■-TWflWKarW., •i^V^ V ^■ .4^' ■k^ f:*' '•-V > , . .>?: .■■^^■ ^l^^-'^.X «•#*'• '.•^4 f*^ ■■k^k..>i.^-.i.k..i.i.>.k'.',k^i.i.ki...kn.^L^^i...kk.'.i.i.i.'.>'.k'.kkk>'.-.Amk>.^'.i Single ^Whip SINGLE WHIP 1 , How many men would be required to move the log in Figure 1 with a direct pull, if the six men are handling it success- fully as shown in Figure 1 ? 2. Why does the nature of the footing to the right of the tree in Figure 1, determine whether or not the Single Whip is of advantage? BLOCKS AND TACKLE 35 Running TaclOe RUNNING TACKLE What is the practical utility of using the single block as a Running Tackle as in Figure 2? What difficulties are introduced into the situation represented in Figure 2 if immediately behind the tree there is a stream into which the log has to be launched? How would you meet these difficulties? What are the relative mechanical advantages of the Single Whip and the Running Tackle? Which needs the stronger rope, the Single Whip or the Run- ning Tackle? Which the stronger tree? 36 PROBLEMS IN PHYSICS QuivTiiclde GUN TACKLE 7. What gain in mechanical advantage over the Single Whip is secured by introducing the second block as shown in the Gun Tackle of Figure 3? What advantage over the Run- ning Tackle? What loss is there in speed? 8. What gain in mechanical advantage over the Single Whip is secured by introducing the second block as shown in the Gun Tackle of Figure 4? What advantage over the Rim- ning Tackle? What loss is there in speed? 9. Compare the two Gun Tackles on the basis of mechanical advantage and speed. 10. The kegs in Figure 3 weigh 120 pounds each. Consider fric- tion and find : (a) with what force the man is pulling, (b) the tension in each return. 11. The kegs shown in Figure 3 weigh 120 pounds each. The rope on which the man is pulling is at an angle of 45 de- grees. What is the stress in the rope supporting the upper BLOCKS AND TACKLE 37 Gtm Tackte ^>4I|( block? What is the force acting on the hook of the lower block? Neglect friction and weights of parts. "127 Suggest a desirable change in the rigging of the Gxxn Tackle shown in Figure 4, in case the tree, is in a swampy place and there is no good footing for twenty or thirty feet on the side toward the I beam. How much harder will the men have to pull 'with the new rigging? 13. The men shown in Figure 4 are each pulling with a force of 50 pounds. Taking account of friction find; (a) the force exerted on the I beam, (b) the force exerted on the tree, (c) the tension in each return. 14. How many men would be required to drag an 800 pound steel I beam across a cement foundation, using the Gun Tackle? Look up necessary data. 15. Some 40 poimd kegs are to be raised from a flat car to the third floor of a building. Would you use the Whip on Whip or the Gun Tackle? Why? 38 PROBLEMS IN PHYSICS R. -«^ r -* Whip on^^)bip WHIP ON WHIP 16. What is the mechanical advantage of the Whip on Whip? 17. What can you accomplish with the Whip on Whip which you cannot accomplish with the Running Tackle? 18. If you are going to use a horse to move a load requiring a force of 800 pounds and have available plenty of rope which will stand 300 poimds, will you use the Whip on Whip, the Running Tackle, or the Gun Tackle? Which will you use if the resistance is 500 pounds? 200 pounds? 19. It requires a force of 1,000 pounds to drag a gun 60 feet to the base of a high wall in which there is a stay bolt con- veniently located. There is available 75 feet of heavy rope capable of standing a load of 1,500 pounds and 60 feet of rope which will stand 600 pounds. Sketch the rigging you would use for the job. Is this the only rigging which could be used advantageously? BLOCKS AND TACKLE 39 20. The men represented in Figure 5 are each exerting a force of 50 pounds. Neglect friction and find: (a) The force which the snub must stand. (b) The tension in each rope. (c) The force acting on the gun mount. (d) The force which the wall is called upon to withstand. Assume the resistance found in (c) and, taking account of friction, find (e) the force which each man must exert. 40 PROBLEMS IN PHYSICS LUFF TACKLE 21. Show that two different mechanical advantages are possible with the Luff Tackle. What is their ratio? 22. Does the pulley P aid in securing the mechanical advantage attained in the rigging shown in Figure 6? 23. An imloading derrick is to be hastily constructed and the blocks and tackle for but one Luff Tackle are available. What mechanical advantage can be secured? Sketch the layout. 24. To what use would you put an additional single block? 25. What is the value of the mast-to-boom Luff Tackle in such a situation as is shown in Figure 6? 26. The drum operating the mast-to-boom tackle shown in Figure 6 is geared to have one fourth the speed of the other drxmi. What simpler mast-to-boom tackle would you use and why? Why is it desirable to use the Luff Tackle in case the gearing is the same? BLOCKS AND TACKLE 41 PORT TACKLE 27. What are the practical advantages of the Port Tackle? 28. (a) If the barrels in Figure 7 each weigh 30 pounds, what force must the man exert? Neglect friction. (b) How strong must the rope be which supports the double block? Assume that the man is pulling at an angle of 30 degrees to the horizontal. 29. (a) Why must the man in Figure 7 stand in line with the mast? (b) What is the practical difference whether he stands close to or far away from the mast? 43 PROBLEMS IN PHYSICS DowMeLuff (2F9ldT»cWo) DOUBLE LUFF OR TWO FOLD TACKLE 30. Sketch two ways of rigging the Double Luff to drag a field piece up a hill. Compare the two as to relative mechanical advantage, and practical utility. 31. Show by sketch how you would use the Double Luff for hoisting. 32. What part of the total load is carried by each of the returns? What is the relation between the mechanical advantage and the number of returns supporting the load? What percentage of the effective mechanical advantage is lost as a result of friction? BLOCKS AND TACKLE 43 R^ r ^ Single Burton (Type A) SINGLE BURTON, TYPE A 33. What is the mechanical advantage of the Single Burton, Type A? 34. Compare the mechanical advantages of the Whip on Whip and the Single Burton, Type A. 35. Why would the Single Burton, Type A, be of no practical utility in the job shown in Figure 5 if the men are able to move briskly when using the Whip on Whip? 36. What are the relative tensions in the two ropes of the Single Burton, Type A? 37. Show that the job of hauling the I beam to the tree (Figure 4) can be done more quickly with the Gun Tackle than the Single Burton, Type A. 38. Which is the faster, the Gun Tackle of Figure 3 or the Single Burton of Figure 9? With which tackle can one man lift a heavy load more easily? In which is the friction loss the greater? 49. Compare the different hoisting tackles which have been studied 44 PROBLEMS IN PHYSICS R^ Single Burton (Type B) as to: (a) height of lift, (b) strength of rope required, (c) length of rope required, (d) force required (man power), (e) convenience and speed. SINGLE BURTON, TYPE B. 39. What is the mechanical advantage of the Single Burton, Type B? 40. What are the relative tensions in the two lengths of rope? 41. If there were plenty of the stronger rope, how would you change the rigging of the Single Burton in order to in- crease the mechanical advantage? Is there any loss of speed through this change? 42. How much oftener would the new rigging have to be over- hauled? 43. Show that a still greater mechanical advantage could be secured with the equipment of Figure 10, if one were per- mitted to cut one of the ropes. 44. What is the relation between the mechanical advantage of the Burton, and the number of returns supporting the load? BLOCKS AND TACKLE 45 THREE FOLD PURCHASE 45. Why is the Three Fold Purchase of greater practical utility for high lifts than the more mechanically advantageous Burton? 46. Why would the Luff on Luff (Figure 17) be unsuitable for such hoisting work? 47. How strong a cable would be necessary to raise a one ton girder with the Three Fold Purchase? 48. How heavy a load could two men conveniently raise with the Three Fold Purchase? 46 PROBLEMS IN PHYSICS R^ PoiirFolcl Purchase FOUR FOLD PURCHASE 50. In the Three Fold Purchase what is the percentage loss in effective mechanical advantage caused by friction? 51. How does the friction loss in the Three Fold Purchase com- pare with the friction loss in a Single Burton with the same mechanical advantage? 52. How much of a load can be lifted by the arrangement shown in Figure 12? The drum diameter is 8 inches, the length of the crank handles 16 inches. 53. Compare the Four Fold Purchase and the Three Fold Pur- chase for mechanical advantage and practical utility. 54. How much more mechanical advantage would the Four Fold Purchase have than the Two Fold Purchase if friction could be neglected? Taking account of friction what is the difference in the mechanical advantages? 55. How strong must be the fastening of the single block, the fast- ening of the upper quadruple block, the lower quadruple block, in Figure 12? BLOCKS AND TACKLE 47 56. In the Three and Four Fold Purchase what is the relation be- tween the number of returns supporting the load and the mechanical advantages? What part of the total load is carried by each of the returns? 57. How strong must the cable of a Four Fold Purchase be in order to just support a load of two tons? Take account of friction and find the strength necessary if the load is to be raised. 48 PROBLEMS IN PHYSICS Dotvhle Burton (Type A) I& DOUBLE BURTON, TYPES A AND B 58. What is the difference in the effective mechanical advantage of a Four Fold Purchase as found by taking account of friction by each of the two methods mentioned on page 33. 59. What are the respective mechanical advantages of the Double Burton, Types A and B? 60. How is the load distributed among the four returns in the Double Burtons, Types A and B.^ 61. Explain how the difference in mechanical advantage in Types A and B of the Double Burton is secured. 62. Is there any relation between the number of returns and the mechanical advantage? 63. Show that the Burton allows you to make use of a short length of rope to advantage. 64. Compare the Double Burtons, Types A and B, as to: (a) mechanical advantage, (b) distance load can be moved without overhauling, (c) speed. BLOCKS AND TACKLE 49 J^=>" R-*— (3 y^ ■r^ — DouMo BurtonCTVpeB) ri^.l4 65. Compare the two Double Burtons, Types A and B as to per- centage loss of effective mechanical advantage, as a result of friction. 66. Change the Double Burton, Type B, by attaching the standing end of the first rope to a snub instead of to the tackle block. Give your judgment as to comparative practical utility con- sidering : (a) mechanical advantage, (b) distance load can be moved without overhauling, (c) speed. 67. Using the equipment of Figure 13 and assuming that you have a sufficient length of rope rig the blocks into a two-fold purchase. Compare with the Burton as to: (a) mechan- ical advantage, (b) distance load can be moved without overhauling, (c) speed. 68. Compare the losses in effective mechanical advantage of a Double Burton, Type A, and a two-block tackle with the same theoretical mechanical advantage. Which shows the greater loss? By what percentage? so PROBLEMS IN PHYSICS D oiible Burton (TYpc C) 69, 70 DOUBLE BURTON, TYPE C What is the mechanical advantage of the Double Burton as shown at the top of Figure 15? As shown in actual use in Figure 15? (a) Find the loss of effective mechanical advantage caused by friction in the rigging shown at the top of Fig. 15. (b) Compare with the loss in a two-block tackle with the same theoretical mechanical advantage. 71. Consider the practical situation shown in Figure 15. Why would consideration of practical utility make you dispense with the lighter rope as soon as possible and apply the heavier rope to the drum as soon as possible? How much mechanical advantage would be lost? 72. Consider the practical situation shown in Figure 15. (a) If you had plenty of heavy rope how would you rig for this job and why? BLOCKS AND TACKLE 51 (b) What is the mechanical advantage as shown in the figure? (c) What would be the mechanical advantage if you proposed rigging? (d) Why is the mechanical advantage not the most im- portant consideration in this situation? 73. A heavy load is to be moved with the Double Burton, using one single and two double-blocks. (a) Sketch the rigging that will give maximum distance without overhauling. (b) Put this same equipment into a rigging that will give a mechanical advantage of six and require no over- hauling. (c) Rig as a Double Burton to enable the load to be moved with the fewest number of men. (d) Assimiing that three suitable lengths of rope are available rig for the greatest possible mechanical advan- tage. (e) Compare the riggings for practical utility. 52 PROBLEMS IN PHYSICS r-* VL^ DOUBLE BURTON, TYPE D. 74. What is the mechanical advantage of the Double Burton shown in Figure 16? 75. If the blocks are separated ten feet, how high can the cannon be raised before overhauling will be necessary? 76. If there were sufficient heavy rope to rig for maximum mechanical advantage, how much easier would it be for the men? Assiune that they each are exerting a force of 60 pounds. 77. Rig the equipment of Figure 16 as a Three Fold Purchase. Compare with other possible riggings as to practical utility. 78. What is the effective mechanical advantage of the Double Burton, shown in Figure 16? 79. The cannon in Figure 16 weighs 1,800 pounds; the lighter rope can stand only 200 poimds. Sketch the rigging that will require the least overhauling. What is its mechanical advantage? How strong must the heavier rope be? BLOCKS AND TACKLE 53 80. What will be the stress on the rope supporting the upper block? On the hook of the lower block? 81. In your opinion how heavy a cannon could be raised using the rigging shown in Figure 16? Study the sketch and make necessary estimates and assumptions. 82. What is the maximum mechanical advantage you can secure with the equipment of Figure 16 if you have another length of rope? 83. If you have a load of 1,200 pounds to move a considerable distance and have plenty of rope that will stand 200 pounds, how will you rig using the blocks shown in Figure 16? 84. Why is a Three or Four Fold Purchase preferable to the more mechanically advantageous Burtons for high lifts? In what respects are the Burtons more advantageous when the lifts are small? 85. Is the loss of effective mechanical advantage due to friction greater in the case of the Burtons or two-block tackles? 54 PROBLEMS IN PHYSICS LUFF ON LUFF 86. What is the mechanical advantage of the Luff on Luff? Why would it usually not be worth while to rig the equipment shown in Figure 17, so as to secure a greater mechanical advantage? 87. How much of a pull can be exerted on the gun carriage shown in Figure 17? What is the strain on the first rope? On the second rope? What is the strain on each block? 88. What is the great practical utility of the Luff on Luff? Ex- plain why a piece of very heavy rope or cable is necessary in order to secure this advantage. BLOCKS AND TACKLE 55 MISCELLANEOUS PROBLEMS ON BLOCKS AND TACKLE 89. A carload of 100 pound barrels is to be unloaded to a platform twenty feet above the tracks. You are assigned to the job with three helpers, two of whom are to do the pull- ing. What tackle will you use? State your reasons for" the choice and sketch the rigging. 90. If you had only one helper for the job what change would you make in the tackle rigging? 91. A carload of 30-pound boxes is to be unloaded to a platform twenty feet above the tracks. You are assigned to the job and given one helper. What tackle will you use? State your reasons for the choice. 92. Your equipment consists of a double and a single block and plenty of rope capable of standing a force of 200 poimds. Rig the tackle so as to secure the greatest mechanical advantage and state the load which could be lifted. 93. Your equipment consists of a double and two triple blocks and plenty of rope capable of standing a force of 200 pounds. Rig the tackle for the greatest mechanical ad- vantage and state the load which could be lifted. 94. Suppose you had plenty of men available and plenty of tackle, what rigging will you use to drag a cannon 50 feet, assum- ing that a force of 1,000 pounds is necessary and the rope can stand 400 poimds? 95. You must drag a heavy steel girder over the ground with the fewest men practicable. The available equipment consists of two double blocks and one single block and two ropes, one of 1,000 pounds tensile strength, the other of 300 pounds strength. Sketch the rigging you would use, and state the maximum safe load of the proposed arrangement. 96. What equipment and source of power would you prefer to employ to raise a one-ton safe to a third-story window? 97. What equipment and rigging would you prefer to employ to raise heavy marble cornice blocks to position? 36 PROBLEMS IN PHYSICS 98. A cannon is to be moved to a moiinting 100 feet away. The equipment consists of 110 feet of rope which will stand a force of 200 pounds and 110 feet of rope which will stand 400 pounds, together with two single blocks. (a) Show that if the resistance offered by the cannon is 600 pounds it can be moved half the distance without overhauling. (b) Show that it can be moved practically the whole distance without overhauling if the resistance is 400 pounds. (c) How many men will be required to each case? (d) If you had plenty of the larger rope how would you rig the tackle for the fewest men? How many men would be needed? (e) Could you move a cannon offering a resistance of 800 pounds with this equipment? If so, sketch the rigging. How many men would be required? 99. A cannon is to be dragged 100 feet to the base of a wall in which there is a tackle bolt. A force of 1,000 pounds is required. If you had one horse with which to do the job and your choice of blocks and tackle, what equipment would you employ? Specify the blocks, and lengths and strength of ropes. 100. What rigging would you select for the job shown in Figure 5 if you had to carry the equipment some distance? The force required is 150 pounds, the haul is 75 feet. Specify blocks, and lengths and strengths of ropes. 101. What rigging would you select for the job shown in Figure 5 if you had a horse for the job? The force required is 1,000 pounds, the haul is 75 feet. Specify blocks and lengths and strengths of ropes. 102. What rigging would you select for the job shown in Figure 5 if you had to do it with four helpers? The equipment must be carried a quarter of a mile. A force of 1,200 pounds is required. Specify blocks, and lengths and strengths of ropes. BLOCKS AND TACKLE 57 103. What rigging would you use for the above job if you had a horse? 104. A log is 150 feet from a wall against which it is to be placed. Two pieces of rope each 160 feet long are available and the necessary blocks. How will you rig to get the greatest speed? How will you rig so as to use the fewest number of men? 105. Devise the cheapest practical hoist for a two-story building, using an extension of the ridge pole for the support, which will enable one man to handle 200-pound barrels. 106. Draw a suitable rigging for pulling a 2S-foot launch out of the water for the winter. 107. What is the usual arrangement of the rigging of a pile driver with a 2,000 pound hammer? What considerations are in- volved in the choice of such a rigging? 108. With a winch capable of exerting a force of 1,000 pounds on the cable, how heavy a load could be lifted using the Three Fold Purchase? Allow for friction. 109. How fast could a 10-H. P. motor raise the load, assuming a force at the winch of 1,000 pounds? 110. Show that a force of more than 1,000 pounds is necessary while the load is gaining speed. What will be the average force if it acquires speed in the first half second? 111. An "A" frame is used to raise building material. There are two cranks, radius 16 inches, the gear ratio is 1 to 10, the diameter of the winding drum in 8 inches. What type of rigging would you employ if two men could be con- veniently assigned to the work? If the men are to raise a 1-ton block of marble, what rigging should be employed. How long a rope would be required for a four-story build- ing? How strong a rope? 112. Draw a diagram of the guy ropes for the "A" frame assuming available ropes have tensile strength of 500 pounds. 113. Draw a diagram of the rigging used in house moving, giving the reason for the choice of the different parts. How is the rigging accommodated to houses of different weights? S8 PROBLEMS IN PHYSICS 114. You must raise a 25-ton steam turbine from a car and lower it 10 feet to its foundation. You have available any length of cable of 20,000 pounds tensile strength and such blocks as you need. Draw a sketch of the rigging. What applied force will be necessary? 115. You must raise a 25-ton steam turbine from a car and lower it 10 feet to its foundation. You have available 25 feet of cable with 20,000 pounds tensile strength, two heavy single blocks and two light double blocks. You must buy suf- ficient cable of 5,000 poimds tensile strength. Show that with a little over 80 feet you can do the job without over- hauling. Sketch the rig. 116. A launch is to be pvdled out of the water. The necessary force is one ton. There is a large double block and two large single blocks. There is sufficient rope which will probably stand 500 pounds, but should be strained as little as pos- sible. There are two small double pulleys and several single pulleys and plenty of rope that will stand 100 pounds. Rig so that one man can do the job of pulling. 117. You must raise a 25-ton steam turbine from a car and lower it 10 feet to its foundation. You have available 19 feet of cable with 20,000 pounds tensile strength, one heavy block, plenty of cable of 5,000 pounds tensile strength and several light blocks. Show how the job can be done without over- hauling. 118. A howitzer weighing 10 tons is to be lifted from a road to a flat car. The road is so situated with respect to the car that there will be a lift of 5 feet and a swing of 10 feet in order to place the gun on the car. Arrange a single boom derrick and blocks and tackle to do the job. Specify strengths of tackle, ropes and guy ropes. With your rig- ging how much force will be required? How will you supply it? PART III. AERIAL BOMBING AERIAL BOMBING GLOSSARY OF TERMS AIR-LAG — The horizontal distance, at any height, which the bomb lags behind a vertical line dropped from the airplane, assuming the airplane to continue at uniform velocity after dropping the bomb. AIR-SPEED — The speed of the airplane relative to the air. It is read on an air-speed indicator. BACK-SIGHT — ^A sighting rod or wire on a bomb-sight which has to ap- pear in line with the fore-sight and the target at the correct moment for releasing the bomb. BOMBING ANGLE! — The angle between the vertical and the line joining the airplane and target at the correct moment for release of the bomb. BOMB-SIGHT — An instrument designed to indicate the correct instant at which a bomb should be released in order to hit the target. DRIFT-ANGLE — ^The angle between the fuselage and the direction of mo- tion of the airplane relative to the ground. The angle between the direction of the air-speed and the direction of the ground-speed. DRIFT-BAR — A bar which can be set to indicate the direction of motion of the machine over the ground. FORE-SIGHT — The transverse sighting rod or wire on a bomb-sight furthest from the observer's eye. GROUND-SPEED — The speed of the airplane relative to the ground. It is determined by the air-speed and wind-speed. TIME-LAG^-The difference between the actual time of fall of a bomb and the time of fall from the same height in vacuum. TRAIL The horizontal distance from the spot where the bomb strikes the ground to the point it would have reached in the same time under vacuimi conditions. TRAIL-ANGLE; — The small angle by which the bomb, as viewed from a uniformly moving aircraft, appears to trail behind the vertical. Specifically, the angle subtended at the airplane by the trail. TRAJECTORY — ^The path of the falling bomb. WIND-SPEED — The speed of the wind relative to the ground. 6i 62 PROBLEMS IN PHYSICS AERIAL BOMBING Aerial bombing operations fall under two heads, those in which it is not necessary to hit any particular object, and those in which it is essential to destroy some definite target. Examples of the firstclass are the German raids on London, the reprisal raids and the nightly low altitude raids near the front. The avowed aim of this type of raid is to destroy the morale of the enemy rather than to damage any object of direct military importance. The second type of bomb raid is the expedition which is considered to have failed if some special target is not destroyed. Examples are, raids to destroy railway junctions or bridges, munition factories, lock gates, and the like. These raids were seldom completely suc- cessful as it was not possible to place more than a small percentage of bombs near the objective. Realizing the tremendous advantage which would be gained by the army which could first secure accuracy in bomb fire the various countries engaged in the war were and are still active in the devel- opment of bombs and bomb-sights. The problem divides itself naturally into two parts, bomb-sight design and bomb design, the latter including the study of bomb trajectories. £-,- §^ wg &2 Im Q5 ■•-» G^n fl "H fl> +j,-i! CO a S Q§ Hi o. o o fto 32 o ^ *^ Og (N -^9 o U --I b 3o" imS E«r N ■t-t si on AERIAL BOMBING 63 BOMB TRAJECTORIES At Langley Field, Virginia, the Air Service has conducted, under the direction of Dr. A. W. Duff and Capt. L. P. Sieg, extensive experiments upon the trajectories of drop-bombs. This work is peculiarly interesting to students of physics as it is the first experi- mental data, obtained by photographic means, on the motion of a falling body from a height of more than a few feet. The bombs are fitted with special electric lights of about 2,000 candle power, carried at the tail between the guide vanes. They are dropped at night and appear like brilliant shooting stars. The path of the light is photographed upon the plates of two cameras at the ends of a base line 2630 feet long. The cameras take the place of surveying instruments and may be regarded as equivalent to two transits. In order that the true path of the bomb may be determined, it is necessary that corresponding points for the two plates be iden- tified. Moreover, the time element must be introduced if velocities and accelerations are to be found. Both results are attained by producing breaks in the traces on the photographic plates by simultaneously closing the shutters of the two cameras at intervals known to an accuracy of two or three thousandths of a second. The plates having been accurately measured, and a number of small but essential corrections applied, it is possible by suitable calculations to determine the actual path of the bomb in space, and its position at any instant, to an accuracy of about two feet. The velocity and acceleration of the bomb, at any point of the trajectory, can also be found to a high degree of accuracy. It is needless to explain that such information is of the utmost value in the study of air resistance. The immediate information gained is the trail-angle and the time-lag of the bomb. From these can be computed all desired information concerning drop-bomb trajectories. The airplane also carries an electric light which makes its trace upon the plate. In this way the path of the airplane and its ground-speed are determined. Similar records at different altitudes together with air-speed and compass readings make it possible to 64 PROBLEMS IN PHYSICS find the wind velocity at the different levels. Due to variations in the wind velocity and other variable influences such as lack of perfect symmetry in the bomb, the bomb always deviates a little from the plane in which it starts to fall and a three dimensioned diagram is required for the trajectory. This deviation has been ignored in Figure 2 in which is shown the trajectory of a Mark III 50-pound stream-line bomb dropped at a height of 5,539 feet from an airplane having a ground-speed of 98.28 feet per second. PROBLEMS 1. Where would the bomb of Figure 2 have struck the ground if there had been no air resistance? 2. From the data on the trajectory of the Mark III 50-pound bomb, given in Figure 2, determine the trail. 3. Determine the air-lag at a point half way to the ground. Com- pare with the trail at the ground. 4. (a) Determine the air-lag at four or five points and for each point find the trail-angle. (b) Does the trail-angle increase or decrease as the bomb descends? (c) It is customary to assume that the trail-angle of a bomb is constant for different heights of release. Is this a reasonable assumption? 5. What would have been the time of fall of the bomb of Figure 2 if there had been no air resistance? 6. What is the time-lag, in seconds, of the Mark III 50-pound bomb whose trajectory is plotted in Figure 2 ? 7. What is the bombing angle for the actual condition revealed in Figure 2? 8. What would be the bombing angle for a bomb with twice the trail-angle of the bomb whose trajectory is given in Figure 2? 9. What would be the bombing angle for a bomb with twice the time-lag of the bomb whose trajectory is given in Figure 2? 10. What would be the bombing angle if the bomb were dropped in vacuo under the conditions represented in Figure 2? X 1000 — I — Lme of fhght of Plane Ground Speed 9828 ff /sec Trajector^^ of Bomb dropped from Airplane From Photographs by Two Cameras Cameras 2630 ft.apart g = 321 2 ft/sec. T \.„ Y Ifrfll 000 1 000 98 16 2.000 196 64 3.000 294 144 4 000 392 256 5 000 490 400 6.000 587 576 7.000 684 762 e.ooo 780 1019 9.000 875 I2B7 10.000 970 1585 11.000 1065 1912 12 000 use 2268 13.000 1251 2652 14.000 1343 3064 15.000 1433 3502 16.000 1523 3965 17.000 1611 4453 18.000 1698 4965 19.000 1783 5499 19.075 fgreuna} 1790 5539 3000 ..3500 ..4000 ..4500 ;.:-yV *"*,■'■ - ground at ss 39 feet Figure 2 66 PROBLEMS IN PHYSICS 11. What would be the bombing angle if the Mark III 50-pound bomb were released from a plane with a ground-speed of 120 miles per hour at an altitude of 18,000 feet? At 6,000 feet? 12. What would be the bombing angle if the Mark III 50-pound bomb were released from a plane with a ground-speed of 30 miles per hour at an altitude of 18,000 feet? At 6,000 feet? 13. What would be the bombing angle if an airplane were flsdng at 12,000 feet with air-speed of 60 miles per hour in a head wind of 60 miles per hour? 14. Upon which does the trail-angle depend, the air-speed or the ground speed? Explain fully for; (a) flight against the wind, (b) flight with the wind, (c) flight across the wind? 15. The conditions are the same as those represented in Figure 2 except that the plane, due to "bumpy" air, is ascending at the rate of one foot per second at the instant of release in addition to the horjzontal ground-speed of 98.28 feet per second. Consider only the effect of this upon the trajectory and proceed as outlined below to find how much the bomb will miss the target, i. e., how far from the point of impact indicated in Figure 2 it will hit. (a) Give good reasons for assuming that the trajectory will be practically identical with that shown in Figure 2, after the path of the bomb has become parallel to the ground? (b) What is the actual speed of the bomb at the instant of release? (c) At what angle to the horizontal is it moving at the instant of release? (d) Give good reasons for assuming that air resistance can be neglected in computing that part of the trajectory passed over before the path of the bomb becomes horizontal? (e) How high above the point of release will it ascend? (f) How long will it take it to reach this height? AERIAL BOMBING 67 (g) How far will it have traveled horizontally during this time? (h) What angle with the horizontal is made by the path of the bomb at the instant it is at its greatest height? (i) What will be its ground-speed at this instant? (j) How high above the ground will it be? (k) In what respects will the trajectory beyond this point differ from the trajectory shown in Figure 2 ? (1) How far short of the ground will the bomb be when it has finished the part of its trajectory corresponding to the trajectory of Figure 2? (m) In covering this vertical distance how far will it go horizontally? (n) What is the total horizontal distance covered by the bomb? (o) What was the horizontal distance planned upon when the bomb was released? (p) By what distance does the bomb miss the target? 16. The conditions are the same as those represented in Figure 2 except that at the instant of release the airplane is descend- ing at the rate of one foot per second in addition to its hori- zontal ground-speed of 98.28 feet per second. Consider only the effect upon the trajectory and find how much the bomb will miss the target, i. e., how far from the point indicated in Figure 2 it will hit. 17. An airplane is flying with an air-speed of 60 miles per hour in a head-wind of 30 miles per hour. (a) What angle does the plane in which the bomb starts to fall make with the fuselage? With the direction of the ground-speed? (b) If lack of symmetry in the bomb is neglected, will the path of the bomb remain in the vertical plane in which it starts to fall? 18. The airplane is fl3nng with an air-speed of 60 miles per hour in a cross-wind of 30 miles per hour. (a) What angle does the plane in which the bomb starts to drop make with the fuselage? 68 PROBLEMS IN PHYSICS (b) What angle does this plane make with the direction of the ground-speed? (c) Will the path of the bomb remain in the vertical plane in which it starts to fall or will the bomb be turned from its course? Consider for wind uniform all the way down and for variable winds. Neglect effects of lack of symmetry in the bomb. " 19. Why is it that the trail depends upon air-speed rather than ground-speed? Why does the wind-speed have no influence on the trail? 20. A 50-pound bomb is released horizontally with a velocity of 98.28 feet per second from a height of 5,539 feet and is found to travel 1,790 feet horizontally before reaching the ground, the time of descent being 19.075 seconds. (a) Calculate the mean vertical acceleration. (b) Compare the mean vertical acceleration with that of gravity which is 32.12 feet per second per second at Langley Field. (c) Calculate the mean vertical air resistance. (d) Calculate the mean horizontal acceleration. (e) Calculate the mean horizontal air resistance. 21. A bomb is released at a height of 6,000 feet from an airplane on a glide of 5 degrees. The (projected) ground-speed is 100 feet per second. Calculate the time of fall of the bomb and horizontal range, neglecting air resistance. Assuming the values of air resistance found in Problem 20, calculate the trail and time-lag. 22. Which of the bombs illustrated in Figure 1 has the smallest time-lag? Why? 23. Two bombs are released at the same instant, one hung vertically by its tail, the other suspended as shown in Figure 5. (a) Which has the greater trail? (b) Which swings the more easily into its trajectory? (c) In your opinion which suspension is preferable? 24. In making dummy bombs for experimental purposes where must the center of gravity be located? Figure 3. One of the Two Cameras at Langley Field Va II^pH . Photograph Bomb Trajectories ' ' ^^^^ *° AERIAL BOMBING 6g THE LOOP Problems dealing with the forces acting on an airplane while it is performing a loop are introduced at this point because the only experimental data ever obtained upon the actual performance of the airplane were secured by use of the same methods of photo- graphic triangulation described in connection with bomb trajec- tories. Figure 4 shows the path of a Curtiss J N-4 H airplane executing a loop. The path is reduced to still air conditions. Such information upon the actual performance of an airplane is of utmost importance in giving information concerning the stresses to which the airplane is subjected. Parts of an airplane which are amply strong enough to stand the stresses of plain flying may give way when subjected to unusually large forces produced by acrobatics. The forces which come into play when a plane sud- denly changes its velocity, either in direction or magnitude, may become dangerously great. Some idea of the large factor of safety necessary in airplane construction can be gained from considera- tion of the following problems. In solving them it is to be assumed that the plane weighs 2,500 pounds and that the wings are the only supporting surfaces. Only the weight of the airplane and the force on the wings, in the direction of the radius of curvature, are to be considered. PROBLEMS 25. Is it the air-speed or the ground-speed upon which depend the forces acting upon the wings of an airplane? 26. At what point does the airplane in Figure 4 have the maximum air-speed? The minimum air-speed? 27. At what point does the plane have the maximum ground- speed? The minimum ground-speed? 28. What is the vertical force acting on the wings when an airplane is flying on a level course? 29. What is the vertical force on the wings when an airplane is on an even glide of 20 degrees? 30. What is the vertical force on the wings when the plane is climbing steadily 400 feet per minute? — _ ^^ ~~" "~~ "~" J 1 — — ~ H c o OI ^ o V O) V) 00 \ \ 'k 5 ' o ? r V. i2c o <0 / °> i f tv.- 0. ?*/ o o> A lO 1 i or — — — ^^ A r^ «'' A < "Ti y 00 00 s I. L r\ - - " \ o 2? \ % cry k oi \ \ \ o 5 s k c<7 q A \ i~ o OJ QO J ^TJ o S ^\s r _ +» o o o o o o o o o o 4) cJ" in * CO 1 1 (VJ J J ^ cog •^ c8 1- £ cfi p AERIAL BOMBING 71 31. If the elevator (horizontal rudder) is suddenly lowered so that the plane dives will the load on the wings be increased or decreased? 32. Why will the wings be called upon to withstand a greater load when the elevator is suddenly raised? 33. What force would be required to support the airplane at point 1.97 seconds, Figure 4, if it were stationary with respect to the earth? How much at 4.93 seconds? At 5.92 seconds? 34. What is the approximate radius of curvature of the path of the airplane at point 1.97 seconds? 35. What is the centrifugal force exerted by the airplane at posi- tion 1.97 seconds? 36. What is the amount of the total load upon the wings of the airplane at position 1.97 seconds? What is the direction of the force? How many times the weight W of the plane is the force? 37. What is the magnitude and direction of the force with which the air reacts upon the airplane at position 4.93 seconds? Express in terms of W, the weight of the plane. 38. What is the magoitude and direction of the force with which the air reacts upon the airplane at position 5.92 seconds? Express in terms of W, the weight of the plane. 39. What is the magnitude and direction of the force with which the air reacts on the airplane at point 9.87 seconds? Ex- press in terms of W, the weight of the plane. 40. At what point in the path of the plane, as it makes the loop shown in Figure 4, are the wings called upon to withstand the greatest forces? How many times the weight of the plane does the force become? 41. At what point in the path of the plane, as it makes the loop shown in Figure 4, are the wings called upon to withstand the smallest forces? How many times the weight of the plane is the minimum force? 72 PROBLEMS IN PHYSICS 42. Sketch the path of the airplane making a loop in a head-wind of 30 miles per hour. In a head-wind of 60 miles per hour. 43. Sketch the path of the airplane making a loop down-wind in a wind of 30 miles per hour. Sixty miles per hour. 44. Does the shape of the path relative to the ground have any effect upon the reactions between air and plane? Explain. AERIAL BOMBING 73 THE EFFECT OF WIND ON THE MOTION OF THE AIRPLANE The actual velocity of an airplane relative to the ground is the resultant of the velocity of the plane with reference to the air and the velocity of the wind. Needless to say, bombing operations necessitate accurate knowledge of both air-speed and ground-speed. The following problems are designed to bring out some of the more general considerations. PROBLEMS 45. An airplane is flying with an air-speed of 70 miles per hour. The wind is blowing from the North with a velocity of 30 miles per hour. What is the ground-speed and direction of the ground-speed when the airplane is headed in the following directions: (a) North, (b) South, (c) East, (d) Northeast? 46. An airplane is flying with an air-speed of 60 miles per hour. The wind is blowing from the East with a velocity of 60 miles per hour. What is the ground-speed and direction of the ground-speed when the plane is flying in the follow- ing directions: (a) North, (b) South, (c) East, (d) West? 47. An airplane is flying with an air-speed of 120 miles per hour. The wind is blowing from the East with a velocity of 60 miles per hour. What is the ground-speed and the direc- tion of the ground-speed when the plane is flying in the following directions: (a) North, (b) South, (c) East, (d) West? 48. An airplane flying at an air-speed of 70 miles per hour, at 335 degrees from North through East, is found by photographic triangulation to have a ground-speed of 55 miles per hour due North. Find the wind-speed, the direction of the wind, and the angle of drift of the airplane. 49. Same as Problem 48 except that the ground-speed is 30 miles per hour due East. 74 PROBLEMS IN -PHYSICS 50. Same as Problem 48 except that the ground-speed is 50 miles an hour Southwest. 51. If the wind is blowing at 30 miles per hour and the air-speed of the airplane is 70 miles per hour what is the radius of the circle which can be drawn through the points which can be reached by the plane in one hour? Where is the center of the circle located with reference to the starting point? 52. An airplane with an air-speed of 60 miles per hour is to fly at an altitude where the wind is blowing from the East at 60 miles per hour. (a) Draw the diagram which will show the ground- speed which it can make in any direction. (b) Use the diagram to find in what direction the plane must be headed in order to actually travel Northwest. What ground-speed can it make? (c) What ground-speed can the plane make North? West? East? 53. Make a similar diagram for a plane with an air-speed of 120 miles per hour in an East wind of 60 miles per hour. (a) In what direction must the plane head to go North- west? What ground-speed can it attain? (b) What ground-speed can the plane make North? West? East? AERIAL BOMBING 75 BOMB-SIGHTS On page 88 will be found a detailed description of the Wimperis- type bomb-sight in the form adopted by the U. S. Army. Certain points in connection with bombing can, however, be brought out more effectively if considered apart from the bomb-sight. The problem of dropping a bomb at the right instant and right place resolves itself into two parts ; getting the airplane on the right course and dropping the bomb at the right time. If the plane is not flying in the correct course the bomb will fall to the right or left of the target producing what is known as "line" or direction error. If the bomb is not dropped at the right instant the bomb will either fall short of the target or go beyond it. This is called "range" error. The two sighting operations are entirely independent. The plane must first be brought into the right course. This having been accomplished the entire attention of the bomber is given to determining the correct instant for releasing the bomb. THE DRIFT-BAR A drift-bar is a device by which the pilot can find the angle be- tween the direction of the air-speed and the ground-speed of the airplane. This angle, with the wind direction and air-speed, determines the wind-speed. A knowledge of the latter is necessary for a correct setting of the back-sights. A drift-bar is nothing more than a horizontal bar capable of rotation about a vertical axis. See Figure 7, page 80. PROBLEMS 54. A pilot is flying a straight course in still air. The drift-bar is set at zero, i. e., lies parallel to the axis of the fuselage. Do objects on the ground appear to move along the drift- bar from end to end or do they move across the bar at a definite angle? 55. What relation exists between the direction in which the plane is moving and the direction of the apparent motion of objects on the ground? 76 PROBLEMS IN PHYSICS 56. A pilot is flying a straight course directly into a strong head- wind. How do objects on the ground appear to move relative to the drift-bar, which is set at zero? The pilot turns the plane to the left. How does this affect the apparent motion of objects relative to the drift-bar? 57. The pilot adjusts the drift-bar until objects on the ground appear to move along the bar. What is the relation be- tween the angle at which the drift-bar is set and the drift angle of the airplane? 58. An airplane is headed 115 degrees from North through East at an air-speed of 70 miles per hour in a 30 mile per hour wind from the Northeast. What is the angle of drift? 59. At what angle to the axis of the fuselage will the drift-bar be set when the plane is headed 20 degrees away from the direction from which the wind is blowing? When the plane is headed 20 degrees away from the direction toward which the wind is blowing? 60. The air-speed meter indicates 70 miles per hour, the compass shows that the plane is headed 90 degrees from North, through East, the drift-bar of the bomb-sight makes an angle of 20 degrees with the fuselage. What is the ground- speed and its direction? 61. A pilot is flying a straight course directly away from the wind. Which way must he turn in order to make use of the drift- bar of the bomb-sight shown in Figure 7? 62. A pilot flies with the wind in such a direction that objects seem to move along the drift-bar, set at zero, from end to end. The compass reads due North. The pilot heads the plane due East and adjusts the drift-bar until objects on the ground appear to move along it. If the drift-bar is found to be set at an angle of 30 degrees with its zero position and the air-speed has been constant at 70 miles per hour, what is the wind-speed and the direction of the wind?^ Figure 5. Drop Bombs in Place in Release Mechanism. Figure 6. Types of American Bombs. (From left to right, two fragmentation bombs, dummy bomb, two incendiary bombs, airplane flare. Note the arming devices like wind mills, which unscrew in flight and arm the bomb.) AERIAL BOMBING 77 63. A pilot flies into the wind in such a direction that objects on the ground appear to move parallel to the drift-bar, set at zero. The compass reads due North. The pilot heads the plane due West and adjusts the drift-bar until objects ap- pear to move parallel to it. If the drift-bar is found to be set at an angle of 30 degrees with its zero position and the air-speed has been constant at 70 miles per hour, what is the wind-speed and the direction of the wind?"- 1 In the Wimperis type bomb-sight the wind-speed is found in the manner described. By a clever mechanical arrangement the setting of the drift-bar automatically separates the "up" and "down" back-sights the cor- rect amount. 78 PROBLEMS IN PHYSICS DIRECTION SIGHTING A pilot using the Wimperis-type bomb-sight must approach the target either directly up-wind or directly down-wind. If at the instant the bomb is released the course of the plane is such as would carry it directly over the target there will be no "line" or direction error. Direction sighting is accomplished by means of the direction wire and the bubble of the lateral spirit level. The direction wire is fixed in position parallel to the axis of the fuselage. The lateral spirit-level is for the purpose of making the line of sight past the direction wire vertical. See Figure 7, page 80. PROBLEMS 64. Why is it not necessary for the pilot's eye to be directly above the drift-bar when he is making a setting of the drift-bar? 65. What relation would the path of the airplane bear to the points on the ground which appear to move along the drift-bar, if the pilot's eye were in the vertical plane de- termined by the drift bar? 66. A pilot is flying a straight course in still air. How do objects on the ground appear to move relative to the direction wire? 67. If a wind is blowing, how must the pilot fly in order for objects on the ground to appear to move along the direction wire? 68. A pilot using the Wimperis-type bomb-sight must approach the target, at the moment the bomb is released, in a straight course, either up- or down-wind. (a) How will objects appear to move relative to the direction wire? (b) Where must the pilot's eye be placed, with reference to the direction wire, if the target is to appear to move along the direction wire when the approach is correct? (c) Where must the center of curvatvire of the lateral spirit level of the bomb-sight be located if a line of sight past the bubble and the direction wire is to be in a vertical plane? 69. What relation does the path of the airplane bear to the target if the target appears to move along the direction wire when the pilot sights past the bubble of the lateral spirit level? What significance has this in connection with the accuracy of the fire? AERIAL BOMBING 79 RANGE SIGHTING A bomb-sight must indicate to the bomber the instant at which to release the bomb. This should be when the horizontal distance from the target is equal to the distance which the bomb will, after release, travel forward in its passage to the earth. It might at first seem that the bomb would drop vertically from the air-plane to the ground but such is not the case for the conditions under which a plane could be stationary with respect to the earth rarely occur. Normally a plane is moving over the ground at a speed of many miles per hour for it must keep in rapid motion with respect to the air or it will fall. Let us first consider the simplest conditions, namely, still air and an airplane flying a straight level course at constant speed. At the instant the bomb is released it partakes of the full speed of the plane and if it were not for air resistance would travel forward, in its flight to the ground, a distance equal to that covered by the plane during the same time. Viewed from the ground its trajec- tory would be a parabola. Viewed from the airplane the bomb would appear to drop vertically to the earth and to burst im- mediately below the plane. Under these ideal conditions the hori- zontal distance between the target and the airplane at the instant at which the bomb should be released would depend solely upon the ground-speed of the airplane and its altitude, the latter, of course, determining the time. As a matter of fact a great many other considerations are in- volved. If there is a wind, its speed and direction affect the speed of the airplane relative to the ground, and the bomb-sight must be provided with corresponding adjustments. In addition the pres- ence of the air causes a departure from the theoretical parabolic trajectory in vacuo. When viewed from the airplane the bomb appears to be moving backv/ard at a slow and fairly uniform velocity. The total dis- tance on the ground from the point of impact to the point vertically below the airplane at the time of impact is known as the trail. It is, of course, assumed that the airplane has moved with constant I < en ^3 a •FN AERIAL BOMBING 8i velocity. This lagging of the bomb behind the vertical may also be measured by the trail-angle which is the angle at the airplane subtended by two lines joining it to the extremities of the trail. Another characteristic of the bomb is the time-lag or the difference in the time of fall along the actual trajectory and along the para- bola of vacuum conditions. PROBLEMS Note : — In the Wimperis-type bomb-sight the adjustment of the back-sights for air-speed is made by sliding the two back-sights, and attached parts, forward or back a distance of .17 inch for each 10 miles per hour of air-speed. The fore-sight is movable up and down in a guide which is tilted at an angle of 2.8 degrees to the perpendicular, the lower end being nearer the tail of the machine. This corrects for the trail of the bomb, 2.8 degrees being a good average value of the trail-angle. The bomb-sight is leveled up in the fore and aft directions by means of the longitudinal spirit level. 70. Draw a diagram to scale showing the relative position of the fore-sight and the two back-sights, of the Wimperis-type bomb-sight, for bombing at an altitude of 12,000 feet. There is no wind and the airplane is flying with an air speed of 100 miles per hour. Assume a trail-angle of 2.8 degrees. 71. Draw a diagram, similar to that of Problem 70, to fit the follow- ing conditions. There is no wind and the airplane is flying at an air-speed of 50 miles per hour at an altitude of 3,000 feet. Assume a trail-angle of 2.8 degrees. 72. How much must the two back-sights be separated if the wind- speed is 10 miles per hour? Fifty miles per hour? 73. Draw a diagram, similar to that of Problem 70, to fit the fol- lowing conditions. The airplane is flying at a height of 9,000 feet with an air-speed of 60 miles per hour in a 30- mile wind. In a 60-mile wind. In the latter case, which one of the back-sights is practically over the fore-sight? 74. Make a rough sketch showing the surface of the ground, the line of flight of an airplane, the actual trajectory of a bomb, and the theoretical parabolic trajectory in vacuo. 82 PROBLEMS IN PHYSICS (a) Mark the position of the plane at time the bomb strikes the ground. (b) Mark the point at which the bomb strikes the ground. (c) Mark the point of theoretical impact, assuming the theoretical time of fall for the assumed altitude. What is the position of this point in relation to the airplane? (d) Mark the point of theoretical impact, assuming that the bomb falls in vacuo for a time equal to the actual time of fall. What is the position of this point relative to the airplane? Why is this point below the surface of the ground? (e) Mark the trail, trail-angle, and air-lag. 75. Draw or trace the trajectory of Figure 2 accurately and pro- ceed as follows: (a) Plot the position of plane at time of impact of the bomb. (b) Show the point of theoretical impact, neglecting air resistance, computed on the basis of altitude. (c) Plot the position of the point of actual impact, neglecting air resistance, computed on the basis of actual time of fall. (d) Plot the theoretical path from a few computed points. AERIAL BOMBING 83 PROBLEMS ON ERRORS IN BOMBING 76. The accuracy of aerial bomb fire may be stated in terms of the circle within which 50 per cent of the bombs are likely to fall. With present sighting methods the radius of the circle is approximately 2 per cent of the altitude. What is the radius of the circle within which 50 per cent of the bombs will fall when dropped from a height of 6,000 feet? 12,000 feet? 77. The accuracy of aerial bomb fire is often expressed in terms of the angle at the airplane subtended by the line joining the target and point of impact. To what angle does the error mentioned in Problem 76 correspond? 78. A Wimperis-type bomb-sight is set at the ground for an ele- vation of 10,000 feet, an air-speed of 60 miles per hour and a wind-speed of 30 miles per hour, on the basis of informa- tion from the Meteorological Service. By how much will the bomb miss the target as a result of each of the following sources of error? Consider both up-wind and down-wind attack. (a) The average error of altimeters (aneroid barometers) is about 300 feet at 10,000 feet. (b) The maximum error of altimeters is about 1,000 feet at 10,000 feet. (c) An air-speed meter may be in error as much as 5 miles per hour. (d) The wind-speed as furnished by the Meteorological Service may be in error by 5 miles per hour. (e) The direction of the wind may be wrong by as much as 10 degrees. 79. An airplane is flying at an altitude of 10,000 feet with an air- speed of 100 feet per second. The sight is taken correctly and the bomb released at the right instant but owing to "bumpy" air the plane is moving upward at the rate of 20 feet per second at the instant of release. What is the corresponding ground error? 84 PROBLEMS IN PHYSICS 80. An airplane with a ground-speed of SO miles per hour drops a bomb when flying at an altitude of 10,000 feet. What is the maximum distance by which the bomb can miss the target as a result of the pitching of the plane through an angle of one degree? Consider only the effect due to inaccuracy of sighting due to the pitching. 81. If "bumpy" conditions cause a variation in the ground-speed of 0.6 miles per hour, what is the corresponding error for an airplane with a ground-speed of 60 miles per hour at an altitude of 10,000 feet? 82. With certain bomb-sights the ground-speed is determined by noting the time taken by an object to pass from an angle 15 degrees ahead of the plane to a point immediately below the plane. If the plane is flying at 10,000 feet altitude, at a ground-speed of 60 miles per hour, what is the maximum possible error in the determination of the ground-speed caused by a forward and aft pitching of the plane amount- ing to one degree? 83. The ground-speed is being found by measuring the time taken for an object to pass from an angle 15 degrees ahead to a position under the machine. If the ground-speed is found to be 50 miles per hour based on an altimeter reading of 10,000 feet which is 500 feet too low, what is the true ground-speed? 84. The bomb-sight is of the Wimperis-type. The pilot lo6ks down past the bubble of the lateral spirit level and the direc- tion wire and notices that he is going to pass 300 feet to the right of the target. He banks and turns to the left. (a) Why is a line of sight past the bubble of the lateral spirit level and direction wire no longer vertical? (b) If the pilot makes a perfect blank, what angle does the plane, determined by the wire and bubble, make with the perpendicular? AERIAL BOMBING ^S (c) If the pilot banks at as small an angle as 5 degrees, what "line" or direction error on the ground is indicated by the sight? Altitude of airplane 10,000 feet. (d) Show that the pilot will probably, on coming out of the bank, find that he has turned too far. 85. Why should the lateral spirit level never be used in sighting unless the airplane is flying a straight course? 85 PROBLEMS IN PHYSICS CROSS-WIND BOMBING Attempts have been made to devise satisfactory sights for cross- wind bombing. Many interesting considerations arise which do not enter into the problem of up- and down-wind bombing with the Wimperis-type sight. ! PROBLEMS 86. An important consideration that arises in cross-wind bombing is whether or not the airplane passes directly over the point at which the bomb strikes, assuming of course that the air- plane continues in a straight course. (a) How far from a vertical line through the point of impact does the plane pass if it is flying with an air-speed of 60 miles per hour, at a height of 12,000 feet, in a head- wind of 30 miles per hour? (b) Same question and conditions except that the wind makes an angle of 30 degrees with the direction in which the plane is pointed. (c) Same question and conditions as in (a) except that the plane is flying down-wind with the wind at an angle of 30 degrees with the fuselage. 87. The relation of the direction of the trail to the direction in which the airplane is headed at the moment the bomb is re- leased is of great importance in cross-wind bombing. Find this relation by answering the following questions in re- gard to a plane headed Northwest and flying with an air- speed of 60 miles per hour in a South wind of 30 miles per hour. (a) What is the direction in which the plane is actually moving? What is its ground-speed? (b) At the instant the bomb is dropped what is its direc- tion of motion? (c) At the instant of release what is the velocity of the bomb in the direction of the wind? (d) How does this compare with the wind velocity? AERIAL BOMBING 87 (e) What resistance will the bomb encounter in the direction of the wind? (f) What will be the air-lag in the direction of the wind? (g) From what direction will the air apparently strike the bomb? Is this direction the same as that in which the airplane is headed? (h) What will be the relation between the direction of the trail and the direction in which the plane was headed at the moment of release? 88. Give evidence to show that the "trail" is always in the direction occupied by the fuselage at the instant the bomb is released. Consider the following case. A plane is headed Northwest and flying with an air-speed of 60 miles per hour in a South wind of 30 miles per hour. (a) What is the direction in which the plane is actually moving? What is its ground-speed? (b) At the instant the bomb is dropped what is its direc- tion of motion? (c) At the instant of release what is the velocity of the bomb in the direction of the wind? (d) How does this compare with the wind velocity? (e) What resistance will the bomb encounter in the direction of the wind? (f) What will be the air-lag in the direction of the wind? (g) From what direction will the air apparently strike the bomb? Is this direction the same as that in which the airplane is headed? (h) What will be the relation between the direction of the trail and the direction in which the plane was headed at the moment of release? 88 PROBLEMS IN PHYSICS DESCRIPTION OF THE U. S. ARMY WIMPERIS-TYPE BOMB-SIGHT MARK I A A number of different types of bomb-sights have been developed and used. Experience has shown that those which embody a stop watch and require approach to the target in a straight course for a considerable distance are not used by pilots under fire. The Wimperis-type high-altitude bomb-sight was designed with the object of providing a sight which can be set almost instantly and permits the pilot to make the preliminary approach toward his tar- get from any direction and in any manner he chooses, so long as he straightens out into a level straight course toward the target either directly up- or down-wind, for ten or fifteen seconds. It is a sight which pilots will use under fire. The Wimperis-type bomb-sight in the form in which it was ap- proved for production in the United States Army is shown in Figure 7, page 80. The sight is mounted on the right side of the fuselage in a position best understood by reference to the two spirit levels. This sight is used for both direction sighting and range sighting. Direction sighting is accomplished with the direc- tion wire and the lateral bubble. The pilot swings into position, either up-wind or down-wind from the target, and straightens out into a level course directed toward the target. If he has chosen his position correctly a sight past the bubble of the lateral spirit level and the direction wire falls upon the target, which appears to move along the wire. This is due to the fact that the center of curvature of the tube of the lateral spirit-level is in the line of the direction wire. Con- sequently the bubble is always directly above the line of the direc- tion wire unless the plane is subjected to accelerations. If the pilot finds that his course is not directed over the target he must turn quickly. This requires banking which makes the bubble useless until the plane straightens out again. It can then be de- termined whether the course was altered the right amount. (See Problems 84 and 85.) Range sighting is accomplished by the use of three sight wires. AERIAL BOMBING 89 the fore-sight and two back-sights, one of the back-sights for use when the airplane is flying against the wind and the other for down- wind attack. The altitude adjustment is made by moving the fore-sight up and down by means of the altitude setting lever, the proper posi- tion of which is indicated on the altitude scale. The fore-sight also takes care of the adjustment for the trail-angle of the bojnb. This is accomplished by giving the guide which carries the fore-sight a permanent tilt at an angle of 2.8 degrees with the vertical. This value is sufficiently close to the trail-angle of the bombs used with this sight. The air-speed and wind-speed adjustments are made by moving the back-sights horizontally. The air-speed adjustment is made by grasping the wind-speed adjusting wheel and pushing all that part of the sight which has to do with the back-sights forward or back on the guides. Ten miles per hour air-speed is represented on the air-speed scale by a distance of .17 inch. If the meteorological service is able to furnish information re- garding the wind velocity at the point where the bombing is to be done the wind-speed adjustment is made before the airplane leaves the ground, by turning the wind-speed adjusting wheel until the drift-bar indicates the right figure on the wind-speed scale. If the wind-speed is not known accurately enough from met- eorological observation it can be determined by the operator. He first fllies directly with the wind or against it, determining the proper direction by observing the drift of objects on the ground in relation to the direction wire. When objects seem to move along this wire the airplane must be flying in the direction of the wind. The operator notes his course and turns at an angle of 90 de- grees, by compass, so that the wind strikes the machine on the right, this being a right-hand sight. By operating the hand wheel he ad- justs the drift-bar until objects on the ground appear to move along it. This operation automatically moves the "up" and "down" sight- wires apart and records the wind-speed on the wind-speed scale. The "up" sight is moved forward automatically imtil its distance from the zero point of the air-speed scale is proportional to the 90 PROBLEMS IN PHYSICS ground-speed for up-wind flight, the ground speed being equal to the wind-speed subtracted from the plane's air-speed. The "down" sight is moved back simultaneously and automatically until its distance from the zero of the air-speed scale is proportional to the ground-speed for down-wind flight, the ground-speed being equal to the wind-speed added to the plane's air-speed. It is impossible to adequately describe the clever mechanical features of the Wimperis sight. It is hoped that every college de- siring a Wimperis sight will be able to secure one from the Ord- nance Department. (See note below.) With the Wimperis-type bomb-sight the plane attacks either up- or down-wind and approaches the target on a straight level course which would carry it directly over the target. Just before the bomb is to be released the attention of the operator is directed entirely to the matter of range. At the instant the proper back sight, either "up" or "down" according as he is bombing up- or down-wind, comes in line with the fore-sight and the target the bomb is re- leased. Great care must be exercised at this time to preserve the level of the plane and maintain uniform air-speed. Note: Arrangements will probably be made so that U. S. Army Wim- peris-Type Bomb-Sights Mark I A can be obtained from the Ordnance De- partment of the U. S. Army. Requests from institutions where there are Reserve Officers' Training Corps Units should be made through the Com- mandant, and addressed to the office of the Chief of Ordnance, United States Army, Washington, D. C: Attention of the Training Section of the Administrative Division. It is possible that moving picture films showing a falling bomb as seen from the airplane will also be available. PART IV. AERIAL PHOTOGRAPHY AERIAL PHOTOGRAPHY The great part which aerial photography played in the recent war is too well known to need to be elaborated upon. Its useful- ness has by no means ended for it promises to be a very powerful aid to map making and will have many other applications as well. The success which has been met in aerial photographic work has resulted from the painstaking study of a large number of phy- sical problems. By no means all of these have been solved. For example, it still remains for some one to develop a satisfactory means of keeping a camera pointed vertically or, failing in that, of recording its angle with the vertical. If a photographic map or mosaic such as is shown in preparation in Figure 2 is to be made, the airplane flies over the territory and vertical pictures are taken in rapid enough succession to overlap each other. The pictures so obtained are matched together, giving a photographic map of a strip of territory. If more territory is to be mapped than can be covered by a single strip, several strips are made by successive flights of the plane over parallel courses. A great variety of types and sizes of camera for vertical use has been developed, ranging in focal length from 8 inches to 48 inches. Toward the end of the war, the British and American practice was standardized to correspond with the French, viz: 18 X 24 centimeter negatives, with 50 centimeter focal length lenses for use when a large territory has to be covered quickly, and a few 120 centimeter lenses for certain occasions when great detail is needed. These rather long focal lengths were adopted partly be- cause of the great heights (frequently 18,000 to 20,000 feet) at which photographic reconnaissance had to be carried on over territory well protected by anti-aircraft batteries and enemy planes. The development of the art of aerial photography has been largely dependent upon the application of principles of physics. The problems which are given below are based on some of the simpler aspects of the development work and upon the situations met in carrying out photographic work in the field. 93 94 PROBLEMS IN PHYSICS GENERAL PROBLEMS 1. Exposures for a photographic mosaic of an area of 10 miles by 15 miles on a scale of 1 to 5000 are to be made using the American Type K-1 camera, Figure 7, which takes a picture 18 X 24 centimeters. (a) How many exposures are needed if 25 per cent over- lap is required from picture to picture, from strip to strip, and beyond the edge of the area? (b) If the airplane flies at 70 miles per hour air-speed, what time interval- must elapse between exposures if there is no wind? (c) Assuming a uniform rate of climb of 600 feet per minute and allowing 5 minutes for making a turn and start- ing back for a new strip, what flying time will be required? The camera is fltted with a 20-inch lens and is capable of 100 exposures in a flight. The flying fleld is 15 miles from the area to be photographed. (d) If there is a wind of 15 miles per hour and the air- plane flies at an air-speed of 70 miles per hour, what will be the time interval between exposures for strips made flying against, and with the wind, respectively? The camera is placed so that the short side of the picture is parallel to the direction of the ground-speed. (e) What will be the time interval between exposures if the strips are made in a direction perpendicular to the wind by "crabbing" across the wind? The camera is turned so that the short side of the picture is parallel to the ground- speed. 2. How much more rapidly can the above territory be covered using a 20-inch focal length lens than with a 40-inch lens if the plane flies at the same altitude in each case? What will be the scale of the map made with the 40-inch lens? 3. How large an area can be photographed on a single plate from an airplane flying at 6,000 feet altitude, using an 18x24 centimeter plate and a lens of 50 centimeter focal length? Using a lens of 25 centimeter focal length? Figure 1. American Type L Camera in Operation. Figure 2. Preparing a Photographic Map or Mosaic. AERIAL PHOTOGRAPHY 95 4. A photographic mosaic has been made with a 50 centimeter focal length lens with the plane flying at an altitude of 8,000 feet. More pictures are needed, to the same scale as the mosaic, at points of enemy activity. On account of the dan- ger to a low-flying plane it is proposed to use a 120 centi- meter lens. At what height must the pilot fly? 5. If photographic reconnaissance cannot be carried on below 18,000 feet, on account of anti-aircraft guns, what is the largest scale on which you can get a mosaic if you have lenses of 25, 50 and 120 centimeters focal length? Which lens is used? 6. If the operator knows that his camera is likely to deviate as much as 5 degrees from the perpendicular, what overlap must he plan for in order to be certain to obtain an overlap of 15 per cent in the finished prints; (a) using an 18 x 24 centimeter plate and a 120 centimeter lens, (b) using an 18 X 24 centimeter plate and a 50 centimeter lens? 96 PROBLEMS IN PHYSICS TIME OF EXPOSURE Exposures in aerial photography must always be very short. Not only does the ground-speed of the airplane put a definite limit on the allowable time of exposure, but the angular motion of the whole plane, i. e., rolling and pitching, and of the camera alone, caused by vibration, are sources of very great difficulty. Lieutenant J. P. Brinsmade, of the Air Service, carried on extensive experiments upon the effect of vibration of the camera. Brilliant electric lights were placed in tree tops and photographed as the airplane passed over. The camera shutter being open, each light traced a wavy line on the film, and characteristics of which gave an indication of the magnitude and nature of the vibration. Occultation of one of the lights, ten times per second, by a revolv- ing disc introduced the necessary time element. PROBLEMS 7. The light conditions are such that you wish to give the longest possible exposure while preserving a sharpness correspond- ing to an image movement of not more than 1/250 inch. When the airplane is flying at an altitude of 10,000 feet, with a ground-speed of 70 miles per hour, what is the longest exposure which can be given if the camera has a 20-inch lens? 8. A series of oblique views are to be taken with a hand camera from a plane flying at an air-speed of 70 miles per hour, at an elevation of 2,000 feet. The camera is held at an angle of 45 degrees to the vertical. It is equipped with a 10-inch lens and carries a 4x5 plate with the 5-inch side horizontal and parallel to the fuselage. What are the longest exposures which can be made without blurring if an image movement of 1/250 inch is permissible? Disregard everything except the ground-speed of the air plane. 9. Under the above circumstances, what depth of territory is cov- ered by the picture from top to bottom? » -I fl ^ .is o o'fe iw ^ fl) C o> *-" G 2 ffl « S ft • bo a a a S S P S » s S « m a §5 ais o 3 S ^ia (S « rj C -O a! . d Jh en u Sua) s5 >> AERIAL PHOTOGRAPHY 97 10. A camera mounting is being designed for a camera with a 20- inch lens. A sharpness corresponding to an image move- ment of not more than 1/250 inch is required. What is the maximum permissible angular velocity of the vibration of the camera if it is to be used at a height of 10,000 feet with exposures as long as 1/100 second; (a) When the direction of vibration is at right angles to the motion of the air plane? (b) When parallel? Assume a maximum ground- speed of 90 miles per hour. 11. A camera mounting is being designed for a camera with a 20- inch lens. A sharpness corresponding to an image move- ment of not more than 1/250 inch is required with exposures of 1/100 second. What is the maximum permissible angular amplitude of vibration if it is known that the frequency of the vibration will be 50 per second ; (a) When the direction of vibration is at right angles to the motion of the airplane? (b) When parallel? Assume a maximum ground-speed of 90 miles per hour. 12. The vibration of a camera is often far from simple harmonic. In such cases it is important to know whether it is the amplitude or the angular velocity of the vibration which is the determining factor. Which of the two is the determin- ing factor in the case of a vibration with a frequency of 60 per second, if the time of exposure is 1/50 second? When the frequency is 10 per second and the time of exposure the same? 13. Examination of one of the plates made in studying the effects of camera vibration showed the trace to be an approximate sine wave with a double amplitude of 1/16 inch and a wave length of J4 inch. There were gaps every J4 inch, meas- ured along the line of the average path, corresponding to the occultation of the light every 1/10 second. With this mounting, what is the longest time of exposure which can be given if the image movement must not be more than 1/250 inch? 98 PROBLEMS IN PHYSICS 14. Examination of one of the plates revealed a trace with a maximum angular departure of 45 degrees from the mean direction. The vibration was of such a long period that the maximum angular velocity was the determining factor. The gaps in the trace, corresponding to the occultation of the light, occvirred every 0.2 inch long the line of the aver- age path. What is the longest exposure which can be given with this camera if the image motion must not be greater than 1/250 inch? 15. In carrying out the work mentioned above, it was found desirable to do the work in the daytime. (a) How did the use of red-sensitive plates, a red filter, a small stop, and a brilliant light make possible the carry- ing out of the experiments by daylight? Discuss the factors separately. (b) Why were clear glass bulbs employed, rather than red ones? (c) Show that, other factors being equal, the intensity of the trace obtained in such an experiment varies inversely with the altitude of the camera. (d) Why was the nature of the background against which the light was placed of importance? What back- ground would you suggest? Give your reason. 16. Refer to the statements made in connection with the last two problems. Assume that the photographic density is propor- tional to the intensity of the image and the time of exposure and that the extent of woods or dark land is sufficient to form a background for all altitudes and all exposure-times used. (a) How does the density of the trace vary with the altitude? (b) Why is the density of the background independent of the altitude? (c) Show that the density of the trace is independent of its length, but that its contrast with the background is inversely proportional to its length? Figure 5. Hand-held Camera Model A-1. (8 to 10 inch lens. Takes all standard 4x5 Graflex equipment). Figure 6. American Type L Camera. (Copied from Camera most used by British at the front. 8x12 inch lens. 4x5 plates, charges automatically by wind propeller. ) AERIAL PHOTOGRAPHY 99 (d) If the length of trace on the plate remains the same, does the contrast with the background vary with the altitude? If so, how? 17. Why do the short wave lengths predominate in the light scat- tered by "haze"? 18. Why does haze interfere less with the work referred to in Problem 15 than with ordinary aerial photographs taken with regular plates?' 19. If haze is to be considered, how will you revise the answers to problems 15 and 16? ' One of the greatest difficulties encountered in aerial photography is the great amount of haze. The scattered light is predominantly of short wave length so that by the use of yellow, green, orange and even red, screens (made of colored gelatine or glass), combined with plates that are sensitive to the longer wave lengths, it is possible to eliminate to a very large extent the effect of haze. Perhaps the greatest photographic advance produced by the war, was the high commercial development of so-called panchromatic plates, some of which are sensitive even beyond the red end of the visible spectrum. See Part VI, Ray Filters, and Figures i and 2, page 130. PROBLEMS IN PHYSICS PROBLEMS ON CERTAIN RESULTS FROM THE USE OF THE FOCAL PLANE SHUTTER. 20. Answer the following questions in order to ascertain whether or not the distortion resulting from the use of a focal plane shutter is negligible. (a) A focal plane shutter with a half-inch slit gives an exposure of 1/100 of a second to (each point on) a plate 18 centimeters wide. What is the time of travel of the shutter across the plate? (b) If the exposure is made from airplane with a ground-speed of 70 miles per hour at a height of 6,000 feet using a 50-centimeter lens, what will be the nature of the distortion; (1) shutter moving in direction of flight? (2) shutter moving in the opposite direction to that of flight? (c) By measuring on the print, with a scale, the distance between objects whose positions are accurately known, it is found that the scale is accurate when the distances on the print are in a direction perpendicular to the direction of flight. It also appears that the same scale is not accurate for measuring distances, on the same print, in a direction parallel to the direction of flight. What is the greatest pos- sible error, in meters, on the ground? Use data under (a) and (b). 21. If double images are found in successive strips across a plate, taken with a focal plane shutter, and it is expected to elimi- nate the trouble with future negatives, what is the most probable cause of the difficulty? Why do the double images not occur all over the plate? 22. If a "between-the-lens" shutter were used with the same camera would double images occur? When would they occur? How would they be distributed over the plate? 23. If you are using a focal plane shutter 24 centimeters wide, with a f^-inch slit, on an 18x24 centimeter plate, for exposures of 1/100 second, in how many places on the plate will there be blurring if the camera is vibrating with a frequency of 50 vibrations per second through an amplitude of 1/10 degree? G Y. AERIAL PHOTOGRAPHY THE NEGATIVE LENS FINDER When isolated objectives are to be photographed some sort of sight is necessary. It is especially convenient if the operator can look down through a hole in the bottom of the plane but the con- struction of the plane seldom permits of a large enough hole. This difficulty was partially overcome by the use of a rectangular negative lens in the floor of the plane. PROBLEMS 24. A 5x6 rectangular lens with a focal length of minus 11 inches, is to be used as a "finder" for a 18x24 centimeter plate camera with a 20-inch focal length lens. The rectangular lens is to be placed in the floor of the fuselage, 34 inches be- low the eye of the photographer. What size should a rectangle at the surface of the lens be made if it is to just outline the field of the camera? Note: This lens serves the same purpose as the "direct view finder" of the ordinary hand camera. 25. What is the size of the hole in the floor of the cockpit to give the same angular view as the 5x6 inch lens, when placed with its 5-inch sides parallel to the axes of the fuselage? 26. Where should the lens be placed, flush with the floor or flush with the outside bottom of the fuselage, which may be as much as 5 or 6 inches below the cockpit floor? 21. In bombing it is often very desirable that the bomber should be able to look ahead at a considerable angle through the bottom of the plane. The construction of a plane some- times makes it impossible for a hole to be cut allowing a forward view beyond 20 degrees. How does the use of a 11 -inch negative lens extend the view? By what angle? PROBLEMS IN PHYSICS PROBLEMS ON THE VENTURI AND SUCTION PLATE OF THE AMERICAN AIRPLANE CAMERA 28. Why is it more important to hold a film flat when using a very rapid lens at full aperture than when using a slow lens? Use a diagram to show this. 29. What is the maximum total pressure on the face of an 18x24 centimeter film if the suction is equivalent to 4 inches of water and there are 289 holes, each 1/64 inch in diameter, in the plate with which the film is backed up? 30. How does a single Venturi tube, like the smaller one in Figure 8, produce suction? 31. How does the outer tube of the double Venturi aid in produc- ing a greater suction? 32. Make a sketch showing how a Venturi could be connected to an aneroid barometer in such a way as to make an air-speed indicator. 33. Make a sketch showing how a Venturi and a Pitot tube could be combined with an aneroid barometer to make an air- speed indicator. 34. Which is better as a siurface for the perforated suction plate and as a "wiper" to remove the electric charge, as the film unrolls, a graphited cloth or a sheet of smooth metal? Why? What is the purpose of the graphite? 35. Why are "static marks" more troublesome in winter than in summer? 36. Why are static difficulties experienced with films used in an airplane when no such difficulty is experienced on the same day in using a film camera on the groxmd? Figure 8. Venturi Tube. (Produces the suction to hold the film flat in the American type K-1 Camera.) AERIAL PHOTOGRAPHY 103 THE PROBLEM OF THE VERTICAL In attempting to make maps by aerial photography, it is neces- sary, if any great accuracy is desired, to take the photographs with the focal plane of the camera horizontal. Therefore, some means of determining the true horizontal or true vertical is of the greatest importance. Such means are much needed for other purposes as well. For example, an artificial horizon will prove of the greatest assistance in aerial navigation and an accurate vertical or hori- zontal will make possible the accurate dropping of bombs from airplanes. The present methods of sighting are such that no great accuracy can be secured. The natural horizon would, of course, be the simplest way of locating the direction were it not that it is frequently obscured by smoke or haze. A pendulum is of no avail for it will be influenced by every change of velocity. PROBLEMS 37. An airplane flying at an air-speed of 70 miles per hour in still air makes a perfect bank in making a turn with a radius of curvature of one mile. (a) What is the ratio of the centrifugal force to that of gravity? (b) What is the angle between the resultant of these two forces and the perpendicular? (c) What angle must the wings make with the resultant force if there is to be no side slipping? (d) At what angle must the plane bank in making the turn? 38. An airplane flying East at an air-speed of 60 miles per hour, in a wind of 60 miles per hour from the North, makes a complete turn to the left. (a) If it banks at an angle of 10 degrees what is the radius of curvature of the path relative to the air? (b) Sketch the path relative to the air. (c) Sketch the path relative to the ground. 104 PROBLEMS IN PHYSICS 39. It is necessary that certain photographs be taken when the camera is pointing not more than two degrees from the vertical. (a) If the camera is mounted rigidly on the fuselage what is the minimum radius of curvature which the path of the plane can have, in still air, at the instant a photograph is taken? (b) If the plane is flying in a 60-mile wind is the de- termining factor the radius of curvature of the path relative to the air or the radius of curvature of the path relative to the ground? 40. An airplane, equipped with a pendulously-mounted camera, is flying at an air-speed of 70 miles per hour in still air. It makes a perfect bank in making a turn with a radius of curvature of one mile. (a) What is the ratio of the horizontal acceleration to that of gravity? (b) What is the direction of the resultant force acting on the camera? (c) What is the position of the camera relative to the plane? (d) What is the deviation of the camera from the vertical? (e) Compare this angle with the angle through which the plane is tipped in making the bank. 41. An airplane, equipped with a pendulously-mounted camera, flies East at an air-speed of 60 miles per hour in a wind of 60 miles per hour from the North. It then makes a com- plete turn to the left. (a) Sketch the path of the plane relative to the air. (b) Sketch the path of the plane relative to the ground. (c) Which path is to be considered in determining the deviation of the camera from the vertical? (d) At what point in the path does the plane suffer the greatest horizontal acceleration? Give reasons for your answer. AERIAL PHOTOGRAPHY 105 (e) At what point in the path does the camera swing farthest from the perpendicular? Give reasons for your answer. (f) Why is there a point at which the plane is stationary with reference to the ground? (g) How does the camera point when the plane is in the position mentioned in (f) ? (h) In what direction, relative to the vertical and the fuselage, does the camera deviate from the vertical just be- fore this point is reached? Just after leaving this point? 42. An airplane is flying 70 miles per hour in a direct cross wind of 15 miles per hour and the pilot attempts to fly a straight course by keeping the nose of the plane headed for an object 15 miles away. How far does a pendulouSly-mounted camera depart from the true vertical? 43. A camera weighing 90 pounds has a radius of gyration of 12 inches. It is to be hung pendulously in gimbals. How far above the center of gravity must the gimbal bearings be placed in order to give it a double swing period of 10 seconds? PART V. BALLOONS THE U. S. ARMY SPHERICAL BALLOON The U. S. Army Spherical Balloon consists of a spherical envelope of rubberized cotton or silk containing the gas. The envelope is covered by a net which acts as a suspension for the con- centrating ring, to which is attached the basket car to carry pilot and passengers. The valve is at the top of the envelope and is operated from the basket by a cord. The envelope ends in an ap- pendix through which gas escapes as the balloon ascends and air enters as it descends. There are three standard sizes of 9,000, 19,000 and 35,000 cubic feet capacity respectively. The length of time a spherical or free balloon can remain in the air and the distance it can cover depend largely upon the gas capacity of the envelope and the amount of loose weight or ballast which can be carried. In order that a spherical or free balloon shall leave the ground with sufficient speed for safety there must be a resultant upward force of from 20 to 100 pounds according to the wind conditions. This is called the ascensional force and is equal to the difference between the "lift" and the total weight of envelope, rigging, car, passengers, etc. PROBLEMS 1. A spherical balloon is 50 feet in diameter. Assume ground conditions as in the table, page 125. (a) What is the weight of the air displaced? (b) What is the weight of the gas in the balloon if it is filled with pure hydrogen? If it is filled with illuminating gas? (c) What is the total lift in each case ? 2. A spherical balloon 50 feet in diameter reaches a height of 10,000 feet. If it is filled with pure hydrogen what is the total lift at this height? What is the lift with illuminating gas? Consult table, page 125. log PROBLEMS IN PHYSICS 3. How much gas does a spherical balloon of 35,000 cubic feet . capacity lose in rising 20,000 feet? What lift at the ground does this loss represent? Consult table. 4. What is the lift of pure hydrogen in pounds per thousand cubic feet? The lift of illuminating gas? Assume ground condi- tions as given in the table. 5. What is the lift in pounds per thousand cubic feet of each of these gases at an altitude of 10,000 feet? Consult table. 6. A spherical balloon filled with commercial hydrogen ascends to a point where the aneroid barometer reads 14.5 inches. (a) At what height is the balloon? Consult table. (b) What is the approximate temperature? Consult table. (c) What percentage of the gas has been lost? (d) If the capacity of the balloon is 50,000 cubic feet what was the total lift at the ground? Assume ground con- ditions as in table. (e) What is the lift at the height attained? (f) What will be the lift when the balloon returns to the ground ? (g) How much gas will have to be valved to just bring the balloon to the ground? 7. The distance which a free balloon can travel depends to a large extent on the ballast which can be carried at the start. Find the relative superiority of commercial hydrogen over illuminating gas for a 35,000 cubic foot spherical balloon in terms of the relative amounts of ballast which can be car- ried. The balloon and gear weigh 400 pounds, the two passengers weigh 300 pounds. Assume that an ascensional force of 50 poimds is required. 8. A spherical balloon has a capacity of 35,000 cubic feet. The balloon and car weigh 400 pounds, and the two passengers each 150 pounds. How high will the balloon ascend if filled with commercial hydrogen? With illuminating gas? Consult table. Figure 1. U. S. Army Spherical Balloon. BALLOONS 9. If the balloon and car of a 19,000 cubic foot spherical balloon weigh 300 pounds, and the two passengers each 150 pounds, how high can the balloon ascend if filled with commercial hydrogen? With illuminating gas? Consult table. 10. How high would the above balloon ascend with one passenger? 11. If two free balloons of different volume, both filled with 98 per cent hydrogen, are capable of ascending with exactly the same amount of ballast, which will attain the greater altitude? Why? 12. Why does a spherical balloon "over-shoot" the point of equi- librium, tending to make its flight a series of ascents and descents ? This over-shooting means waste of gas or ballast and is prevented as much as possible by a skillful pilot. 13. Why does "over-shooting" result in waste of gas and ballast? 14. What effect have the sun's rays on a balloon? Assume that a free balloon has just enough ascensional force to carry it through a cloud. If the sun heats it 20 degrees Centigrade and it is filled with 35,000 cubic feet of pure hydrogen, how much will the ascensional force be increased? If the top of the cloud is 4,000 feet above the earth how high will the bal- loon ascend? Disregard the over-shooting. 15. Why is the tension in the fabric in the top of the balloon greater than at the bottom? What is the factor of safety in a SO-foot hydrogen-filled balloon if the fabric tests 38 pounds per running inch, assuming that the fabric does not bulge through the net? Study the photograph, estimate the bulge, and find the approximate factor of safety. What is the tension in the fabric at a point near the appendix? 16. Why is it that a large balloon will lift a considerable weight while a small balloon made from the same fabric will not support even its own weight? 17. Why does the height to which a spherical or free balloon can ascend depend almost entirely upon the size of the balloon? PROBLEMS IN PHYSICS THE U. S. ARMY OBSERVATION BALLOON The U. S. Army observation balloon, Type R, is modeled after the French Caquot balloon. It consists of a stream-line envelope with a total length of 90 feet, a maximum diameter of 29 feet, and a gas capacity of 37,000 cubic feet. In the forward end of the balloon there is a ballonet or air bag much like a huge blister on the inside of the under surface of the envelope. One of the functions of the ballonet is to take care of the variations in the volume of the gas, with change of altitude and temperature. If an observation balloon were open to the air like a spherical balloon, each time it was hauled down a large volume of air would enter the envelope and mingle with the gas. A ballonet makes it possible for air to enter the body of the balloon and not contaminate the gas. When the balloon ascends a second time no gas is lost until all the air is expelled from the ballonet. It is customary to make ballonets of a size to take care of the variations in gas volume encountered under normal conditions and heights of flight. A second purpose which the ballonet serves is to maintain the pressure in the envelope. The wind often blows against a captive balloon with great force and would cup in the nose were it not that the ballonet automatically maintains the gas pressure sufficiently high to prevent this. The pressure in the ballonet is produced by an air scoop which is placed under the balloon in the zone where the wind pressure on the envelope is the greatest. The valve is placed in the nose of the balloon and opens auto- matically when the gas pressure is excessive. It may also be oper- ated by hand. The type R observation balloon, rigging and basket weigh ap- proximately 1,000 pounds. PROBLEMS 18. It is common practice to assume the lift of a hydrogen-filled balloon to be 64.4 pounds per thousand cubic feet. Com- pute the lifting force of hydrogen, at sea level and determine the percentage of purity which is assumed in the case of the above mentioned lift. Consult table, page 125. lUl^^ t.' & hAk ^ ,.lr Figure 2. U. S. Army Observation Balloon. Type R BALLOONS 113 19. What is the ascensional force in an observation balloon of 37,000 cubic feet capacity? Weight of cordage, car and observer 1,300 pounds, lift of the gas 64.4 pounds per 1,000 cubic feet. 20. What is the ascensional force when the above mentioned bal- loon has reached 5,000 feet, assuming that the balloon was full when it left the ground? How much gas does a balloon lose in rising 5,000 feet when fully inflated with 37,000 cubic feet of gas? 21. What must be the cubical capacity of a ballonet which will just take care of the variation in gas volume of a hydrogen bal- loon which is to operate with a maximum elevation of 5,000 feet andwhich has a maximvmi capacity of 37,000 cubic feet? 22. It is often assumed in rough calculations that a balloon loses 1/8000 of its ascensional force for each meter of altitude. Does this apply to a fully or partially inflated balloon? Consult the table on page 125 and find the maximum error, as a result of this assumption, for altitudes up to 5,000 feet. Up to 10,000 feet. 23. An observation balloon equipped with a ballonet is fully inflated at the ground, the ascensional force is 1,000 kilograms, the cable weighs 1/10 pound per foot. To what altitude will the balloon go? 24. If the same balloon is filled only ^ full of gas how high will it ascend? A 37,000 cubic foot observation balloon is to ascend to a height of 5,000 feet. With how many cubic feet of 98 per cent hydrogen should it be inflated to secure maximum lift with no loss of gas? 25. The above balloon is to be filled from a number of cylinders containing hydrogen gas at 2,000 pounds pressure at an atmospheric temperature of 80° F. If the actual volume of the tanks is 2 cubic feet how many will be required? 26. A hydrogen-filled observation balloon breaks away at a height of 10,000 meters. The balloon is full and the valve is blocked shut. The pressure at the equator of the balloon is 12 milli- 114 PROBLEMS IN PHYSICS meters. How high will the balloon ascend before bursting if the greatest diameter is 29 feet and the fabric tests SO pounds per linear inch? 27. Why is it that an observation balloon, if it breaks away, will turn nose up? Why is this an advantage? 28. A hydrogen-filled observation balloon of 37,000 cubic feet capacity breaks away and rises with a lift force of 600 pounds. If it attains equilibrium at 8,000 feet how much gas has been lost? If more gas is allowed to escape and the balloon comes down, the lower end will become flabby and the balloon will point more and more towards the ver- tical. Why does this occur? 29. The fabric of an observation balloon with a maximum diameter of 29 feet will stand a tension of 50 pounds per running inch. What is the maximum pressure in inches of water to which the balloon can be safely inflated with hydrogen if a factor of safety of 7^ is to be maintained and the mano- meter is level with the under surface of the balloon? 30. A winch weighing 5,000 kilograms is placed at right angles to the wind. If the wheels are 2 meters apart and the cable extends at an angle of 45 degrees in a line which intersects the groimd at a point half way between the wheels, can the winch be overturned? The cable will stand a tension of 3,200 kilograms. 31. When a winch fails to operate the cable is passed through a snatch block loaded with sand bags. A number of men move along with the block and thus bring the balloon down. If the ascensional force is 600 pounds and the cable is at an angle of 45 degrees, how much must the sand bags weigh to just drag on the ground? How many men must be assigned to the task? (See page 33.) 32. The forces which act on a type R captive balloon on ascension, the air being calm, and the axis of the balloon horizontal, are as follows: Ascensional force — 1,100 kilograms, 11.6 meters from the BALLOONS 115 Weight of fabric and rigging — 400 kilograms, 14 meters from the nose. Weight of basket and equipment — 200 kilograms, 18.6 meters from the nose. Tension of the cable. (a) What is the total force acting downward (exclusive of the tension of the cable), the direction of the force, and the distance of its direction line from the nose? (b) What is the magnitude and direction of the force exerted by the cable and the distance of its direction line from the nose? 33. From what height must a man jump to make the impact equivalent to that of a parachute landing? The rate of descent of parachute is approximately 1,000 feet per minute. 34. The observer lands in a 12 mile wind and the parachute topples over and drags him. With about how much force does the parachute pull him along? 35. A captive balloon is situated 4,000 meters from the enemy lines at the height of 1,500 meters. The wind is blowing directly toward the enemy lines with a velocity of 25 miles per hour. If the observer is forced to jump, where will he land with reference to the enemy lines? A parachute descends at a speed of about 1,000 feet per minute. 36. A captive balloon is situated 6,000 meters behind its own lines at the height of 1,500 meters. If the wind is blowing at an angle of 30 degrees with a line joining the balloon and its own front line trenches, how strong can the wind be and permit the observer to drop in friendly territory? A par- achute descends at a speed of about 1,000 feet per minute. ii6 PROBLEMS IN PHYSICS THE FORMATION OF EXPLOSIVE MIXTURES. Great danger from explosions exists if the hydrogen in a balloon contains more than 18 per cent of air. The following problems serve to call attention to certain causes of explosive mixtures. PROBLEMS 37. A captive balloon 30 feet high is adjusted so that the pressure recorded by the gauge is 11 millimeters of water. The point of attachment of the gauge and the open end of the gauge are on a level with the middle of the balloon. Calculate the excess pressure in the balloon over atmospheric pressure, (a) at the top, (b) at the bottom of the balloon. 38. Repeat the calculations of Problem 37 for a gauge reading of 3 millimeters of water. What conclusions would you draw in this case as to the effect of making a hole in the lower part of the balloon? 39. Starting with a balloon in the condition represented in Problem 37 trace qualitatively the processes taking place during deflation when, (a) a hole is made in the top of the balloon, (b) a hole is made in the bottom of the balloon, (c) one hole is made at the top and another hole at the bottom of the balloon. 40. A captive balloon 29 feet high is filled with hydrogen until a gauge at the middle reads 11 millimeters of water. The valve is adjusted to open at IS millimeters pressure. The balloon ascends to an altitude of 3,000 feet and returns to the ground. Calculate the minimum volume which must be provided in the ballonet in order that the pressure at the bottom of the balloon shall not be less than that just outside when the balloon returns to earth. 41. A balloon is filled as in Problem 40. The gauge is then placed in the basket 50 feet below the point of attachment to the balloon. What is the change in reading of the gauge? How would the result be effected if the tube leading from the gauge to the balloon was filled with air? BALLOONS "7 42. A balloon of 37,000 cubic feet capacity has a hole 1/10 of an inch in diameter in its side where the excess pressure is 11 millimeters. Calculate the fall in pressure per day as a re- sult of this hole. 43. The hole mentioned in Problem 42 might easily happen to open into a comparatively closed pocket like the fins, of say 15 cubic feet capacity. About how long a time would elapse before the mixture in the closed pocket became explosive. A mixture containing more than 18 per cent of hydrogen is explosive. 44. How does pressure difference affect the passage of gas through a hole in the fabric? Do the same considerations apply to pure diffusion? Explain. 45. Assuming that 9 liters of hydrogen pass through one square meter of fabric by diffusion in 24 hours, at what rate would you expect air to enter the balloon owing to diffusion? How long would it take for diffusion to result in an impurity of 18 per cent of air in a spherical balloon of 37,000 cubic feet capacity? ii8 PROBLEMS IN PHYSICS THE U. S. ARMY 84,000 CU. FT. AIRSHIP The U. S. Army 84,000 cubic foot airship or dirigible is illustrated in Figure 3. This airship is of the non-rigid type, the shape of the envelope being maintained by the gas pressure, which is always greater than that of the atmosphere. When the airship is under way a pressure of at least 18 millimeters is maintained. If the pressure reaches 38 millimeters, approximately, gas is valved auto- matically. Two ballonets ^ are used ; one in the nose and one near the tail. These are connected with a small blower and also with a "scoop" placed in the slip stream of the propeller. By either of these means pressure can be maintained in the ballonets. This pressure is com- municated to the gas and must be sufficient to maintain the shape of the balloon against the wind pressure. The ballonets are also employed in altitude control. Valves are arranged so that either ballonet can be inflated at will. Trans- ferring 1,000 cubic feet of air from one to the other tilts the balloon 5 degrees. When the balloon is under way this furnishes a very effective means for vertical steering, making the use of the elevators unnecessary and doing away with the resistance attending their use. A skillful pilot will depend almost entirely upon the ballonets. ^See page 112. BALLOONS 119 PROBLEMS 46. How much lift at the ground would an 84,000 cubic foot airship have if inflated with pure hydrogen? With pure helium? 47. How much would the lift be reduced for each cubic foot of air in the ballonets, (a) if the airship were inflated with pure hydrogen, (b) with pure helium? 48. What is the lift at the ground of the Army 84,000 cubic foot airship when the gas is commercial hydrogen and the bal- lonets are full? When commercial helium is used and the ballonets are full? 49. How high can an 84,000 cubic foot airship, filled with com- mercial hydrogen, ascend without losing gas if it valves at 38 millimeters and the manometer reads 18 millimeters when the airship leaves the ground, with ballonets full? 50. How high can an 84,000 cubic foot airship, filled with com- mercial helium, ascend without losing gas if it valves at 38 millimeters and the manometer reads 18 millimeters when the airship leaves the ground, with ballonets full? 51. The 84,000 cubic foot airship is to fly at altitudes not to exceed 5,000 feet. Maximum lift is desired with no loss of gas. How much air should be left in the ballonets if the envelope is inflated with commercial hydrogen at a pressure of 18 millimeters and the pressure is not to exceed 30 millimeters at the maximum elevation of 5,000 feet? 52. What will be the answer to problem 51 if helium is substituted for hydrogen? 53. How many cylinders of hydrogen gas will be required to fully inflate the Army airship when the atmospheric pressure is 740 millimeters and the temperature is 10° C? The cylin- ders were filled with 6.4 cubic meters of free gas at a pres- sure of 760 millimeters and temperature of 15° C. 54. Some gas cylinders are filled with gas at a pressure of 150 kilograms per square centimeter at a temperature of 15° C. If at this pressure the factor of safety is 5, is there danger of bursting when the temperature of the cylinder is raised 40 degrees Centigrade by the sun? PROBLEMS IN PHYSICS 55. How much more does it cost to completely inflate the 84,000 cubic foot airship with helium than with hydrogen? Helium costs $100 per 1,000 cubic feet and hydrogen $8. 56. How much less lift has commercial helium than commercial hydrogen? Express in percentage of hydrogen lift. 57. In view of the facts brought out in the answers to the last two problems, why should it be proposed to use helium in all captive balloons and airships? 58. A mixture of helium and hydrogen containing 15 per cent of the latter will not ignite. (a) What is the relative lifting power of commercial helium, commercial hydrogen, and the mixture? Assume the density of impurities to be that of air. (b) If the same lift which is secured with 1,000 cubic feet of commercial helium is obtained by the use of the mixture what is the saving in cost? 59. Helixmi is obtained by liquifying and distilling off all the other gaseous constituents of a natural gas obtained in the Southwest. The helium is obtained in a practically pure state. The other gases are nitrogen, methane, ethane, pro- pane, butane and pentane. What are the physical char- acteristics of these other gases and of helium which make this process possible? 60. When ballonets are used in a balloon they are usually made of such a capacity as to become deflated at the maximum height at which the balloon is to be used. What percentage of the total balloon capacity must be alloted to the ballonet in the case of an observation balloon to operate at a maximum height of 1,500 meters? 61. The Italian Type M airship is designed for a height of 18,000 feet on account of the high mountains to the North. Why are very large ballonets employed ? About what percentage of the total balloon capacity must be alloted to the ballonet? Assume a maximum pressure of 38 millimeters and that the pressure may reduce to zero when the ship returns to the ground. This latter condition is made possible by the fact that the Italian ships are semi-rigid. BALLOONS 62. Why will a submarine, not under way, either float to the sur- face or sink to the bottom while a balloon will, if it ascends at all, tend to reach a certain level at which it will float steadily? 63. Why can the observer in a free balloon locate the point on the ground immediately below him by sighting with the trail rope, while a trail rope or its equivalent will be of no use in a captive balloon, an airplane, or a dirigible? 64. Give reasons why the cars of a dirigible should be placed some little distance in front of the center of lift. 65. Approximately how many pounds are added to the gross lift of the 84,000 cubic foot airship for each drop of temperature of 10 degrees Fahrenheit? 66. The instructions regarding the operation of the dirigible are not to start after sunrise with less than 100 pounds of quickly available ballast and that double the amount will usually be necessary in the late afternoon. Why is more ballast needed in the afternoon than in the morning? 67. Why does every 1,000 feet gain in altitude with the bag full of gas mean a loss of lift of about 160 pounds? Why must this equivalent of load be discharged before landing? 68. Why are instructions given to never force a dirigible up higher by power than it would go by use of ballast? 69. How near does the consumption of fuel, etc., keep place with the loss of lift if the leakage amounts to 3,000 cubic feet per day? PROBLEMS IN PHYSICS NAVIGATION CHART A navigation chart showing the net speed that can be made in any direction under different wind conditions is of great assistance in the proper navigation of airships and airplanes. The normal speed of the machine is taken as 1. The angles between the course of the wind and the direction of the destination are plotted hori- zontally, and the resulting net speed of the airship is plotted ver- tically. The wind velocity is expressed in terms of the air-speed of the machine. Wind velocities equal to 2, IJ/^, 1, J^, 1/3, and 0, times the air-speed are convenient values. Some students may find it interesting to prepare a complete chart. Certain of the following problems can be answered without the use of the chart. 70. Prepare a navigation chart as described above. 71. Can a line be drawn on the chart which represents the maxi- mum speed which can be attained with any wind, no matter how high? If so, draw the line on the chart. 72. Why does the ordinate of this curve for any angle give the wind which will give maximum speed for that particular angle? 73. Under what conditions is a wind blowing at more than 90 degrees to the course unfavorable? Is a wind at less than 90 degrees always favorable? Explain. 74. Why is it that a wind of very high velocity, compared to that of the ship, is always unfavorable except when the angle is zero? 75. Why do curves for 1^ and 2 times the air speed of the ship suddenly end? 76. Within how many degrees of the course must the wind be blowing to be favorable if the wind velocity is equal to the air speed of the ship? 77. If the wind velocity equals the air speed of the ship can the ship be held to its course for wind directions from 90 to 180 degrees from the course? Will there be any progress? BALLOONS 123 DATA ON THE 84,000 CU. FT. AIRSHIP 1. Linear — Length 163 ft. Mean diameter of maximum section 31J^ ft. Maximum width (across fins) 41 ft. Maximum height 46 ft. Length of car 28 ft. 2. Volumes — Envelope (total) 84,000 cu. ft. Forward ballonet 8,500 cu. ft. Rear ballonet 12,500 cu. ft. 3. Total Fin Surfaces- Fixed horizontal 304 sq. ft. Elevators 70 sq. ft. Fixed vertical 152 sq. ft. Rudder 56 sq. ft. 4. Power Plant — Curtiss OXX-3 engine, N-9 pusher, pro- propeller, 8' X 4'-7", direct connected. 1,415 r. p. m. at full speed. Maximum brake horse-power, 105. 5. Weights — Gas bag proper 1,550 lbs. Gas bag and associated parts 1,760 lbs. Fin surfaces 310 lbs. Car, engine, tanks, etc 1,280 lbs. Instruments, parachutes, tools, etc 350 lbs. Two men 320 lbs. Necessary ballast 100 lbs. Fuel and oil (full) 650 lbs. Gas, 84,000 cu. ft. of hydrogen (97 per cent quality) 630 lbs. 6. Gross Displacement at 70° F. and 30" Baro- meter 6,300 lbs. 124 PROBLEMS IN PHYSICS 7. Speed and Resistance — Maximum air speed 48 m. p. h. Minimum resistance at 48 m. p. h 540 Its. Resistance at other speeds R=.33 ^•* Ordinary cruising speed 39 m. p. h. Vertical resistance of balloon without power, 3.5 S*, in which S is the ver- tical speed in feet per second. 8. Variations in Lift and Load — Leakage of gas 2,000 to 5,000 cu. ft per day Fuel consumption at full power 65 lbs. per hour Fuel consumption at cruising speed . . 46 lbs. per hour Evening contraction may produce a sur- plus load of as much as 400 lbs. Rain may add a load of 400 lbs. Every 1,000 feet altitude with the bag full of gas means a loss of lift of about 160 lbs. BALLOONS 125 AVERAGE AIR TEMPERATURES AND DENSITIES AT DIFFERENT ALTITUDES. ^ (Standard density=L293 Kg. per cu. m., 0°C., 76 cm. pressure.) Atmospheric density Altitude Pressure Tempera- Vapor ture pressure Per cent Per cent standard surface Feet Inches op Inches 29.92 59.0 0.36 94-4 1 00.0 1,000 28.86 56.0 .32 91.6 97.1 2,000 27.83 52.9 .28 88.g 94.2 3,000 26.83 49.8 .25 86.2 91.4 4,000 25.86 47-3 .22 83.6 88.6 5,000 24.92 44-9 .19 80.9 85.8 6,000 24.02 42.5 .16 78.4 83.1 7,000 23.12 40.0 .14 75-9 80.4 8,000 22.28 37.3 .12 73-5 77-9 9,000 21.46 34.3 ■105 71.3 75-5 10,000 20.66 31.2 .086 69.1 73.2 11,000 19.88 27.9 .072 66.9 70.9 12,000 19.13 24.6 .060 64.8 68.7 13,000 18.40 21.3 .050 62.8 66.6 14,000 17.69 17.8 •045 60.8 64.S 15.000 17.00 14.2 .040 S8.9 62.4 16,000 16.35 10.8 •03s 57-1 60.5 17,000 15.72 7-4 .030 55-3 58.6 18,000 15.10 4.0 .025 53.5 56.7 ig,ooo 14.50 0.4 .020 51.8 54-9 20,000 13.92 — 3-4 .017 50.1 S3. 1 21,000 13.36 — 7.2 .015 48.5 SI.4 22,000 12.82 — 1 1.0 .013 47.0 49.8 23,000 12.29 -14.8 .010 45-4 48.1 24,000 11.79 —18.4 .008 43-9 46.5 25,000 11.30 — 22.0 .007 42.4 45-0 26,000 10.83 —25.6 .006 41.0 43.S 27,000 10.37 — 29.2 .005 39.6 42.0 28,000 9-93 — 32.6 .004 38.2 40.S 29,000 9.51 — 36.0 .003 36.9 39.1 30,000 9.10 —39.2 .002 35.4 37-7 DENSITY OF GASES, 0°C., 76 CM. PRESSURE. Hydrogen 0056 pounds per cu. ft. Helium 0112 pounds per cu. ft. Illuminating gas (approximately) 0500 pounds per ca ft. Air 0807 pounds per cu. ft. (Commercial hydrogen is 98 per cent pure, heliimi 92 per cent. In all problems assiune impurities to have the density of air.) 1 From the Monthly Weather Review, March, 1919, 47 : 157. PART VI. RAY FILTERS RAY FILTERS The information necessary for the answering of the following questions can be found in any good optical text. Preston's "Theory of Light" or Wood's "Physical Optics" are suggested as suitable books. It is believed that an instructor will have no particular difficulty in using the following questions in an elementary course if a little time is devoted to furnishing the necessary backgroun4- The use of ray filters in photography is also treated under the sub- ject of Aerial Photography. Figures 1 and 2, show bow success- fully the effects of "haze" have been eliminated. In order to illustrate the subject matter of the last four ques- tions, the instructor should have at hand sample filters. Small discs of cobalt blue glass and of the various noviol glasses manufactured by the Corning Glass Works, Corning, Pa., are recommended. By combining the blue glass with the different noviol glasses, very interesting filters are produced. The most striking results are obtained when different green pigments, apparently the same to the eye, are examined through these filters. PROBLEMS 1. Why does the light scattered by fine particles in the air inter- fere with the distinctness with which distant objects can be seen? 2. What particular color or portion of spectrum would you expect to predominate in the scattered light? 3. Can this scattered light be eliminated by means of a suitable ray filter? 4. Characterize roughly the spectral transmission which would seem desirable in a ray filter for observing distant objects. 5. Why will distant objects appear more distinct when viewed through such a ray filter? 6. What will be the color of such a ray filter when viewed by transmitted light? 1 29 130 PROBLEMS IN PHYSICS 7. State in general terms how the apparent color of red objects will be affected. Of blue objects. 8. In photographing a distant view why is a ray filter desirable? 9. Why is it that the common yellow ray filter used on a camera to secure "cloud effects" by reducing the intensity of the blue light of the sky would be useful in securing better definition of distant objects? 10. What are the optical characteristics of such a ray filter? 11. Why should the relative sensitivity of the plate for different portions of the spectrum be taken into account in order to determine whether the spectral transmission of the ray filter is satisfactory? 12. State briefly the optical characteristics of a ray filter to be used with orthochromatic plates, which are sensitive well down into the red end of the spectrum. 13. What different characteristics would you expect in a filter to be used with ordinary plates, the maximum sensitivity of which lies in the blue or even in the ultra-violet portion of the spectrum? 14. Suppose the filter designed for ordinary plates is used for both ordinary and orthochromatic plates, which would require the greater increase in exposure? 15. Why should one take into account the visibility curve of the eye in selecting a filter to be used for visual observation? 16. State briefly what modifications might be made in the require- ments to be satisfied by a filter when the visibility curve is taken into consideration, as compared with those based upon the assumption of uniform sensitivity throughout the visible spectrum. 17 In the above questions it has been tacitly assumed that the sun is the source of illumination. Suppose a searchhght is to be used at night. In what part of the spectrum will the scat- tered light be most abundant? 18 What can you say of the relative advantages of viewing the dUtant object from a point near the searchlight and from a point some distance to one side of the searchlight? Figure 1. Area near Langley Field. Va. Photographed with an ordinary plate, with no filter. (Exposure 1/340 second; altitude 5,500 feet. Low altitude gives an ad- vantage over plate used for photograph below.) Figure 2. Same area photographed with a s;:ecial American Panchro- matic plate, using a red filter. (Exposure 1/30 second; altitude 10,003 feet.) RAY FILTERS 131 19. What are the optical characteristics of a ray filter to be used when viewing a distant object illuminated by a searchlight? 20. How could one modify the glass in front of a searchlight so as to secure the same result as is obtained with a ray filter in front of the eye? 21. What characteristics should be given to the arc in order to secure this same result? 22. What characteristics could be given to the reflector in order to secure this same result? 23. The French did, in fact, substitute gold for silver on their searchlight mirrors. How does the effect produced by the gold harmonize with the characteristics which would be de- sirable in a reflector? 24. This gold reflecting surface worked well when the searchlights were used for the observation of terrestrial objects, but when used for anti-aircraft work, the enemy quickly appreciated the lack of a portion of the spectrum and painted their air- planes so that they were invisible when illimiinated with these searchlights. What color did they paint the airplanes? 25. Buildings surrounded by green foliage are frequently painted green in order to lessen the contract between them and the trees. When viewed through an appropriate filter, the foliage may appear black while the painted surfaces appear red. What does this seem to show regarding the relative amounts of red and green light reflected by green foliage and the pigment of the paint? 26. With other painted surfaces and different filters the foliage may appear red and the paint black. What does this show? 27. What can one say of the transmission of the filter in each case? 28. In general what should be the characteristics of a filter designed to increase contrast between the apparently similar colors ? 29. Describe in general terms how signalling can be accomplished by the use of a light which appears practically uniform in intensity to the enemy, but is seen by the friendly observer as a series of flashes. PART VII. OPTICAL SYSTEMS OF INSTRUMENTS OPTICAL SYSTEMS OF INSTRUMENTS An attempt has been made in the following pages to furnish material which will be of assistance to the instructor who wishes to introduce into a course in Light, subject-matter dealing with the simpler optical systems used in ordinary optical instruments and in military instruments. Much of the material is suited to an element- ary course. The following books are mentioned as references : Bureau of Standards, "The Properties and Testing of Optical In- struments, Circular No. 27." Drude, P. K. L., "The Theory of Optics," Translated by C. R. Mann and R. A. Millikan, Longmans Green & Co. Gleichen, Alexander, "The Theory of Modern Optical Instruments," Translated by H. H. Emsley and W. Swaine. His Majesty's Stationery Office, London. Nutting, P. G., "Outlines of Applied Optics," P. Blakiston Son & Co., Philadelphia, Pa. Southall, T. P. C, "Mirrors, Prisms and Lenses," The Macmillan Company, New York, N. Y. The instructor not already familiar with military instruments will find the book by Gleichen indispensable. It was translated by the British Government in order to supply information to Army officers and manufacturers of Army instruments and contains two chapters on range finders which constitute one of the best sources in English for information in regard to this instrument. It also contains a chapter on other military instruments as, for example, the panoramic sight and the battery commander's telescope. No attempt has been made to give an extended description of the different instruments or of their use. However, there are fur- nished diagrams of the optical systems of the instruments and of the different types of prisms. " These will be found useful in connec- tion with the problems. The student will have to depend upon reference books and the instructor for the necessary background. It is felt that wherever possible the actual instruments and prisms should be placed in the hands of the students. It will be difficult for an instructor to adequately present to a class the mate- 135 136 PROBLEMS IN PHYSICS rial dealt with in the questions unless he has at hand the actual prisms and instruments as outlined above. The list is as follows' : Opera glass to illustrate the Galilean telescope. An inverting telescope. A terrestrial telescope with lens erecting system. Right angle telescope.^ A prism binocular to illustrate the Porro erecting system. Right angle prism. Roof prism. Penta prism. Porro prism system. Battery commander's telescope. Panoramic sight. An 80-centimeter or 100-centimeter horizontal base range finder. Set of panoramic sight optics mounted in skeleton form so that the system forms a practicable telescope. The objective prism and rotating prism should be mounted in such a way that they can be rotated, but it is not necessary to have them connected by gears as in the completed instrument. ^ An institution having a Reserve Officers' Training Corps Unit should enlist the assistance of the Commandant in procuring as much of this equip- ment as possible. - If desired this may be omitted as the lower half of the panoramic sight is a complete right angled telescope. Figure 1. Panoramic Sight. OPTICAL SYSTEMS '37 f OBJECTIVE EYEPIECE. Figure 2 THE GALILEAN TELESCOPE 1. Locate the image formed by the objective of the telescope. 2. Trace the course of the rays through the instrument showing that the final image is erect. Is this final image real or virtual? 3. When the adjustment is "telescopic," i. e., when the focal planes of eyepiece and objective coincide, and the entering pencil is parallel, is the emergent pencil parallel or con- vergent? 4. Locate the image formed by the telescope (not the objective) when adjustment is "telescopic." 5. Is the image formed by the telescope any nearer the eye than the object viewed? 6. How then does the telescope magnify? 7. Give the formula for the magnification. 8. Is there any difference in the "accommodation" of the eye when viewing a distant object and viewing the image through the telescope in "telescopic" adjustment? 9. If one is near sighted, in what direction must the ocular, in telescopic adjustment, be moved for comfortable vision? 10. Locate the exit pupil of the Galilean telescope. 11. Why cannot the pupil of the eye be brough to coincide with the exit pupil in this type of telescope? 12. What effect does this fact have upon the field of view? 13. What effect upon the illumination of the field? 138 PROBLEMS IN PHYSICS 14. Is there any plane within the instrument in which an object could be placed and appear sharp to the observer's eye when the eye is accommodated for the distant object under observation? 1 5. What bearing does this have upon the place at which a reticule, having cross-lines, should be put? 16. What bearing does this have upon the place at which a diaphragm should be placed in order to provide a sharp well- defined boundary for the field of view? 17. Assuming that the maximum field of view for the eye is 45 degrees, what is the maximum actual field for a six-power instrument? 18. What is the relation existing between the exit pupil, entrance pupil, and magnification? 19. Assuming that the exit pupil is to be 6 millimeters in diameter, what must be the diameter of the objective of a six-power instrument? 20. What will be the maximum resolving power of the objective ? 21. What will be apparent value of the angle subtended by two points just resolved by the objective when viewed through the six-power binocular? OPTICAL SYSTEMS ^39 h-9 OBJECTIVE BVEPieCt Figure 3 INVERTING OR ASTRONOMICAL TELESCOPE 22. Locate the image formed by the objective. 23. Where is the plane within the instrument which is in focus for the observer's eye when the eye is accommodated for the distant object? 24. Where should a recticule having cross lines or scale be placed? 25. Why do the cross lines appear stationary with respect to the object when the eye is moved? 26. State clearly what is meant by parallax. 27. Why is there parallax when the reticule is displaced from its normal position? 28. If, as the eye is moved from side to side in front of the eye- piece, the cross lines appear to move, relative to the distant object, in the same direction with the eye, is the reticule nearer or farther from the objective than the focal plane? 29. Where in the instrument should a diaphragm be located in order to provide a sharp boundary for the field? 30. What must be the diameter of this diaphragm if the focal length of the objective is ten inches and the field is four degrees ? 31. Locate the exit pupil of this telescope. 32. Why can the pupil of the eye be brought into coincidence with the exit pupil in this type of telescope? 33. What effect does this fact have upon the field of view ? 34. What effect upon the illumination of the field? 35. What is the formula for the magnification of this instrument? 140 PROBLEMS IN PHYSICS 36. Assuming that the exit pupil is as large as the pupil of the eye, is the brightness of the image increased by enlarging the objective? 37. If you believe that the brightness is not increased, draw a diagram showing clearly why the extra area of the objective does not contribute to the illumination of the image. 38. If two telescopes have exit pupils of the same size, upon what may a difference of illumination obtained with the two instrimients depend? 39. Why does an increase in the size of a photographic aperture always increase the brightness of the image? 40. Wherein is the difference between this case and that of enlarging the objective of the telescope? OPTICAL SYSTEMS 141 m f OBJECnVE ERECTING SrSTEM Figure 4 ErEPiecE TELESCOPE WITH LENS ERECTING SYSTEM 41. Trace rays through this system and show that the final image is erect. 42. Locate two planes, each of which is in focus when the ob- server's eye is accommodated for the distant object? 43. Why can a reticule be placed in either of these planes? Should a reticule with a marked scale be placed in the instrument as it is to appear or should it be reversed or turned upside down or both ? 44. In what place could a diaphragm be placed to sharply limit the field of view? 45. How does the position of the erecting system influence the magnification produced by the instrument? 46. Develop a formula for the magnification of a telescope with a lens erecting system. 47. Locate the exit pupil of this telescope. 142 PROBLEMS IN PHYSICS PORRO PRISM OBJECTIVE ERECTING SYSTEM Figure 5 TELESCOPE WITH PORRO PRISM ERECTING SYSTEM 48. Trace the rays through a pair of porro prisms. Is the image erected? 49. How many reflections do the rays undergo? Figure 6. One Meter Horizontal Base Range Finder. OPTICAL SYSTEMS 143 Figure 7. Porro Prism PRISMS 50. If the reflection of a printed page is viewed in a mirror, the letters are observed to be reversed. This is commonly spoken of as perversion of the image. Is the image per- verted after a single reflection in a prism? 51. Is it perverted after two reflection? 52. Is the image perverted after an odd number of reflections? 53. Is the image perverted after an even number? 54. Is the real image formed by a lens perverted? 55. Is a virtual image formed by a lens perverted? 56. Does any combination of lenses ever pervert an image? 144 PROBLEMS IN PHYSICS Figure 8. Right Angle Prism 57. Is the image formed by a telescope with a lens erecting system perverted? 58. The erection of the image is to be accomplished by means of prisms. Should an even or an odd nimiber of reflections be employed, if the image is to be unperverted? 59. If a telescope gives an erect and unperverted image, in what direction does the field move when the telescope is turned to the right? 60. Is the relationship between movement of field and movement of telescope a natural one? 61. If the telescope gives an image erect, but perverted, in what direction does the field move when the telescope is moved to the right? OPTICAL SYSTEMS 145 62. 63. 64. 65. Figure 9. Roof Prism Is the relationship between movement of field and movement of telescope a natural one ? Which type of telescope would be more advantageous for lay- ing a gun, that of Problem 59 or 61 ? In general, what statement may we make regarding the number of reflections which light must undergo in a military tele- scope? In the drawing of a right angle prism, BA is a ray incident normally upon the face of the prism and emerging after a reflection on the hypothenus face. Will there be total re- flection if the index of the glass is 1.52? 146 PROBLEMS IN PHYSICS f\ Figure 10. Penta Prism 66. CA is a second incident ray (not traced through the prism) lying in the plane ABCD and making an angle CAB with the ray BA. What is the maximum value of angle CAB, if total reflection is to be secured at the hypothenus face? 67. Suppose we have any other ray, incident at A, making an angle with BA less than or equal to this maximum value, but not lying in the plane ABCD, will it be totally reflected? 68. What limit does this set upon the maximum angular value of the field which may be viewed, fully illuminated, by means of an unsilvered right angle prism? 69. What is the limit for a prism made of glass with an index of reflection of 1.52? 70. Will this angular extent of field be increased if flint glass, with an index of refraction of 1.62, is used? 71. What will the angular extent of field be for 1.62 glass? 72. Can the field of a right angle prism be increased by silvering the hypothenuse face? OPTICAL SYSTEMS 147 73. The roof prism bends a ray, incident normally upon one face, through 90 degrees, as does the right angle prism. How- ever, in the roof prism there are two reflections, whereas in the right angle prism there is only one. What can be said of the difference between the image formed by the one prism and that formed by the other? 74. In the penta prism the reflection takes place at two faces in- clined to each other at 45 degrees. What is the total de- viation of the ray? 75. Is the image shifted when the penta prism is rotated slightly about an axis parallel to the intersection of the two reflect- ing faces? 76. Is the deviation of the rays altered when the prism is rotated? 77. Is the image viewed in the penta prism perverted? 148 PROBLEMS IN PHYSICS OBJECTIVE. ROOF PRISn EYEPIECE Figure 11 RIGHT ANGLE TELESCOPE 78. In the right angle telescope shown, the prism used is a roof prism. Why is the roof prism required instead of an ordi- nary right angle prism? )?ure 12. Battery Commander's Telescope. OPTICAL SYSTEMS 149 OBJECTIVE PRISM OBJECTIVE ERECTING PRISM EYEPIECE. Figure 13 BATTERY COMMANDER'S TELESCOPE 79. Trace a pair of rays through the Battery Commander's tele- scope and discover whether the image is erect or not. 80. Count the number of reflections and determine whether the image is perverted. OPTICAL SYSTEMS 151 THE PANORAMIC SIGHT 81. Will the image be erect in the hypothetical panoramic sight shown in Figure 14 (a), which has two right angle prisms and the objective prism turned for a back sight? 82. Will the image be perverted? 83. If the objective prism is turned around so that observer looks straight ahead, as in Figure 14 (b), will the image be erect? 84. Will it be perverted? 85. What will be the position of the image for an intermediate position of the objective prism? 86. The system actually employed in the panoramic sight is shown in Figure 14 (c). It is to eliminate rotation of the image that the rotating prism is added, which is so geared to the objective prism that it rotates at half the angular velocity of the objective prism. If the two ordinary right angle prisms are retained, will the image now be perverted? 87. How will the substitution of a roof prism for the lower right angle prism remedy this difficulty? Try to picture to your- self the manner in which the rotation of the rotating prism keeps the image erect as the objective prism is turned. ■^ OPTICAL SYSTEMS i53 THE RANGE FINDER 88. Why are penta prisms instead of right angle prisms used at the ends of the base line of the range finder? 89. If an ordinary right angle prism were used instead of the penta prism, through how great an angle would it have to rotate in order to displace the reflected ray 1 second? 90. If the square faces of the prism are 2x2 inches, and one of the edges is held stationary, how far would the other edges have to move in order to permit this much rotation? 91. In an instrument of the type which shows one half of the field inverted, do both halves of the range finder have the same number of reflections? 92. With the sharp dividing line employed in the range finder the eye can detect a lack of coincidence between two points subtending an angle of 15 seconds in the apparent field. To what actual angle in the real field does this correspond, if the magnification is fifteen? 93. If the base is 9 feet, and the object is 4,000 yards away, how much nearer must the object be brought in order that its parallax from the two ends of the base line may change 1 second ? 94. If the object is 8,000 yards away, how much nearer must the object be brought in order that its parallax may change 1 second? 95. What will b«. the angular error in the final adjustment if the adjusting lath is one-half millimeter shorter than the base of the ra^ige finder and is set up at a distance of 30 meters for adjus-jng the range finder? 96. In the adjustment of the range finder, it is assumed that the two principal rays, proceeding from the two marks on the lath to tile respective ends of the range finder are parallel and make the infinity adjustment. If the range finder has a one-meter base, at what distance from the range finder will these rays actually intersect under conditions of Problem 95? 97. To what linear error will this angular error correspond, if the object is distant 3,000 meters from the range finder? 154 PROBLEMS IN PHYSICS 98. If the adjusting lath is set up 200 meters from the range finder, what will be the angular error in adjustment? 99. To what linear error will this correspond when the object is distant 3,000 meters? 100. The adjusting lath for a one-meter range finder is of the cor- rect length but, instead of being parallel to the range finder, it is rotated about a vertical axis through an angle A, thus producing foreshortening. If the adjusting lath is set up 200 meters from the range finder, how great will the angle A have to be in order to produce an angular error corre- sponding to a three per cent error at a range of 3,000 yards ? The Engineer School at Camp Humphreys A REPORT ON METHODS OF TEACHING ENGINEERING . WAR DEPARTMENT COMMITTEE ON EDUCATION AND SPECIAL TRAILING WASHINGTON ^L The Engineer School at Camp Humphreys A REPORT ON METHODS OF TEACHING ENGINEERING WAR DEPARTMENT COMMITTEE ON EDUCATION AND SPECIAL TRAINING WASHINGTON LETTER OF TRANSMITTAL. Washington, D. C, June 30, 1919. The Honorable, The Secretary of War. My dear Mr. Secretary: Herewith is submitted a report on the work of The Engineer School at Camp A. A. Humphreys. This has been prepared under the direction of the Advisory Board of the Committee on Education and Special Training in response to an invitation from the Chief of Engineers. The work now being done at this school is pioneer work in higher technical education and it is, therefore, of great significance to the future of engineering education both in the army and in civilian schools. It is recommended that a small edition be printed and distributed to those who may be interested. Respectfully, C. R. MANN, Chairman, Advisory Board. TABLE OF CONTENTS Page PART I. The Engineer School at Camp A. A. Humphreys 7 PART II. The Course in Mechanics of Engineering: Outlines of Class Work in Mechanics of Engineering ... 21 The First Study Problem 23 Teachers Notes on the First Study Problem 25 The Second Study Problem 29 The Third Study Problem Co The Fourth Study Problem 31 The Fifth Study Problem 32 Specifications for Mechanics Work 33 Chart 36 PART III. Courses in Structural Engineering: A. Topical Outline of the Course in Plain Masonry Structures 45 I. Statement of the Minor Problem 47 Minor Problem No. 1 48 II. Instructors Notes on Minor Problem No. 1 50 III. Statement of the Subsequent Minor Problems . .53 Minor Problem No. II S3 Minor Problem No. Ill 56 Minor Problem No. IV 60 Minor Problem No. V 63 B. Synopsis of the Course in Materials — Timber: 1. Analysis of Problem No. I into Minor Problems 68 2. Instructor's Notes on Minor Problem No. I . . . . 73 THE ENGINEER SCHOOL AT CAMP A. A. HUMPHREYS Immediately after the Civil War, Congress authorized the maintenance of a permanent battalion of engineers as a part of our regular army. An engineer post under the direct control of the Chief of Engineers was established at Willets Point, New York, where three companies were permanently stationed. In the fall of 1866 plans were discussed for a school of application for officers and men of the Reserve Corps. It was also planned to make the school a special laboratory of the Engineer Corps for investigations and experimental research. The officer instruction at first was carried on through the Essayons Club, a voluntary organization, which encouraged individual reading and preparation of papers on professional subjects for discussion. The Engineer School at Willets Point developed gradually from the Essayons Club status into a school of application covering the use of astronomical and surveying instruments and important investigations in electricity as applied to the operation of submarine mines. This electrical work at the school resulted in the first prac- tical system of electrically controlled submarine mines adopted by the United States for the defense of its important harbors. The experimental work associated with the school developed by 1881 to a point that made it seem desirable to detail cutillery officers to the school for special training in torpedo work, mine planting, etc. The curriculum gradually expanded to keep pace with the growth of scientific and engineering knowledge. In 1901 the school was moved to Washington Barracks, D. C, where a two year course was given in military, civil, electrical and mechanical engineering. Regular examinations were given and graduation from the course was noted in the army register as an important factor in the officer's military record. The students admitted to this course were graduates of West Point, who had been assigned to the Corps of Engineers. After graduation they were usually sent for one year's training with troops in the field and then assigned to the school at Washington CAMP HUMPHREYS REPORT Barracks. The method of instruction there was that usually fol- lowed in colleges in their seminar courses. Officers were assigned certain courses of reading and attended conferences with their instructors at stated intervals. In connection with this reading course, a considerable amount of practical laboratory work was done in the electrical courses and a quite complete course in prac- tical field astronomy and the use of astronomical instruments in geodetic surveying was given. After completion of the course, the engineer was assigned as apprentice to an older engineer on prac- tical work, and was as a rule not assigned to responsible charge of engineer projects until years after graduation from West Point. The war interrupted the work of The Engineer School. In its stead a large program of reserve officer training had to be inaugu- rated. Thousands of men who had had technical training in civilian schools had to be given intensive military training in order to pre- pare them for commissions and active service with the army. With the signing of the armistice the Chief of Engineers was again con- fronted with the problem of re-establishing the engineer school to supply the professional training needed to make an engineer officer out of a West Point graduate. This problem was rendered more acute by the fact that the West Point course had been cut off at the end of two years as an emergency measure, and 62 graduates of the two-year course had been commissioned as second lieutenants in the Corps of Engineers with but very slight instruction in the applied sciences. Since the emergency had passed these men had to be trained for service as engineers on the lines of work for which the Corps is responsible in times of peace. Under these conditions, Major General Wm. M. Black, Chief of Engineers, decided to establish at Camp Humphreys a new school of engineers, with a three-year course of instruction, designed to develop officers who would be able to perform the extraordinarily varied and specialized duties required of the Corps of Engineers. In organizing this new school. General Black desired to apply the lessons of the war-time experience in intensive officer training, as well as the earlier experience of the engineer school, to the problem THE ENGINEER SCHOOL of training engineers who should be well grounded in the funda- mental principles of engineering science and able to tackle any problem which falls in the Held of the Engineer Corps and to get results. In order to accomplish these ends, Colonel V. L. Peterson, who made an exceptional record as commandant of the Officers' Train- ing School at Camp Lee, was assigned as commandant of the new school at Camp Humphreys. A number of engineer officers were detailed to co-operate with Colonel Peterson in planning the cur- riculum and the course of study. The majority of these officers had no experience with teaching or with schools, but all had demon- strated their ability as practical engineers, and all had clear concep- tions of the result that was required. In the selection of officers to do the actual teaching a similar policy was pursued. Men were selected primarily because of suc- cessful practical experience in the various lines of work which they were called upon to teach. Their work as teachers is carefully supervised and frequent conferences are held both among the officer instructors and with the commandant. The problem and practical application method of instruction, which before the war had been used successfully in some courses in the old engineer school at Washington Barracks, and in some of the best civilian institutions, was adopted as the basic method of treat- ment. The curriculum was planned to meet the requirements of men who had completed the emergency two-year course at West Point and had been commissioned as second lieutenants in the Corps of Engineers. After only three weeks of planning and preparation, the school was opened on December 7 with 62 lieutenants and 10 captains as students and 20 instructors. Later 18 more captains, who had graduated from the emergency three-year course at West Point and had seen some service with troops, were added to the student body. The subjects included in the first-year program and the amount of time devoted to each are as follows : CAMP HUMPHREYS REPORT Hours Total Subject. per week. Weeks. Hours. Mechanical Drawing 10 15 150 Chemistry (class) 12 12 144 Chemistry (laboratory) 5 4 20 English 1 16 16 Engineering Mechanics 12 25 300 Shop Work 8 10 80 Sound and Light 5 9 45 Equitation 2^^ 20 50 Because of the speed with which the project was executed, the perfection of the details of courses and administration proceeded in parallel with the operation of the school. It has, therefore, been possible to make changes quickly whenever faults appear and to maintain a fine spirit of investigation in the entire enterprise. The whole organization is operating as a well-trained team, determined to achieve a clearly defined result in the best possible way. Mechanical drawing was intended to supplement the work which the men had already had at West Point. A few simple ex- ercises with lines and circles in pen and ink were given to assure familiarity with instruments. Each student was then required to construct from notes and specifications placed on the blackboard sections of structural steel, crane hooks and chains, nuts, bolts and screws. There was no copy work. Drill in visualizing from drawings was given by working up orthographic projections from isometrics and the reverse. The objects for these exercises were generally rather complicated machine parts. Finally three plates of stereotomy were required. In all of these a student was required to complete the entire drawing, and to make isometrics, templet, patterns, and bevels for the most complicated stones. The final problem of this first stage of the course called for the complete de- sign of a structural steel roof truss, the student being guided in his work by notes published by the school. About April first the mechanical drawing was replaced by a course of Sound and Light, which treated of the military applica- tions in sound ranging and optics, which have developed so rapidly during the war. This course is a combination of lectures, recita- tions on assigned readings and laboratory work very similar to the THE ENGINEER SCHOOL physics laboratory work found in any American college. Each student received a mimeographed direction sheet for each experiment. The purpose of the work in chemistry was to give the student a clear picture of the chemical industries of the country and a gen- eral view of the trend of chemical work. The army engineer does not need the detailed and exact facts which the chemist or chemical engineer must have. He need not be an expert laboratory work- man. He should, however, know how, where and why certain products are manufactured, the general outlines of qualitative and quantitative analysis, some organic chemistry, materials to be em- , ployed for the manufacture of chemical apparatus, etc. He should also understand the fundamental principles of manufacture relating to the handling of labor and the shipping, storage and costs of raw materials and finished products. He should know that yield figures are of importance only when connected with data on production and costs. He must realize that text-book equations are very in- complete expressions of reactions, indicating results under ideal conditions. In order to achieve these ends, the course gave less attention to the chemical reactions as such and paid greater attention to com- mercial methods of production, the actual application of the ele- ments to purposes of warfare, the manner of shipping, storing and preserving. All the elements were discussed in this manner before the general study of compounds began. Lengthy introductions were avoided and the problem presented as it would be in the fac- tory. For example: Given a calcium phosphate rock of known purity; what weight of rock is needed to produce enough phos- phorus to fill a given number of smoke grenades of given capacity? In addition to the class discussions, the students spent altogether about 20 hours in the laboratory learning the simple standard reac- tions and the elementary conceptions of qualitative analysis. For work in English, the student is required to write reports on subjects with which he is familiar. For example: A trip to the Bureau of Standards was the subject of one report. These reports are criticized and retxu-ned for correction and consideration. In CAMP HUMPHREYS REPORT order to develop ability in oral English also, the students are di- vided into sections of 18 each, and each section discusses orally the questions of importance to its members, such as : Should officers be promoted by seniority or by selection? A committee is ap- pointed from the section to investigate the subject under considera- tion and prepare a report. After the report is presented it is dis- cussed by all members of the section. A vote is taken as to whether the meeting will accept the findings of the report or not. While the instruction in all departments of the school is in accord with progressive tendencies of current educational practice, the course in Mechanics of Engineering is unique and stands out as a striking contribution to methods of teaching this difficult sub- ject. Full details of this work are given in Part II. It is, therefore, probably sufficient to mention here that the fundamental conception back of the course is to train students to analyze prob- lems by engineering methods and to gain self-confidence so that they do not hesitate to tackle difficult situations. To accomplish these ends the work begins with a real problem — a small highway bridge near the camp— which they examine. In the classroom a simple type of bridge was taken for investigation. A heavy piece of artillery must be drawn across the bridge. Will the bridge stand it? Is it safe? In trying to answer this question the student soon discovers that he must analyze the problem and then secure tools in the way of fundamental principles and data concerning materials. He is, therefore, glad to be guided in an analysis and to be shown where these tools and this information can be secured. As he proceeds and his collection of principles and information becomes more ex- tensive, he gradually acquires greater confidence in his ability to analyze and meet any ordinary situation. Before the close of the course he is taken through a standard text-book as a review and as a means of organizing into a logical system the material which he has learned by use. There are many other phases of this mechanics work that are worthy of note. Specifications are issued concerning the manner in which all computations must be performed. No credit is given for THE ENGINEER SCHOOL 13 an exercise unless the numerical result as well as the method of solution is correct. In the early stages all solutions are made on the basis of fundamental analyses and no derived formulae are used. Later, formulae and standard hand books are freely used in order that the students may secure a proper working knowledge of them. Early in March it was decided to give the students some shop work in order that they might have a general working knowledge of the essential operations and the time required to complete shop jobs of various kinds, and also that they might become familiar with the properties and limitations of different kinds of machine tools commonly used in working both wood and metal. Since the work was to begin April first, it was decided to follow the outline of exercises that was already in use in one of the well-known en- gineering schools. In accordance with this plan, the students fol- lowed directions and blueprints which would carry them through a series of typical experiences in ordinary shops. It is planned next year to substitute for these typical exercises productive jobs required for the repair and maintenance of the reg- ular camp machinery and equipment, thereby introducing the prob- lem idea and giving the greater incentive that comes from doing necessary jobs. In grading the students the standard West Point system is used. Each man receives a numerical grade for every oral or writ- ten recitation. The scale used is from zero to three. The arith- metical sum of all grades received during the month determines the standing for the month and the order of merit is that of the sums from the highest to the lowest. In the mechanics course this system was modified by assigning different weights to different portions; of the work. The entire course was divided into five periods, and the marks during the first period were assigned a weight of 1, those during the second period a weight of 2, those during the third period a weight of 3, etc. For the final records only the grades assigned during the last period were used. The standard army intelligence test was given to all of the 14 CAMP HUMPHREYS REPORT Students during the last week of the course. The result indicated that all but two of the students were of grade A, which is in accord with the general record made by the entire Engineer Corps during the war. The school closed its first year on June 15, and the students were sent to France in charge of Colonel Peterson to make prac- tical studies of the engineer work done over there during the war. The course for the second year will be opened in September, and will consist almost entirely of engineering subjects treated by the method that has proven so successful in the engineering mechanics. From 20 to 30 experienced engineer officers have been working for a number of months preparing in detail the major, minor and development problems which constitute the backbone of the course. Special reports giving details of the curriculum as at present planned and samples of sections of the courses are appended. In making this study the Committee on Education and Special Training has had the co-operation of the following specialists : S. L. Conner, Professor of Railroad Engineering, Tufts College, Medford, Massachusetts. F. H. Evans, Consulting Engineer, Ransom & Randolph Co., Toledo, Ohio. W. K. Hatt, Professor of Civil Engineering, Purdue Uni- versity, Lafayette, Indiana. Wm. A, McCall, Instructor in Educational Psychology, Columbia University, New York. H. N. Ogden, Professor of Sanitary Engineering, Cornell University, Ithaca, New York. These experts devoted from one to four weeks to this work, and each of them spent a number of days at Camp Hvunphreys in a close study of the school. Part II presents the details of the course in mechanics of engineering as actually given during the past six months. No time for preparation of this course was available before instruc- tion actually began, and therefore this outline is a record of work as it progressed from day to day. The outline must not be taken THE ENGINEER SCHOOL iS as a final statement of how the work will be handled because the details are constantly being revised and improved. Part III gives the outlines so far prepared for next year's work in civil en- gineering. These courses have not yet been given and will doubtless be modified considerably both before beginning the classes and during the progress of the work. Similar series of problems are in preparation for the classes in electrical and me- chanical engineering. During the last week of the course a questionnaire was circu- lated among the students by Mr. McCall asking their impressions of the relative merit of the Camp Humphreys course and that of West Point, and also their estimate of the work in mechanics. The results indicated that the students, saw little difference between the two schools in general, but that the mechanics course at Camp Humphreys was unanimously voted to be more stimulating to interest and speed of learning. These student opinions may be taken for what they are worth, as it is far too early to secure objective evidence that will warrant positive conclusions. It is also the vmanimous opinion of the civilians who studied the work that the methods of instruction developed in the me- chanics course are a real contribution to engineering education because they win and hold the students' interest; and that there- fore these methods, as it is planned to apply them next year to the engineering courses, are a valuable contribution to the solution of the difficult problem of developing young engineers who are well grounded in fundamental engineering sciences and who know how to tackle a new problem and get results. PART II THE COURSE IN MECHANICS OF ENGINEERING THE COURSE IN MECHANICS OF ENGINEERING The course in engineering mechanics is designed to develop mastery of the fundamental principles and facility in their use in solving unfamiliar problems. Hence it begins with the analysis of real problems and introduces mathematical and physical prin- ciples when the need for them as tools has become apparent. The series of problems are so selected as to require the use of the essential conceptions and principles of mechanics. The first problems are worked through without a text. Later hand books and tables are used freely. The last five weeks of the course are devoted to a review with a standard text for the purpose of fixing the subject in mind and organizing it in logical form. In the following pages a portion of the analysis of the first problem is given in detail in order to show the successive steps and methods of procedure. Owing to the fact that instructors soon grasped the main ideas of the method of presentation, sub- sequent study problems were not outlined so carefully. It was found that the main features were more easily covered in con- ference at which the instructors made such notes as they needed. Skeleton outlines of these problems are shown on the chart, in which the organization of the course and the analysis of the separate problems are indicated graphically. These outlines are significant because they indicate the novel method of organization. The main feature lies in the fact that the unifying center of each problem is a material structure, such as a bridge, a water tower or a dam, and that around this center are grouped numerous mechanics concepts and principles. In ordinary methods of mechanics instruction the subject-matter is organized about a mechanics principle as a center, and then some special details of an engineering structure are cited as examples of the application of the principle in question. The outline of the first few weeks instruction in the mechanics work will be found on page 21. 19 CAMP HUMPHREYS REPORT Analysis of the outline shows that the method of procedure was as follows: (a) A problem was described and presented. (b) The instructor stimulated the students to go as far in solving the problems as they could without any other aid than their own knowledge. (c) The students were helped in overcoming recognized obstacles when they had spent as much time as was profitable under the circumstances in attempting to overcome them. A student may be helped over an obstacle in one of two ways. One way is for the instructor to give a demonstration or even a hint that will lead the student to apply principles used in previous solutions. The other way is to give a practical method without proof for the student to use. In a later problem the theorem of three mo- ments was presented in this way. Students desiring the proof found it much easier after the theorem had become familiar through being used in solving actual problems. (d) When a new principle has been brought to the student's attention during the solution of an en- gineering problem, an effort is made to fix the principle in the student's mind by presenting other problems, not of the same type, but involving new situations in which he must use the same principles. In this way idea memory is obtained rather than mechanical memory. All work which the student turns in must comply with the specifications given on page 33. A text, Poorman's Mechanics, was introduced near the last of the course. This tied together what had been covered previously and provided a ready reference in addition to the student's notebook. MECHANICS OF ENGINEERING OUTLINES OF CLASS WORK IN MECHANICS OF ENGINEERING The first meeting of the Engineering Mechanics Sections was held on Saturday morning, December 7, 1918, at the bridge over Accotink Creek, near the village of Accotink. The attention of each member of the class was called to the following information concerning the bridge, each part or feature being explained: Highway bridge. Pony truss bridge. Parallel chord bridge. Trusses and truss members. Chords, top (or upper) and bottom (or lower). Web systems and web members. End posts, posts, columns, struts. Hangers. Main diagonals, ties. Counters. End shoes. End bearing plates. Anchor bolts. Floor planks; also longitudinal planks for reinforcing floor. Stringers. Floor beams. Lower lateral system of wind bracing. Span of bridge, center to center end bearings. Depth of bridge, center to center of chords. Width of bridge, center to center of trusses. Panels, panel points (upper and lower). Guard rails and hand rails. Loop rods. Turnbuckles. Upset rods. Tie plates or batten plates. CAMP HUMPHREYS REPORT Lattice bars. Pin joints. Pin plates. Riveting. Bolts for erection of bridge. Channels, angles, "I" beams, round bars, square bars. Connections of one part of bridge to another. Splice in top chord. The following defects in the bridge or departures from good practice were noted: Rusted plates. Bent floor stringer. Bent rod in lower chord. Lower later diagonals not in plane of lower chord. Tie plates too far apart. The class was then divided into four sections of 18 men each and one section at a time was taken onto the bridge and put thru the following quiz: Why are some members rod and some members built up out of shapes? What is best form for a tension member? What is best form for a compression member? Why is top chord so wide? Why are lattice bars and tie plates used? Why are counters put in? When do they act? Why are the counters "Upset" at the turnbuckle? How does the "Load" get from its point of application to the ground? Trace its path from member to member. How does force go from one member to another when both are connected to a pin? How is floor fastened on? How may a weak floor be reinforced? Attention was called to the great importance of making all con- nections between parts of the bridge thoroughly safe. Special effort was made to have each member of the class clearly understand the action of a "Pin Joint" and how stresses are transferred from one member to another through the pin and how the pin is subjected to shearing and bending forces. MECHANICS OF ENGINEERING 23 THE FIRST STUDY PROBLEM The second meeting of the class in Engineering Mechanics was held on Monday morning, December 9, 1918. Four sections of nine men each met from 8:00 to 9:30 and four sections from 10:15 to 11 :45. A King Post-Pony Truss-Highway Bridge, was taken up as the first engineering problem. The following notes were given as suggestions to the instruc- tors, with the understanding that the details of the work should be changed to suit conditions, always keeping the main object in view, that is, the development and training of the student. Each instructor was expected to supplement the work outlined in the notes by bringing in additional illustrations and explanations derived from his own experience. In other words, the individuality of the instructor was to be used to the fullest extent possible in order to make him an effective leader or coach for his men. In the first problem the following mechanics concepts are introduced : Weight of Timber and Steel. Forces. "Free Body" idea. Things necessary to know in order to know a force. Force represented by an arrow. Definition of "Two Force Piece." Transmission of the effect of forces by means of triangular frames. Direct Tension and compression. Internal Stress holds in equilibrium the External Loads. Unit Stress, Ultimate Stress, Proportional Limit. Factor of Safety. Upset rods — reason for, and design. Investigation and design of steel bars in tension. Laws of Equilibrium for forces in a plane. Summation of components of forces in any direction equal to zero. 24 CAMP HUMPHREYS REPORT Graphic determination of stress, three forces at a point, in a plane. Analytic determination of same. Resolution and composi- tion of forces. Investigation and design of long columns in timber by straight line formula. Physical ideas of Bending and Shear. This problem was used as a study problem for four days, December 9, 10, 11, and 12, 1918. MECHANICS OF ENGINEERING 25 TEACHER'S NOTES ON THE FIRST STUDY PROBLEM Before every session of the class a conference of instructors was held for the purpose of drawing up a series of questions to indicate the order in which the various ideas might best be presented. Under each question notes were made to suggest to the instructors subject matter that should be mentioned. The following develop- ment questions and notes, used in the first lessons are appended as a sample of the method. Similar questions and notes were made for the analysis of the other parts of the bridge. After a few class sessions the instructors became used to the method. Then no formal notes on the con- ferences were needed. Span 24' C-C end bearings (2 panels at 12'). Depth, 6'; width, 16" C. C. Trusses. Concrete abutments on rock foundation. Bridge is over gorge 100' deep, with very steep, rocky sides. Upper Chord (End Posts), 4"x6" timber. Lower Chord, ^" round bar, not upset. Hanger, 1" round bar, not upset. Floor beam, 2'-8"xl4" timber. Stringers, 4"xl2" timbers, 2'0" on center. Floor Plank, 4"xl0" timber. Guard rail, 4"x6" timber. Sill on abutment, 6"x6" timber. Question : Military necessity requires that a 12-inch howitzer (fully loaded for traveling) be taken across this bridge. Question: Is the bridge safe? NOTE — Suggest that students make notes of ideas that come to them while thinking about this. NOTE — Encourage them to try — to start something. Question: In how many ways is it possible for bridge to feiil? List them. note: — Follow load from point of application until force gets into ground. (Floor plank, stringers, floor beam, hanger, upper chord, shoe, bearing plates, abutment, and all connections between these parts, also lower chord rods). 26 CAMP HUMPHREYS REPORT Question: How may the floor planks fail? Question: Make sketch showing worst position of live load on planks. NOTE — The analysis of bending stress in the planks can be postponed temporarily. Question : If planks were too light, how could they be quickly strengthened? Question: How may the stringers fail? NOTE — (Carry this through in same manner as for floor planks). Question: How may floor beam fail? NOTE — (Carry this through in same manner as for planks and stringers). Question : What shall we do in order to find out whether the hanger is safe? Question : How much load at lower end of hanger rod? NOTE — (Dead load: Weight of planks, stringers, floor beam and guard rail, which properly goes to hanger). Question: How get weight of timber? How figure F. B. M.? Question: (If live load has been forgotten) — How about ef- fect of live load? Question: What position of howitzer will give greatest load on hanger? Question: What is total load on lower end of hanger? What load on upper end? Question: How about the effect of Impact? Question : Take hanger out as "Free Body" and show forces acting on it. NOTE A "Free Body" sketch is one which shows some particular body by itself with all other bodies previously connected with it taken away, the effect of the removed bodies being replaced by the proper forces (represented by arrows). NOTE — Never take away any part of a body without putting in a force to represent it. Never put in a force where nothing has been taken away. MECHANICS OF ENGINEERING 27 NOTte — A force is fully defined when the following is known: (a) point of application. (b) direction in space. (c) sense, or direction along action line. (d) amotint, or magnitude. A force may be represented by an arrow which denotes these four things. Question : What force is acting at upper end of hanger? NOTE — If weight of bar itself is included by any students, have them figure its weight and compare with the load on hanger. A bar of steel one square inch in cross section and one foot long, weighs 3.4 pounds. (In this case, weight of bar may be neglected, but the student should arrive at this conclusion himself). NOTE — The rod in the bridge doesn't move (is in equilibriimi). The free body in sketch represents the rod in the bridge, therefore the free body does not move (is in equilibrium, etc.). NOTE — Conditions for equilibrium of two forces are: (a) must act in same line. (b) must be opposite in sense; and (c) must be equal in amount (magnitude). NOTE — A rigid body which is in equilibrium under the action of two forces only is technically called a "Two Force Piece." Question : How much force is acting internally in the bar? NOTE — Have two men pull on a cord and ask whether tension in cord is different from pulls at each end. Substitute spring balances. (Take out parts of the hanger as free bodies. Wherever the section is made the following will be true). NOTE — Internal stress in bar holds in equilibrium the external load on bar. NOTE — The internal stress in a "Two Force Piece" equals the Ex- ternal load at EITHER end of the piece. (If weight of piece is neglected). The hanger is a case of direct tension. Tension stress is uniformly distributed over area of cross section, therefore : (Total Stress) equals (Unit Stress) times (area of Cross Section). Question: Is the hanger safe? What is your conclusion? NOTE — A kip equals 1,000 pounds; abbreviation "k." NOTE — Compare unit stress with ultimate tensile stress (60 kips per square inch). 28 CAMP HUMPHREYS REPORT NOTE — Unit stress should be compared with proportional limit rather than ultimate stress. When proportional limit is reached the danger point is reached. Proportional limit of this steel is about one-half its ultimate strength or (30 kips per square inch). Question: What is proportional limit? Elastic limit? NOTE — The recommended use of proportional limit instead of elastic limit to mark the end of straight line variation in stress and deformation. Question: (Discuss Factor of Safety). Question: (Discuss — upset rods, and area at root of thread). NOTE — Allowed safe stress equals 16 kips per square inch, giving a factor of safety of about 3.75. note; — The hanger stress is higher than allowed in good practice, but below the proportional limit, and could be called safe for this particular emergency. Question: What size should hanger be to conform with good practice? Question: Is hanger safe if howitzer gets oS the middle of roadway and runs near side of roadway? MECHANICS OF ENGINEERING 29 THE SECOND STUDY PROBLEM. Report on the Safety of a Timber Tower Supporting a Water Tank. The principles involved in this problem being largely the same as in the first one, no outline was prepared for the instructor's use. The problem was discussed by the instructors in conference on De- cember 12, particular attention being given to the new ideas which the problem brought in. This problem involves the following mechanics concepts (those introduced for the first time are marked with a *) : — * Moments. * For Equilibrium, moments of all forces equals zero. Weight Timber and Steel. * Weight of Water. * Wind pressure on Flat and Cylindrical Surfaces. Application of the Laws of Equilibrium. * Increased reactions due to wind ; also uplift due to wind. * Pressure on Soil and Safe Bearing Power of Soil. * Investigation of safety of timber in side bearing. * Investigation of safety of concrete in bearing. * Determination of stresses in truss. Investigation of timber columns. Physical ideas of bending and shear. This problem was used as a study problem on December 13 and 14, 1918. 30 CAMP HUMPHREYS REPORT THE THIRD STUDY PROBLEM Report on the Safety of a Concrete Dam. The design of this dam was submitted in connection with a proposed water supply system for a city located in the southern part of the United States. This problem involves the following mechanics concepts (those introduced for the first time are marked with a *) : — Weights of concrete and water. * Hydrostatic Pressure. * Hydrostatic Prism. * Friction of Rest. Application of Laws of Equilibrium. Factor of Safety. * The insertion, in a given system, of two equal and oppo- site forces in the same line does not change the pre- vious condition of equilibrium. * Couples in the same plane are equal if their moments are equal and in same direction. Direct Stress (or Uniformly Distributed Pressure). * Bending Stress (or Increased and Decreased Pressure due to tendency to overturn). * Combined Stress (or Resultant of Direct Stress and Bending Stress. Actual distribution of Pressure on base of dam). Safe Bearing Power of Soil. This was used as a study problem on December 20 and 21, 1918. MECHANICS OF ENGINEERING 31 THE FOURTH STUDY PROBLEM (A) Investigation of the Dam in the previous problem as to safety at any section between the top and bottom. This problem furnishes drill in all the features brought out in the previous problem. The special purpose of the problem is to give a clear physi- cal idea of Shear and Bending Moment, which are here introduced. (B) 1. This problem also introduces the following mechanics concepts : * Diagram showing intensities of water pressure at various depths. (Load Diagram). * Diagram showing tendency of the dam to slide off at various horizontal sections. (Shear Diagram). * Diagram showing tendency to break off at various horizontal sections. (Bending Moment Diagram). * Idea that shear is rate of change of moment. * The three Laws of Derived Curves. 2. The profile for an Electric Transmission line used as a means of introducing the idea of "Rate Curves," and as drill in first and second laws of derived curves. 3. Profile of vertical curve, for a railroad track, and its rate curve used to emphasize the idea that an in- clined straight line in one diagram creates a curve in the next higher diagram. 33 CAMP HUMPHREYS REPORT THE FIFTH STUDY PROBLEM Investigate the Safety of a Timber Cofferdam to be Used in Construction of Pier in a River. In this problem the following concepts of mathematics and mechanics are involved (those introduced for the first time are marked with a *) : — Hydrostatic Pressure. Load Diagram. Shear Diagram. Moment Diagram. First Law of Derived Curves. Second Law of Derived Curves. Third Law of Derived Curves. Center of Gravity of Triangle. Moments. Reactions. Parabola (area). Parabolic Spandrel (area). Quadratic Equations (solution of). * Cubic Equation (solution of). * Inflection Point of Bending Moment. Couples. * Investigation Fiber Stresses in Timber Beam. * Safe Fiber Stresses in Timber Beam. • Investigation Timber Columns. Straight Line Formula for Timber Columns. Investigation of Bearing on side of Timber. Safe bearing on side of Timber. * Investigation of Longitudinal Shear in Timber Beam. MECHANICS OF ENGINEERING . 33 SPECIFICATIONS FOR MECHANICS WORK (Supplied to all students.) 1. Unless otherwise specified, use only Standard Mechanics Paper; size, 8%"xll"; color, yellow or orange; punched for Standard I. P. 3-ring Binder. 2. Holes for Ring Binder shall be at left of sheet. 3. Margins shall be ruled as shown on Sample Sheet. Problem Number, Name, Section Number and date shall be placed as shown. (This should be the first work placed on each sheet). 4. Begin each problem on a new sheet. Not more than one prob- lem shall be put on a sheet unless otherwise instructed. 5. Work shall be arranged systematically and clearly on each sheet. (By doing this, errors which grow out of confusion will be avoided). 6. Explanatory headings shall be used throughout to indicate steps taken in the work. Marginal index shall be used to identify results obtained in the various steps. (This leads to accuracy and efficiency and increased speed. It also saves time and effort when checking or referring back to the computations). 7. Rule a space at the left of the sheet (as shown on sample), for the segregation of the so-called "scratch-paper" work. Vary the width of this space to suit the nature of the work. (This work is of great importance and must be done with the same clearness as the other work or else accuracy will be sacri- ficed. Proper care is good insurance). 8. Rule horizontal lines entirely across the sheet to separate parts of a problem (or where there is a break in the work). Do not rule vertical division lines. 9. Use no short cuts. Perform one operation at a time and make a complete record of it. (Neat and careful work leads to neat and careful thinking and vice versa). 34 CAMP HUMPHREYS REPORT 10. All work shall be done with a pencil which gives a clear and black mark. Enough pressure must be put on the pencil to make the marks black. Pencil points must be kept sharp so as to give clear marks. (Pencils which are too hard or too soft will not give satisfactory results). 11. All sketches shall be made with triangles or straight edges unless otherwise specified. Outlines must be clear and black. Strong contrast between real and imaginary lines. 12. Dimension figures must always have the right of way and must be kept clear of all lines. 13. Decimals must have a distinct point. (The decimal point is of such great importance, and errors from its omission are so costly, that it is a good plan to exaggerate it). 14. Fractions shall be written with a horizontal line and not with an inclined line. 15. Statements of "Proportion" shall be shown in fractional form with the sign of equality and not with proportion signs. The unknown shall be placed in the numerator on the left side of the equation. 16. Make large sketches. (The sketch is an aid to clear think- ing, not merely a picture of what has already been done. A "working sketch" is only relatively to scale. Certain parts should be exaggerated in order to make the work convenient and easily xmderstood). 17. Use only Standard Engineering Lettering and large fig- ures for all problem work. 18. Stresses in framed structures shall be noted on the proper members of a "Space Diagram" (or "Stress Diagram"). The Space Diagram must be large enough to show this informa- tion clearly. Compression Stresses shall be marked C; Tension Stresses T. 19. Answers to problems and the results of various steps of a problem shall be made prominent by the device shown on sample sheet, except that no such device shall be used for MECHANICS OF ENGINEERING 35 results noted on diagrams (such as stress or curve diagrams). 20. Units shall be clearly indicated for all given data and for all results. 21. Accuracy is absolutely essential in engineering work. (Preci- sion may not be necessary). The engineer who cannot be depended upon for results is worthless. The student must learn the cost of errors. Incorrect results ; no credit. 22. Use check methods whenever possible and surroiuid all work with as many safeguards as can be used efHciently. PART III COURSES IN STRUCTURAL ENGINEERING COURSES IN STRUCTURAL ENGINEERING The courses in Structural Engineering are under preparation, and will be given for the first time beginning September, 1919. Classified as Structural Engineering are the following: Number of Length of Total Subject. Periods. Periods. Hours. Materials of Construction 23 3 hours 69 Roads and Pavements 26 2 hours 52 Foundations 26 2 hours 52 Wharves and Piers 15 2 hours 30 Plain Masonry 18 2 hours 36 Reinforced Concrete 12 2 hours 24 Roofs and Bridges 25 2 hours 50 Building Construction 24 2 hours 48 The subjects are pursued intensively, in the sequence as listed. A morning period is 1 hour 50 minutes, and an afternoon period 3 hours in length. A morning subject occurs three days in the week, and alternates with another, and an afternoon subject alternates with the same other during 5 days, 3 periods one week and 2 the next. The time allotted is tentative. The school year is 11 months. These courses are preceded by training in Mathematics and Mechanics. These courses are being prepared by engineers of extended practical experience but of no teaching experience with army reserve commissions, on active duty at Camp Humphreys. They are working under a general plan as fixed by Major General Black. The preparation of each course includes: A frame work of major and minor problems, through which the student approaches the text. Writing of school texts Selection of reference texts The school texts contain a discussion of the elements that con- trol the design or method of construction, and are unusually valuable in that they bring to the student's attention many im- portant practical considerations that are absent from the ordinary text. 39 40 CAMP HUMPHREYS REPORT The distinctive feature of each course is one or more major problems, constituting a framework upon which the student hangs the subject matter of the text. The major problem is generally a complete structure that the student is to design, or to specify its method of construction. A complete description of the situation is given. In his progress, he is required to make decisions, and is thrown back to the text for the facts, or theories, or principles that control the decision. For this purpose, the major problem is fur- ther analysed into a number of minor problems that are parts of the whole and serve to keep the student's interest alive, and to guide him to a reasonable degree in the sequence of the necessary decis- ions in the face of a real situation. The latter are brought out by a series of development questions. This is the job method of teaching and is applied to the engi- neering courses ordinarily listed for the senior year in engineering schools. These courses offer a hopeful solution of the difficulty of teach- ing such courses as Foundations, Wharves and Piers, to the student in the civilian engineering school. It is the general experience that such courses have not the same value as courses in Applied Me- chanics, when considered as educational tools ; it is difficult to get reaction from the student. Generally the civilian student informs himself by reading texts, and the subject is discussed, and lectured upon by the pro- fessor in class on the basis of the text. A continuous reaction from the student is not obtained. The matter is descriptive. The actual process that the engineer goes through in deciding between conflict- ing conditions of the problem, or choosing controlling elements, are not generally evident from the text. Nor has the professor as a rule such live and real problems as are available in the course in Struc- tural Engineering now being prepared for The Engineer School at Camp Humphreys. Instead of reading and discussing a text for classified knowl- edge upon which he is examined, the army engineer student goes back to the text for the material for a definite decision, for facts, or for a tool to accomplish a purpose. STRUCTURAL ENGINEERING 41 In civilian institutions, also, courses such as Bridges and Build- ings require from the student an extended performance in the draw- ing of the details. In the courses in The Engineer School at Camp Humphreys the designs are sketched, but not drawn to com- plete detail. These courses thus take the middle ground between reading courses and detailed design courses. They represent the work of the engineer rather than that of the drafting office. When looked at from the standpoint of the courses as ordinarily taught in civilian schools, it might appear that too little time was allotted to the subjects ; and that a superficiality, which has resulted in the past from a too general reading of a treatise, might again re- sult. But these courses should correct the superficiality. In the first place, the time-consuming detailed drawings of structures by the student are omitted, as has been said, and sketches are used. In the second place, the student is led into the background of the school text for decisions. And this school text is a short summary of the controlling elements rather than a detailed treatment. An instructor should be able to direct the use of the fuller reference treatise when necessary. It should be said also that under the conditions of the student's life at The Engineer School, he is less subjected to distractions such as those that diminish so greatly the effectiveness of student time in civilian colleges. The physical conditions of the engineer stu- dent will be favorable. He is also a very carefully selected man. His power of attainment will correspond to that of our civilian stu- dents in the training camps. At first glance, the decisions expected of students seem to be beyond their capacity, and to demand a judgment that could only be obtained from experience. Professors who have tried similar courses are surprised at the extent to which many students reach wise de- cisions after a study of the situation and the text. The instructor is furnished with a guide to the correct decisions, and in turn can guide the student. The process of approach to a decision, the knowledge of controlling elements, are learned, even if the decision is incorrect. 42 CAMP HUMPHREYS REPORT These courses must also be viewed in the light of the product that it is desired to produce ; namely the engineer officer. It is the usual expectation that the graduates of a civilian school of Civil Engineering will immediately and fairly continuously deal with the detail of a subject, as in surveying operations, or in a designing, or detailing office of a bridge or building construction company. He must learn the detailed processes. The army engineer, however, has a much wider range of duty. He may have to select the equipment for a power plant, or deal with a difficult foundation, and may do this years after graduation, and only once. He should be trained to handle the problem from the broad standpoint, without the "tricks of the trade," or skill in details. That is to say, he must be trained as an engineer, rather than as a draftsman. It would seem that such a broad understanding of the various fields of construction, and an ability to think through these problems would be developed by these courses, with an avoidance of the superficiality and lack of interest and reaction that comes from mere reading of treatises. In brief, these courses aim to accomplish the following : The student must think out a decision in the face of a real sit- uation. The subject matter is presented to bring out the fundamental principle, and to force the student to analyze the problem to its con- trolling elements. He is continually confronted with a problem, and goes from this to the text for a decision only after exhausting the possibilities of his own experience and judgment. The practice and the types of structure are presented. No doubt when the courses are operated, adjustments of subject mat- ter and coordination of the courses will be necessary. The relation of the laboratory for testing materials to the courses should be studied. The general question of the student's critical study of data upon which design rules are based, and the measurement by the student of the forces of nature, and the subject of inspection trips to engineering works, will have to be considered. STRUCTURAL ENGINEERING 43 For the benefit of civilian instructors, in engineering schools, extracts from text and problems of some of these courses are given on page — , under the following headings : A. The topical outline of the course in Masonry Structures followed by: I. The statement of the first major problem, the Black Warrier Dam, with the analysis of the first of the minor problems into development questions. See page 47. II. Extracts from instructor's notes on the first minor problem. See page 50. III. The statements of the subsequent minor problems. See page 53. B. The outline of the Section on Timber from the course on Materials, followed by : I. The analysis of the major problem into minor problems and development questions. See page 68. II. Extracts from instructor's notes on the first of these problems. See page 73. The text is a very excellent and well-balanced discussion of quality and use of wood. The instructions to the teacher will aid in a practical design and guide the student to a wise decision. The discussion of flooring, sash, framing, etc., brings in the qualities of minor species. Cast iron and steel enter in columns, wrought iron in hangers, wood for tanks, considered in sprinkler system. Shrinkage allowed for. The text of the courses and the references take the student into the consideration of the elements necessary for a decision. There is supplied to the teacher a discussion and reasons for the correct decision upon each element of the problem. By these an instructor other than the experienced constructor who has prepared the course can satisfactorily administer the course. The student's problem is 44 CAMP HUMPHREYS REPORT well analyzed into a framework of subsidiary questions so that he will not be too much at sea. A record of these, with the instruc- tions to the teacher, follows. This course is marked by a well-matured plan for bringing the student to a decision upon the controlling elements of the problems, and sending him to the background for laws and data upon which decisions must be based. The time allotted to this course consists of 12 hours in class, 6 hours in laboratory, and 6 hours of night study. The instruction extends over a period of one-half month, with three periods each week of three hours each. STRUCTURAL ENGINEERING 45 A. TOPICAL OUTLINE OF THE COURSE IN PLAIN MASONRY STRUCTURES. I. DAMS. 1. Historical (brief). 2. Classification of dams. 3. Types considered. 4. Design of dams. 5. Preliminary investigations. 6. Stream diversion. 7. Foundation, hard. 8. Construction of rubble masonry dams, (brief) 9. Procurement of materials. 10. Construction plant and equipment. 11. Cyclopean masonry. 12. Delivery and deposition of materials. 13. Expansion joints. 14. Drainage of foundation and dam. 15. Overflow dam. 16. Dams on pervious foundations. 17. Construction plant. 18. Present tendencies in construction. 19. Estimates and costs. II. RETAINING WALLS. 1. Kinds of retaining wall. 2. Method of treatment. 3. Equivalent fluid pressure. 4. Surcharge. 5. Stability of retaining wall. 6. Foundations. 7. Design of plain concrete walls. 8. Foundation for walls. 46 CAMP HUMPHREYS REPORT III. ABUTMENTS. 1. Kinds of abutments. INTEREST aroused and maintained by contact with Engineering Situations INDEPENDENT thought and judgment stimulated by analysis of raw Problems t: SUBJECTl^--^ MATTER/*^^*^ MOTIVATION '^^^ SETTING — A concrete engineering situation Project or Problem S-l Military necessity re- quires transporta- tion of 12" howit- zer Floor sys. Safety of Planking Stringers Floorbeanis Truss, Safety of Hanger End Post Lower Cord As a Whole Across King Po«t Truss Highway Bridge of 24' span, over gorge 100' deep with very steep rocky sides. Bridge 5' years old and in gqod condition. 4" Plank on 4"xl2" Stringers 2'^-0" c-c In Part Is it safe? Probable effect of load On the bridge EFFECTIVE HABITS of work and study, and PRACTICAL uses of working tools established THE ANALYSIS Process Make list of possible sources of failure. (See explanatory' note) Failure by bending. 4"xl2"*t2', Sup- ported each end 2-8"xl4" Sup- ported each end by hanger. 1" round steel bar (not upset) 4"x6" wood. }i" Round steel bar (not upset) Failure by bending. Failure by bending. Determination of elTect of dead load. Determination of effect of live load. Force tending to break hanger. Is hanger safe? Design safe hanger in conformity with good practice. Is it safe? a. Trace forces from point of application to the ground. b. Ktfect on various members. Position of load to break. Position of load to break. Position of load to break. Calculation of amount and distribution of dead load Position of amount of live load giving maximum load on hanger. Impact. External force resisted by internal stress. a. Distribution of stress over' cross-sec- tion. b. Determination of breaking strength hanger. Determination of necessary area of cross-section. a. Find forces acting upon upper chord — analytic and graphic solutions. Is it safe? b. Find apparent unit stress equals force area Why so large a stick? Working Tools Working drawings. Previous experi- ence and judgment. Previous experience and judgment. Sketches of possible failure. Sketches. Sketches. Sketches. Working drawings. Methods of calculating amounts and weights of materials. Working drawings, judigment. Inspection and Free body sketch. ACQUAINTANCE with Fundamental Principles, and KNOWLEDGE of their relations to solution of Problems PRINCIPLES Basic Conditions of equilibrium Tests of steel (tension) Test of steel (tension). Specifications based on tests of steel and good judgment. F. B. Sketch upper joint. Force polygon upper joint. c. Design end post in accordance with specifications. a. Find forces acting upon it. b. Find unit stress and compare with allowable. C. Design lower chord. Judgment. Experiment with various models of columns. Empirical Formula. Standard formula. F. B. Sketch of joint at end post. Force poly, of joint. Given minimum cross sectional area and tests of steel. Standard Specifications. Forces are vector quantities and may be represented by lines. Stress uniformly distributed. Material safe within propor- tional limit. Stress uniformly distributed. Equilibrium Stress in long columns is com- bination of direct stress and bunding. Equilibrium — Direct Tension. Derived 10 Physical idea of bending. Physical idea of bending. Physical idea of bending. Proportional Distribution of Loads 2 forces, equal and oppo- site, in same action line. I'orce is known when, a I't ol App.. b direction, c sense, d magnitude, are known. Unit stresa=total stress di- vided by area of cross section. Working Factor of Safet> Total Stress=;allowablc unit stress times area of cross section. 1' V = o r H - o Graphic and analytic. Strength of long columns is dependent on: — length, shape of x sect, and area of cross section, and material. CO-ORDINATION and Fixation of Ideas Rules, Formulas, Refer- ences, Data, Text. 11 Handbook data for timber and steel. Rules for showing forces in F B. Sketches. Detinition of " 2-F(trce Piece. I'ltimate strength and prop. Limit for steel. Specifications. Straight line formula. (Same as tor hanger.) (Same as lor nanger.) ;2 V - o. i 11 o Graphic and analytic. (Same as for hanger.) (Same »c ff\r V,'..- OUTLOOK Expectancy concerning future studies. Deferred- Analysis 12 Bending Stresses Bendiiig Stresses Bend in\i Stresses Adv. Theory and Research 13 Material for ad vapced theory and research ap- pear in siib- sequent problems S-2 S-3 Bearing of truss on sills S-4- A water tank on frame tower and concrete foun- dations- fell over in a high wind. Inves- tigate and report whv it failed. A design -for .1 concrete dam has been sub- mitted in connec- tion with a proposed water supply sys- tem for a certain city located in the southern part of the United States. Dam for water supf)ly Sills 6"x6" Circular tank 10' diam. and 16' high, 50' tower consists of timber frames — 4 tiers — posts are 10' apart at top and 20' at base Wreckage made it diffi- cult to decide what part failed first The dam is straight, .SOO feet long and creates a reservoir extend- ing half a mile up stream from the dam Traper-oidal Ba^e^l' Section [ Height .W F.lcvation of cresl of dam ; 800' above sea level. Tests have shown the founda- tion to be solid granite. Concrete dam in S-^( Is it safe? 1. \Vh,-it c.iust's runlri- buted to the fniliire i)f the tank? 2. Tower may have tipped over on ils foundations. 3. Koundations may have failed thru ex- ccssi\rsoil pressure. 4. Tower may have been overstressed as a truss. 5. Beams in floor 1. Is dam safe? Invest! gate and report 2. Will it slide on its base? b. Find unit stress and compare with allowable. c. Design lower chord. a. Find pressure of truss on sill. b. Find unit pressure and compare with safe. Make a list of the items which might ha\e been responsible. (St'f ('X|)l;iriatory nitri-) a. Find forces lending lo IidUI l.uik in place, full and empty b. Find forces tending to upset the tower. c. Which produce greatest effect? How do forces produce rotation? d. Compare condition of tank full with tank empty. What factor of safety? What precautions to prevent failure? a. Mnd total pressure exerted b\' each footing. b. I""ind maximum unit pressuie on soil. Is it safe? c. If unsafe, how remedy? a. Find stress in columns. b. Find stress in bracing. c. Find stress in struts. d. How remedy weak members? a. Failure by bending. b. Failure by crushing on top of posts. LisI possible sources of failure (See explanatory note) a. Find lorces which produce sliding b. Find forces which hold agaiusi slid- ing 3. Will it overturn? 4. Is the pressure too great on the founda- tion? Is dam safe al any section between top and bottom? Inves- tigate and report. , C. Find ratio between b .ind a a. Find moments of all forces tending to overturn. b. Find mom. of all forces teTulii\^ tn stability C. Find ratio of stabilizing l.i over- turning moments. Find distribution of pressure on base. Fin'cl max. and min. pressun-s per unit area. a. Analyze as in S .? for >.liding .11 sec- tions 6', 12', IK', 24'. and .id' be- low top of dam. b. As in S-.i for overturning .ihoiit toe of each Section C. As in S -.? liiid ma.^. and niin p on each section cut. Given minimum cross sectional area and tests of steel. Standard Specifications. F B. Sketch of entire truss. Kmpha- Test of bearing strength. Working drawing of the lank uid tower including foundations. Judgment and experience. Drawing of tank. Determinations of weights of materials. rests of wind pressure on Hat and curved surfaces. Idea of levers and effect of forces acting on cranks in general. Seesaw. Judgment. F B. Sketch. Principle of moments Craphic determination of reactions — String polygon. Tests of safe loads on various soils. Judgment. Specifications— Judgment. F B. Sketch — Laws of equilibrium. Force Polygon. Method of sections Principle of moments. Specifications. Sketches Allow unit-bearing stresses. I..1WS of equilibrium. Judgment and experience. F B. Sketch. Hydrostatic prism. Fxperiments in friction. Judgment determines [iroper factor of safety f B. Sketch — Laws of equilibrium. Ditto judgment as to allowable Factor of Safety. Fx peri men ts — judgment — straigh t line variation, an acceptable assumption. Kquivalent systems. Make tables of sliding lorces — sketch of hydrosiatic prism for each sec- tion. Tabulate moments and factors of safety. F. B. Sketches. 1. Tabulate Direct Pres. Bending mo- ments due to water. Bending mo- ments due to eccentricity of dam, about center of base — Table of net bending mom. at center of base. F. B. Sketch of each section. (Same as for hanger.) (Same as ior hanger.) .\ s\-slem of forces ma>' I>e re- placed li\- its resultant. I-'luid pressures ("i>nditioiis for e' i)e replaced by .1 single force acting thrii their C of C Pressures depend upon char- acter and position of ex- posed surfaces and selo- ity of wind. Summation of moments .dioiit any pt.^=2ero. Downward reactions require tension connections to footings. i' .M ^ o .Analytic - is in equi- librium. I U'droslatic I'ressure. M.i about toe of Dam. i' Mil about toe of Dan _Mi. Ma F S. Pressure is coml^ination ol Direct Stress and beml- ing. Couples, in same plane are equivalent if their moments are equal and in same vlirection. 1 iandbook data. ."Mlowable coefticient of Iric tion from handbook. l-'.ielor ol s,ifet\ should be Sate \*.'ilues taki-n h-om hantl- book. Drill in friction. Drill in I". R. Sketch and moments. Drill in moments and I-. B. Sketches. Drill. Benfling Stresses F.l'lect of ice pres- sure. Uplift due to water pressure Stresses on other than horizon- tal section. s-s SiniplifiL'utioii of inves- tigation. Derivfi! ciir\ os as (odIs Ditto Timber cofferdam Concrete (lam, S-,i Le\'el notes of siir\i'V Vertical curve on R. K. location. 9'x30' inside sheet pil- ing. +"xl2" sheet piles 6"x8" wales ()"x8" struts 2 wales 6' and 12 l>eIow water (re sptc'tively.) 1. Coortliiiale calcula- tions for sliding and bending moments — I'or sections in "A " I'rolik- and rate cnrvt Ditlii a. Construct diagram showing "intensi- ties" of water pressure. b. Above the load diagram, construct diagram showing tendenc\' of each section to slide off. c. What relations between a and b? d. Above the shear diagram construct diagram of bending moments or tendencies to "break off. " e. What relations be(\vcen d and b? f. What relations between d and a? g. Coordinate the relations between load — shear — moment. a. Plot profile b. Plot rate curve below profile. c. From rate curve, find difierence in elevation between any two stations. a. Plot profile and rate of change curves 1. Is the cofferdam safe.-' (Sci- c.'C|ilari.(t<>r\ note) 2. I ru Instigate struts and report as to safetv'. b. Use diagrams to calculate interme- diate elevations e. Profile approaches parabola. rate cur\'e approaches si. line. Make a list of all possible sources of failure. Discuss cofferdam construction. Deterniinalion of load. b Kirtd allowable Stress in C(»Uimn Make recommendation as tostrcnglh- ening. iiienrs uue lo wacer. oenamg mo- ments due to eccentricity of dam, about center of base — Table of net (tending mom. at center of base. I*". B. Sketch of each section. 2. Tabulate combined effect of direct stress and bending. Hydrostatic prism. Graphic represenla- tation of quantities. Summation of forces on a section. Geometry and Algebra. Use data obtained in "A" Geometry and Algebra. Geometry and Algebra. Physical ideas of load, shear and mo- ments. 1st and 2nd Laws of Derived Curve 2nd La' 1st and 2nd Laws. ditto ditto Working drawing. Judgment and pre- vious experience K. H. Sketch -Triangiil.tr pressitre |jrism Standard specifications Judgnicnt. Equiv alent systems. luiiiiiibritim-- hv'droslatic" pressu re Cotitbined bending and di- rect stress. Combined stres: Load diagram. 1 u o Transverse Shear diagram. 1st and 2nd laws of derived curves. Moment diagram. 1st and 2nd laws of derived curves. 3rd law of derived curve? Shear — Rate o( change of moment Load — Rate ol change of shear. Klevation diagram. Grade rate diagram. Ktnpincal reductiofi iornuila Drill in combined stresses. Drill in Laws .old use of derived curves Drill in use ol straight line column formula Timber under bending. A. Sheet piling, 2 Sup- ports. Triangular loading. 1. Will the piling be safe under the effect ol bending:* I'ind external bending moment of forces acting on a sheet pile t.tken as a beam. L.iws of etjuilibrium. !•'. B. Sketches. Laws of derived curves — Load, shear and moment diagrams. For l''.quilii)rium. 1 V U, X H ' o. Drill in determination of max. shear and mom. in. a beam and use of laws. 2. I'^ibre stress due to bending. <.\i{ beam transversel>' at any point and determine internal forces acting on fibres. F. B. Sketch showing intern.il stresses. Laws of equilibrium. ICxIernal Bending Moment^ Internal Resist. Moment at anv section. Max. fibri.' sticss occurs at point ol max. bending. Max. bending occurs where shear passes thru (). Refer to specifications for allowable fibre stress in bending. The previously deferred prob lem in bending has become a major prob- lem. 3. Longitutlitial shear (tendency to split.) a. Take short section of beam and de- termine forces acting on each face. Ditto Ditto, b. Take section of a with lower face at neutral axis and find unit stress along this face. Ditto L.'iws of equilibrium. Longitudinal shear is distrib- uted unilormly laterally over longitudinal section. 4. Bearing on wales. Determine area of bearing surface and load. Specifications. B. Waling as beam. 4 Supports. 1. A continuous beam. Which is stronger, a series of simple beams or one continuous? Models of beams of small cross sections Simple beams show greater bending. Analysis of Cont. Beam deferred 2. A series of simple be.ims Analyse for fibre stress and long -shear. In same manner as for sheet piling ahov e Dale STORAGE BATTERIES FOR TRUCKS A JOB SHEET MANUAL WAR DEPARTMENT COMMITTEE ON EDUCATION AND SPECIAL TRAINING WASHINGTON STORAGE BATTERIES FOR TRUCKS A JOB SHEET MANUAL WAR DEPARTMENT COMMITTEE ON EDUCATION AND SPECIAL TRAINING WASHINGTON PREFACE One of the lessons taught by the intensive war train- ing experience was that rapid progress in learning can be made when men are trained for definite jobs. Hence a better result will be secured from the technical instruc- tion for the Reserve Officers' Training Corps if the product needed by the army is first defined in terms of the jobs and operations which an officer may have to perform in the conduct of his daily routine. Such definitions will also assist college teachers in their regular work by supplying problems and other material which will enable them to connect their instruction with the broad field of application in which the mastery of scientific principles is objectively revealed. Instruction based on problems and job sheets of graded difficulty seem to offer as effective a means as can be found of de- veloping the ability to do things in civilian life as well as in the army. The job sheets herein printed have been prepared by Prof. L. W. W. Morrow of Yale University. In this work he has had the hearty cooperation of Mr. A. L. Pearson, Electrical Engineer of the Construction Division of the Army and of Mr. G. W. Vinal, Associate Physicist of the Bureau of Standards. Further information on this subject may be had from a circular of information on tractor batteries, for use in storage battery maintenance stations, prepared by Mr. Pearson and published by the Bureau of Standards. C. R. MANN, Chairman, Advisory Board. -nisii iBw avianaJni adi ^d id-guBi anozaal adi io snO nsD gnimBsI ni saaigoiq biqBi JeriJ 8sw aonaiiaqxa gni E sonaH .adoi aJinilsb loi bsnisiJ aiB nam nariw sbfim sd -auiJani IsDinrfoaJ ariJ moil baiuoaa ad Iliw jluasi isjjsd adi ii gqioD gninisiT 'aisofHO sviaasH srij loi nob arrnaJ ni baniiab taih ai ^^rms srij yd babasn Jouboiq oj svEff Ysm i3Dfflo nB rioiriw anoiJBiaqo bns adoi ^^^ i° .sniJuoi Y^iEfa aid io Joubnoa sriJ ni miohsq lisrt:^ ni siadoBsi agalloo JaiaaB oalB Iliw anoiJinSab riou2 iBiiSjBm isriJo bns amsldoiq gniylqqua yd jIiow lElugsi riJiw noiJouiJani I'ladi Joannoo oJ msriJ aldBna Iliw rioiriv/ Io yisJafira ariJ rioiriw ni noiJBQilqqs io bbii bsotd adi noiJoutJanl .balBavai ylsvijosido ai aalqioniiq oSiinsioa YJluoiflib bsbfiis io aJaaria doi bns amaldoiq no bsasd -ab io bnuoi ad nso as ansam b aviitoalia aB laBo oi maaa Haw BB aiil nBiIivio ni agniriJ ob ot yJilidB arii gniqoiav .ymiB ariJ ni ee \d baiBqaTq naad avsri baJniiq niaiari aJaaria doi ariT jiiow airiJ nl .^^ii^^^v'mU alBY io wonoM .W .W .J .ioi'I ,noaiBa*I .J .A .iM io noiJsiaqooD yJiBari arij bfirl afirf an arlj io noiaivia noiJouiJanoD adi io laanignS lBaiiJoaI3 ad* io Jaioi8\(ri JOB No. i6 (c) What differences are allowable in cell readings of volts, temperatures and specific gravities? (d) Why do these • differences occur, and how can they be remedied? (e) Are they detrimental to normal operation? 6. (a) Can you compute the remaining ampere hours in the battery from the data taken? (b) The kilowatt hours? (c) How do they compare in value? 7. (a) If the battery were tested on a hot day, say 100° F., would the capacity be changed? How much? Why? (b) If the battery were tested on a cold day, say 20° F., would the capacity be the same? (c) Can you predict capacity at normal temperature from a test made at abnormal temperature conditions? 8. (a) How can you check your predicted capacity? (b) How do your results check? (c) Write specifications for testing an Edison A6 battery for condition and state of charge under normal operating conditions. JOB NO. 17. Put a Gould 17 V149 Truck Battery in Dry Storage. Manufacturers' Data: 222.5 ampere hours. 1270-1280 specific gravity, charged. 1120-1130 specific gravity, discharged. 5 hour discharge. 40 and 16 amperes charging rate. 1. (a) When are batteries put in dry storage? (b) Why is wet storage not better than dry storage for long storage periods? 2. (a) Should the battery be charged or discharged before being prepared for dry storage? Why? (b) How long should the battery be charged? (c) How long after gravity and voltage are constant should the charge be continued? (d) What should be the readings of the voltages? Of the specific gravity? (e) How high above the plates should the electrolyte be at the beginning of the charge? 3. (a) Will you keep a record of the specific gravity of the electrolyte in each cell at the end of the charge? If so, why? (b) Will you preserve the electrolyte? Why? (c) How long will you wait after the electrolyte is removed before adding water? (d) May heating occur? Why? (e) Is it essential to get all the electrolyte out of the cell be- fore adding water? (f) What kind of water should be added? (g) How high above the plates should the water stand in the cells ? (h) If any electrolyte is spilled on the case, how will you re- move it? 4. (a) How long should the battery stand when filled with water? Why? 59 6o JOB No. 17 (b) Would the battery keep in good condition if stored with only water in it? (c) Should battery be charged or discharged when filled with water? (d) Would charging or discharging when filled with water shorten the time taken in preparing for dry storage? (e) Can the battery also be placed in dry storage by removing cells from case, then removing the elements and washing them several times in distilled water? If so, which is the better method? 5. How would you dismantle the battery after the water is emptied? (See Job No. 1). 6. (a) In what kind of a place should the plates be stored? (b) Should they be put on top of each other? (c) Can the separators be stored and used again? How? Is it advisable? (d) Can the perforated rubber sheets be stored and used again? (e) Can the jars be used again? (f) Will all other parts of the battery be suitable for use after storage? (g) Should the jars be stored dry? 7. (a) For wet storage purposes, compare the method of a monthly charge with that of placing the batteries on a so-called trickle charge as to efficiency and operating advantages. (b) What minimum value of current should be used for trickle charge storage? (c) What value of current should be used for the monthly charge method of wet storage? JOB NO. 18. A Gould 17 V149 truck battery has been in dry storage for 14 months. Install the battery in a truck for service purposes. Manufacturers' Data: 222.5 ampere hours. 5 hour discharge. 1270-1280 specific gravity, charged. 1120-1130 specific gravity, discharges. 40 and 16 amperes, charging rate. 1. (a) In order to reassemble the battery, what new parts might be needed? (b) Where can new parts, if desired, be obtained? (c) Can they be kept in stock? 2. (a) What specific gravity electrolyte will you use for re- filling the jars? (b) What effect has temperature on the specific gravity desired? (c) If no record is available of gravity before storage, what specific gravity can you use? 3. Assemble the battery. (See Job No. 2). 4. (a) How soon after filling the battery with electrolyte will you charge the battery? (b) Why must time elapse? (c) Has the temperature anything to do with the length of time the battery must stand before being charged? 5. (a) At what rate will the charge be made? Why? (b) What would a boosting charge do to the battery? (c) How long will a charge be continued? Why? (d) In using constant potential charging, what precautions must be taken at start of charge? (e) When using constant current, will the finishing rate be different from the initial rate? If so, why? 6. (a) What measurements will indicate how long the charge will be continued? 6i 63 JOB No. i8 (b) If a new battery can be conditioned in 60 hours, why will an old one often take 75 hours? (c) Why should temperature readings be taken during charge? (d) What will you do if the temperature becomes greater than 110 degrees F. during the charge? Why? 7. (a) After charging is the battery ready for service? (b) What should be the level of the electrolyte? (c) Should the specific gravity be read before adding water or after? Why? (d) How will you determine the real specific gravity after water has been added to the electrolyte? How long a time is neces- sary if you charge the battery? (e) Will a reading of specific gravity after the battery has been discharged for a short time give as good an indication of specific gravity as a reading based on a charge of the same length of time? (f) What will be the specific gravity when the battery is charged and properly filled? 8. If the temperature is different from normal, how can you correct readings of specific gravity? 9. (a) Why should the top and sides of battery be wiped off before putting the battery in service? (b) Can you use ammonia on the cloth? Why? (c) Is the battery ready for service? (d) Should any coating be put on the exposed terminals of the battery? JOB NO. 19. Install a new General Lead Batteries Co.'s Type BH-IS, 12-Cell Truck Battery. Manufacturers' Data: 220 ampere hours. 4J^ hour discharge. 1270-1280 specific gravity, charged. 1120-1130 specific gravity, discharged. 43 and 15 amperes, charging rate. 1. (a) What information does the name plate give you about the battery? (b) Do you understand the meaning of all the symbols on the name plate? 2. (a) What are you going to do with the battery in order to have it ready for service? 3. (a) What procedure would you follow in unpacking the battery? (b) Why should you unpack the battery in an upright position? (c) When should covers to the filling plugs be removed? 4. (a) Why should all the packing material be removed and the top and sides of the battery wiped off and the whole unit care- fully inspected? (b) What would you do with the battery if a jar were broken? (c) If a filling plug were broken? (d) If a jar leaked? (e) If the terminals were corroded? 5. After battery has been inspected for mechanical defects, what is the next item to inspect? 6. (a) Are batteries ever shipped unfilled? When? (b) How high above the battery plates should be the elec- trolyte? (c) If the electrolyte is low, will you add water immediately? If so, why? (d) In case there is indication that the electrolyte has been spilled, would you add water? (e) How can you determine whether evaporation or spilling has caused lowering in the height of electrolyte? 64 JOB No. ig 7. (a) What should a hydrometer read when placed in the cells? (b) Will you take hydrometer readings before or after adding water or electrolyte, or both? Why? (c) How can you insure getting a true reading of specific gravity after adding water? 8. (a) Is the battery shipped in a charged condition, so that it is ready for service? (b) Does a battery decrease in capacity when standing charged, but unused? If so, how much and at what rate? 9. (a) What rate is best used for the conditioning charge? (b) Should the filling plugs be in or out during the charge? Why? (c) How long will the charge be continued? (d) Where should specific gravity and voltage be measured? (e) What indications as to voltage and specific gravity will show that the conditioning charge has been completed? (f) How often should readings be taken? (g) How long a time will the charge be continued after no appreciable change occurs in specific gravity or voltage? 10. (a) How can excessive gassing be prevented during the last part of the conditioning charge? (b) What should be the finishing rate as compared to the nor- mal rate? (c) What effect will temperature have on making the condi- tioning charge? (d) Should water ever be added while charging? Why? (e) If the specific gravity is too high at the end of the charge, how will you bring it to the proper point? (f) Why is water the only thing needed by a normal battery if no leakage has occurred? 11. (a) What will you do to remove any water or electrolyte spilled on top of the battery after conditioning charge? (b) Is the battery now ready to be installed in a truck? (c) Should anything such as vaseline be put on terminals? 12. How often and why should a battery be given an equalizing charge? JOB NO. 20. Determine the efficiencies and characteristics of a General Lead Batteries Co.'s Type BH-15, 12-cell lead battery under normal test conditions. Manufacturers' Data: 220 ampere hours. 4J4 hour discharge, normal. 1270-1280 specific gravity, charged. 1120-1130 specific gravity, discharged. 1.7 end point of voltage of cells for normal dis- charge. 43 and 15 amperes, charging rate. 80° F. normal temperature. 1. (a) Can the ampere hour and the watt hour efficiencies be determined by either the constant current method or the constant potential method of charging? (b) What is meant by the term "efficiency?" 2. Which method lends itself most readily to test operations and to numerical computations? 3. What mechanical inspection of the battery is essential be- fore testing it? How high above the plates should be the elec- trolyte? 4. What electrical and chemical tests should be made before determining the efficiency of the battery? 5. (a) Is there any reason for charging and discharging the battery several times at normal rates before taking data for an efficiency determination? (b) Will such procedure insure average conditions, or best conditions, of the battery? (c) What readings are you going to take to determine the efficiencies characteristics of the battery? How are efficiencies expressed? (d) Is temperature of any importance in battery tests? (e) Could a constant temperature be maintained? If so, how? (f) Can readings be corrected for temperature changes? Should they be? 65 6i JOB No. 20 (g) What temperature variations should you find between be- ginning and end of charge and of discharge with outside tempera- ture at about 70° F.? 6. (a) Will you first take data on charge or discharge? (b) What advantages are there in starting with a fully charged battery and getting the discharge characteristics before getting the charge characteristics? (c) Should you measure the open circuit voltage, the tempera- ture, and the specific gravity of each cell or of one cell? Are these needed in an efficiency test? (d) Does the voltage fall off rapidly at start of discharge? Why? (e) What time elements should be used between readings at the start of the discharge? (f) What time elements should be used between readings dur- ing the flat part of the discharge curve? (g) Is it advisable to plot observed values to time as the dis- charge continues? Why? (h) Do you desire the total time of discharge and the open circuit readings at the end of discharge? (i) Will you discharge for 4)4 hours or will you discharge until cell voltage drops to 1.7? Why? (j) Should the amount of gassing be noted? Why? What does gassing signify? 7. (a) Will you start the charge immediately after discharge has ceased? What change would occur if time elapsed? (b) What time elements between readings will you use during the different parts of the charge curve? (c) Will you continue the charge at normal rate or will you use a finish rate in this efficiency test? (d) Will you charge for seven hours or will you charge until the voltage and specific gravity remain constant? 8. (a) What would a curve of charge and discharge voltage plotted to time tell you about the battery? (b) Compute the ampere-hour efficiency. (c) Compute the watt-hour efficiency. JOB No. 20 67 (d) Why does the discharge curve drop sharply at start of dis- charge and at the end of discharge? (e) Why does the charge curve change its shape? (f) What would curves of temperature and specific gravity plotted to time tell you about the battery? (g) What effect has thickness of plates on shape of charge and discharge curves? Why? 9. (a) What is meant by "recovery" of a battery and why does it occur? (b) If the battery were charged completely and then dis- charged for two hours at normal rate, and then charged one hour, and the operation repeated throughout a nine-hour day, what would be the approximate state of charge at the end of the day? 10. Explain the effect on efficiencies of charging at high and low rates? Of discharging at high and low rates? 11. (a) What is meant by "voltage efficiency"? (b) What is the relation of the ampere-hour and voltage effi- ciency to the watt- hour efficiency? (c) How do you estimate the minimum cost of charging from the output and the watt-hour efficiency? JOB NO. 21. Determine the efficiencies and characteristics of an A6, 21 -cell Edison truck battery. Manufacturers' Data: 225 ampere hours. 5 hour discharge. 7 hour charge. 45 amperes normal discharge. 45 amperes normal charge. 80° F. normal temperature. 1. (a) Should the battery be charged and discharged several times at normal temperatures before determining its characteristics? (b) Will you take the battery out of service, charge it, and then have the efficiency determined from the discharge and the fol- lowing charge? (c) Do you desire to determine the best performance or the average performance of the battery? (d) Is a determination of battery efficiency of any practical im- portance? If so, is the ampere-hour efficiency of more importance than the watt-hour efficiency? 2. (a) Does the constant current method lend itself better to the efficiency testing than the constant potential method? If so, why? (b) Is it advisable to have the current constant during the whole of the charge, or should a finishing rate be used when making efficiency tests? (c) In what order is it advisable to take the runs, i. e., start with battery charged or start with battery discharged? Why? (d) Will voltage or will time determine the end of the '•H.eicharge? (e) What should be the cell voltage at the end of discharge? 3. (a) What data will you take to detcinTin»> the efficiency and operating characteristics of the battery? (b) Will readings of temperature, cell, specific gravity, cell voltage and battery voltage all be necessary? 70 JOB No. 21 (c) Will the temperature be constant during the test? If not, will your results be affected? (d) Will you allow a temperature range corresponding to nor- mal operating before any correction of readings will be made? (e) Will you read specific gravity, volts and temperature on all cells, or on one cell? (f) Should each cell be filled with electrolyte to normal level before starting the test? 4. (a) What time elements between readings will you use on discharge? (b) What readings will you take at the same time? (c) Why should the time elements between readings be short at the beginning and at the end of the run? (d) Should all data be plotted in the form of curves? Why? (e) Does the shape of the voltage curve depend on the specific gravity? On temperature? On internal resistance? If not, upon what does it depend? 5. (a) Should you start the charge immediately after the discharge? (b) Should you use the same time elements between readings on charge you use on discharge? (c) Should you read the same items on charge that you read during discharge? (d) Should you notice when gassing starts and the relative amounts of gas emitted at different times during the charge? If so, why? (e) Should your data be plotted on the same curve sheet as the discharge data? If so, why? 6. (a) What difference do you find between the ampere-hour efficiency and the watt-hour efficiency? (b) What methods are available for determining these effi- ciencies from the curves? (c) Is a calculation from average ordinates sufficiently accurate? 7. (a) Why does the voltage curve have a peculiar shape dur- ing charge? JOB No. 21 71 (b) Why does the voltage curve on discharge assume a differ- ent shape than the charge curve? (c) Why is the value of the voltage required for constant cur- rent charging constantly changing? (d) Can you determine the internal resistance from the data taken? (e) Does the time elapsing between end of discharge and be- ginning of charge affect your results? If so, why? 8. Would you get the same efficiencies if you charged at higher rate? A lower rate? Why? Explain. 9. Would you get the same efficiencies if you discharged at a higher rate? At a lower rate? Explain. 10. What is the voltage efficiency of the battery? JOB NO. 22. Burn connectors on a lead battery by the arc method and by the blow torch method. 1. (a) Do you consider burned connectors better than bolted connectors for truck batteries? If so, why? (b) Are contact resistances and corrosion effects important items in battery operations? (c) Under what conditions does it become necessary to burn connectors? (d) Should a lead burning outfit be carried as part of the truck equipment? (e) Could any type of lead burning outfit be improvised in an emergency? If so, what? 2. (a) What will you do to the connectors to prepare them for burning? (b) What tool will be used to clean connectors? (c) What effect does acid on the contacts have on the burning operation? (d) Should the battery be protected from the flame by means of a damp cloth? By means of waste in the filling holes? Which is better? (e) Under what conditions of burning should the gases be blown out of the cells? (f) How can the cell gases be removed? 3. (a) How can you build up the battery posts if they are too short for burning? (b) How can you tell the posts are too short? (c) How ought a post, whose connector has been bored out, be treated before burning on a new connector? (d) How ought a post that has had its connector removed by a puller be treated before burning on a connector? (e) What tool can best be used for trimming posts? 4. (a) What equipment is used for arc burning? (b) What is the objection to using a large carbon? A small carbon? (c) How many cells do you need in series to operate the arc? 73 74 JOB No. 22 (d) Do you desire the arc or the hot carbon to do the burning? (e) How far below the top of the connector is the top of the post for arc burning? (f) Why should the top of the post be melted first in putting on a connector? (g) Why is a rotary motion of the carbon and lead filling from the inside outward and upward advisable in arc burning? (h) What would happen if the carbon remained stationary on the connector any length of time ? (i) What do you do to the top of the connector to get a finished job after arc burning is complete? 5. (a) In using an oxygen-illuminating gas burner, what kind of tip is advisable? (b) In adjusting for burning, why is it advisable to use only four or five pounds' pressure of oxygen for the torch? (c) What would likely happen if the tip became closed and oxygen was forced by higher pressure back into the illuminating gas mains? (d) How can this be prevented? (e) Why is it advisable to adjust the flame to about 8-inch length with the inner blue flame about 1 inch long for burning? (f) Has the flame a characteristic hissing sound when properly adjusted? (g) What part of the flame should be applied to the lead when burning? (h) Why must the flame be used rapidly and removed fre- quently from the lead? (i) Should the center of the post be first reduced, and then, using a rotary motion, build up the connector until flush with the top? (j) Can a smooth top be obtained with the flame? (k) What is meant by a hard flame? A soft flame? A reduc- ing flame? 6. (a) Can a hot soldering iron be used for lead burning? (b) Why is it inferior to either the arc or the torch? (c) Could an ordinary gasoline glow torch be used for lead burning? (d) Would an alcohol torch be suitable for lead burning ? JOB NO. 23. A two-ton truck with rated load, equipped with a National Carbon Co.'s Type VV 1215Z, 12-cell battery, has its battery tested at a stopping point on a long trip and finds it reading as follows: Voltage, 21.8. Specific gravity, 1140. The truck has still 10 miles to go, with no charging station in- tervening. At the point where the truck has stopped there is available for charging purposes a Signal Corps 2-Kw., 25 or 115 volt gas engine driven D. C. generator. GET THE TRUCK TO ITS DESTINATION. Manufacturers' Data: 1270-1280 specific gravity, fully charged. 1120-1130 specific gravity, discharged. 220 ampere hours at normal discharge. 4^ hour discharge, normal. 35 and 14 amperes, charging rate. 1. Can the truck reach its destination under its own power without charging the battery? 2. Can the 2-Kw. set be utilized to charge the battery? 3. (a) How many amperes would be available if the 25-volt circuit of the generator were used? (b) If the 115-volt circuit were used? (c) How much overload can be obtained from the charging set? 4. (a) Will you use the 115-volt circuit to charge the battery? (b) How long will it take to charge the battery from this circuit? (c) Will you have to put some resistance in series with the battery? Why? (d) What will you use for this resistance? (e) If there were no question about generator capacity, would you need a series resistance? (f) Will you charge at constant current or at constant poten- tial, using the 115-volt circuit? 75 76 JOB No. 23 5. (a) Will you use the 25-volt circuit to charge the battery? (b) How can you connect the battery to the circuit so it will be charged? (c) If you have a lead burning outfit, will it be quicker to charge with the 115-volt or 25-volt circuit? (d) Can you improvise a lead burning outfit if you cut a con- nector for charging from the 25-volt circuit? (e) What connector will you cut and how will you connect the cells to the charging circuit? 6. (a) Will you use any series resistance if charging from the 25-volt circuit with your new connection of cells? (b) Will you charge at constant current or constant potential? 7. (a) Under the conditions, what method of charging and which circuit of the generator will enable you to reach your desti- nation in the shortest time? 8. Which method involves the maximum labor and trouble? 9. State conditions under which you would use the 25-volt circuit. The 115-volt circuit. JOB NO. 24. Answer some general questions about batteries and their operation. 1. (a) Do storage battery plates keep their shape and weight? Why? (b) Why does not a form of electro-plating occur such as is noticed when zinc and copper are used in acid with electricity? 2. (a) If the material actually changes from lead to lead sul- phate, why does not lead sulphate precipitate as sediment in the cell? (b) Why do not trees and thick and thin places on the plates occur because of the reversible cycle? 3. (a) If the positive plate is lead or lead antimony alloy and contains lead peroxide, why is not the positive plate a storage bat- tery of itself? (b) Why does not it have a local charge and discharge of some magnitude? (c) Why is not some other material than lead used as a grid to hold the lead peroxide? (d) Should the grid be cleaned of sulphate? (e) Should the positive grid have a great amount of surface exposed? 4. (a) If lead sulphate is the resultant of discharge action, why is a "sulphated" cell said to be in bad condition? (b) Why should large sulphate crystals form on plates if a battery is left standing when discharged? (c) Why cannot these large sulphate crystals be readily re- duced by charging? (d) Why is a long-continued charge at low rate used to reduce them rather than a short-time charge at high rate? (e) Does sulphation help hold or cement the active materials together? (f) What is the extreme of this action? 5. (a) Why does not a storage battery discharge itself when standing on open circuit fully charged? (Water can be decom- 77 78 JOB No. 24 posed into gases, when slightly acid, at a potential of only about 1.7 volts, yet the battery has a voltage of 2 and over). (b) Why does it take 2.3 volts to cause a battery to gas on charge? (c) Would impurities in the electrolyte affect the above con- ditions? (d) In the active materials? 6. (a) Why do not the lead grids dissolve in the sulphuric acid? (b) What kind of material forms on the outside of the lead? (c) Why does it protect it from the acid? (d) Why does not this protection also occur w^ith respect to the spongy, active lead or the negative plate? 7. (a) Does a battery cool during discharge and heat during charge? If so, why? (b) If it cools during discharge, what becomes of the energy taken from the air? 8. (a) Why is heat generated when sulphuric acid and water are mixed? (b) Why does not the electrolyte in a battery always remain warm due to the above action? 9. (a) Why is the voltage of a cell a fixed thing approximately independent of the quantity of material or density of electrolyte? (b) What exceptions are there to the above statements? 10. (a) Why does the capacity of a battery change with tem- perature? (b) Does the capacity decrease with both extremes of tem- perature? (c) What is the.physr.cal explanation of such action? (d) What is meant by a "sluggish" battery? (e) Why do some battery men short circuit an Edison battery for an instant just before using? (f) Is there any truth in their reasons? 11. (a) What causes buckling of plates? (b) Is buckling apt to occur in a modern vehicle battery? (c) What limits the current output of a battery? JOB No. 24 79 (d) Will a short circuit necessarily injure a lead battery? An alkaline battery? (e) What differences in behavior is there between a thin plate battery and a thick plate battery? (f) Where are thin plate batteries used? 12. (a) What is the effect of partial discharges on the capacity of a battery? (b) What should be done to a battery that has been operating under conditions of partial discharge? JOB NO. 25. Determine conditions under which a truck equipped with an A 6, 21-cell Edison battery or one equipped with an Electric Storage Battery Co.'s Type MVY-15, 12-cell, will be ordered into service. Motor rating on truck is 45 amperes at 24 volts. Truck guarantee is four miles per hour on level with 4000-pound load. The battery is to operate the truck for a total of four hours actual running time per charge per day. Manufacturers' Data: Edison — A 6, rating, 45 amperes on 5-hour discharge. E. S. B. Co.'s— MVY 15, rating, 49 amperes on 4i^-hour discharge. 1. (a) Assuming identical trucks and their batteries fully charged, a load of 4000 pounds is to be carried from the station a distance of eight miles. The outside temperature is 98° F., which truck would you order into service? (b) Would either truck do the job? (c) Assuming a level road, which would do the job in less time? (d) Under the same conditions, excepting an outside tempera- ture of 18° F., which truck would you order into service? (e) Would either truck do the job? (f) Which truck would do the job in less time on a level road? (g) In case you have time, could you prepare the batteries to do the job in better shape on a hot day? On a cold day? (h) What would you do to the Edison? What would you do to the lead? (i) Would these precautionary measures enable either or both the trucks to perform their four-hour guaranteed service? 2. (a) A load of 4000 pounds is to be taken a distance of 24 mUes in ten hours. A charging station is located 12 miles from the starting point. (b) Which truck would you order into service, assuming nor- mal temperature and level road? Why? (c) Would either truck do the job? 8i 82 JOB No. 25 (d) Which would do the job in the shortest time? (e) What maximum charging time could you allow on the lead at the half-way station? On the Edison? (f) What maximum boosting charge would you utilize on the lead? On the Edison? (g) Assume the road has such a grade that a speed of only three miles per hour can be made. Would this change your choice of truck to be ordered into service? How? (h) If the road is steep and muddy so that you can average only two miles per hour, which truck would you order into service? Why? 3. (a) On a busy day, normal temperature, it is desired to work trucks under conditions such that otily half-hour boosting charges are available every three hours. Which truck could do its guaranteed service for a 12-hour day? Why? (b) Could each do it? (c) Which would give service a longer time? Why? (d) Would such service injure the Edison? The lead? 4. Which truck will have the greatest speed running light on a. level road at normal temperature? Why? 5. Which truck will have the greatest speed on a level road under heavy load conditions at normal temperature? 6. A four-ton truck weighing complete with load 8500 pounds has become stuck in the mud. In the emergency, which truck would you order out for helping the stalled truck? Why? r*^ :*^ .•w^<2^' srK y *^ "^-%. *•: