a Pi 10 I 1 1 "t5 ooco l 4 tpifl I QO <0 / *? ■go. h r o •^ Scale of © '. 92 SHIP FORM, RESISTANCE AND SCREW PROPULSION is perhaps negligible at (p)=*35 and below, but it increases to 3 per cent, and 5 per cent, at and above (jm='45. The hollow entrance gives a bad-looking model, and at all speeds requires 10 per cent, to 12 per cent, more power per ton displacement than either the straight line or medium entrance. Varying Prismatic Coefficient and Shape of Stem. — In all the models with various shaped sterns eddy-making appeared to be present in a more or less marked degree. The two best models were those with (1) the finest after-body prismatic coefficient (■789 ; see curve 5, Fig. 21), and (2) the medium prismatic coeffi- cient (-836) having straighter lines. The [C j curves for these two sterns associated with the same entrance (fore-body prismatic coefficient of -836) are given in Fig. 23. In neither of them was the eddy-making very great, and the lower levels were quite clear of it. If such high after-body coefficients are required, the curve of areas and water line should take forms similar to curves 4 and 5, Fig. 21, but with a somewhat easier shoulder for the latter curve. It must be remembered that one of the main factors in producing eddy-making in such forms as these is the ratio : — i (area of midship section) 2 length of run These model results show that in order that the stream lines shall not break away from the stern, the value of this ratio should not exceed j^ (see also § 16). CHAPTER X POSITION OF MAXIMUM SECTION, AND RELATIVE LENGTH OF ENTRANCE AND RUN § 43. — The experiments of Professor Sadler with equal-ended models having prismatic coefficients of -54 and -61 and no parallel body showed that within practical limits the midship section position had little influence upon the resistance. If anything it appeared to be advantageous to keep it a little aft of mid-length. Similar and more complete experiments have been made at the William Froude tank with a large number of mercantile ship forms. In these experiments the total displacement, length of ship, length of parallel body in any set, midship section shape and area were all kept constant, but the parallel body was shifted to varying fore and aft positions relative to the perpendiculars, the entrance and run remaining the same in form, but being elon- gated or compressed as necessary. The parent forms tried are given in Table 15, p. 94, together with the range of ratio of length of entrance , , ,, — ? — rr — j covered by the experiments. For the finest forms the results agree with those of Sadler, the best ratio of — , ,, — s being 1-1 to 1-2, according to the length of run ° ° speed, the latter becoming the better at really high speeds for the form. Beyond these limits the resistance increases continuously, particularly at wave-making speeds. With series " B," which had a blunter bow than the fine series, the influence of the position of the parallel body was still small, and may be neglected for speeds below that given by a Ck) value of 1-2 (or 9-3 knots for a 400-foot ship). Above this speed no 94 SHIP FORM, RESISTANCE AND SCREW PROPULSION definite rule can be laid down. The experiments showed a very emphatic gain at some speeds by using a short entrance, but this advantage had disappeared at a MM valueof 2-2. This uncertainty is due to one of the wave humps, which depends upon the wave- making length of entrance. As the entrance is shortened and run lengthened, the wave-making, which is more noticeable owing to the blunter lines, occurs at lower speeds, and there is a waviness in the curve of resistance at fixed speed as the ratio of entrance to run changes. Table 15. Length of ship 400 feet Midship section coefficient *98 Number of drafts in the beam . . 2-25 Beam in Feet. Displace- ment in Tons. Prismatic Coefficient . Parallel Body in Feet. Range of Ratio. Length of Entrance Set. Entrance. Bun. Length of Run. ' A B C D E 50 52-26 52-26 52-26 52-26 7,400 8,450 9,570 10,310 11,259 •52 •57 •57 •67 •67 •584 •584 •584 •64 •64 40 41-8 120 120 200 •76 to 1-67 •57 to 1-62 ■55 to 1-63 •6 to 1-67 •6 to 1-65 The total prismatic coefficient of any form in the above table can be obtained by combining the entrance and run with the appropriate length of parallel body which has a prismatic value of unity. The results with the forms having 30 per cent, parallel body combined with the finer ends (set " C ") show that the ratio of length of entrance . „,,-.., • i — ,°- , , . may vary from -9 to 1-2 without any material effect upon the resistance at any fixed speed below that corre- sponding to a fjn value of 1-6. As in any case it would not be economical to run a ship of this form at any speed above that given by Cr) value equal to 2-1 (i.e., a speed of 16-6 knots for a 400-foot ship), the results are fairly definite for this type. POSITION OP MAXIMUM SECTION 95 a Pi * J° 03 ® \ €> ®<© K \\\\ ' -^ v \ \\\\ \ «o s \\ \\\ \ \ \ \ \ \ lf» \ VT V \ \ \ \ \ * \ \ w «, \ V ft o \ \ \\\ 3 3 \ \ H\ 2 n <0 u ® M \ w\U ® ®\\ Hi ft: \ - n > M 5 < ife a / i ■*■ 1 1 / / 1 1 i in / / fl / P / 1 / 111 / / V /. % jo a/eog 1 *> I *? \ o M T3 T3 • ^ s a CO* CJ > n q «j O Ph s O 1C fl H rt -J a? £ > rfl * e O o CJ n o +3 M a> t> H 3 O 96 SHIP FORM, RESISTANCE AND SCREW PROPULSION With a fuller prismatic of both entrance and run, the forms with a short entrance and relatively long run are better than the reverse at all moderate speeds. In set " D " the advantage is but little, and if the speed exceeds that given by Ck) equal to 1-5 the entrance and run should be of equal length. As the form becomes rather wasteful at rKj equal to 1-7 (or 13-6 knots for a 400-foot ship), the above gives, for all practical purposes, a fair indication of the effect of any such change in form. But this gain with short entrance and long run becomes most marked when the parallel body amounts to 50 per cent, of the total length. The (c) curves for these forms are given in Fig. 24, and it will be seen that at low speeds the ratio — £ — -r — z c length oi run should be about -9 for the best results. The explanation of this advantage obtained with short entrance and long run lies in the fact that as the parallel body is added the lines become blunter at the ends and a certain amount of eddy- making takes place. This can be at any rate partially eliminated by elongating the run at the expense of the entrance, and so long as the curtailment of the bow does not increase the wave-making more than is gained by the reduction of the eddy-making at the stern, so long is there something to be gained by the change. So far as could be told, the eddy-making begins when the parallel body amounts to about 30 per cent, of the total length. With a relatively smaller beam than that adopted in the experiments it is probable that a higher proportion of parallel body could be worked without any marked detrimental effect. Moreover, if the form has a very hollow curve of area at the stern it is more liable to this defect than one with practically no hollow at all. As it is of great advantage from the point of view of the efficiency of the propeller to do away with this eddy-making, vessels having a large proportion of parallel, or practically parallel, body in their length should have but the slightest amount of hollow in their curve of areas for the stern. (See also § 16 and § 42.) CHAPTER XI MIDSHIP SECTION AREA AND SHAPE § 44. — This is as a rule settled by considerations more important and quite apart from the question of resistance and propulsion, and model experiments show that within reasonable limits this practice is quite sound. The shape of the midship section can be varied over very wide limits without affecting the resistance provided the beam, water line, and curve of areas remain un- altered. With the full type of midship section commonly adopted in the merchant service a little qualification is required to this, as a too sharp turn of bilge has certain disadvantages which have been already pointed out ; but good results can be obtained with midship section coefficients up to -98 if the rise of floor is nil and a little less than this if the rise of floor is not abnormal. This general rule enables the designer to adopt any type of section which may suit the particular service of the vessel without having to trouble about the question of propulsion. Prom the above it will be seen that the ratio of breadth to draft cannot be a very useful means of comparing different forms. A far better criterion is the ratio beam B Vmidship section area VA m This ratio is independent of the form of midship section, and at the same time is a measure of the relative width and mean depth of the immersed form. The question of absolute size of midship section is intimately connected with the one of longitudinal distribution of displace- ment, and from many points of view cannot be wholly separated from it. It is also closely associated with the stability of the ship, S.P. H 98 SHIP FORM, RESISTANCE AND SCREW PROPULSION since a large midship section coefficient means a comparatively low centre of buoyancy at the deeper drafts, and a large area of midship section with a moderate coefficient will give a higher centre of buoyancy and metacentre. The possible combinations are infinite, but the consideration of some more or less restricted cases will serve to show what is best for propulsion in most cases. The usual type of merchant ship has from 7-5 to 8-5 beams in its length, and 1-9 to 2-8 drafts in the beam with a midship section coefficient of -85 to -98. But, supposing the beam and draft are severally or together increased, will this affect the resistance per ton? § 45. Increase in Midship Section Area, Beam, and Draft without Increase in Total Displacement. — This necessarily involves a fining of the ends of the form and a reduction of the prismatic coefficient, which is favourable to the attainment of high speeds at economical rates. Mr. W. Froude has tested the effect of this on two forms of the following dimensions : — Table 16. Length in Feet. Beam (feet). Draft (feet). Dis- place- ment (tons). Wetted Surface (square feet). Form. Entrance. Parallel Body. Run. Total. A B 144 179-5 72 144 179-5 360 359 37-2 45-9 16-25 18-0 3,980 3,980 18,860 19,130 Both had the same degree of fineness of entrance and run ; the larger midship section of form " B " was balanced by an extension of the entrance and run to amidships, the parallel middle body being entirely eliminated. The change from "A" to "B" involved an increase of wetted area, as indicated by the last column of the above table. Below 13 knots form " A " was very slightly the better, but above this speed form " B " improved continuously compared with " A " owing to the smaller wave- MIDSHIP SECTION AREA AND SHAPE 99 making resistance consequent upon the decrease of the prismatic coefficient. Experience at the Froude tank shows that for vessels of fairly full form running at speeds above or about that given by V=-6S*/L, within reasonable limits, greater beam and finer ends will give better results. § 46. Increasing Beam and Draft at every Section, keeping the Midship Section Coefficient and Form of Level Lines unaltered. — Such a change as this leaves the prismatic coefficient unaltered, but the displacement and angle of entrance of the water lines are both increased. The vessel with the greater beam has the smaller area of wetted surface per ton displacement, which has to be balanced against the increased wave-making due to the larger angle of entrance. Froude's methodical series of model experiments show that with models of prismatic coefficients -55 to -61 the broader the vessel the smaller is the power per ton at all low speeds. Thus at Ajn=2-4 the power per ton decreases as LM) decreases (or beam increases), the reduction for 10 per cent, in displacement (i.e., 5 per cent, increase of both beam and draft) being about 1 per cent. This advantage is a very small one, and as speed increases the increased importance of the wave-making causes the broad vessel to slowly lose in comparison, and it becomes the worst at high speeds. The change over takes place at (mj=5-9 to 7-4, according to the speed, but above Ckj— 3-3 the vessel with the smallest beam is always the best. Taylor's experiments show much the same result. His models had prismatic coefficients of -56 and -68, the former being fine ended, and the latter, although having no parallel middle body, being rather flat amidships and fairly full at both ends. At low speeds the effect was the same as is given above for ^gj=2'4. At high speeds, given by V=l-lVL, with the -56 prismatic coefficient the beam change had very little effect on the power per ton, but with the -68 prismatic coefficient the broadest vessel was the worst. h2 100 SHIP FORM, RESISTANCE AND SCEEW PROPULSION § 47. Decreasing the Midship Section Coefficient by increasing the Beam and Draft together, the Area of each Section remaining the same. — Taylor has made experiments with models varied in this way. Two sets were tested having prismatic coefficients of •56 and -68 respectively. Several ratios of displacement to length, covering all the practical range, were tried. The midship section coefficient was varied from 1-10 to -70, corresponding to / — - values of 1-63 and 2-04. The ratio of beam to draft was maintained the same for all the models, viz., 2>923. The forms with fine midship section coefficient naturally had " peg-top " sections, and those with large midship section coefficient had an under- water bulge amidships. The minimum wetted surface for the models was obtained with midship section coefficients of -9 to «98 for the -56 prismatic coefficient and -86 to -93 for the -68 prismatic coefficient. T> With both prismatic coefficients a change of , — from 1-63 VA m to about 1-76 (midship section coefficients 1-1 to -95) had no effect upon the power per ton. For the finer midship sections not only was the wetted surface greater, but the residuary resistance increased as beam and draft were increased, at all speeds up to the maximum consistent with economy of propulsion (V equal to 1-48 and I* 15 times VPL for the fine and full prismatic coefficient respectively). The excess of the total resistance of the -7 over the «95 midship section coefficient amounted to approximately 7«5 per cent, for the finer vessels and slightly less than this for the full vessels at their normal speeds. At lower speeds the difference was not quite so great in either case. The results show that for the attainment of high speed there is JO nothing to be gained by the adoption of high values of in order to get a fine midship section. o jo it Breadth, . _ § 48. Varying — j=— by increasing Beam and decreasing Draft, MIDSHIP SECTION AEEA AND SHAPE 101 keeping Displacement, Form of Sections, and Levels unaltered.— It can quite easily be seen that a large increase of beam on a fixed displacement and length will generally mean an increase of wetted surface, and generally it can be stated that with given form of section there is a particular value of ratio of -7= which has the VA m advantage of offering a minimum wetted surface, which for low- speed vessels is a very important item. In Colonel Rota's experiments with models having a midship section coefficient of -87, and prismatic coefficient of -56, this best ratio of ,-— is about 1-85, and there is remarkably little change of wetted surface between values of 1-6 and 2-3. So far as Motional resistance is concerned, therefore, these figures give the best proportions of ,— for this form of boat. But the experi- ments showed that the residuary resistance increased with the beam at all speeds, and as a result the minimum value of total resistance for a vessel of 328 feet length occurs at a somewhat lower value of — == than that for minimum wetted surface, viz., 1-38 to 1-8. The extent to which these latter ratios are lower than the ratio for minimum wetted surface must depend upon the form of the ship — i.e., its curve of areas, etc. — but for good forms there can be little doubt that the above result is fairly representative. B Departure from this best value of i-g in the direction of smaller beams was not a matter of very great moment for the range of variation possible in most cases. But the resistance in- creased fairly uniformly with this ratio when it exceeded 1-8, and when it became 2-45 the resistance was 13-5 per cent, above the minimum. This can be seen from Fig. 25, which gives the [Cj values for ship of 328 feet length, to a base of ratio of beam to draft. The forms with the largest beam and smallest draft may 102 SHIP FORM, RESISTANCE AND SCREW PROPULSION be classed as shallow-draft vessels of high speed, as the draft corresponding to 328 feet length is only 9J feet. If the midship section coefficient be increased from -87 to -97 the draft would MIDSHIP SECTION AEEA AND SHAPE 103 become 8-36 feet and the results would still apply within 1 per cent. Mr. Froude's experiments show that a change of ,_ from 1-72 to 1-99, obtained in the same way, caused an increase of resistance of approximately 3 per cent, for vessels of high (m) value or small ratio of displacement to length, and 6 or 8 per cent, for vessels of larger and more usual ratios of displacement to length. The models with which the above experiments were made are described in § 30 and Table 10. § 49. Decreasing Midship Section Area by increasing the Pris- matic Coefficient, all Dimensions and Displacement remaining the same. — Taylor has tested this with models having block co- efficients from -56 to -68. The models had a ratio of beam to draft of 2-4, and the dimensions were arranged so that the product beam x draft X block coefficient was the same in all the models. For any block coefficient the curve of areas had more hollow the larger the midship section coefficient ; and the area curve for the largest block coefficient (•68) had nearly straight ends at -98 midship section coefficient and bluff-rounded ends for smaller midship section coefficients. The water lines followed the area curves in shape. The sections had a slightly bulbous stem, and both stem and sternpost were " vertical. The variation of wetted surface is very small with such changes, being of the order of 1-6 per cent, when the midship section coefficient is varied from -86 to -96 and 3*1 per cent, going from •96 to 1-06 at all block coefficients. Generally speaking the results show that at all moderate speeds a full midship section is good, and a coefficient of -98 is quite safe even for a block coefficient of -56. Except at very high speeds for the form, -96 to -98 may be taken as good working figures. At low speeds the full midship section gave slightly higher resistance. The speeds at which it became advantageous to reduce the area of midship section and fill out the ends of the ship are indicated 104 SHIP FOKM, RESISTANCE AND SCREW PROPULSION V in the table by the heavy lines. Each line is for a definite -W value, and for any block coefficient, that prismatic coefficient is best which lies immediately to the right of the line corresponding to the speed at which the vessel is to run. Table 17. Dimensions and Coefficients of Models. Length . . . 20 feet. Block Coeffi- cient. Breadth (feet). Draft (feet). Midship Section Coefficients. •£6 •92 •98 1-04 110 2-928 2-828 2-739 2-657 1-22 1-179 1141 1107 Pr i ismatic ibove B Coeffici lidship ents co Section rrespon Coeffic ding to ients. •56 •651 •698 •609 •652 •571 •538 •509 •545 V •60 •612 | -577 7i=" 88 ■64 •744 •791 •696 •739 •653 1 -615 •582 „ --72 •68 •694 •654 •618 ., ='6 „ —"48 Thus for a block coefficient of -68 at speeds between —r= equal to -48 and -6 the best prismatic coefficient is -694 to -654, corre- sponding to midship section coefficients of -98 and 1-04 respectively. It must be noted, first, that the possible gain in resistance was always small, and, secondly, that the large midship section coefficients were obtained by large under-water bulging of the form, i.e.., the tumble home commenced well under water, and there were never any sharp or angular corners in the sections at the bilge. B § 50. Varying jj- by Bodily Sinkage of the Ship. — The follow- MIDSHIP SECTION AREA AND SHAPE 105 ing table gives the percentage increase in power for a 10 per cent, variation of displacement obtained in this way : — Table 18. Variation of Effective Power for 10 per cent. Variation in Displacement. Block Speed in Knots. Type of Coeffi- cient. Length (feet). Ship. 10 15 18 20 22 30 40 Battleship . •65 400 70 8-0 120 Cruiser •53 400 — 6-6 7-8 — 110 Small cruiser •51 400 — 8-0 9-0 9-5 11-2 Destroyer •5 400 — 5-6 — 8-1 10-3 10-6 Steam yacht. •5 400 — 6-5 7-8 — 101 Passenger steamer •59 400 6-2 7-7 8-5 12-4 Speed in Knots. 8 10 12 14 16 Intermediate steamer •677 400 5-0 5-5 6-8 6-9 | 19-0 to deep line 12-0 to light line Slow steamer •758 400 4-5 6-5 6-6 7-0 10-0 at 15 knots It will be noticed that the effect for each form varies with speed, and for all forms at low speeds the effective horse-power per ton of displacement decreases as the draft increases, and may be taken as varying with (displacement)*. At those speeds at which wave-making is important the power per ton is roughly constant for all normal variations of draft. The skin friction effect would be the same at high or low speeds, and the increased percentages in the table at high speeds must therefore be due to increase in wave-making. At the low speeds this depends upon the form near the water plane, but at higher speeds upon the cross-sectional area, which increases with the 106 SHIP FOEM, RESISTANCE AND SCREW PROPULSION draft. Larger waves, therefore, are created at the same speed as the draft is increased. For this reason, such a variation of power per ton of displacement as is shown for the " intermediate steamer " at its high speed is found, to a greater or less degree, in all ships, when they are forced beyond their proper speed. CHAPTER XII LEVEL LINES AND BODY PLAN SECTIONS § 51. — Assuming that a satisfactory curve of areas has been decided upon, and that the over-all dimensions are fixed, it remains to draw in the body plan sections and level lines. The most important is the normal level line. This being fixed, the sections may be drawn in almost any manner consistent with fairness and the curve of areas, without any material effect upon the resistance. If the water line coefficient in either body is the same as the prismatic coefficient, the sections tend to become bulbous in character — i.e., broader below the water line than on it — and for this reason the water line coefficient is usually made a little greater than the prismatic coefficient of the body. A slight increase in fulness of the water line enables the bilge curve to be eased, and avoids this tendency to bulbous sections and gives a much better bow line. Still more increase in area of water line will give sections decreasing continuously in width towards the keel. Vessels of Low Speed. — For vessels having prismatic coefficients of about -7 to -8 intended for low speeds given by (pj values up to •5 (or about 11*5 knots for a vessel of 400 feet in length) a com- paratively full-ended bow water fine can be worked without any material disadvantage. It gives bow lines with a good fore and aft slope and easier stream line flow under the form. For this class of vessel care is required in working the lower level lines into the parallel body, especially if the midship section is fairly full. A midship section coefficient of about -98 with a little rise of floor 108 SHIP POEM, EESISTANCE AND SCKEW PEOPULSION to the section gives a very quick turn at the bilge, and in a form having more than about 25 per cent, of parallel body is liable to show a corner where this sharp turn is merged into the tapering entrance and run. This can be avoided by adopting a flat floor line amidships and a bilge curve of larger radius, keeping the midship section coefficient the same ; or of course this coefficient can be reduced, but the latter method involves making the ends fuller to compensate for the reduction of area amidships. It can also be avoided by easing the lower level lines so that the per- fectly parallel body does not extend so far either forward or aft at the bottom as it does at the load level. This gives a good shape, and is to be recommended for all vessels of large prismatic coefficient. The bow lines become easier and the flow of water to the screw is better. § 52. Vessels of Higher Speed. — For these the case is different. In the full vessels easy stream lines are important, but with finer prismatic coefficient assuming a fair form easy stream lines are assured, and the avoidance of wave-making will now require special attention. Table 19. Type. Beam at Half-length Beam Amidships Battleship First-class cruiser , Third-class cruiser Destroyer Skin friction does not enter into the question at all. With a fixed curve of areas the effect of any change of water line coeffi- cient upon the area of wetted surface is very small. With ordinary forms having U-shaped sections in the fore-body, and V or Y- shaped sections in the after-body, the water line coefficient may LEVEL LINES AND BODY PLAN SECTIONS 109 be varied widely and the skin area will remain practically con- stant. But variation of the area of water plane affects the stability, and a comparatively large water plane is usually necessary to secure the required stability in the ship. As a rule it is obtained by filling out the after water line. The amount of filling can be roughly gauged from the figures in Table 19, p. 108, which gives average values of the ratio of beam at the half length of entrance and run to beam amidships for several types of ship : — This fining out of the after water line gives the sections a V or Y shape, according to the relative fulness of after-body and water line. It also has the advantage for all vessels of high or moderate speed that it reduces squatting, and in twin screw vessels the full stern protects the propellers when the ship is going alongside wharves, etc. Taylor's experiments with models having the same dimensions and fore-body, and the same curve of areas for the after-body, showed that the shape of the section had no very large effect on the resistance. The models had a prismatic coefficient of "62, and a midship section coefficient of •98. The best result was obtained with an after-body in which all the sections were geometrically similar to the midship section, i.e., had vertical sides and flat floors, beam and draft being both decreased as necessary to obtain the desired area. This was some 3 per cent, to 5 per cent, better than the conventional form of stern. The worst shape was one in which the full beam and a flat floor were retained in all the sections, this being some 7 per cent, to 10 per cent, worse. So far as resistance is concerned a comparatively full water line aft is slightly better than a fine one for all moderate speeds (see Fig. 26). This requires a little qualification in the case of certain single-screw ships. In such vessels having a screw with the blade tips 2 or 3 feet below the normal load line aft, the water line should be kept fine enough to avoid any dead water, and the body plan sections can be filled out towards the keel without material detriment to the resistance or the screw action. 110 SHIP POEM, RESISTANCE AND SCREW PROPULSION § 53. — So much freedom of treatment of the bow level lines is not possible if good results are to be obtained at moderate or high speeds. A fine entrance is essential for small wave-making. For vessels having 10 to 25 per cent, of parallel middle body a fine entrance with a little hollow in the water line gives better results at the service speed of such vessels than a full entrance with straighter lines, even though in the latter case the entrance is longer than in the former. The essential thing is not so much length of entrance as fine angles, which the former secures. For finer vessels both length and fineness of entrance are required to attain high speeds. Fig. 26 gives the residuary resistance for four of the models tested in connection with the experiments detailed in § 31. These four models have the same area curve. Numbers 1 and 4 have a fine water fine in the stern with fine and full bow water fines respectively. Numbers 3 and 2 have a full water fine in the stern with fine and full bow water lines respectively. These water lines are given in Fig. 18. It will be seen that the full bow water line gives double the residuary resistance obtained with the fine and hollow water line. For high-speed vessels, i.e., those whose normal speed V is greater than -9VL, it is more difficult to lay down a general law. The best form of water fine depends to a certain extent upon the shape of the adopted curve of areas. Taylor's experiments show that with a full-ended curve of areas such as G and D, Fig. 18, at all speeds it is an advantage to keep some hollow in the bow water line. But fine forms, whose area curves are hollow at the ends, as curves A and B, Fig. 18, give best results with only a moderate amount of hollow in the water fine, and for speeds above that given by V=llVL the form with the straight bow water fine is the best. At these high speeds the form was slightly improved by fining down the stern load water fine from its usual full form to a straight or even hollow curve. It must be remem - bered that the above results were obtained with forms whose prismatic coefficients were -60 and -64 having no actual parallel body. The possible reduction of power by variation of the load- LEVEL LINES AND BODY PLAN SECTIONS HI •wsuittijdsip I/O] j>d ry/ jo a/es^ S3 S «T) .9 Hi § ■8 o o M .1° CD 6 M P I 112 SHIP FORM, RESISTANCE AND SCREW PROPULSION line in these experiments amounts to about 6 per cent, of the whole for the practical range of variation. § 54. Hollow versus Straight Lines. — This question has already been considered for slow and intermediate steamers, and this section deals with the case of high-speed liners, cruisers, etc. Vessels of still higher speed, such as destroyers, are considered in § 55. The half-breadth lines in the fore-body of the majority of fast liners, cruisers, and battleships are hollow towards the end. The same remark applies to the lower level lines in the after-body. With low prismatic coefficients hollow level lines are a necessity if a curve of areas suitable for high speeds {i.e., with hollow ends) is adopted, and the fore-foot and dead-wood aft are not cut away. It is possible, as in the case of sailing yachts, to maintain such a curve of areas and yet work the level lines without any hollow. But the block coefficient of such vessels is very low, and the sweeping contours of stem and stern post adopted in them are possible to only a limited extent in large vessels. For fine forms, the experiments by Mr. R. E. Froude, made specially to test the relative merits of hollow and straight-ended forms, give reliable data. His models had the usual cruiser type of stern, and for one set of experiments corresponded to the following dimensions for ship : — Table 20. Length between Perpen- diculars (feet). Beam (feet). Draft (feet). Displace- ment (tons). Midship Section Coefficient. Prismatic Coefficient Form. Fore- body. After- body. D E 490 490 74-5 75-5 260 250 14,458 14,458 •926 •90 •552 •580 •598 •639 Both models had the same displacement and length, and the same height of metacentre, the beam being varied in order to obtain this. In model " E " the level lines were practically LEVEL LINES AND BODY PLAN SECTIONS 113 straight towards the ends in both bodies. The lines of model " D " had the usual amount of hollowness for such forms. As " E " had a greater prismatic coefficient than " D," its draft was reduced in order to maintain the same displacement. The tests showed " E " required 8 per cent, more power to obtain the same speed. This large difference extended down to quite moderate speeds given by V='SVL. Tests made with other models of the same type showed that the major part of this effect was produced by the change in the fore-body. A still greater difference was obtained with two models having the same principal dimensions and midship section. One had perfectly straight ends to all the level lines, and the other had the usual amount of hollow. The increase in displacement was about 7 per cent. (4 per cent, in the bow and 3 per cent in the stern), and the increase of power 13 per cent, at moderate and 16-5 per cent, at high speeds. With regard to the effect on propulsion of the straightening out of the after-body lines, Mr. Froude's conclusion is : " The net upshot may be said to have been purely neutral as between straight and hollow lines for after-body, the balance of efficiency advantage which the screw experiments attributed to the hollow- line after-body being just about cancelled by the shaft tube and web advantage of the straight line one." This increase in resistance with the straight level lines is due to a great extent to the fact that the curve of areas obtained by their use is a bad one for all moderate and high speeds. For very high speeds it may be, and is in certain cases, an advantage. Experiments with these models were also made in what repre- sented a very steep ground swell, all the waves having the same period. The increase in power required to maintain the speed was about the same with both straight and hollow line models, and was always greatest when the period of the waves as encountered by the ship, was some 12 per cent, greater than the natural pitching period of the ship. Although not conclusive, the results give no reason to suppose that with ordinary waves the smooth water advantage of the hollow line form is ever lost. S.F. I CHAPTER XIII RACING AND OTHER HIGH-SPEED VESSELS § 55. — This term includes all such vessels as pinnaces, de- stroyers, motor launches and hydroplanes, i.e., vessels whose highest speeds exceed that defined by the formula (p)=l-5, or V=2VPL. Thus for a vessel of 325 feet length having a prismatic coefficient of -6 this critical speed is 28 knots. At the above speed the hollows and crests of the bow transverse wave system are coincident with those which the stern tends to form, and as a consequence wave-making is abnormal. But above this speed the bow system gets out of phase with the stern system, and as the speed is increased each tends to cancel the other and the height of the transverse waves formed at the stern of the vessel decreases. But the divergent waves emanating from the bow also tend to increase in size, and unless the vessel is specially shaped to prevent it, this increase is continuous. So long as the cancellation of the transverse waves mentioned above exceeds the natural growth in the divergent wave system, the per- formance of the vessel will improve. This is what happens with many destroyers whose lines are very fine. The divergent waves formed are comparatively shallow and have but a small velocity in the forward direction. Fig. 27 is a typical fcj curve for a good type of destroyer, and it will be seen that above rp)=l-5 the f(jj value steadily decreases, but is tending to the horizontal at the highest speeds. With such vessels the percentage of the propulsive power required to overcome the wave-making has been found to be RACING AND OTHER HIGH-SPEED VESSELS ^- 2 /© jo g/e. 'S 1 * to n CM ^ <* \ CO •p 5 Sea eo t- X X o I I CO CO CO o I I k < jr i> ? =1 to is t 1 > * X <> o — s 1 > Ck o I » i rl ^ § /Sea 5 7 eofl >s per ton/ 9 fi IS o 02 8 U -*> .3 IS « o s EE8TEICTED WATEE CHANNELS 133 that it is practically independent of the length of the vessel, and thatitdependschiefly upon the ratio ^an depth of midship section depth of water The greater the ratio the sooner this effect becomes marked, and the greater is the shallow water increment. Prismatic coefficient appears to have little influence at speeds below that given by the preceding formula. This can be seen from Fig. 29, which gives the results of some recent experiments with models in shallow water. The figure gives the increase in resistance per ton dis- placement of ship at two speeds, the ordinates being plotted to a base of mean de f\ ° f f id f fr section . Four block coefficients depth of water varying from -56 to -68 were tried with varying midship section areas. The particulars of these models are given in Table 17. These experiments show that in shallow water there is no gain as regards resistance by adopting a large midship section area, when this means a deep draft, even though it gives better results in deep water. Johann Schiitte's experiments with models of an Atlantic liner and a cargo-boat support the above results, and it will be noticed that even at a speed given by V 2 =2-88d there is a material increase of resistance for all depths of water tried in the experi- ments. For practical speeds Schiitte's experiments show that the following depths of water are required in order to be entirely free from shallow water effects : — Destroyer, more than 14 drafts. Fast liner, about 7-5 drafts. Cargo-boat, more than 5 drafts, but not more than 7. The increase in power required to steam at speeds well below the critical speed for the depth of water is shown by the following trial results of two warships : — H.M.S. Edgar in deep water steams at 21 knots, but in 12 fathoms with the same power she can do only 20-25 knots. The Edgar has a midship section area of approximately 1,150 square feet, mean depth of midship section of 22-5 feet, length between perpen- diculars of 360 feet. 134 SHIP FOEM, RESISTANCE AND SCREW PROPULSION H.M.S. Blenheim in deep water steamed at 21-5 knots with the same power as developed only 20 knots in 9 fathoms. Her mid- ship section area is 1,320 square feet, mean depth of midship section 25-5 feet, length between perpendiculars 375 feet. One important effect of shallow water is the increased sensitive- ness of the stream line flow. Mr. Taylor, in giving the results of his experiments, pointed out that unstable eddies caused the resistance to vary radically at high speeds, and even at low speeds the results required some fairing. This eddy formation must necessarily produce bad manoeuvring in any ship working under the same conditions. § 63. Width and Depth of Channel. — Schiitte has tested several forms in channels of varying width and depth, and in what may be called open and unlimited water. Taking first the case of a cargo-boat. The increase in resistance at any speed over the open water value was approximately the same for a broad and shallow channel as for a narrow and deep channel, provided the ,. depth of water . ,, , , width of channel . ,, ratio j ,. — 7-t-: — m the former and — r j-t-= m the dratt of ship beam of ship latter were the same. This only applies to the ordinary low speeds at which such a vessel would run, when wave-making is not very important. Over this range of speed, the percentage increase of resistance was roughly constant for any given size of channel. At higher speeds, experiments with models of an Atlantic liner and a torpedo-boat show — (1) the speeds at which humps occur rPSlstfliTlCG in the curve of -. — ^ — ^— r- a are slightly lower than in open and deep water, but (2) these humps and the succeeding hollows become more emphatic the narrower the channel. Table 23, p. 135, gives the percentage increase in resistance found with the above two models at various speeds. The figures, however, are not very accurate, being obtained from small scale diagrams, but they serve to show that a width of channel of at least eight beams is required for the liner and ten beams for the torpedo- boat to get the same results as in deep water. EESTEICTED WATEE CHANNELS 135 Table 23. Effect of Width of Channel. Number of Beams in Width of Channel. Percentage Increase on Besistance at fpj Value. 2-0 1-75 1-5 1-25 1-0 •9 •8 •7 Torpedo-boat : Block coefficient -45 . Prismatic coefficient, about -6 Atlantic liner : Block coefficient, -61 Prismatic coefficient, about -64 3-4 ■ 5-67 7-9 3 ■ 5 7 7-0 1-6 •4 16-3 8-0 1-6 7-S 5-1 320 12-0 4-7 9-5 7-4 2-5 20-6 1-6 9-5 7-0 1-6 26-0 6-7 30 16-5 4-3 20 9-2 4-1 Note. — The bad wave-making speed of the torpedo-boat in deep water is given by 0= =1*6. The highest service speed of the liner would be approximately ( P )=-8. When the channel is both narrow and shallow there would be the same tendency to form the shallow water wave, but the actual wave formed would be affected by the width of the channel and the speed at which the vessel was running — i.e., whether this speed was one at which the ship tended to form waves in deep and open water. But the shallowness appears to be more important than the width, and would be the main factor in determining the extra resistance. Some tests were made at Uebigau with a number of similar models of different sizes. These were tried in two channels, one of which had a cross-section area nine times greater than the other, both having a breadth twice the depth. These experiments gave the following results : — (a) An area of channel 200 times the midship section area of the model had no effect up to speeds given by V 2 =5-0d. Above this speed the usual shallow water hump occurred at about V 2 ~l0d, and at higher speeds the resistance was slightly lower in the channel than in open water. The increase of resistance at the hump was 4 per cent, for a model of draft equal to '05d, and 12 per cent, for a model of draft equal to -Id. 136 SHIP FORM, RESISTANCE AND SCREW PROPULSION (6) An area of channel 51 times the midship section area of the model increased the resistance at all practical speeds, this increase being of the order of 8 per cent, at fp)='78. With a fine form (prismatic coefficient -6) the increase of resistance was continuous up to the critical speed for the depth, and exceeded 22 per cent, at this speed. With a fuller and deeper form (prismatic coeffi- cient -8) the resistance hump and hollow at fpj—-8 to 1-1 was exaggerated in the small channel, and the percentage increase of resistance over the open water value varied considerably in consequence. When the speed exceeded that given by V 2 =5d the resistance increased enormously. This model had a draft one-fifth the depth of water in the small channel, the draft of the former one being one-tenth. (c) In a channel of cross-section area 22-8 times that of the model the resistance of the fine and shallow form was increased from 4 per cent, at quite low speeds to 45 per cent, at a speed given by V 2 —5-0d, and much higher figures above this speed. For the fuller and deeper form (draft=-33xd) the resistances were increased 12-5 per cent, and 30 per cent, at speeds given by y -t-=1-15 and 2-6 respectively. . It will be seen that in a confined channel, the deep vessel suffers more than the shallow one, and that a cross-section area of channel about 200 times that of the vessel is required at all normal speeds, if the resistance is not to be affected by the boundaries. At low speeds a smaller size can be allowed, the necessary ratio of areas being about 150. In the previous pages it has been shown that there must be a depth of water equal to 14-0 to 7-0 drafts when there are no side boundaries, and a breadth of channel equal to 10-0 to 8-0 beams when the water depth is very great. When both side and bottom boundaries are present these numbers naturally increase somewhat, as shown by the above results. § 64. Barges and Canals. — It was demonstrated many years ago by Scott Russel that a barge could be towed in a narrow and RESTKICTED WATEE CHANNELS 137 shallow canal much easier at high speeds than at low, and that at a certain critical speed which had to be passed to attain this result the resistance was remarkably high and the wash on the canal banks very destructive. This critical speed he found to be that at which a wave of translation proper to the canal depth would L '•C 1-0 ■9 ■9 r 8zf Values of A f 2 for various Barges in Canal R~r- excess resistance in Canal oyer Open Water Value A - immersed Sectional Area of Barge. V = Speed of Barge in feet per second. o-,y ]0 Cross Section Area of Canal " "En, "/i>"i\£ ar g e Mean Curve shorts AV?-(rri) z For Speeds above 2-3 miles per h- 'the added resistance exceeds that shown by Curve. + Flute © Peniche T Toue V Margotal 1 Jeanne (Light) L » (Mean) r - (Deep J bs. 8 •7 ■6 ■5 ■4 ■7 \ X- << b \ a ■S «*• u \ ■4- "5 CO v, ■3 1 ^ ■3 ■i 1 N % \- ■I •1 ~* *- ■1 3 4- 5 Ifsle nF C ro - is Section Are- < of Canal. 0-i 9 >eaie or j^r 6 ss Section Are a^of tlarge g Fig. 30. — Additional Resistance in Canals. Barge Forms. travel, and is given by the formula in § 60. This speed is, how- ever, too high for the usual run of canal-boats, being 8-1 knots for a depth of 6 feet. In considering this matter it must be remembered that the usual type of canal-boat has a very high block coefficient (generally above -9), which necessitates blunt ends. Irrespective of any effect of the restricted area of the waterway, however, these vessels are not suited for running at high speeds, owing to the growth of wave-making and eddy resistance. Moreover, in many 138 SHIP FOKM, RESISTANCE AND SCREW PROPULSION inland canals there is a definite speed limit which must not be exceeded. This speed has been fixed mainly with the idea of preventing the banks from being destroyed by the wash of the waves created by passing vessels, and averages about three* miles per hour, and it is at this and lower speeds that the effect of the restriction of area is of greatest interest. Reliable data on the subject is scarce, but from such as is available the following conclusions may be drawn : — (1) Canals which are broad and shallow give worse results than deeper and narrower canals of the same sectional area. This is due to the fact that a vessel requires a certain depth of water between it and the canal bed. If this depth of water is not available, the stream flow under the bottom becomes very unsteady and the resistance is increased due to the consequent increase of eddy- making and erratic motion of the vessel. This depth appears to be not less than 1-5 feet, and if possible 2-0 feet for canals of about 7-0 feet total depth. (2) The resistance in the canal depends very largely upon the ratio area of canal waterway m ., , , -. j t-- j , J , . The resistance m a canal may be immersed section ot boat J divided into resistance in open water and added resistance in the canal. Experiments made by M. de Mas show that this added resistance for speeds up to 2-3 miles per hour may be written in the form R and r being resistance in lbs. in shallow and deep water respectively ; A the immersed sectional area of the boat in square feet ; V the velocity in feet per second ; „ . . (area of waterway). n the ratio -. — A * This figure does not apply to intersea canals, the speed limits for these being as follows: — Suez, 5-3 knots; Kiel, 8 knots light draft, 6-5 knots if draft exceeds 16 feet. EESTKICTED WATEE CHANNELS 139 The spots in Fig. 30 are obtained from the experiments with the vessels whose dimensions are given in the following table, and the curve put through them represents the above equation : — Table 24. Dimensions of Barges and Values of -^ in Open Water. Barge. Length (feet). Draft (feet). Cross- section Area (square feet). Dis- place- ment (tons). Block Coeffi- cient. r AV* at Speeds (foot seconds) 1-64 3-28 4-92 6-56 Prussian boat . Toue-boat Alma Rene Adrien FUte Peniche Jeanne No. 2, Fig. 31 . No. 8, Fig. 31 . No. 4, Fig. 31 . 112 118-4 1 124-6 99-4 67-4 123 125 99 | }100 { 100 | 4-27 3-28 4-27 5-25 5-25 5-25 5-25 4-82 5-94 3-28 4-27 5-25 4-67 1-00 405 •87 69 54 70 86 86 86. 86 79 97 53 70 84 106 22 92 20 200 226 286 226 148 256 337 247 45 247 45 •93 •97 •99 •82 •94 •26 •59 ■51 •51 •51 •51 •51 •78 10 ■20 •44 •39 •24 •49 •41 ■38 •39 •38 •38 •51 •71 •43 •39 •35 ■21 •49 •39 •62 •244 ■47 ■41 •37 •375 ■375 •375 •42 •72 •18 •43 •33 •57 ■26 •47 •42 •39 ■40 ■40 •40 ■49 ■77 •23 •36 •42 •50 Notes. Peniche is slightly rounded at each end, and the bottom cut away slightly at stem and stern. The to«e-boat has a square stern, but is cut away more than the Peniche at the bow. In connection with the above, the following results obtained by Herr Gebers with box-shaped models are of interest. The boxes had a perfectly square section through- out, the breadth being equal to the draft. The values of -j™ obtained were — With length equal to ten beams, 1-16. With length equal to five beams, 1-10. This table also gives the values of -jm ^ or * ne Dar g es m open water, so that the percentage increase due to the canal may be 140 SHIP POEM, EESISTANCE AND SCEEW PEOPULSION I Barge, Type 2 ■„-f ^r 3 JZ Barge, Type & j ^ £ Fig. 31. — Barge Forms. obtained. Incidentally the table shows the great decrease in resistance resulting from a slight fining of the bow of the barge. EESTEICTED WATEE CHANNELS 141 The extra resistance which a barge experiences in a canal is partly due to the heaping up of water across the canal in front of the barge, and if a finer entrance was used on these forms the canal resistance would drop considerably, as the water could more easily pass to the rear. This advantage of a fine entrance would be felt in open as well as in restricted waters. (3) Any advantage due to its form which a barge may possess in open water, is to a certain extent masked in the canal, but is never obliterated. In every case the canal boat which towed best in the river Seine was found to tow best in the canals, the difference in resistance of two boats at the same speed being roughly the same under both conditions. Taylor's experiments, already discussed, seem to indicate that this may not be true for much finer vessels, but although there may be limits to the above generalisation, they are so far removed as not to affect its application to the type of vessel considered. (4) The choice of form for a towed barge will depend largely on the character of the traffic, i.e., whether the tow is short or long, and whether there is a train of barges or only one. Taking the case of the short tow, Sadler's experiments show that a form as Type 2, Fig. 31, gives a good performance, either singly or in groups. But Type 4 carries a bigger load on given dimen- sions, and in groups, towed stem to stern, is little worse than Type 2. For a long tow, Forms 2 and 8 are both reasonably good for resistance in deep and shallow water (see Table 24). A better form than either of the above for working singly, especially for deep water, can be obtained by using a little more rake of ends than that of Type 2, and by rounding the ends into the sides and bottom. For long trains of barges, towed stem to stern, Form 4 is as good as any, and for given displacement is decidedly the best in very shallow water. But taken singly, even in shallow water, either Types 8, 2, or 2 modified, are better than Type 4. (5) Where resistance is of any importance, steel barges are much more economical than wood, as the wood surface quickly roughens and splinters, causing a large increase in resistance, 142 SHIP FORM, RESISTANCE AND SCREW PROPULSION this increase, -with a very moderate roughening, being some 20 per cent. (6) In deep water, the power required to tow a train of barges increases, roughly, with the number of barges. In shallow water a long train is much better than a broad one. With only a little water between barge bottom and river bed, a long train, towed stem to stern, will have little more resistance than a short one. PART II THE SCREW PROPELLER CHAPTER XVI SCREW PROPELLER NOMENCLATURE AND GEOMETRY § 65. — The driving face or front of a screw blade is the surface which is seen by an observer looking from aft to forward. The back of a blade is that which is seen by an observer looking from forward to aft. The leading edge of a blade is that which leads or cleaves the water when the vessel is going ahead under the action of its own propellers. The trailing edge is the other edge of the blade. The developed area of a blade is the actual area of the blade surface irrespective of its shape. The developed area of the propeller is the sum of the developed areas of its blades. The projected area of a blade is the area enclosed by perpen- diculars from the edge of the blade on an athwartship plane. The projected area of the propeller is the sum of the projected areas of its blades. The disc area of a propeller is the area of the circular section swept by the blade tips, and equals -j (diameter) 2 . mi .. .. . ,, . developed area of screw The disc area ratio is the fraction §* . disc area The blade width ratio (6) is the fraction maximum width of blade along its surface radius of propeller 144 SHIP FORM, RESISTANCE AND SCREW PROPULSION The developed surface of many blades takes the form of an ellipse having the radius of the propeller as the major axis, the ellipse necessarily being cut away at the boss. In this case b is the ratio of minor to major axis. The mean width ratio is the ratio of the mean width of the blade clear of the boss, to the diameter of the propeller. The root thickness of a blade is its maximum thickness at the boss square to its face, ignoring any rounding at the joint of blade and boss. The blade thickness ratio. If the median lines on the face and back of a blade be pro- duced to the centre of the propeller where their width apart is t (see Fig. 32), then j, is called the blade thickness ratio. Rake. A propeller blade is said to be raked forward or aft, according as the centre line of the blade at the tip is forward or aft of the centre line at the root. The rake is usually expressed in degrees inclination to the trans- verse plane, of the line joining these two points. A helicoidal surface is that traced out by a line AB (Fig. 33), of which one point A moves at uniform rate along a line CD whilst AB is revolving around it at uniform rate. A blade of uniform pitch is one whose face is a portion of a true helicoidal surface, and its pitch is the distance A advances whilst AB makes a complete revolution. A surface is said to have increasing pitch when the pitch at the trailing edge is greater than that at the leading edge, i.e., when the generating line AB (Fig. 33) advances along the line CD from leading edge to trailing edge with increasing speed whilst it con- tinues to revolve at uniform speed. If the point B advances in the direction CD faster than the point E, then the pitch at B is greater than at E, or the pitch is said to increase towards the tip. Fig. 32. SCREW PROPELLER NOMENCLATURE AND GEOMETRY 145 The face pitch of a propeller is the mean of the face pitches of all its blades. The effective or analysis pitch of a propeller is that calculated from the revolutions of no thrust. Thus, if at speed v in feet per minute the propeller develops no thrust when the revolutions are r per minute, the effective pitch is given by -. When the A A Pitch |/*J ! I ' ! / "-Axis c * ! t 1/ Ik! '/ E {*>*:' Blade outline B Fig. 33. thrust of the propeller is zero, the slip calculated from this pitch is also zero. Let P = pitch of the propeller face in feet ; D =diameter of propeller in feet ; N = number of revolutions in hundreds per minute ; V = speed of the ship in knots ; Fj= speed of advance of screw through wake water in knots ; 2V =revolutions for no thrust, in hundreds per minute ; P r =effective pitch of the propeller. Then apparent slip PN-VX 1013 =s ffl =- PN effective slip and S.F. #,!>;= F X X 1-013. 146 SHIP FORM, RESISTANCE AND SCREW PROPULSION Unfortunately the value of P r is very difficult to determine with- out careful trials, and in consequence it is not generally used. The apparent true slip or as it is usually called the slip is given by Py-FtX 1-013 This is the real slip of the propeller if the actual or effective pitch were the same as that of the propeller face. Pig. 34. For definitions of wake, thrust deduction, hull efficiency, etc., see § 71. Slip angle and pitch angle. Consider any portion of the blade surface of a propeller of pitch P and let the diameter of this portion be D. In Fig. 34 draw OL=ttD and FL=P Then if the triangle OFL were cut out and wrapped around a cylinder of diameter D keeping the line FL parallel to the axis of the cylinder, the line OF would form a helix, and a section of the blade would be as shown by AOBC. SCEEW PROPELLER NOMENCLATURE AND GEOMETRY 147 The angle 6 is called the pitch angle of the section. If the section is working at slip s, make FE=s(FL) where c N s=-p- so that The angle EOF is called the slip angle of the section, and is the inclination of the plane of the section to the direction of its motion. Since FE and EL are the same for all parts of the same screw provided it has uniform pitch, it follows that <£ is constant for all parts of the blade having the same diameter, but decreases as D increases. If the pitch of the trailing edge is greater than that of the leading edge, draw LG equal to this new pitch. Then the slip angle of the trailing edge is GOE, and the blade section at this diameter is as shown by AjOBG. L 2 CHAPTER XVII THEORIES OF THE SCREW PROPELLER § 66. — A screw propeller is a means of pushing a ship forward by thrusting water aft. For this two things are required : — (1) An unobstructed and free supply of water ; (2) A mechanism which shall only thrust aft, and not rotate the water, or waste energy by shock. These conditions are ideal, but the more nearly they are approached the more efficient becomes the propeller. The method by which the propeller thrusts the water aft is known only in a general way. Probably the nearest approach to the truth is the ideal propeller theory advanced by Mr. Pv. E. Froude. In this theory it is assumed : — (a) The propeller mechanism is frictionless and that no energy is lost in heating the water or in causing eddies. (6) The race column is complete and has a uniform velocity. (c) The pressure in the outer layer of the race is the same as' that of the surrounding water, i.e., the same as it had before the propeller acted upon it. (d) There is an unlimited supply of water. (a) That at the front the streams are drawn or sucked into the propeller, and at the rear are thrust backwards owing to an excess pressure, the streams contracting towards the race owing to the increase in velocity of the particles. Writing V x =the relative velocity of the screw to open water ; U =the sternward velocity imparted to the water ; T =the thrust of the propeller ; v D =velocity of the water at the propeller ; Q =the quantity of water acted upon per second, THEORIES OP THE SCREW PROPELLER 149 we have T=-QxU . (1) 9 and the work expended per second in slip therefore (^-Fi)=4 .... (2) that is, one half of the sternward velocity has been received by the water before it reaches the propeller. This velocity is largely due to the suction of the propeller. Taylor has explored the pressures existing around a working screw and has found that there is a considerable reduction of pressure in front of it — appreciable to 1-5 diameters ahead of it. This reduction, expressed in terms of the screw thrust, was broadly speaking independent of the pitch ratio and slip of the propeller. The useful work done by the propeller=2 7 x V 1} the total work done by the propeller=2 7 Xi\ D j and the efficiency (3) "(^) This may be turned into a more useful form by writing and equation 3 becomes £!) i=l i_2 (4) If the race is rotational, assuming that the angular and trans- lational velocities imparted are the same throughout the race column, the equations for thrust and efficiency become T-9E(u- rV! \ ... (5) 150 SHIP FORM, RESISTANCE AND SCREW PROPULSION and '~ I \ . (6) V _ l—s e f g/ a « 2 \ ~l_fA *°*) where r is the external radius of the race column and w the angular velocity of the race. It will be seen that the loss due to rotation of the race consists in a term -jl-jr) ■ The bracketed part of this is the tangent of the inclination of the spiral path of the race particles with the line of motion. Fig. 35 represents the motion taking place. v+u «c V, Fig. 35. These formulae 4 and 6 give the ideal efficiencies which are possible under the assumptions made, and show in a general way the dis- advantage of rotation of the race, which becomes more noticeable when for any reason the slip becomes large. This may explain the advantage which is sometimes derived in a screw propeller by fitting guide blades at the rear of the screw. If D=the diameter of the propeller, from equation 2, and multiplying equation 1 throughout by V t «, 1- 1 4 g 1 (1-sJ foot-pounds, which is a formula for the maximum power a propeller will deliver. These formulae do not represent the actual case of a working THEORIES OF THE SCREW PROPELLER 151 propeller owing to the fact that the assumptions made are only partially realised in practice. Every fluid is frictional, eddies are formed, the ship's form impedes the flow of the water, the com- pleteness of the race column depends upon the form and disc area of the propeller, and for all these reasons the actual case differs from the ideal. Provided that the blades of a screw did not interfere with each other's action (which they do), and that their thrust was propor- tional to their slip angle, the race velocity U would be propor- tional to the slip of the blades, and in this case the term s t would be a measure of the slip of the screw. The formulae may therefore be regarded as giving ideal thrust and efficiency in terms of slip (effective), provided the above assumption as regards the actual propeller thrust is true — which is the case for all moderate slips. § 67. — Of the other theories of the screw propeller three only need be mentioned — viz., those of Rankine, Greenhill, and W. Froude. Eankine assumed that the propeller in thrusting the water aft gave it a spiral motion and that there was no change of pressure in the race — i.e., the streams contract suddenly in passing through the screw — and that the race forms a complete column. The centrifugal action causes a change of pressure and the loss of thrust due to this can be calculated, as also can the loss by skin friction. Greenhill assumed that the propeller gave no sternward but only rotary velocity to the water — i.e., there was no contraction of the streams — and that the thrust was due to the increase of pressure in the race. This rotary motion, however, produces a pressure at the axis differing from that at the tip of the screw, except for one particular slip (67 per cent.), and actually, for equilibrium, the outer streams must be accelerated and the inner retarded at all moderate slips. Neither of these can be put to any practical use. They neglect the effect of form and dimensions of blade, pressure limits, and limitations of water supply, and to obtain the effect of these items one is driven to experiments. 152 SHIP FORM, RESISTANCE AND SCREW PROPULSION W. Froude advanced the theory that an element of a screw blade may be considered as a small inclined plate moving through water, and its efficiency and thrust can be calculated by the use of the known normal and frictional forces on such plates. Referring to Fig. 34, the velocity of any element of a propeller blade through the water is given by Vi sin (0— (j>y The normal force on it =P=a(8A) . J.f .. sin 6 ; s ' sin 8 (0— <(>) r the tangential force V 2 sin a {0—Y The thrust of the element along the axis =T=P cos 6—F sin 0. The transverse force =M=P sin 0+F cos 0. Hence f sin cos 0— ^sinfl T=a(BA)V J z - a sin 2 (0— and a and/ are the coefficients of normal and frictional force on a plane surface. Curves of efficiency obtained in this way agree in general character with those obtained by experiments with model screws. The method, if extended to a whole blade, becomes very unwieldy and throws no additional light on the general theory of the pro- peller. It is tacitly assumed that there are no limitations to the THEORIES OF THE SCREW PROPELLER 153 water supply, that interference of one blade with another is nil ; also the fact that additional area becomes useless when a complete column is formed behind the screw is ignored. A simple and useful variation of this theory has been suggested by A. Mallock. Keferring to Fig. 36, If OX is the path along which the plane is moving (0 to X), de=the resistance of the plane measured along OX=R, ea=the reaction normal to OX=L. If this blade is a part of a screw whose longitudinal axis is Y, the reaction of de and ea along the axis = 6a, and reaction normal to the axis=d&. As the plate moves along OX, forces normal to this line do no work, and the efficiency is the ratio of the resolved parts of the forces ba and db along OX „-* "-ft or __bc _ tan a V ~ bd~ tan (<*+£)' Since _ B resistance tan /3= T = L lift the efficiency for any pitch ratio and slip can be calculated for any type of blade whose — yti — [i-e., y) ratio is known. There is a large amount of data in existence giving the value of this factor for various types of blades, and this formula will be em- ployed in later sections to examine the effect of shape, etc. It has the advantage that interference of one blade with another, and effect of shape, can be taken into account by the proper choice of -=■ values. Li The absence of any theory which will take complete account of working conditions, forces the designer to depend upon his general experience or to have recourse to experiments. Keliable infor- mation as to the action of a screw in a given ship is difficult to 154 SHIP POEM, RESISTANCE AND SCREW PROPULSION obtain, unless those making the steam trials go out of their way to get it. Times of delivery and financial considerations limit the possibility of trying several screws on the same ship, and unless this becomes necessary owing to deficiency of speed, such tests are seldom made and still more seldom published. The designer's knowledge is therefore more or less limited, and here Pig. 36. more than anywhere experiments on a small scale should be advantageous. § 68. Applicability of Small Scale Experiments to Full-sized Screws. — But for experiments on a small scale to be of use two things are required : — (a) A law enabling results for a full-sized propeller to be predicted from the model. (b) Exactly similar conditions in the model as in the ship, or a means of allowing for the difference. THEORIES OF THE SCREW PROPELLER 1SS First consider the case of two screws advancing into still water, the one of diameter D at velocity V and revolutions per minute N and the other of diameter d at velocity v and revolutions per minute n, where j=l and v=Vlxv. Then if both screws are similar and work at the same slip the flow past each screw will be similar, the difference being one of scale only, and this similarity holds for any similarly related speed provided the race columns are equally complete or in- complete. For the slips to be the same, n=NVl From the proof of the law of mechanical similitude given in § 8, it will be seen that under these circumstances the two screws will be giving thrusts T and t, which are related by the equation T=Pxt. Provided the losses in friction and eddy-making vary as the (speed) 2 , this relation still holds between the large and small propellers. If the propellers are near the surface the surface deformation will be " similar," since the pressures vary as the scale, and the above relations still hold good. If the screw sets up a rotation in the race, for similar hydro- dynamic conditions the angular velocity of the race should vary as velocity . 1 diameter' *' e,J M V? or as the revolutions at the same slip ratio. Under these con- ditions the formula for thrust given above still holds. This argu- ment is quite sound for the ideal case of the complete race column, but with the incomplete column the race rotation and trans- lational velocity is not the same for all particles in the column, and although this is the case in both large and small screws, and with perfect streaming flow the action would be the same in both cases, there is no guarantee of this perfect flow. The extent to 156 SHIP FORM, RESISTANCE AND SCREW PROPULSION which this possible loss of similarity may affect the above law of comparison can best be judged by experimental results. § 69. Experimental Tests of the Law of Comparison.— Mr. Taylor has tried in the Washington tank screws varying in diameter from 8 inches to 24 inches. He found some slight varia- T tion in the value of jwf™ and efficiency at the same slip and corresponding velocities, as the size was varied. These tests were not made under quite similar conditions, as the centres of the screws were all at the same immersion, 12 inches — i.e., the im- mersion of the blade tips became smaller with the larger propellers. Preliminary experiments with the 16-inch screw having the blade T tips at varying immersion, showed a very slight reduction of j^m with reduced immersion. The variation found with the different sized screws at fixed immersion was of the same character and order as the above effect due to immersion, and the latter possibly accounts for the former in these experiments. The variation was only 2 per cent., and the law of comparison holds more closely than the results indicate, and may be accepted for the range covered by the experiments. Other experiments made by Mr. Taylor with the 16-inch diameter screw at various speeds showed that the thrust at given slip varied as (speed) 2 over a considerable range of speed, as theoretical considerations lead one to expect. Herr Gebers' experiments with models of a turbine type of screw varying in diameter from 12 to 3 inches gave practically the same efficiency at corresponding speeds and slips, and the thrusts calculated for the largest screw from the measured thrusts with the smaller ones came within 3 per cent, of that obtained by experiment, over the useful range of slip. An important test of the law has recently been made by experi- ments in air with exactly similar propellers of 15 feet and 2 feet diameter, the larger one on the whirling arm at Messrs. Vickers, Maxim and the smaller one on the whirling arm at the National Physical Laboratory. The tests were made at corresponding THEOEIES OF THE SCEEW PEOPELLEE 157 speeds, and the thrust and horse-power for the smaller propeller were estimated from the tests of the larger propeller, and com- pared as follows : — Item. Thrust in lbs. Horse-power Absorbed. Efficiency. Deduced from the full-size propeller by the law of comparison . From experiments with small model .... 205 1-97 •1123 •1115 •64 •62 The falling off in the small model is slight and may be neglected. For this case the law undoubtedly held good. M. Dorand has compared similar propellers of different diameter in air, under very dissimilar conditions to the above. His pro- pellers were 6-2 and 14 feet diameter respectively and practically the same in design. The results show a difference in comparative thrust of only 2 per cent., and the efficiencies were almost identical. Although these tests were made in air, they lend considerable weight to the practice of using the law for propellers in open water, i.e., with no ship in front of them. § 70. — The second condition which must hold if the results of model propeller tests are to be of use in predicting results for full-sized screws is — all the conditions in the model tests should be similar to those holding in the ship, or there should be some known method of allowing for the difference. Screw experiments may be divided into two quite distinct classes, viz., those made to test the screw and those made to test the reaction between the screw and model. The former are made in open or undisturbed water, the latter with the screw of the correct size in its correct position at the stern of the ship. In the latter experiments the object is to measure two primary things — (a) The amount by which a screw situated in a given position augments the resistance of the model when it is itself producing a thrust sufficient to propel the model. 158 SHIP FORM, RESISTANCE AND SCREW PROPULSION (b) The average speed of the streams in which the screw is working, i.e., to obtain the wake fraction. With regard to both a and b one condition is essential, i.e., that the position and diameter of the model screw shall be to scale for ship. This is all that is really necessary from the hydrodynamic point of view, and the pressure gradients and accelerations produced at the stern of the model will then be similar to those in the ship. In other words, both ship and model will experience the same increase in resistance due to the action of the screw. But with the wake the same cannot be said. It can confidently be stated that the wake of a model so far as this is due to skin friction is greater than that for the ship. In the majority of cases some portion of the propeller works in the frictional belt, and a portion of the area of the model screw will be working in this frictional wake, and the total or mean wake obtained for the whole area of the screw will be exaggerated by this to some extent, so far as the result is applicable to the ship. If the screws are well removed from the hull, the wake is largely due to stream line or wave action, and in this case the difference between model and ship conditions is negligible. But the smaller the screws and their clearance from the hull become, the more the difference must be felt, and some correction of the result should be made to obtain the true wake for the ship with similar screws. In single- screw ships this must be the case, as the propeller then works in a large area of the frictional belt. As in the general run of ships the error is probably not a great one, and in many cases must be small, it is the wiser course to accept the results than to hazard a correction which may lead farther from the truth. Leaving the question of shaft web and bracket influence on one side, it can therefore be said that as the necessary conditions of similarity hold fairly closely between model and ship, the augment of resistance due to the screw obtained with the model holds for the ship, and generally speaking the same may be said of the wake. CHAPTER XVIII THE ELEMENTS OF PROPULSION § 71. — The whole question of the propulsion of the ship requires the consideration of engines, propeller, and hull, the net propul- sive efficiency being the product of the efficiencies of these three things. The hull has been considered in the earlier chapters. The engine efficiency depends largely upon the type of engine used, whether it is a triple or quadruple expansion reciprocating engine, a turbine, gas, oil or electric engine, or any combination of these. The type of engine chosen affects the revolutions of the engine shafts, and in this respect also affects the screw, but the latter is otherwise independent of the engine and may be considered as a distinctly separate subject. The propulsive force exerted by the propellers of a ship when the latter is travelling at a uniform speed, must be exactly equal to the resistance the ship experiences at that speed. The resist- ance of a ship when towed is due to the motion which it produces in the water as it passes through it. This water motion is to a considerable extent longitudinal, and shows itself abaft the stern in what is commonly called the " wake of the ship " or the current of water which follows it. If the ship is propelled by its own screws these cause considerable changes in the pressure of the water around the stern, whereby its resistance and therefore the screw thrust necessary for propulsion, become greater than the tow-rope resistance. Not only does the action of the screws affect the ship's resistance, but the presence of the ship affects the working of the screws. These have to work in this wake water, and their action will therefore depend to some extent upon the magnitude and direction of the currents in that portion of the wake on which they act. 160 SHIP POEM, EESISTANCE AND SCEEW PEOPULSION The net efficiency of a screw as a propelling agent will depend upon two factors, of which one expresses the efficiency of the propeller itself if working in undisturbed water under similar conditions as regards thrust and revolutions. The other expresses the modification of this efficiency due to the action of screw upon ship, and ship upon screw. Mr. R. E. Froude, to whom this method of treatment is due, calls these two factors " the screw efficiency proper " and the " hull efficiency " respectively. It will be seen later that for many purposes these two factors may be regarded as separate elements, and this subdivision simplifies the work both of the designer and the experimenter. Consider the case of a ship propelled by a screw. Let T =the thrust of the screw in lbs. ; JV = revolutions in hundreds per minute ; V =the speed of the ship in knots ; R =resistance of the ship in lbs. at the speed V with no screws, i.e., the tow-rope resistance ; 8 = shaft horse-power delivered to the screw when pro- pelling the ship ; E =the effective or tow-rope power, including bossing and keel resistance. Suppose the screw to be now removed and set working in un- disturbed or " open water," the revolutions being maintained the same but the speed of advance V ± adjusted so that the screw develops the same thrust as it did behind the ship. Let S 1 — shaft horse-power absorbed by it under these conditions. So far as the development of thrust is concerned, the screw behind the ship might equally well be advancing into undisturbed water of velocity V v and this velocity is usually taken as the mean velocity of the water past the screw in the wake of the ship. If the following current left by the ship were of uniform speed throughout the area operated upon by the screws, the above would be quite true, and the power required to drive the screw in open water at speed V v or behind the ship at speed V would be the same. It is a fact proved by many experiments on screws working behind THE ELEMENTS OP PEOPULSION 161 models and in open water, that the shaft horse-power of a screw propelling a model differs extremely little from that of the same screw in undisturbed water under the above conditions. The propulsive efficiency of the screw is given by tow-rope power E shaft horse-power 8 which may be split up into the factors given in the following equation : — -§=¥=©x(!;Mf)x(§)- The first bracketed term here is the ratio of the tow-rope resistance of the ship to the thrust of the screw. If t is the fractional measure of the excess of the screw thrust over the tow-rope resistance, t is called the thrust deduction fraction, and is given by 1-t-X The second bracketed term is the ratio of the velocity of the ship to the mean velocity of its wake water taken over the screw disc, and writing 7=7 1 (l+w) w is called the wake fraction, and denotes the fractional excess of the velocity of the ship over that of its wake water at the screw. The third term is merely the efficiency of the screw in open water. The fourth term is the relative measure of the power required to develop the screw thrust in open water and in the disturbed water behind the ship. This is known as the relative rotative efficiency. The propulsive efficiency of any screw can therefore be written : _ /screw efficiency\ . . ,■,,<< /relative rotative\ ''""V in open ) ( )( + ' \ efficiency /" The speed of advance of the screw through the water in which it is working is equivalent to a speed V x in undisturbed water, and 162 SHIP FORM, RESISTANCE AND SCREW PROPULSION the work which it does in propelling the ship is measured by the product This is called the thrust horse-power of the ship. The product R X V is a measure of the effective horse-power of the ship, and the net efficiency can therefore be written in a new form thus : — _ E.H.P . /screw efficiency \ /relative rotative\ T.H.P- \ in open / V efficiency / This first term is defined as the hull efficiency of the ship, and since the latter term is generally unity the efficiency can be written 7j=hull efficiency x screw efficiency in open, where hull efficiency A=(l— i)(l+w>). The net propulsive efficiency of the ship (e) is the product of the propulsive efficiency of the screw and the efficiency of the engine including thrust block and shaft friction, and can be written _ /screw efficiency^ / hull \ / engine \ \ in open / \efficiency/ ^efficiency/ ' The cost of propelling the ship any distance depends equally on each of these terms. Of these the most important and most liable to variation is the screw efficiency, and this is considered in the next section. CHAPTER XIX SCREW PROPELLERS IN OPEN WATER § 72. — Several broad conclusions can be drawn from the various theories of the action of propellers, and the considerable number of experiments which have been made on model propellers, and a few on large-sized propellers, enable these conclusions to be com- pared with empirical results. Of these the most important are the following : — (a) The thrust and efficiency of any given screw, advancing through the water at any given speed and turning at various revolutions, will depend upon the slip ratio corresponding to the revolutions at any given moment. (6) The thrust of a given screw working at a given slip varies as the square of the speed of advance through the water. (c) The thrust at given speed of advance and slip ratio, will vary as the square of the diameter, for screws exactly similar in design. (d) The efficiency at any slip ratio is unaffected by varia- tions of speed or of size of screw. Setting aside all question of cavitation, experiments show that the first three of these conclusions are true for actual screws, and although the efficiency varies slightly with speed, for all ordinary purposes this variation is small and can be neglected. It follows that the thrusts obtained from all screws of similar design at any given slip will be connected by the formula T j)iy£~ ' M 2 164 SHIP FORM, EESISTANCE AND SCREW PROPULSION where c is a constant depending on the slip and design of screw. Its variation with pitch, diameter, blade area, thickness of blade, and any other feature is one of the main and most difficult pro- blems in propeller design. No theory yet formulated will give reliable quantitative values for pressure or efficiency. The only useful theory that will give relative efficiency values is that due to Mr. Mallock (see § 67). By the use of this theory a fair guide can be obtained as to what may be expected from any variation in design, and, failing experimental results on any point, it has been used in this way when dealing with the subject. Experimental Results. — In using experimental results close attention must be given to the experimenter's method of tabu- lating and giving data, and more particularly as to how he defines the various terms used. The absence of uniformity of definition is responsible for no small amount of the doubt that has been thrown upon experimental results. Mr. Taylor uses the face pitch for both pitch and slip ratio. So also does Herr Gebers. Mr. Froude uses a pitch calculated from the revolutions and speed of advance so that slip shall be zero when thrust is zero. There can be no doubt that the latter is the more correct, as the back of a blade is just as important as the front, and should be taken into account in giving the blade its pitch value. Moreover, this method is more in accord with sound theory, and is less likely to give contradictory results. In applying results obtained by any model screw experiments to full-size screws, the pitch ratios obtained require multiplying by some coefficient, and Mr. Froude has stated that pitch ratios obtained by his method of analysis should be taken as 1-02 times the nominal or driving face pitch for the ship. This result, which is based upon experience in the analysis of ship trials, is better than any estimate based upon the relation of face to real pitch. This method has the advantage, too, of taking account of differences in boss arrangement and in blade thickness. For these reasons, and because the results are more compact, Froude's method has been adopted throughout the book, and the constants given in his paper read before the Institution of Naval Architects in 1908 have also been adopted. SCREW PROPELLERS IN OPEN WATER 165 Of the experimental results published, Froude's, Taylor's, and Durand's are the most important. To a large extent they cover the same ground, and when analysed in the same way corroborate each other as regards denning the effect of variations of pitch, width of blade, etc. The screws used by them differ mainly in blade thickness ratio and in the size of screw, and the effect of these factors will be considered in detail later. § 73. Froude's Experiments on Model Screw Propellers. — These experiments were made in open water, the screw being mounted on the fore end of a driving shaft so that there was no obstruction, either in front of it, or for some distance to the rear. The diameter of screw was, uniformly, -8 foot. The boss diameter was, uniformly, -91 inch. The root thickness was, uniformly, -27 inch. The immersion to centre of screw was -8 of the diameter. The speed of advance was 300 feet per minute. The face pitch ratios covered a range from -8 to 1-4 ; the disc area ratio varied from -3 to -75. Four-bladed and three-bladed propellers were tested. The developed blade shape was elliptical for all the four-bladed screws. The three-bladed included the elliptical and the wide-tip pattern. For the elliptical pattern the developed outlines were ellipses of major axis equal to propeller radius (see Fig. 42). The wide-tip blades were formed from these by making at any radius=r wide tip width _ 1 . r elliptical width - STB' where B equals the propeller radius. Each screw was tested through a range of slip ratios, and thrust, revolutions, and turning moment were recorded. Special experi- ments were made to obtain the friction of the apparatus and the resistance of the frame and shaft carrying the screw. The thrusts obtained were expressed in a formula T n (P+2l\ v 1-02 a (1--08 a) ,-. DW? =±S V~p/ X (l-5) a ' * ' {) 166 SHIP FOEM, RESISTANCE AND SCREW PROPULSION W cS ^05 HO H5 h20 h25 ~fco 735 ikd ~ffi TSo T55 Tid t65 Set Fig. 40.— Curve of Z" & 0095 ■009 0085 008 0075 v2y = N 2 H P 3 y = N. P. D. A ' V, s B(P*2I) A V, where H= thrust horse power per screw /V= revolutions in hundreds per minute Y, = speed in knots through the wake water B= blade factor given by Fig. 37. D = diameter in feet P = pitch ratio An example of the use of the curve is given in § 75. 065 Fig. 40. — Curve of X*—Y for obtaining Propeller Dimensions. SCREW PROPELLERS IN OPEN WATER 173 is for the screw behind the ship, and must be taken as speed of screw through the wake water, and not as speed of ship. Some wake factors are given in Tables 29, 30, 35 A, B, C, D, to enable F x for the screw to be obtained from the ship's speed. But the whole section dealing with wake should be read in order that a sound estimate of this factor in any particular case may be made from the data given. (6) The driving face pitch of the ship screws, as already explained, is y^ times that obtained from these calculations. This figure is based upon Admiralty trials before 1906, when pitch ratios of 1-0 to 1-2 combined with moderate disc area ratios were general. The author has found that for turbine vessels having screws of smaller pitch ratios (-85 to -95), and larger disc area ratios, a somewhat higher denominator (1-04) gives better agreement between estimate and trial results. When the driving face is cut away slightly near the leading edge, as is done in some propellers, the effect is to slightly increase the true pitch, and the factor then becomes somewhat less than y-^ ; and, in a similar way, cutting away the driving face at the trailing edge increases the factor to j^- or less. For model screws Mr. Froude's results give an average figure of , -__ . Mr. Taylor's results as analysed by Mr. Abell, show a factor varying from j^r= for large disc areas, to pr^ for small disc areas of 1-2 pitch ratio, and -^— for small disc areas of -8 pitch ratio. Herr Gebers' experiments show a factor of . os , his screws being of unity pitch ratio, and fairly large disc area ratio. In the absence of definite and complete results from steam trials these figures may be regarded as Hmiting values to the coefficient showing how it probably varies, and not as figures to be used for full-sized screws. 174 SHIP POEM, RESISTANCE AND SCREW PROPULSION (c) It must be understood that these efficiencies are for clean, smooth blades in which the skin friction is normal. The effect of a rough surface is shown by the following experiment. A 6 feet diameter propeller was roughened so that the surface was equivalent to coarse sand. It was used to propel an 18-5 ton vessel of about 60 feet length. To get the same speed as was obtained with the same propeller, but with a smooth surface, it was necessary to increase the power from 12 to 20 per cent, and the revolutions 8 per cent. Experiments with a flat blade in air at small angles showed that varying the surface from " varnished mahogany " to " rubber surface fabric " made practically no difference to the thrust or lift, but increased the resistance from 18 per cent, at small angles to 7 per cent, at an inclination of 12 degrees ; very few screws work with their blades inclined to their direction of motion at an angle greater than 12 degrees. (d) For a three-bladed propeller of radius r, having a blade width ratio of, say, -4, the developed area assuming there was no boss 3 [|x(-4)r 2 l=-3w 2 and the disc area ratio • 3 <=-3. ■nr' The disc area ratios used by Mr. Froude in plotting his results were obtained in this way, and this fact must be borne in mind in using the data. If the developed outline of the blades be produced to the shaft centre and the boss line be drawn on the diagram, it will be found that the proportion of the whole outline cut off by the boss varies from 20 per cent, for Admiralty pattern screws of moderate revolutions, to about 15 per cent, for wide-tipped turbine-driven screws cast on the boss. The actual figure can easily be obtained in any particular case by measurement from similar screws. When using Froude' s data for obtaining the dimensions of propellers to satisfy given conditions, some such discount must be put upon the area obtained by calculation in order to obtain the correct SCREW PROPELLERS IN OPEN WATER 175 developed area of the blade outside of the boss line. Similarly, when analysing trial results, the actual area of the blades should be increased by a similar percentage (which can be obtained with fair accuracy from the plan of the propeller), and this increased value should be used for obtaining the disc area ratio from which the " B " value is obtained. Great accuracy is not required in obtaining these disc area ratios, as the thrust is not very sensi- tive to area unless the blades are very narrow or cavitation is present. Screw Dimensions by Means of the X 2 — Y Curve. — It is required to find suitable dimensions for four screws to run at 315 revolu- tions per minute, to develop a speed of 20 knots in a turbine- driven vessel whose effective horse-power is 10,000. Allow for bilge keels 2 per cent. ; for bossings, 3 per cent. ; air resistance (fine weather), 2 per cent. — total, 7 per cent. Hull efficiency assumed, -98. /T.H.P. to be delivered by each\ 10,000x 107 =2 13Q=H \ of the four screws / "98x4 With a clearance of about 14 inches the wake factor for this vessel may be taken as -16. 20 Speed through wake water, V 1 =j^rQ= 17-24 knots. rm. i- • lx. 2,730x33,000 -,-.„,, Thrust on each screw m lbs.= 17 . 2 4y iqt.o =51,540 lbs. The screws are well buried and a cavitation pressure of 13 lbs. per square inch may be assumed. 51 540 Minimum blade area— '. . =27-55 square feet per screw. NW (3-15)2x2,730 V x 5 ~ (17-24) 5 Xx_5. 47 tf~ 547 The results are plotted in Pig. 41. Other disc area ratios can be used in the calculations if desired. The screw should be chosen 176 SHIP POEM, EESISTANCE AND SCEEW PEOPULSION from the diagram to the right of the cavitation line, with as large a pitch ratio as possible, consistent with good efficiency. Table 25. Calculation for Three-bladed Screws. Disc Area Ratio assumed : ■5 •6 " B " Value for mode- rately Wide - tipped Screws from Fig. 37 . •11 •113 N*H SF? .... •1619 •1576 p assumed . • . ■8 •9 10 11 •8 •9 10 11 j>S •0235 •0333 ■0455 •0603 •0235 •0333 •0455 •0603 p+21 p+21 x BVi i •0038 ■0054 ■0074 •0098 •0037 •0052 •0072 •0095 Hence from Fig. 40, X= 1-435 1-62 1-602 1-685 1-43 1-511 1-594 1-676 Np 9-8 9-23 8-76 8-38 9-75 9-18 8-72 8-33 Face pitch j^r* 7-61 8-07 8-51 8-95 7-57 8-03 8-47 8-9 Developed area of 3 blades in square feet -85 x jD 2 X disc area ratio = 320 28-4 25-6 23-4 38-2 33-9 30-6 27-9 Efficiency for above X values at corresponding p values, from Fig. 39 . •65 •655 •654 •628 •65 •656 •655 •631 Correction for disc area ratio, from Fig. 37 -•008 -•006 -•005 -•003 -■028 -•023 -•018 -■013 Corrected screw efficiency ■n ... . •642 •649 •649 •625 •622 •633 •637 •618 S.H.P. required at the propeller=— = . 4,260 4,210 4,210 4,370 4,390 4,310 4,290 4,420 SCEEW PEOPELLEES IN OPEN WATEE A 177 Fig. 41. — Typical Diagram of Screw Dimensions and Efficiency. Good dimensions would be — diameter, 8-75 feet ; pitch, 8«45 feet ; developed area, 29-5 square feet per screw ; disc area ratio, •575 ; efficiency of screw, '63. These dimensions are obtained from the above by interpolation. s.p. K CHAPTER XX PROPELLER BLADES § 76. Pitch Ratio. — It will be seen from the theoretical formula in § 72 that the thrust produced by a screw at any slip will be directly proportional to the pitch if the revolutions remain the same. The same fact may be stated in another way. If a ship's speed and power are to remain the same, and the screw pitch is altered without affecting the diameter or blade area, then as the pitch is increased the revolutions will decrease, and the slip will increase. The effect of the change upon the efficiency would depend upon the initial pitch ratio and slip. For ordinary screws of pitch ratios 1-0 to 1-3, working at slips of 20 per cent, and above, there would be little change, the loss due to higher slip and the gain due to higher pitch ratio being practically equal. But at slips exceeding 30 per cent, there is a fair loss of efficiency with increase of slip, but practically no advantage due to using higher pitch ratios than 1-1. Increase in pitch ratio would therefore, in this case, mean loss of efficiency. All blades, and particularly wide ones, of pitch ratio -8 to 1-0 gain considerably in efficiency by increase of pitch ratio, and since they do not reach their best efficiency until the slip is 25 per cent, it follows that it is a distinct advantage to keep the pitch as high as possible, even though it means a fairly high slip ratio. Thus a propeller of -75 disc area ratio of 1-0 pitch ratio, has as good efficiency at 38 per cent, slip, as a propeller of the same area and •8 pitch ratio has at 25 per cent, slip, and at any slip lower than 38 per cent, the 1-0 pitch ratio is always better, its advantage being over 10 per cent, at 25 to 30 per cent. slip. This disadvantage of small pitch ratio is due to two main causes : — First, small pitch ratios involve small slip angles, unless PEOPELLEK BLADES 179 the slip ratio is large, and no blade works well at small angles. Thus a pitch ratio of -8 has slip angles of 2°-09 and 4°-98 at slip ratios of 15 per cent, and 35 per cent. A slip angle of 2°-9 is required for a reasonable efficiency, which will remain fairly good until the slip angle exceeds about 6°-0. Secondly, small pitch ratios involve small pitch angles, which give less clearance or smaller gaps between consecutive blades, a point dealt with later (see page 182). § 77. Rake and Skew-back. — Experiments with model screws show that efficiency and thrust are not affected by raking the blades either forward or aft up to 15 degrees. Rake aft may be of advantage in twin-screw ships in obtaining greater clearance of propeller tip from hull, and in single screw ships gives a greater distance between the body post and the leading edge of the blades, a desirable thing, particularly for vessels having full after lines. It has the disadvantage, however, of throwing greater stress upon the propeller blades due to the centrifugal forces. If the thickness of the root sections of the blades have to be increased to resist the additional strain brought about by the rake, the efficiency will not be improved, and in high revolution propellers will fall slightly. No material advantage is gained in the ordinary vessel by bending the blade in the transverse plane. For vessels working in waters containing a lot of weed, etc., a certain amount of skew- back may be found advantageous, as it helps the blade tips to clear themselves of the weed. Developed Outline. — The relative merits of the elliptical and wide-tipped pattern blades have already been considered (§§ 73 and 74). The thrusts obtained by Taylor with screws of a different type of outline (see Fig. 42) were slightly lower than those for Froude's elliptical blades, the efficiency being about the same for both. The root thickness of Taylor's blades was slightly less than that of the others, which may account for this difference, and generally speaking the two outlines may be said to give approximately the same results. N 2 180 SHIP FOEM, EESISTANCE AND 8CEEW PEOPULSION The blade outline should be well rounded at the corners, as such shapes as the " very wide tipped " in Fig. 42 tend to produce . Fraud e Elliptical Wide Tipped Taylor Normal Very Wide Tipped Fig. 42.— Outlines of Blades. vibration, particularly if the clearance between the blade tips and the hull plating is less than about 12 inches. Such corners if they exist at the leading edge of the blade are a source of weakness, and are liable to bend across a line as A A. The propeller thrust and suction per square foot are both greatest PROPELLEK BLADES 181 at a point approximately "092 of the diameter from the tip, and at any radius is greatest near the leading edge, so that with a corner there is a tendency to local concentration of force at this part. By rounding the edge at the tip the thrust is distributed better over the blade, the length of the section on such a line as A A (cutting off a constant area) is much greater, and the stress on it less. Disc Area Ratio. — Large disc area ratio may be obtained by (a) Increasing the number of the blades ; (6) Increasing the area of individual blades. All model experiments show that, with a fixed number of blades of moderate width, at any slip the variation of efficiency with disc area ratio is negligible. But for disc area ratios of -55 and above there is a loss of efficiency which becomes more im- portant the smaller the pitch ratio (see Fig. 37). Thus, for propellers of -8 pitch ratio the maximum possible efficiencies at •4 and -8 disc area ratios are -66 and -56 respectively. With engines running at high revolutions, the tendency is towards small pitch ratios of large disc area ratio, and the propulsive efficiency necessarily suffers through the low screw efficiency. The reader's attention is directed to § 73, where the relative merits of three and four bladed screws are considered. It is there shown : — (1) That somewhat more thrust is developed by four blades than by three, the diameter and total area being the same, there being only a very slight difference in efficiency in favour of three blades. (2) That above a disc area ratio of about -55 large increase in area produces but small increase in thrust. For this reason a wide blade propeller is stronger than a narrow one of the same root thickness ; there is very little increase in thrust and a con- siderable increase in root area to stand the strain. Large area ratios increase the backing power of the screws, and may be required for this reason. But, unless the propeller is 182 SHIP FORM, RESISTANCE AND SCREW PROPULSION working near the cavitation limit and the diameter is restricted, large disc area ratios have no other propulsive advantage. The effect of wide blades upon efficiency is given by Mr. Froude as largely independent of slip but varying with pitch ratio, and must therefore be due to variations made in the design of the blades when varying the widths. Increase of width was accom- panied by ' , „ „ ,. . blade thickness (1) Smaller ratios of , , ■■ .,.. ; v ' blade width .„, T ,. . blade width b (2) Larger ratios of n j = — = - ; x ' ° propeller radius r ,„, on i.- j: blade width (3) Smaller ratio of . gap By " gap " is meant the normal distance between the spiral surfaces of consecutive blades. A propeller of n blades having a pitch angle 6 at any radius r, has a normal gap between the blades . , , . ,. i , 2irr sin 6 , ,, ,. blade width , ,, at this radius equal to and the ratio at the u n gap radius r equals =; ; — ^. ^ 2,-nr sm 6 The effect of — has been tested with a number of gap aerofoil blades (i.e., with biplanes), and by means of Mallock's method the results can be used to give an indication of the effect of this ratio on a screw. If the pitch and slip be maintained the same, and is varied from 4 to # by reduction of blade 5 gap 3 6 J width, the thrust per square foot will be increased 25 per cent, so far as gap alone affects it. In the latter case there is only half the area of blade, but the thrust is Jx 1-25= fths that of the wider blade. „,, . . . ,, . blade width . , j This increase in thrust per square foot as is decreased is accompanied by an increase in efficiency of about 2 per cent, at high pitch ratios (1-2) and 7 per cent, at low pitch ratios (-8). „ , . . , , , . ,., . , .. -mean blade width But increase m blade width gives a larger ratio of prope ii er ra diu 7 PROPELLER BLADES 183 and tests with blades in both air and water show that the thrust and efficiency depend upon this ratio. This can be seen from the following table : — Table 26. Thrust per Unit Area and ~ — r-r for Blades having different .Resistance ° Ratios of Width to Length. Flat Blades in Water. Rounded Back Blades in Air. Ratio — . r Thrust per Thrust Thrust per Thrust Unit Area. Resistance' Unit Area. Resistance' 20 •104 5-2 10 •165 6-2 •5 •24 8-3 •33 — — •28 100 •25 — — •32 11-5 •20 — — •325 12-9 •167 — ~~ •33 140 The thrusts in columns 2 and 4 are in the same units : b is measured in the direction of motion and r across it. Reducing the ratio — from 1-0 to -5 gives an increase in thrust per square foot of •24 165 :l-45. The smaller blade therefore gives 1-45 =•725^ the thrust of the larger blade of double the area, and there is a considerable increase in thrust and therefore resistance efficiency with the narrow width. The definite figures given above are not intended to be anything but a guide to what happens with a screw, but taking them as they stand, the thrust for a narrow-bladed screw and one of twice the width of blade (-=1-0) are in the ratio :- I X 1-45 = '9 blade width effect & effect gap r 184 SHIP FORM, RESISTANCE AND SCREW PROPULSION Froude's " B " values for the corresponding blade widths are in the ratio *91. It will be seen that whatever tends to decrease the value of 2-nr sin nb tends to decrease the efficiency and the thrust per square foot at any slip of the propeller. Wide blades and small pitches (except at high slips) each give poor efficiencies, without con- sidering the effect of the blades upon each other, and when this interference effect is taken into account they become still more undesirable. Small pitch ratios mean small pitch angles (6), and when combined with wide blades (or large b values) can never give good results. § 78. Thickness and Shape of Blade Section. — Some experiments have been made by Mr. Taylor to test the effect of blade thickness. Fig. 43. His screws were 16 inches in diameter, varying in pitch ratio from •6 to 1*2, having developed blade areas of 39-3 and 62-9 square inches in three blades (mean width of blade 2-5 and 3-73 inches respectively). Three root thicknesses were tried— viz., ^, -fg, and 1 inch (see Fig. 43). It was found that (a) The effective pitch of the screw increased with the thickness, so that fewer revolutions would be required with the thick blades to produce the same thrust as the thin ones, the difference in revolutions being about 12 per cent, for the extreme variation of thickness tried. PROPELLER BLADES 185 /i\ t> ■ i i .li .l- maximum thickness at half radius ,. , (o) Provided the ratio — rjvr — nn dld v ' mean width ot blade not exceed -045 the efficiency remained practically the same when thrust, pitch, and area were the same. When this ratio exceeded about *07 the efficiency fell off badly. Experiments with blades in air support the above conclusions. These also show an increase in effective angle (or slip) when the thickness is increased. The efficiency of such blades at the same CD thrust improves very slightly for small slips till the ratio -^-g in Fig. 44 equals about -06, after which it decreases slowly. But for slip angles much in excess of 12 degrees (effective) the efficiency Leading t__,„- , C- . Edge ADBG : Section of Screw 139. AiJDBO: Section of Screw 143. Fig. 44. breaks down rapidly when the thickness exceeds that given by the above ratio (-06). It must be remembered that the above results only hold pro- vided proper screw action is taking place ; the differences due to the thickness may be smoothed out as cavitation sets in. The effect of shape of blade section has been tested on a set of screws of rather fine pitch ratio (-7875 on the face), the blade width ratio being -6. A screw is usually required to develop a given thrust, and comparing the results at constant thrust the following conclusions are arrived at : — (1) Setting back the driving face at the leading edge from B to B r (Pig. 44) has little effect upon the revolutions, and gives slightly better efficiency at all moderate slips. But with a pro- peller of higher pitch ratio =1-2 on the face, there was a serious 186 SHIP FORM, RESISTANCE AND SCREW PROPULSION falling off of efficiency at high slips, the loss being 7 per cent, at 14 per cent. slip. (2) Setting back the trailing edge from A to A x requires higher revolutions to produce the same thrust, but has little or no effect upon the efficiency except at very low thrusts, when the results are rather indeterminate, but seem to indicate that a little set- back may do good but too much will cause a serious loss of efficiency. The increase in revolutions passing from section 139 AA to 143 is 10 to 15 per cent., and varies with the ratio -j^ for intermediate sections. Experiments with blades in air support the above conclusion as regards increase in revolutions to obtain the same thrust when the driving face is cut back at the trailing edge. Such experi- ments also show a slight gain in efficiency at small thrusts with AA small set-back (up to -rw"—'^) an< ^ a l° ss °* efficiency at high thrusts, which becomes serious if the set-back exceeds a ratio of AB ~ 05> Position of Maximum Thickness in Section of Blade. — The shape of the section of a blade is usually symmetrical about the axial line. This is adopted mainly on the score of strength going ahead and astern. There are no published results of tests with propellers having the maximum thickness elsewhere than in the middle of the section, which would show if anything can be gained by keep- ing the maximum thickness near the leading or trailing edge. Some guidance can be found in tests of flat blades in air, and the following paragraphs give the general conclusions to which such tests lead one : — (a) There is a fair gain in efficiency by moving the maximum thickness towards the leading edge, provided the ratio-r-is greater than -3 (see Fig. 44). If-r-is made smaller than -3 the efficiency drops, particularly at very high slips. PROPELLER BLADES 187 (b) The thrust is improved by making-^-equal to -38, but for small values of this ratio the thrust falls off badly at the higher slips. It appears, therefore, that when going ahead more work can be put into the screw with a fair gain in efficiency by keeping the point G a little to the leading edge, provided that-^-is not made less than *38. (c) Thickening the section on the back towards the trailing edge has very little effect upon either the thrust or efficiency, within the limits of the experiments. These are shown by sections 1 and 3, Fig. 45. • Section 3 • Section I Driving face leading edge. ElG. 45. Hollowness of Driving Face. — It is not uncommon for screws of moderate width to have increasing pitch from the leading to the trailing edge, i.e., to be hollow on the driving face. Thorny- croft's model screws show slightly better efficiency with the pitch of the driving face varied in this way, but the experimental results are not given in sufficient detail to allow of a comparison of thrusts, and in any case the blades have other special characteristics besides that being discussed. Experiments with flat blades show that the hollow face has little or no advantage in efficiency, but develops a given thrust at a slightly smaller angle than the flat face (measured on the chord AB in Fig. 46 in both cases). At slip angles exceeding 12 degrees the hollow face has a considerably better thrust coefficient than the other. 188 SHIP FORM, RESISTANCE AND SCREW PROPULSION A hollow face, therefore, would have no advantage at the root of a screw blade where the slip angle is small, but could be worked Pig. 46. with advantage to the thrust over the central portion of the blade. The screw would then develop a given power with slightly less revolutions than the flat face. CHAPTER XXI HTTLL EFFICIENCY, WAKE AND THRTTST DEDUCTION § 79. — The second term in the net efficiency of propulsion given on page 162 is the hull efficiency, i.e., the ratio work done in towing the ship at any speed actual work done by the screw in propelling the ship at that speed. It has already been shown that this factor may be written in the form h=(l+w)(l~t). One of these terms depends upon the wake velocity, the other upon the extent to which the action of the screw augments the resistance of the ship. The two terms are not independent of each other, and any condition which tends to increase the wake factor w generally tends to increase the thrust deduction factor t, so that h remains fairly constant, varying as a rule between -95 and 1-0. For twin-screw vessels of moderate prismatic coeffi- cients at speeds above that given by F(knotB)=*/L(feet). provided that the propeller clearance is good -96 may be taken, and for lower speeds -97 to -98. These figures are for vessels in which eddy-making at the stern is absent ; with after-body prismatic coefficients much in excess of -7 they become smaller. Hull efficiency as a whole is therefore not of great interest to the designer. But the separate factors which go to its make-up, owing to their influence in other directions are always important. A proper valuation of w is necessary in order that the velocity of the screw through the water may be obtained. If the thrust on the screw is approaching the cavitation limit, then the augmenta- 190 SHIP FOEM, RESISTANCE AND SCREW PROPULSION tion of the resistance becomes important, and anything which will reduce this, means smaller thrusts for given speed and power developed. Wake. — The natural stream line flow of the water past the ship, produces around the after-body a forward velocity which differs in magnitude at different parts of the stern, but which at any point is a fairly constant percentage of the ship's velocity. The wake velocity due to this is always positive, i.e., in the direction of motion, but is smaller the further forward the screws are placed. It has its greatest value near the ship, and smallest outboard at the keel level. Two or three other causes, however, are at work, their effect varying according to the type of ship. The surface of every ship being frictional, is bound to produce a forward velocity in the water with which it may come into contact. This forward velocity is transmitted in a minor degree to the surrounding particles. Hence the " frictional belt " tends to increase in thickness continuously towards the stern, losing at the same time any definite line of demarcation between it and the surround- ing water. But with very full lines, stream line flow becomes impossible near the body post, and the vessel tends to drag some water along at a velocity equal to its own. This is particularly the case in the region of the water line, where full lines may be required for stability or other reasons. At high speeds, waves are formed by the ship, and the particles of water constituting any wave have an orbital velocity. At the crest of a wave this orbital velocity is forward, i.e., in the direction of motion ; in the hollow of the wave the particles move back- wards. It follows that the wake effect of this orbital velocity will depend upon the position of the wave crests and hollows at the stern of the ship. A screw working directly under a wave crest will have a large forward wake, but if it is placed near a wave hollow, the wave effect will tend to cancel the frictional belt and stream line effect and give a negative wake. Thus all destroyers at high speeds travel with the stern in a small wave hollow, and HULL EFFICIENCY, WAKE AND THEUST DEDUCTION 191 the wake factor for these is sometimes negative, and seldom more than 2 per cent, positive. These causes together produce a wake of varying intensity at different points around the stern, and the experiments of Calvert have shown the extent of this variation. He measured by means Section at 2 inches out From centre to fc fi4 i4s tie zte 4a 14/ ivi /js 4* t« -+7 140 l\3 Zf/ 5+7 64* 46 -& Q2 06 247 b}7 i\f 140 V H42H 143 142 >4Z qs 14a 2i 443 143 143 145 148 W 140 m H2 142 W W Fig. 47. — Calvert's Wake Experiments. The figures on the sections give the forward movement (or positive wake) of the water at any point, as a percentage of the forward movement of the boat. of Pitot tubes the velocity at various points around the stern of a ship, and Fig. 47 shows the wake values he obtained. The designer is mainly concerned with that part of the wake in which the screw works, and the wake factors determined by screw experiments, or by the analysis of steam trials, give the mean wake over this area, and are used as already explained. In Tables 35 A, B, C D, is given a list of ships and the wake factors (w) obtained generally by model experiments. The speed V x of the screw through the water is given by V Vi= 1+ttT 192 SHIP FORM, RESISTANCE AND SCREW PROPULSION These values apply generally to screws with good clearances between hull and tip of blades, such as are usually worked in twin- screw ships, viz., from 1 to 2 feet, not having any obstruction in front which might materially affect the flow of water. § 80. — The following additional remarks are based upon Froude's and Luke's experiments : — (1) The wake factors are practically independent of the screw pitch, and number or area of blades, as theory would lead one to expect. (2) Wake decreases very slightly with speed for all practical speeds. (3) With a single screw, diminishing the diameter increases the wake value, but decreases the thrust deduction value as well, the hull efficiency increasing somewhat with smaller diameters. It must be remembered that this result could not be obtained in a ship having very full after lines owing to the dead water effect. Decrease of diameter in any ship would be accompanied by higher slip, and probably lower screw efficiency, which discounts some, if not all. of this apparent gain in hull efficiency. (4) For low-speed vessels working with a slip of about 22 per cent., there is the danger of getting on the low slip side of the efficiency hump. This can be avoided either by designing the screw for a slightly higher slip than that which gives the maximum possible efficiency, or by using a wake factor slightly lower than the tables give. The loss in efficiency by doing this is not impor- tant, and a good result is assured. (5) The fore-body of the ship has practically no influence upon hull efficiency or wake. (6) Increase of the prismatic coefficient of the after-body, keeping the screw diameter and tip clearance the same, and with the same fore and aft position of the screw, leads to lower hull efficiency values, the loss becoming more marked at those speeds at which heavy wave-making occurs. This loss is due partly to slightly lower wake factors, but more to higher thrust deduction values with the fuller form. If the screws be kept on the same HULL EFFICIENCY, WAKE AND THEUST DEDUCTION 193 centre line as the stern is filled out, and are shifted further aft so as to maintain the same clearance of the blade tips, the hull efficiency does not alter to any great extent. This is an important matter, and must be borne in mind when the stern is filled out to obtain lower towing resistance. (7) Variation of clearance between the tip of the propeller and the ship has a considerable effect upon the wake and thrust deduction. This effect is generally the same whether obtained by varying the spread, fore and aft position, or diameter of the screws. Small clearances give higher wake factors and higher thrust deduction values. The greater the clearance becomes, the nearer to unity does the hull efficiency approach. So that a low hull efficiency can be improved by giving the screw a greater clearance, but, unless a smaller wake factor is desired, or a smaller thrust deduction, there is nothing to be gained by increased clearance if the hull efficiency is already close to unity (see effect upon cavitation). (8) The smaller the wake experienced by a screw, the smaller is the real slip at any ship speed and revolutions, and the higher can the revolutions be worked before reaching the cavitation limit. If this smaller wake factor is obtained by large clearance, the presence of the hull has less effect upon the thrust exerted by the propeller tips as they pass the hull — i.e., the pressure on each blade remains more uniform throughout its revolution. This is important in high-speed ships, and is dealt with in the section on Cavitation. (9) The lower a screw can be kept relative to the hull, the smaller will both thrust deduction and wake become, and the nearer to unity will the hull efficiency approach. A low position of the screws also has the advantage that the screws have less chance of breaking the water surface when the vessel is at a light draft or pitching. This effect in a more or less exaggerated form can be seen from the following table, which gives the results of trials of two self- propelled barges of -9 block coefficient : — S.F. O 194 ship Form, resistance and screw propulsion Table 27. Trials of U.S. Navy Oil Barges Nos. 2 and 3. Number of Column : — 2 3 4 5 6 (diameter (feet) . Propeller J pitch (feet) dimensions 1 dev. area (square feet) . (number of blades I.H.P Speed in knots .... 5-5 4-25 12-9 4 204 134 4-42 6-17 3-5 100 3 213 150 512 5-75 3-5 6-6 3 211 131 4-70 6-25 3-33 20-3 4 206 175 5^24 6-75 3-5 14-0 3 206 178 6-24 These vessels failed to get their speed of 6 knots on the first trials, and although alteration of propeller dimensions effected some improvement, the true solution was found in lowering the pro- peller by angling the shaft downwards until the blades projected below the keel, the results for which are given in column 6 of the table. § 81. Inward and Outward Turning Screws. — An inward turning screw is one in which the blades are moving inwards at the top of the screw disc when going ahead. Twin screws placed at some distance before the after-perpendicular must work in water which, near the hull at least, is not moving perpendicularly to the screw disc. This inward movement of the water is invariably greatest near the water line, i.e., at the top part of the screw disc. The transverse movement in the stream flow is therefore in the same direction as that of inward turning blades at the top of the screw disc, when the screw is going ahead, and in the opposite direction to that of outward turning blades in the same position. Taking first the case of screws working without any bossings or brackets in front of them. Froude's experiments show that, in so far as there is any difference, the inward turning has a slight advantage on hull efficiency, mainly due to a slight increase in wake factor. This advantage did not vary in any consistent way with spread of screws or type of vessel, and its mean value taken over a large number of cases is about 1-4 per cent., the mean increase in wake being -6 per cent. Vessels having A brackets to support the outer ends of the shafts, with only small bossings or HULL EFFICIENCY, WAKE AND THKUST DEDUCTION 195 " swellings " where these break through the hull, may be con- sidered as working under conditions which approximate to the above, and the above conclusions will hold good in their case. When large bossings are adopted the case is very different. These bossings are liable to interfere considerably with the natural flow of the water around the stern. This natural flow has been found to be upwards and inwards in more or less diagonal planes. A horizontal web at about half -draft prevents a good deal of this upward flow from taking place. The surface streams must then move in more rapidly than before, in order to avoid a cavity, and at the after end of the web where there is no restriction the lower streams will have a more marked upward movement. In the same way, a vertical web exaggerates the upward and for- ward flow along the buttock lines below the web, and there will be more rapid movement inwards just aft of the end of the web, particularly at the top of the screw disc. The effect of such changes upon the towing resistance has already been given in Table 22. But this is not by any means the only effect of the bossings. The exaggerated inward flow near the surface with horizontal bossings and the equally impor- tant changes in stream flow due to vertical bossings, affect the wake and screw efficiency. The presence of the bossings in front of the screw will naturally increase the thrust deduction slightly, and, being a source of resistance, will increase the wake also, but it is in the effect upon the relative advantages of the two directions of rotation that it becomes important. Fig. 48 shows the results of some experiments made in the Clydebank tank with bossings inclined at different angles on a model whose principal dimensions were : — Length, 15-3 feet ; beam, 2-5 feet ; draft, -75 feet ; Cm J value, 6-2. Prismatic coefficient — fore-body, -627 ; after-body, -719. Propeller dimensions — diameter, *5 foot ; spread, -417 foot from centre line ; screw centre before A. P., -125 foot; immer- sion — tips, -167 foot ; centre -417 foot. o 2 196 SHIP FORM, EESISTANCE AND SCEEW PROPULSION Speed of model in knots = • 8 a/length in feet. The bossings were all -125 x (screw diameter) in thickness, rounded at the outer edge, well tapered off aft. f Dotted lines inward turning) Full » outward » ) Total resistance compared with resistance of naked model. 22$ 45 67? Angles of bossing. ^L ZZL 30 22t 45 67% Angles of bossing. Net effect.ie Hull efficiency divided by total resistance. is: 5 30 Pig. 48.- 22~£ 45 6lf Angles of bossing. Angle of Shaft Bossing and Hull Efficiency Elements. 3D For all angles of the bossings the thrust deduction was increased some 2 per cent, over that for naked model, but the wake values differed with angle, the variation being in opposite directions with inward and outward turning. The exaggerated inward motion at the top of the screw disc produced by the horizontal webs gives an enlarged wake outward turning, and a decreased wake inward HULL EFFICIENCY, WAKE AND THEUST DEDUCTION 197 turning. The vertical web has the opposite effect upon the wake. The effect upon the hull efficiency and the product of hull efficiency and total resistance, are shown by the figure. These results are for model, and it is possible that the wake effects are somewhat greater than they would be in the ship, but there can be no doubt that the broad conclusions will be the same for both ship and model. Neglecting screw efficiency, the results warrant the conclusion that inward turning screws require an angle of bossing of about 45 degrees, and outward turning do best with smaller angles than this. Taking screw efficiency into account, as one must in a ship, it will be noted that with horizontal bossings and outward turning screws, or vertical bossings and inward turning screws, there is a high wake, which, with such forms as that under test, will mean either a very high slip and low efficiency of screw, or larger diameter with smaller pitch and larger bossings, the screw efficiency dropping, but not so much as before. This loss may be considerable, and Froude has stated that it just about balanced the gain in hull efficiency in cases he has tried (comparing the horizontal and 45 degree bossings). It follows that either inward turning combined with horizontal webs or outward turning and vertical webs, will always give bad results. This to some extent explains the relatively bad results ob- tained by Mr. Duncan with inward turning screws and " fairly horizontal " bossings. With inward turning screws the speed obtained was 9-34 knots ; by changing over the propellers so that they ran outward, and running the engines at the same revolutions as before, the speed was 10-34 knots. A similar case has been given by Mr. Taylor. The Niagara II., a steam yacht of 2,000 tons displacement, 250 feet length, did 12-8 knots with inward turning screws, the I.H.P. being 2,100. With the same screws outward turning, the speed was 14- 1 knots with 1,950 I.H.P. The vessel was fitted with " wide horizontal bossings." Wake values for a great number of ships of various types are given in Tables 35 A, B, C, D. § 82. Multiple Screws. — The number of shafts adopted in propelling a vessel depends to a certain extent upon the type of 198 SHIP FOEM, EESISTANCE AND SCREW PROPULSION main engine to be used, and upon the actual power to be delivered by the screws. Large thrusts require large areas of screw blade, which means either large diameter with a given number of screws or smaller diameters and more shafts. But there are usually fairly rigid restrictions on the maximum diameter which can be worked on any ship. Long lengths of outboard shafting are very undesirable both from the resistance and vibration points of view, and generally the screw disc must come within the maximum beam and above the keel line. Screws of large diameter require high shaft lines in the hull and therefore reduce the cargo space a little, and in certain vessels would require more care in laying the vessel alongside a jetty to avoid fouling the screws. On the other hand, the fewer the number of shafts the less expensive, as a rule, is the installation, the supervision is less, and the shaft bossing resistance is less. Assuming that the main engines require high revolutions for good efficiency, it is known that the possibility of getting good efficiency out of the screw is limited by two things : — The thrust cannot be increased beyond a certain amount per square foot of blade surface. The pitch must be such as to give a reasonable slip. But it is seldom good to keep the pitch very low relative to diameter, and as the power to be delivered by the screws is increased, there will come a time when it is advisable to increase the number of shafts rather than to increase the diameter or pitch of the existing propellers. With low revolutions of the main engines a large diameter of propeller and high pitch ratio can be adopted, and higher thrusts can be delivered on a single shaft with quite reasonable screw efficiency. It is of little or no use adopting a type of main engine suitable for high revolutions, and sacrificing considerable effi- ciency by working it at low revolutions to suit the screw. The gain, if it exists, would not warrant the extra cost usually involved. If an economical high revolution engine is to be used, its revolu* tions must be reduced to what gives reasonable efficiency of the screw, by some means external to the engine. HULL EFFICIENCY, WAKE AND THRUST DEDUCTION 199 The propulsive efficiency of triple or quadruple screws can be obtained exactly the same as for twin screws. It is necessary to know the wake factor and hull efficiency for each screw position. With these the screw efficiency can be obtained from Froude's results (Figs. 37 and 40). The doubtful point at present is the hull efficiency. The best data upon this for quadruple screws is given in a recent paper by Mr. Luke. A comparatively fine lined model was tried in the Clydebank tank with twin and quadruple screws. The particulars of the model and screws are given in the table. Table 28. Quadruple Screw Experiments. Model dimensions : — Length .... Beam .... Draft .... Block coefficient Propeller particulars : — Diameter (feet) Number of blades Spread from centre line (feet) Centre before A. P. (feet) . Clearance from hull . The inner and outer screw discs when projected on the transverse plane just touched each other. Experiments were made with the forward and after screws separately, each giving a thrust equal to half the resistance of the model plus the augment caused by these screws. The aggregate thrusts of the forward and after screws thus equal the total augmented resistance. This assumes complete non-interference, and as this was a doubtful point, further experiments were made to observe the effect on the performance of the forward screws, of a pair of revolving screws placed in the after position, and also on the after screws of a pair placed in the forward position. The results of the twin-screw experiments call for no special comment except that the high hull efficiencies are probably due to the close proximity of relatively small propellers to the hull of a very wide model. Table 29 gives the hull efficiency elements . . 16-67 feet . . 2-5 „ , •75 foot • ■60 Inner. Outer. •333 •333 . 3 3 •25 •583 •25 . . 1-5 •125 diam. -125 diam 200 SHIP FORM, RESISTANCE AND SCREW PROPULSION for each position with the four screws revolving. It will be observed that the forward screws have a material influence on the wake of those in the after position, and the hull efficiency of these screws is considerably reduced ; but the after screws have very little effect upon the forward ones. Some light upon two most important points in connection with the propulsion of vessels by quadruple screws is obtained from these experiments. Table 29. Results of Quadruple Screw Experiments. (Model and screw data are given in Table 28.) After screws only f outward turning I inward turning Forward screws only { outwa , rd t turnin S J I inward turning Thrust Wake. Deduc- tion. •21 •14 •20 •11 •24 •13 •24 •10 Hull Effi- ciency. 104 1-07 1-08 1-12 The effect of action of neighbouring screws on above results : — Thrust Hull Wake. Deduc- tion. Effi- ciency. forward screws (out- r outward. ward turning) •16 •13 101 Wake, turning forward screws (in- etc., of ward turning) •13 •12 •99 after forward screws (out- screws inward i turning ward turning) forward screws (in- •15 •12 101 ward turning) •10 10 •99 after screws (out- ■ outward ward turning) •22 •13 106 Wake, turning after screws (inward etc., of turning •22 •12 107 forward 1 after screws (out- screws inward . turning ward turning) after screws (inward •23 •12 1-08 turning) ■23 •10 110 HULL EFFICIENCY, WAKE AND THEU8T DEDUCTION 201 In the first place the relative wake values to use in propeller design are approximated to, and in the second place the combina- tions of directions of rotation to ensure the highest gross hull efficiency can be obtained. With this particular model, the gross hull efficiency values obtained with the various possible combina- tions of inward and outward turning screws in either position are almost identical, although it is not possible to say that this is a general rule. The fact that the clearances and diameters were the same for both positions, and that the effect of the bossings is to be superposed upon these results, must be borne in mind when using them in any case. In several ships whose trials have been analysed the author has found that the forward screws have influenced the wake of the after ones, reducing it to about equality with that of the forward, and in the case of a high-speed triple-screw vessel to 4 per cent, less than that of the wing screws, the wake of which was 2 per cent, positive. This influence of the forward screws upon the after ones cannot be good for the screw efficiency itself. It would only be felt upon the outer part of the screw disc, and the blade tips would pass through this sternward wash from the forward screws, into the strong forward wake near the ship's hull, with every revolution. When projected upon the transverse plane, in the case of triple screws, the discs should clear each other by at least -2 of the diameter. With quadruple screws good results have, been obtained when the projections of the screws on a transverse plane only clear each other by a few inches, but as a rule the forward screws have been several diameters ahead of the after ones and somewhat higher in the hull. The natural stream fine flow will tend to wash the race from the forward screws upwards as well as inwards, and the raised position of the forward screws com- bined with the distance between the two positions, all tend to help the race of the one to clear the other. The results of some model experiments made in the Spezia tank are given in Table 30. These experiments were made in order to compare triple and quadruple screws. It will be seen that the 202 SHIP FOEM, RESISTANCE AND SCREW PROPULSION mean wake values are higher for three screws than for four, and this was largely due to an increase in the wake of the centre screw of about 7-8 per cent. As the thrust deduction was about the same with either three or four screws, the hull efficiency was therefore better with the former. Triple screws also had the advantage of lower appendage resistance, and would have a decided advantage in propulsive efficiency in this case, if they could be designed to avoid cavitation and do their work with as high screw efficiency proper as quadruple screws would give. This would need investigation for any ship on the lines already given, before a complete comparison could be made. Table 30. Form : — A B Length in feet 630 620 Beam in feet 93-3 900 Draft in feet . 27-6 27-9 Displacement in tons 24,700 24,600 Block coefficient ■536 •555 Number of screws : — 4 3 4 3 Transverse spread of Projection of Projection of Centres of Wing screws screws. discs nearly discs just outer screws 2-64 diameter touching each touching each 4-2 diameter apart. other, centre other. apart, of outer inner screws screws 1-6 diameter. 3-7 diameter apart. Centre of screw from after end outer Ill feet 77-4 feet 86-3 feet 62 feet of water line inner 61 „ 42-6 „ 44-0 „ 37-5 „ (cruiser stern) Ratio of resistance of naked ship to resistance with appendages, cor- rected for ship •925 •95 •95 •975 Speed in knots : — 12 24 12 24 12 24 12 24 Mean wake values . •12 •09 •17 ■13 •10 •10 •18 •18 Mean hull efficiency 1-05 •96 M0 ■98 ■98 ■95 1-09 10 Product of hull efficiency and appendage coeffi- cient .... •971 •888 1-004 •93 •93 •903 106 •975 CHAPTER XXII MAIN ENGINE § 83. — It is only intended here to run over the main effect which type of engine has upon the propulsive efficiency in general, and not to consider the reasons for this effect so far as the engines are concerned. Every type of engine, whether it is steam recipro- cating with three or four cranks, steam turbine, oil, gas, or electric, has a certain range of revolutions over which it will work at its best economy, and there is a penalty to pay, if for any reason the revolutions are fixed outside this range. In some types this penalty is a comparatively small one, and in others assumes serious proportions. There are two different sides to the question which have to be considered : — (1) The cost of producing one brake horse-power per hour on the propeller shaft ; (2) The economical utilisation of the whole power developed by the engines. Good propulsive efficiency is of little practical use if it is obtained, either by the wasteful consumption of cheap fuel and water, or by the economical consumption of an expensive fuel. On the other hand, a cheap means of producing power has to be combined with an efficient mechanism for thrusting the ship along, or it is of no use to the naval architect. For very large powers only two types of engine are available, namely, the reciprocating and turbine engines, and of these the reciprocating is approaching its upper limit both as regards piston 204 SHIP FORM, RESISTANCE AND SCREW PROPULSION speed and revolution. For more moderate powers the oil engine becomes a competitor, and for still smaller powers the gas and electric engine are available. The power limitations of the last three types are not necessarily set by any inherent qualities of the engines, but because of their comparatively smaller develop- ment. The Reciprocating Engine is fairly efficient at all moderate speeds, its mechanical efficiency varying from -8 for low to •88 for full power in triple-expansion, and to -92 for quadruple- expansion engines, exclusive of thrust block friction, which might be taken as absorbing 2 per cent, of the power. Its coal consumption is about 1-3 lbs. per I.H.P. per hour for a three-crank engine, exclusive of auxiliaries, or 1-54 lbs. per S.H.P. Taken on a prolonged voyage and for all purposes, the consumption of coal may be taken as roughly 1-5 lbs. per I.H.P. for triple and 1-34 lbs. for quadruple-expansion engines. This gain in coal consumption with the quadruple- expansion engine has to be balanced against the extra cost and larger engine-room involved, and would be realised only on long voyages. Going astern its power is about -89 of that going ahead. The Turbine. — For high powers to be delivered at high speeds, the turbine has a lower coal consumption per S.H.P., and its efficiency is at least equal to, and sometimes more than that of the quadruple-expansion engine. It produces an almost uniform torque on the propeller shaft, enabling higher mean thrusts to be used on the propeller blades and causing less vibration. On the other hand, it is not reversible, and an astern turbine or a transformer must be fitted. A turbine gives better efficiency as the blade speed approximates to the steam speed, and for this reason high revolutions are better than low. A land steam turbine developing powers of 10,000 H.P., gives the best performance at 1,000 revolutions per minute or above, and for smaller powers at still higher revolutions, the coal consumption being as low as 1-0 lb. per S.H.P. per hour. MAIN ENGINE 205 But if a vessel is of only moderate speed the turbines cannot be run at such high revolutions without serious loss in screw efficiency, and to avoid this loss transmission gear between turbines and screw has been adopted in recent years. This loss at low speed can be seen from the following results for the Amethyst and Topaze : — Table 31. Distance Travelled per Ton of Coal. Speed in Knots. Amethyst, with Turbine Engines and direct Drive to Souews. Topaze, with Four-crank Recipro- cating Engines. 10 14 18 20 7-42 6-6 4-8 4-2 9-75 6-8 3-7 2-9 Trials with other vessels show generally the same variation. Thus at one-fifth power the " Invincibles," with turbines and direct drive to screws, require 2-4 lbs. of ooal per S.H.P., and the " Minotaurs," with reciprocating engines, require only 1-9 lbs. At high speeds the corresponding figures are 1-2* lbs. and 1-75 lbs. respectively. The water consumption varies in the same way, but not to the same extent, the figures at high speed being about 12-0 lbs. and 15-8 lbs. respectively. All of this gain in the turbine at high speed shown by the con- sumption per S.H.P. is not necessarily realised. Larger powers are required owing to the lower propulsive efficiency compared with that obtained with reciprocating engines at lower revolutions. The propulsive efficiency of the Utah, with turbines (taken as the E H P \ ratio ' ' ' )> is '62, and that of the Delaware, with reciprocating D.xi.lr./ * The coal consumption of the Lusitania, with Scotch boilers and tur- bine engines, is 1-43 lbs. per S.H.P. per hour. 206 SHIP FORM, RESISTANCE AND SCREW PROPULSION S H P engines, is -69, assuming that T Vrp ^ s "90- This loss* in pro- pulsive efficiency must be set against any gain in consumption per S.H.P. In some cases it exceeds the latter. A comparison of the results of the Caronia and Carmania will illustrate this. The former has quadruple - expansion engines driving two screws at 80 revolutions per minute at 18 knots ; the latter has compound turbine engines driving three screws at 175 revolutions per minute. The coal consumption of the latter is stated to be "considerably greater" than that of the former. The crossing-over point at which the purely reciprocating and purely turbine ship are about equally economical in coal appears to be in the neighbourhood of 15 to 18 knots for the intermediate class of passenger-cargo steamers. For steamers of moderate power and speed, the two propulsive defects of a turbine with direct drive to the screw — non-reversibility and high revolutions — can be removed wholly by fitting a transformer of the " Fottin- ger " or electric type between the turbine and propeller, or in part by the introduction of mechanical gearing. The relative propulsive advantage of the reciprocating and turbine engine, with or without transmission gear, depends to some extent upon whether the former can be arranged to give the best screw effi- ciency. If this is the case, whatever is to be gained by change of type of engine must be obtained from the turbines and trans- mission, and to whatever extent it is not the case there is further possible gain with the latter. The additional weight of the trans- former, whether water pump, electrical, or mechanical gearing, is roughly speaking compensated for by reduction of weight of turbines. In some cases there has been a fair gain in weight by fitting a high revolution turbine and a transformer of some kind, * The Italian cruiser San Marco, with turbines on four shafts, haB practically the same propulsive efficiency as the sister ship San Oiorgio, with reciprocating engines on two shafts, the S.H.P. of the former being •89 of the I.H.P. of the latter at 22 knots, the mean revolutions per minute being 380 and 140 respectively. MAIN ENGINE 207 but the area of engine and boiler room remains about the same in vessels of moderate speed. The " Fottinger " Reducing and Reversing Gear can be arranged for reduction ratios from 3 to 1 up to 12 to 1 and has the following efficiency : — Small powers about 150 H.P. . . efficiency=-865 Larger powers about 600 H.P. . . „ =-88 Powers above 1,000 H.P. ... „ =-90 The above efficiencies include the effect of thrust block friction. A small portion (1| to 2 per cent.) of the loss in the transformer can be recovered by using transformer water for feeding the boiler. No astern turbine is required in this case, the transformer taking its place, and in a recent case the astern power has been as much as 80 per cent, of the ahead power. This astern power can be maintained for prolonged periods without detriment to the engines. With an installation developing 2,400 S.H.P. the water con- sumption was 12-46 lbs. per S.H.P. for turbines and transformer alone, and the coal consumption was 1-38 lbs. per S.H.P. including auxiliaries, the coal not being of very good quality. If the trans- former is to be any advantage in propulsion, the known loss in it of about 1 1 per cent, must be made good by greater efficiency in the screw and turbine. The above figures, which are believed to be reliable, compare very favourably indeed with the water and coal consumption of a reciprocating engine, and the efficiency of the screw with the turbines and transformer would be at least as good as with the reciprocating engines, and much better than with direct turbine drive. Installations of 10,000 H.P. on one shaft are in hand for the 25,000 ton steamer Admiral von Tirpitz, and the shop tests show an over-all efficiency of 92 per cent, for these. Mechanical Gearing. — Gearing up to S.H.P. of 2,000 on each pinion and to 4,000 per shaft by working two pinions to one gear wheel is now in use on the Anyo Maru, and pinions to take up to 3,000 H.P. are stated to be under consideration. Reduction 208 SHIP FORM, RESISTANCE AND SCREW PROPULSION ratios varying from 20-0 to 4-5 are in use. The loss of power in the gearing is about 2 per cent, and there is an additional small loss in the ordinary thrust block, which may bring the total loss to 4 per cent, or 5 per cent. If pivoted blocks are used in the thrust bearing, the loss in it is very small, being from -2 to -3 per cent. The gain in efficiency of the turbine by running it at the high revolutions possible with the gearing is considerably greater than the above loss, and the screw can be arranged to work at its best efficiency. This eliminates the most serious disadvantage of the turbine for low and moderate speed vessels, but the astern turbine is still a necessity and leads to some complication, and as a rule to loss of astern power, compared with the reciprocating engine. The astern power is usually about 60 per cent, of the ahead power, but more can be arranged if desired. The cost of the installation is from 5 per cent, to 10 per cent, greater than that of reciprocating engines of the same power and somewhat larger boilers. The gain in consumption can be seen from the. results of the trials of the Caimgowan and Caimross. These are sister ships of length 370 feet, beam 51 feet, block coefficient -784 and -779 respectively, having a sea speed of 10 knots, the boilers and propeller being the same on the two ships. The former had a triple-expansion engine, the latter high-speed turbines with Parson's mechanical gearing between the turbine and propeller shafts. The coal consumption of the former with all auxiliaries was 15 per cent, higher than that of the latter with the propellers making the same revolutions. The S.H.P. of the latter was 87-7 per cent, of the I.H.P. of the former, and, using this figure in the Caimross to calculate the equivalent I.H.P. for a reciprocating engine, the lbs. of coal per I.H.P. for all purposes becomes 1-45 and 1-70 for the geared turbines and reciprocating engines respec- tively. The Caimross had somewhat finer lines, which no doubt helped her, but, making all due allowance for this and for the com- paratively high consumption of the reciprocating engine, there is still a balance of about 9 per cent, in favour of the geared turbine. MAIN ENGINE 209 Electrical Transformers. — These have been tested on several ships of comparatively moderate powers. The efficiency of the electrical gear is claimed to be 88 per cent. Just as with any other transformer, the turbine can be run at very high revolutions. With electrical gear, however, the ship's speed can be altered or reversed with the turbines running in their normal direction. No astern turbine is required with it, and the full power of the main engine is available for going astern. For vessels of high power a number of independent high-revolution turbine generators can be used in any convenient part of the ship, and some of these can be cut out for low speeds. The system can be used with internal combustion or any other engine as the prime mover. It has the disadvantage of introducing high-voltage alternating current into the engine room. The United States coal collier Jupiter (length, 520 feet ; displacement, 19,000 tons loaded) is fitted with one turbo-generator making 1,990 revolutions per minute at full speed (14 knots estimated), driving two motors with an approximate reduction ratio of 18-0. The shop tests of turbine and generator show a steam consumption of 12 lbs. per S.H.P. The weight of machinery is said to be 156 tons compared with 280 tons in the sister ship Cyclops, driven by two triple-expansion engines, and she has maintained 14-8 knots on her trials against 14-6 knots of the latter, the S.H.P. of the former being 6,300 and the I.H.P. of the latter 6,700. The cargo boat Tynemount is fitted with two 300 B.H.P. oil engines making 400 revolutions per minute, supplying current to one 500 B.H.P. induction motor on the propeller shaft. This vessel is said to have passed her trials satisfactorily. Consump- tion and efficiency figures have not been published. Combination of Turbine and Reciprocating Engines. — In this system the steam is first taken to a reciprocating engine and then to a low-pressure turbine. Each type of engine is then run under its best conditions, and large expansions of the steam are possible. No astern turbine is required with this arrangement, but the astern power is necessarily limited to 89 per cent, of the ahead power of the reciprocating engines. Unless there is sufficient S.F. p 210 SHIP FOKM, RESISTANCE AND SCEEW PROPULSION beam to place them more or less abreast each other, the engines are liable to require a long engine-room, and cargo and passenger space then suffers. The system is most useful for vessels of moderate speed (15 to 21 knots) and fairly large power. Comparatively high revolu- tions are necessary for economy, the drive being direct from turbine to screw as a rule. The saving in coal in a good example is given by the comparison of the Laurentic and M egantic. These vessels are 565 feet in length, 20,000 tons displacement, the former having triple-expansion engines on the wing shafts and a low- pressure turbine on the centre shaft. The latter has quadruple- expansion engines with two screws, and consumes 12 per cent, more coal than the former. The same system is fitted in the Otaki (length, 465 feet, displacement, 11,750 tons on trial), and the advantage in its favour compared with quadruple-expansion engines is stated to be 20 per cent, in steam consumption. The Olympic (length, 852 feet, speed, 21 knots) and several other large vessels making long voyages also have such engines. Oil Engines. — The oil engine has the great advantage that it is self-contained, requires no intermediate process of transformation between fuel and engine, has low stand-by losses, and requires smaller space than the reciprocating engine and boilers. The fuel can be quickly stored in places not suited for coal and requires no trimming. Against these advantages must be set the facts that the supply is only possible at certain ports, and the cost per ton is much higher than that of coal, outside of certain restricted areas. Low flash-point oil cannot be carried under holds owing to the danger of vapour getting into the latter. The power which can be generated in one cylinder is limited at present to about 500 B.H.P., and by grouping smaller cylinders powers up to 2,000 B.H.P. can be developed on one shaft. The type involves reciprocating parts, with the possible attendant vibration. The two-stroke is more simple and has a more equal turning moment than the four-stroke, but its consumption is about 10 per cent, higher and the piston temperatures are higher. Engines of moderate power — up to 1,250 S.H.P. on each shaft — MAIN ENGINE 211 have now shown themselves to be fairly reliable on service. The oil consumption and efficiency can be seen from the following figures : — The Selandia (length, 370 feet, displacement, 9,800 tons loaded) is fitted with two shafts each driven by a four-stroke cycle " Diesel " oil engine making 140 revolutions per minute at about 11 knots, developing 2,500 I.H.P. The mechanical efficiency of one of the main engines was found to be -85. This is exclusive of thrust block friction and auxiliaries, and in comparing it with the similar figures for the steam reciprocating engine it should be reduced some 3 to 5 per cent, to allow for the latter. The oil fuel consumption including auxiliaries was *44 lb. per S.H.P. The France, (length 430 feet, displacement, 10,700 tons loaded) is fitted with a two-cycle engine on a centre fine shaft, and makes 230 revolutions per minute, developing 1,450 B.H.P. at a speed of 10-2 knots. The mechanical efficiency of the engine was found to be -71, the engine being run on lamp oil and consuming -47 lb. perS.H.P. In considering the application of oil engines to low-speed ships the effect of revolutions upon efficiency of the propeller must be carefully borne in mind. Increase of revolutions above a certain limit, which depends upon the power and speed, is bound to lower the screw efficiency. Developing the power on two shafts, as in the case of the Selandia, raises this revolution limit considerably above its value for a single shaft transmitting the whole power at the same speed. Gas Engines. — No engine of high power for use on board ship has yet been developed. Such an engine for general use requires a producer to burn bituminous coal on a large scale without caking, and the absence of such an one of reasonable proportions and weight stands in the way of any considerable advance. The majority of gas engines are dependent on a clutch for reversing, and special means are required for setting the engines in motion. The stand-by losses are about the same as for a vessel with an ordinary steam boiler. Where a good supply of coke, coke breeze or anthracite coal p 2 212 SHIP FORM, RESISTANCE AND SCREW PROPULSION is available this type of engine is used with great fuel economy. For small powers — up to about 450 H.P. — the consumption is -8 lb. of anthracite and 1 lb. of bituminous coal per I.H.P. per hour. Effect of Revolutions. — In the preceding section it has been stated that the propulsive advantages which might be gained by the adoption of certain types of prime movers are affected (some- times adversely) by the revolutions which are necessary to obtain reasonable efficiency in the engine. Two cases have been chosen to illustrate this effect. One of these represents a comparatively low-speed vessel, the other a vessel of intermediate type, both having twin screws. Ship Particulars. Item. Case 1. Case 2. Speed in knots (V) ..... Thrust horse-power to be developed by two screws (2H) ..... Wake factor ...... Speed in knots through wake water (F x ) . Minimum area in square feet for cavitation (assuming 12 lbs. to the square inch) Screws three-bladed of uniform pitch. 15 7,500 •18 12-71 56 20-6 16,000 •144 18-0 84 For both cases, diameters and efficiencies for several pitch ratios have been calculated for various revolutions, and are plotted in Fig. 49. For any revolutions of the engine, the diameter and efficiency of the propeller will be given by the curves for the particular pitch ratio chosen. When considering the results two things have to be borne in mind — first, that the efficiency curves are for screw only, and any loss in this direction must be balanced against the lighter and smaller engine possible at the higher revolutions, and a better efficiency of engine in the case of turbine drive ; secondly, that the small diameters would be associated with smaller bossings or brackets, which gives them a slight advantage, and with proper Scale of Revolutions per minute Fig. 49. — Revolutions and Screw Efficiency. Note.— The figures on the curves are effective pitch ratios, equal to 1-03 times the face pitch ratio. 214 SHIP POEM, RESISTANCE AND SCREW PROPULSION clearances there is no reason to suppose there will be any loss in hull efficiency with them. Somewhat more clearance will be required with the small screws than with the large ones. There is no definite published data on this point, but as both screws will be developing the same total thrust, the intensity of the water pressures around the smaller screw will be greater, and more clearance will be required to avoid an increase in the thrust deduction factor, which would counterbalance the gain due to the higher wake factor with the closer set screws. Case 1. — The developed blade area per screw must exceed 56 square feet, corresponding to diameters of 14-6 feet and 12*0 feet for -4 and -6 disc area ratios respectively. These limits are shown by the thick vertical lines. As revolutions increase, the maximum possible efficiency steadily decreases, until the cavitation limit is reached. It is then necessary to increase the disc area ratio, if further increase is made in the revolutions, and this entails a more rapid drop in the efficiency. The curves also serve to show that moderate changes in the pitch ratio of a screw of fixed diameter and area have little effect on efficiency down to diameters of 17 feet. For smaller diameters, pitch ratio must be decreased as revolutions are increased, in order to obtain the best efficiency. Case 2. — The minimum blade area for avoidance of cavitation in this case, gives diameters of 15-9 feet and 12-5 feet for disc area ratios of -5 and *8 respectively, as shown by the full vertical lines. As before, the maximum possible efficiency falls off as revolutions are increased, and increase in the disc area ratio carries with it a still more noticeable drop in efficiency. This is shown for the 1-0 pitch ratio by the fine dotted line, which holds for screws of fixed blade area with decreasing diameter as revolutions are increased. It will be seen that very small pitch ratio is never good in this case, and is particularly bad when associated with low revolutions or large area ratios. In both cases, variation of blade area has little effect upon the diameter or revolutions for given pitch ratio. These curves are based upon the data given in Figs. 37 and 39 ; MAIN ENGINE 215 they have been worked out as shown by the example in Table 25, and other cases can be dealt with in the same way. Such separate treatment is necessary in any case where there is any departure from general practice, particularly if there is any liability to cavitation. CHAPTER XXIII CAVITATION § 84. — " Cavitation " is the name given to the phenomenon which makes itself felt by the absence of proper increase in screw thrust with increase of torque. The cause of it is not thoroughly understood, but the following explanation appears to be sound, and does not run counter to good theory : — Reynold's experiments show that the admission of air to a screw causes it to race heavily. If this air is carried round by the blades, it is compressed, and when released from the pressure expands and pushes the water back and out as well as forward, and thus retards the flow through the screw. If, therefore, the blade tips cut the water surface, or are near enough to the surface to suck down air, loss of efficiency will result. Under these con- ditions the thrust and revolutions of the screw are very sensitive to its immersion, and slight variations of the latter, caused by pitching or the passage of waves, will tend to cause considerable variation in the revolutions, producing what is commonly called " racing of the engines." This " racing " is a species of cavitation, but all cavitation is not due to the blades breaking the surface or sucking down air. Screws have been known to cavitate badly when there has been no question of the water surface being broken. Such phenomenon may be due to several causes. Cause 1. — An advancing and rotating screw produces in front of it a suction which causes the water to move towards the screw. The movement of the water is mainly longitudinal, and the acceleration of the particles at any point depends upon the difference of the still- water pressure and the suction of the screw at that point. This still-water pressure is that due to the depth of water, added to the atmospheric pressure, which averages CAVITATION 217 14-6 lbs. per square inch. Thus at 10 feet immersion the pressure is 19-4 lbs. When the suction at any point has reached the still-water pressure, increase of rotation will not produce more suction, and it follows that the acceleration of the water particles will not be increased, or, in other words, the water supply to the screw at this point remains the same although the revolutions have been increased. One of two things may then take place, either the water will rotate partially with the screw blade or a cavity will tend to form. The formation of the cavity will cause a break up of the stream flow at the point and consequent eddy-making. Both the rotary action and the formation of cavities mean loss of efficiency. If every part of the screw blade surface exerted precisely the same amount of force, this limiting suction would be attained all over it. But the water which passes the screw blades is forced into more or less definite stream lines, and the pressures in these streams vary according to their distance from the blade surfaces and screw centre. The thrust which the screw exerts is made up of two parts — viz., the suction on the back and thrust on the face. Owing to the circumferential velocity these are greatest near * the tip, and, owing to the stream line action, at any radius the pressure across the blade is greatest near the leading edge. The greatest suction will therefore occur at the back of the blade towards the tip of the leading edge, and the greatest thrust at the same position, but on the face of the blade. // the back of the blade is very full near the leading edge, it tends to produce at all small slips a negative pressure or suction on the driving face near the leading edge, and such a feature should be avoided. For most blades tested lineally in air at small angles, this suction effect constitutes more than half the thrust of the blades, and there can be little doubt that the efficient working of the * Some recent experiments with blades in air show that the maximum forces are not experienced at the tip of the blade, but at some distance in. For a rotating blade this distance would be approximately one-eighth to one-sixth the radius of blade from the tip. 218 SHIP POEM, RESISTANCE AND SCREW PROPULSION screw depends upon the attainment of good suction on the back of the blades. Since cavitation will take place when the suction at any point reaches a certain limit, the back of the blade must be such as to attain good suction without any marked high local value. For this a sharp leading edge and a rounded back with no sudden change of shape are required. The driving face appears to make little difference to the phenomenon provided it is either flat or hollow in section, i.e., of uniform or gaining pitch passing from leading to following edge. Since all corners and abrupt features tend to produce local high velocities, it follows that the contour of the leading edge at the blade tip must be well rounded to avoid cavitation. Above a certain limit (when the thickness exceeds -1 of the width of the blade) the thicker the blade the smaller is the slip angle at which these high local suction values are likely to be attained, and the earlier is the break- down in the efficiency of the screw. Cause 2. — The above assumes that the screw is rotating uni- formly, so that the maximum cavitation pressure limit can be reached by the screws. This is fairly representative of turbine screws of small diameter, whose revolutions are generally constant. But with reciprocating engines the rate of rotation of the screw varies considerably during a single revolution. This can be seen from Table 32, p. 219, giving the results of measurements taken by Mr. G. H. Heck. This variation in rate of rotation affects the slip at which the screw works, and hence its thrust. Thus with a mean slip of say 20 per cent, a 2 per cent, increase in revolutions brings the slip to 21-6 per cent, and increases the thrust of the propeller 12 per cent. The mean thrust of the propeller is therefore less than its maximum by an amount depending upon the variation in rate of rotation during a revolution. To a similar extent, the thrust when cavita- tion becomes present is less than what it might be with uniform angular velocity. The following table shows that the main factors in obtaining uniform rotation, are good balance of engines and good immer- sion. High revolutions also help in this direction, due to the CAVITATION 219 inertia of the rotating mass, particularly in the case of turbine engines. Table 32. Variation in Rate of Rotation of Screw Shafts. Percentage Variation from Type of Vessel. Type of Engine. Revo- lutions Propeller Tips. Mean of Revolution. per Minute. Taken over J Rev. Taken over iRev. Cargo-boat two-crank com- pound. 58 well immersed. 12 8-6 Cargo-passenger . triple-expansion three-crank. 66 well immersed. 4-6 21 w >» 68 24 inches out 7 to 9 (not racing) of water. Large cargo three-crank 71 20 inches out of water. 5-6 2-15 Large cargo four - crank bal- anced. 66 65 inches out of water. 4-6 1-2 Small high-speed four - crank bal- 104 immersed 4 4-8 1-7 passenger. anced. inches. Cause 3. — A good clearance between hull and blade tip is a necessity for any screw working at moderate thrusts. With reduction of clearance the supply of water to the blades as they pass the hull becomes more restricted, and eventually becomes insufficient. Each blade then breaks up the streams in the effort to supply itself with water. This water is then not thrust back- wards, but whirled round by the blade, which for some portion of its revolution, after passing the hull, has every appearance of " cavitating." It is nearly always possible to tell if this is taking place, if one can get to the inside of the hull plating near where the screw blades pass. The plating is subject to sharp and rapid vibration, and an emphatic crackling noise can be heard as the water is broken up. The higher the tip velocity of a screw the greater become the forces involved and the larger the clearance it requires. For this reason a section of the hull which follows the sweep of the pro- 220 SHIP POEM, RESISTANCE AND SCREW PROPULSION peller tip for any distance, is likely to cause trouble unless the clearance is considerable. In destroyers with clearances of only 10 inches, this phenomena has been obviously present, and it has been observed in larger ships having the same and slightly greater clearances. Turbine-driven screws having 30 inches clearance have not shown this defect although cavitating for other reasons. Cavitation Pressure Limits. — With high revolution, directly driven turbine screws, well immersed, having a clearance of at least 24 inches and good easy buttocks to the hull, a thrust of 13-2 lbs. per square inch can be allowed. With the same con- ditions but deeper immersions 13-5 lbs. may be taken, and reputed pressures of 13-8 lbs. are said to have been realised. With a clearance of 12 inches a pressure of 13 lbs. can be realised under favourable conditions (the screw tips being immersed at least 2 or 3 feet). With a well-balanced quadruple reciprocating engine running at high revolutions, Barnaby found that the pressure limit was given by : — Pressure per square inch of projected area=10-85+|xMbs. where h is the immersion of blade tip in feet. These figures are considerably lower than the preceding, but are based upon trials with the Daring, in which the blade tips were immersed only 1 foot and the hull clearance was about 10 inches. For propellers driven by four-cycle explosion engines, in which the turning moment varies considerably, Barnaby gives a figure of 8 to 9 lbs. per square inch, unless a large number of cylinders is used. CHAPTER XXIV MEASURED MILE TRIALS § 85. — Trials upon the measured mile are intentionally made under the best possible circumstances as regards weather and sea and with a clean bottom. Under such equable conditions the performances of different vessels may be compared with one another and with tank results. Most large vessels are now tested by a series of " progressive trials," i.e., trials made at a series of speeds from the lowest to the maximum possible. A single trial at high speed serves but very little use, except to show that a certain engine power and general efficiency (as may be laid down in terms of power and speed in the ship's contract) have been obtained. Progressive trials, if properly analysed, can be made to give valuable data, not only as regards the ship tested, but such as will be useful in future designs. The real object of such trials is to measure the propulsive efficiency of the vessel, and for this complete records of revolutions of each shaft, ship speed, and indicated or shaft horse-power are required. All the trials should be made at as near as possible to the same displacement, which should be carefully checked by taking the drafts before leaving and on returning to the moorings. In the case of high-powered vessels, if the trials at different speeds are run on the same day after each other, the time between each set should be noted, in order that the displacement may be corrected for the fuel and water consumed during the intervals. Every care is required in carrying out such trials to see that errors shall not creep into the results. With good judgment 222 SHIP FOKM, EESISTANCE AND SCKEW PKOPULSION many of these can be avoided. The more important of them are : (a) Insufficient length of run, after making the turn to go over the course again. The vessel must attain uniform speed and be on its course parallel to the posts before starting on the mile, otherwise the speed will be low. (b) Variation in tide. The tide on the mile is never con- stant either in direction or in speed. It can be eliminated from the measured speed by making an even number of runs on the mile, and using the mean-of-means method of obtaining the average speed. If an odd number of runs is used to deduce the speed the result will be in error, being on the small side if the larger number of runs is made against the tide. (c) When there is any variation of tide at different parts of the measured course, the runs both with and against the tide should be made in the same part of the channel. (d) The steam valves should not be touched once the vessel has settled on her course and is approaching the mile. (e) The rudder should not be put over more than 2 or 3 degrees whilst the ship is approaching or on the mile. Analysis of Data. — The records of speed, revolutions, and power obtained during the trials should all be averaged by the mean-of- means method. Thus, if four runs are made at approximately the same speed the average is obtained as follows : — Measured Speed or Power, etc. First Mean. Second Mean. Third Mean and Average. 0i Xp I H P attitude of the curves of -y- and ' v ' 3 for ship. Both of these increase rapidly in value when cavitation commences. But a rapid increase in their value at high speeds is not in itself a sure indication of cavitation ; it may be due to the ship resistance increasing at an abnormal rate. E H P This would be shown by the "^ curve, which should be either constant in ordinate value or increase gradually with speed. ■p Tip A sudden increase in value of ' T ra denotes that the form is for some reason unsuitable for the speed and the resistance abnormal. BxP I H P In this case the — y- and ' v ' 3 will also increase rapidly, and other means than that indicated above must be adopted to detect E H P the presence of cavitation. But if the ' v ' 3 curve is fairly straight at those speeds at which the revolutions and power show a rapid increase, it is fairly certain that cavitation has developed. A further check can be obtained from the values of (I.H.P.— D.H.P.). When cavitation is present the power estimated from MEASURED MILE TRIALS 227 the revolutions exceeds that actually developed in the screws, and the estimated D.H.P. becomes too great and gives a fictitious, and correspondingly low value of (I.H.P.— D.H.P.) and an equally , , .E.H.P. low value of — 5 — . Such an analysis as the above therefore gives a reliable indica- tion of the worst evil a screw may meet, and also serves to give data as to both the engine and propeller efficiency, and enables these to be partially separated from each other. It also tells the designer the approximate ratio of driving face pitch to analysis pitch which must be used in making estimates from Froude's data for any particular make and style of propeller. Tabulation and Plotting of Trial Results. — Without model experiments analysis of steam trial results cannot be carried very far, and what is usually done can only be regarded as tabulation of results for record and comparison. Some of the curves pre- viously mentioned can, however, be plotted in order to check the jtrp results in themselves. For record purposes values of -ri — W, I.H.P. or preferably /wetted \ / V3 \ should be tabulated, or plotted as ^surface J x \ y J y ordinates to a base of , n . P being the prismatic coefficient VPxL of the form and L the immersed length on which this coefficient has been calculated. This plotting takes account of two important factors in resistance, viz., the actual wetted surface, and the wave- making speed at which the ship may be running. If any humps occur in the plotted curve, they should fall at known values of ■p , viz., 1-34, «95, -76, etc. (see also Table 8). Many factors influence the value of the ordinate, but the above is a ready and approximate method of comparing all types, and a fairly accurate one for comparing a number of forms of any given type. Table 34 gives particulars of a number of ships treated in this way. Q2 228 SHIP FORM, RESISTANCE AND SCREW PROPULSION Example of the Analysis of Steam Trial Results. Displacement on trial . . . 8,500 tons. Engines ..... triple expansion. Propeller particulars : — Diameter . . . .16-0 feet. Driving face pitch . . 20-25 feet uniform. Number of blades . . .3 Developed blade area . . 70 square feet. Clearance of blade tips and hull plating . . . .13 inches. Lines 2, 3, and 4 of the following table give the measured speed, indicated horse-power, and revolutions of engines. The analysis pitch of the propeller=20-25x l-02=20-67 feet. 20-67 The analysis pitch ratio=^r^r=l-29=p. The disc area ratio= .3".,, = -414. w(8 - 0) a The 13 square feet added in the last line is the allowance for the blade outline if produced to the shaft centre (see note (d) § 75). Thrust factor from Fig. 36, i.e., " JS ". . . -106 Hull efficiency assumed -98 £±li JBD 2 = ?^x-106x(16-0) a =469 (see § 75). Thrust horse-power delivered by the screw (line 15 of the table) = 469 X 7 X ( F x ) 3 . The trials show a transmission efficiency of -85 at service speeds, which is fairly good. The thrust block friction, which amounts to about 3 per cent, of the power transmitted, is taken into account in the above efficiency. The further analysis of this is dealt with on page 225. Line 7 gives the power estimated from the tank experiments, and should agree with the figures in line 15, i.e., the powers calculated from the known particulars of the propellers. The discrepancy may be due in part to rough water or to the screw not developing the calculated powers owing to too little clearance, which will also lower the efficiency. The latter assumption gives about the same D.H.P. value, but makes the "H" value lower. It may also be due to the reputed pitch being too high. A slightly lower pitch would improve line 21, but would reduce the engine efficiency shown by line 20. If the figures in line 7 were divided by AjF 8 and plotted to a base of speed with the figures in line 9, the two curvea should MEASURED MILE TRIALS Table 33. 229 Runs. Line Item. 1&2 3&4 5&6 7&8 9&10 2 3 4 5 6 7 Speed in knots .... I.H.P., one shaft Revolutions in hundreds per minute $ (E.H.P.), from tank tests. E with 8 per cent, added for air and shaft tube resistance Line 6 divided by hull efficiency (•98) . . . . . 7 / B E T.H.P 11-0 900 •60 400 432 441 12-5 1,350 •695 625 675 689 14-0 1,940 •795 925 1,000 1,020 150 2,310 •850 1,175 1,270 1,294 15-5 2,640 •89 1,325 1,432 1,461 8 BP 7 1,129 1-15 1-17 1-17 1-187 9 I AfT 8 Line 7 (velocity) 8 ~ Wake factor assumed •00161 •00165 •00169 ■00169 •00169 10 T.H.P ■332 •17 •352 •16 •372 •16 •383 •15 •393 11 w ■14 12 ( jj— -J speed of screw through wake water .... Vi 9-40 10-78 12-07 1304 13-6 13 x=. BP Vi 1-319 1-333 1-357 1-345 1-351 14 Prom Fig. 39 ... . •00125 •00131 •00142 •00138 0014 15 P Efficiency of screw from Kg. 39, cor- responding to above "X" values Correction for disc area from Fig. 37 H 486 770 1,168 1,437 1,651 16 17 — •73 ■002 •73 •002 ■727 •002 •73 •002 •729 •002 18 19 Correct efficiency Power on the shaft at the screw= V •732 •732 •729 •732 •731 n Efficiency of engine, including thrust block and shaft friction. D.H.P. 664 1,052 1,602 1,960 2,259 20 D.H.P. •74 •78 ■825 •85 ■855 / 21 Line 7 divided by line 15 . Propulsive coefficient (line 5 divided by line 3) . T.H.P. •91 ■90 ■88 •91 -89 22 H •444 •463 ■477 •51 •503 show about the same attitude to the base. The same remark applies to line 15, the attitude of which can be altered a little by adjusting the wake at the different speeds, so as to bring the results into better agreement. This example, containing as it does some discrepancies, has been chosen in order to show how to deal with them. 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> ► M ••S'-S s 00 CS CS CO «3 CO OS OS OS r^ ^ a.2 cs CS OS CS OS OS OS OS OS © FH 43 CJ f-H >> S as* CO 00 r- ■* to in 00 00 F** cs CS cs OS OS OS OS OS o © FH FH (» § n fH cs 00 t- OS 1-4 ■>* 00 o © fH o o o o r-i o o £3 "Sa o © o © o IN >o -* 10 00 00 « o" fH* OS os" in" 1— i fH FH 43 .-£, >a t~ fH to « o so ■# F- M to t> fH IN IN CM CN (N 5 • r£ ^* ■* lO M lO 00 fH (3 O IN eb fH l> CO © ti «*H ** c- t- CD CO t~ W" • • " * • "as OS m .& T— 1 eN cs a P< & QQ fH 3 IN a eo s M 03 M EQ w 03 4) 0) CS J2 cs ,a • 2 33 .3 "3 m CS 3 a J is '3 S3 236 SHIP FORM, RESISTANCE AND SCREW PROPULSION Table 36. Correction of (g) Value, passing from a Ship Length of 400 Feet to any other Length. Length of Ship Addition to Length of Ship Deduction from (feet). f°} Value. (feet). C^T) Value. 100 •09 400 150 •066 450 •007 200 •045 500 •013 250 •03 600 •024 300 •018 700 •033 350 •009 800 •041 400 — 900 •048 ~ — ~ -— 1,000 ■054 INDEX. A. Abnormal increase in resistance Adding parallel body between fixed ends Admission of air under hydroplanes to screw. After-body, definition of . and bull efficiency water line in fine vessels Ahlborn's experiments on eddy-making friction . Air blade tests on thickness of blade propeller tests and law of comparison Angle of bottom for hydroplanes and plates diverging waves entrance and diverging waves . for moderate speeds lines in run for no eddy-making shaft webs Applicability of small scale screw experiments Area curve, best for moderate speeds destroyers and racing vessels for low prismatic coefficient . use for stream line plotting . variation in after-body, fine forms of resistance with versme of water channel for low resistance . midship section, and length of run . shape decreased, ends filled out increased, displacement constant increased Augmented surface . Number of section. . 28 . 36 . 56 . 84 1 . 80 . 52 . 17 . 9 . 78 . 69 . 56 . 21 . 21 . 63 . 16 58, 81 68,70 . 32 . 55 30,31 . 4 . 31 . 27 . 29 63, 64 . 42 . 44 . 49 . 45 . 46 . 10 B. Balloon-shaped forms, eddy-making at stern . Barges, shape of . - . in canals ....... Beam and draft increased, sectional area constant . increased and prismatic coefficient decreased at all sections draft decreased, area constant , 16 64 64 47 45 46 48 238 INDEX Beam necessary on motor boats to draft ratio, effect on resistance Bilge keel, head resistance of . resistance trace .... turn and lower level lines rise of floor eddy-making at stream lines at Blades of propellers, developed outline (see 0) number of {see N). Block coefficient, definition Body plan sections, form of Boss allowance, and Froude's disc area ratio Bossings and direction of rotation . Boundaries, effect on stream line motion Bow water line, high-speed vessels . low-speed vessels . variation on fine forms . Breadth of canals and channels, effect on resistance Buttock lines, importance at high speeds Number of section. . 56 30 17 59 17 51 51 16 7 . 1 51, 52 . 75 56, 81 . 6 . 53 . 51 . 31 63, 64 . 55 C. Canals and resistance 64 Cargo-boats, minimum depth of water for low resistance . .62 Cavitation, causes of .84 indicated by trial analysis 85 pressure limits 84 Channel steamers .30, 31, 33 width, depth, and area for low resistance . . . .63 Clearance of tip, and blade outline 77 cavitation 79, 84 hull efficiency 80 Combination of turbine and reciprocating engines . . . .83 wave systems 18 Comparative tests of models 26 Comparison, law of 8 " Constant " notation 2 Constants for skin friction 9 Consumption of main engines 83 Correction of skin friction for length 25 Corresponding speeds 8 Cossack trials 61 Critical speed in shallow water, theoretical 23 actual 60, 61 of ship for economy 28 Cruiser forms 30 stern 32, 33 D. Definitions 1, 65 Depth of channel and resistance 63 water, minimum for low resistance 62 INDEX 239 Destroyers after-body curve of areas . and shallow water .... Developed outline of propeller blades (see 0). Diameter of single screw and bull efficiency versus disc area ratio Dimensions of experiment tanks Direction of rotation and shaft brackets Disc area ratio, effect on propeller efficiency thrust (Froude's) allowance for boss Displacement, importance in racing vessels increased by increasing beam and draft to length ratio in Channel steamers . effect with parallel body Distribution of pressure on propeller blade Diverging waves in shallow water .... velocity of ..... Draft and beam increased at all sections . sectional area constant decreased, beam increased, sectional area constant effect of in channels increased by bodily sinkage . Number of section. . 65 . 34 61, 62 . 80 . 73 . 24 . 81 . 74 73,77 . 75 . 55 . 46 . 33 . 35 . 84 . 21 . 23 . 21 . 46 . 47 . 48 . 63 . 50 E. Economical length of parallel body 35 speeds 28 Eddy-making and shallow water 60 at stern in general 16 behind plates 17 effect on propeller 16 with full stern 42 Efficiency (hull) {see H). model screw experiments on 74 net propulsive 71 of element of propeller 67 ideal propeller 66 main engines 83, 85 propeller with foul surface 75 relative rotative 71 Electrical transformers 83 Energy in a wave 18 Entrance and run filled out, maximum area decreased . . .49 relative length of 43 angle and diverging waves 21 definition of 1 length in racing boats 56 necessary 28 reduction of length with parallel body . . . .37 varying fulness, fine forms 40 full forms 41, 42 240 INDEX Number of section. Errors in speed trials 85 Estimating from model screw data 75 Experiments on friction, Proude's 9 with small screws, applicability 68 F. Fashioning 57 Fine and full ends and total resistance . . . .31, 40, 41, 42 wetted area 31 water line at ends 52, 63 forms and hollow water lines 53, 54 vessels without parallel body 30 Fining ends and filling shoulders 35 Fore and aft position of Bcrew and hull efficiency . . . .80 Fore-body, definition 1 effect on hull efficiency 80 introduction of parallel body in 35 Form, best for moderate speeds 32 Fottinger transmission gear 83 Foul bottom 15 screw blades and efficiency 75 Four and three-bladed propellers, efficiency and thrust . . 73, 74 Frictional resistance 9, 10, 11, 12 and shallow water 60 and wake 79 Friction losses in engines 83, 85 Froude's constants 2 experiments with model screws 73 Full ends versus fine ends with parallel body . . . .29,35 Fulness and eddy -making 16 effect on skin friction 10, 14 G. Gap between screw blades and efficiency 77 Gas engines 83 Geber's experiments on friction 9 Generation of waves 20 Qreyhound experiments 26 Ground swell and resistance of fine vessels 54 H. Havelock and wave resistance .... Head resistance High speeds and hollow lines .... no parallel body .... Hollow and full-ended forms, no parallel body. with parallel body driving face of screw blades lines and snubbing .... versus straight lines, long parallel body no parallel body . short parallel body 22 17 39 31 31 35 78 29 41,42 53,54 . 39 INDEX 241 Number of section. Horizontal shaft webs 58, 81 Hull efficiency, general 71, 79, 80 and shaft webs 81 Humps, effect of shallow and narrow water on .... 63 in resistance curves 28 Hydro-aeroplane floats 56 Hydroplanes 56 I. Ideal propeller Increasing pitch of screw prismatic coefficient by adding parallel body Interference of bow and stern wave systems . . Inward turning propellers and angle of webs . . 66 . 78 34, 36 . 28 58, 81 Kelvin's wave system 20 Large prismatic coefficient, and parallel body bow water line eddy-making with Largest section, position of Law of comparison for screws, tests of . ship skin friction resistance Stanton's Leading edge of propeller blade, setting back Length and speed of waves correction of skin resistance for . effect on resistance humps . increased by addition of parallel body relative, of entrance and run Level lines and body plan sections . Limited fluid, effect on stream line pressures Liners, minimum depth of water for low resistance 35, 42 . 51 . 16 . 43 8, 25, 26 . 9 . 12 . 78 . 18 . 25 . 36 34, 36 . 43 . 61 . 6 . 62 M. Main engines, efficiency and consumption Manoeuvring, effect of eddy-making on . Mathematical wave systems Mean speed on measured mile . Mechanical gearing Metacentre and midship section coefficient Midship section and shallow water resistance area and size of water channel decreased, ends filled out increased, with constant displacement coefficient and long parallel body wetted surface position of ... • shape and area 83 16 20 85 83 44 62 63 49 45 61 47 43 44 S.F. B 242 INDEX Number of section. Model experiments 24 screw experiments 73 Moderate speed vessels and shallow water 62 Motor boats 66 Multiple screws 57, 82 N. Number of blades in propeller, efficiency and thrust . . 73, 74 0. Obliquity of diverging waves 21 Ocean waves 18 Oil engines . 83 Outline of blades 77, 84 Outward turning screws and angle of shaft webs . . . 58, 81 P. Paints, skin resistance of 15 Parallel body, definition 1 adding between fixed ends 36 and bilge turn 51 long, with varying ends 41, 42 methods of introducing 34 short, with varying ends 39, 40 varying, on fixed total length . . . 37, 38 Period and length of waves 18 Pitch, definition of 65 ratio and efficiency 74 effective and thickness of blade 78 high, advantages of 76 nominal and effective 75 Planing 66 Plates, diverging waves created by 21 head resistance of 17 moving on surface of water 21, 56 Position of screw, effect on wake, etc 80 Power absorbed by skin friction 14 Pressure curves, characteristics of 5 for limited fluid 6 various forms 4, 5 distribution on propeller blade 84 limits for cavitation 84 Prismatic coefficient definitions 1 decreased by increase of beam . . .45 effect on economical speed . . . .28 pressure distribution .... 5 skin resistance 10 increase by snubbing 29 INDEX 243 Number of section. Propagation of ocean waves 18 Propeller, effect of eddy-making on 16 experiments, Froude's 73 in open water, general laws 72 Q. Quadruple screws 82 R. Racing of propeller 84 vessels 55 Rake of Borew blades 77 Rankine's augmented surface 10 Reciprocating engine, efficiency and consumption of . . .83 Reduction and reversing gear . . . . . . . .83 Relative rotative efficiency of propeller 71 Revolutions and cavitation 84 speed on trials 85 wake value ........ 80 effect on efficiency 85 Root thickness of blades 78 Rotation of screw race 66 in small and large screws 68 screws, variation during revolution . . . .84 Rudder resistance 59 Run, and entrance filled out, largest section decreased . . .49 definition of 1 length of necessary 28 reduction of length of, due to parallel body . . . .37 relative length of entrance and 43 varying with fixed entrance 40, 42 S. Sadler's models, displacement constant, varying parallel body Screw propeller theory (see T). Section of propeller blade, and efficiency position of maximum thickness Shaft brackets and direction of rotation . tube and fashioning, resistance webs, cross flow at . reduction with straight lines aft Shallow and deep draught vessels in channels draught vessels . water, effect on stream lines resistance due to waves Shape of after-body sections . Skew-back of propeller blades . Skin friction, correction for length resistance in general . 35 . 78 . 78 . 81 . 58 . 17 . 54 . 63 . 48 . 6 60, 61, 62 . 23 . 52 . 77 . 25 . 9 244 INDEX Number of section. Small scale screw experiments, applicability of .... 68 Snubbing, effect on area curve and resistance . . . 29, 30 Sources and sinks 4 Speed and length of waves 18 wake 80 of diverging waves 21 variation of eddy-making with 16 skin resistance with 9 wave-making with 28 Squatting and after water line 62 Stanton's experiments and law 12 Stern, cruiser form of 32 water lines 32 Stream line diagrams 4 flow and wake 79 around racing vessels 56 sensitive in shallow water . ... 62 motion in general 3, 4 lines for fish and ship -shaped forms 7 Suction in front of propeller 66, 84 Surface wetted, calculation for 13 T. Taylor's models, varying parallel body, displacement constant . 35 stream lines 4 Theories of screw propeller 66, 67 Thickness of propeller blade 77, 78 Thrust and number of blades 73 deduction fraction 71 experimental law for 73 of propeller in open water 72 variation with width of blade 77 Tidemans experiments on friction 9 Trailing edge of propeller blade 78 Tramp steamer, fore-body curve of areas 34 Transmission gear 83 Transverse wave resistance 22 Trial data analysis 75, 85 Trials on measured mile, errors, etc. 85 Trochoidal wave 18 Twin versus single screws 67 Types of main engine 83 U. U-shaped sections in fore-body 62 V. V-shaped sections in after-body 62 Variation of rate of rotation of propeller 84 Versine curve of areas 29 INDEX 245 Number of section. Vertical shaft webs 58, 81 Vibration and blade outline 77 small clearances 84 W. Wake, and direction of rotation 81 Calvert's experiments 79 causes of 79 for quadruple screws 82 fraction definition 71 of model and ship, comparison of 70 revolutions and speed 80 Water line and bilge turn 51 coefficient and wetted surface 52 proportions 53 variation in bow and stern 31 Wave-making in racing vessels 55 Wave motion and law of comparison 8 fine vessels 54 resistance in shallow water 60 Waves, theoretical formulae, etc., for ... 18, 19, 20 Web, shaft, reduction with straight lines aft 54 Wetted surface and fine ends 31 increase of beam and draft . . . .46 midship section coefficient . . . .47 calculation 13 filling ends and reducing midship section . . 49 variation with parallel body 35 Wide-bladed propellers and pitch ratio 76 tipped propeller blades (Froude's) 73 Width of channel and resistance 63 ratio of blades, and thrust 77 X and T. X—T and X*— Y curves Y-shaped sections in after-body Yachts, absence of hollow in water line after-body curve of areas . Yarrow's towing experiments . 75 52 54 34 26 SPECIAL INDEX This index gives the numbers of the sections in which reference is made to vessels of definite prismatic coefficient. Prismatic coefficient. Subject. Number of section. •50, -55 •60, -55 ■50, etc •50, etc. •50, etc. •53 •548 •55, etc. •55 to -61 •56 •56 •56, etc. •575 •60 •60 •60 •60 and -64 •60, etc. •60, etc. •60 and -66 •60 to -68 •61 •615 •62 •62 •62 and •65 •65 •652 •67 •68 •68 •68 •67 to •70 ■704 and • ■7, etc. •7, etc. •72, -75, -76 •74 to -78 •74 •75, -76 •80 •80, etc. •82 •828 •828 •81 to -84 •94 •68 •72 756 Pressure curves for forms . Fulness and skin friction . Snubbing Reducing midship section coefficient Hollow flues .... Economical speed Adding parallel body . Froude's methodical series . Increasing all cross-sections Constant area, varying beam and draft Increasing beam, decreasing draft Shallow water effect . Hollow versus straight lines Eeducing midship section coefficient Liner and width of channel Torpedo-boat and width of channel Variation of water plane Angle of obliquity of waves Introducing parallel body . Fulness and skin friction . Shallow water .... Hollow versus straight lines Froude's methodical series . Relative length of entrance and run Shape of after-body sections Introducing parallel body . Pressure curves for stream form Adding parallel body Rudder resistance Variation of after-body Best length of parallel body Increasing all cross-sections Constant area, increasing beam and draft Varying fulness of entrance and run Increasing beam, fining ends Relative length of entrance and run Reducing midship section coefficient Bow water line for low speed Fulness and skin friction . Varying fulness of entrance and run Best curve of areas Pressure curves for stream forms Best curve of areas Bow water line .... Fulness and skin friction . Relative length of entrance and run Hollow lines in stern . Varying fulness of entrance and run Barge 5 10 29 49 54 28 36 30, 48 46 47 48 62 54 49 63 63 31, 53 21 34 10 62 54 30, 48 43 52 37 5 36 59 35 35 46 47 40 45 43 49 51 10 41 35 5 35 51 10 43 43 42 64 BBADBUBY, AGNEW, & CO. LD., PRINTERS, LONDON AND TONBR1DOE. D. VAN NOSTRAND COMPANY 25 PARK PLAGE New York SHORT=TITLE CATALOG OF T^txklk^&ms m& ^wquxxt&twm OF SCIENTIFIC AND ENGINEERING BOOKS This list includes the technical publications of the following English publishers: SCOTT, GREENWOOD & CO. CONSTABLE & COMPANY, Ltd. TECHNICAL PUBLISHING CO. ELECTRICIAN PRINTING & PUBLISHING CO. for whom D. Van Nostrand Company are American agents. AufiUST, 1914 5H0RT=TITLE CATALOG OF THE Publications and Importations OF D. VAN NOSTRAND COMPANY 25 PARK PLACE, N. Y. Prices marked buith an asterisk (*) are JVET. All bindings are in cloth unless othertuise noted. Abbott, A. V. 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