BOUGHT WITH THE INCOME FROM THE SAGE ENDOWMENT FUND THE GIFT OF Hctirg W. Sage 1891 AU.'^A/.:^'.. AoM Cornell University Library VM755 .B97 The Resistance and ttie proportions of sc olln 3 1924 030 903 417 Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924030903417 THE RESISTANCE AND THE PROPORTIONS OP SCREW PROPELLERS. THE KESISTANCE AND THE PEOPOETIONS OF SCEEW PEOPELLERS. BY WILLIAM BURY, CONSULTING MARINE KNGINEEE ; AUTHOK OF " THE POWEK AND SPEED OF STEAM VESSELS.' LONDON: E. & F. N. SPON, 16, CHAEING CROSS. NEW YOEK : 35, MUERAY STEEET. 1883. The right of Publication and of Translation u reserved. INTEODUCTION, O^KO About four years ago the writer published a treatise on the Power and Speed of Steam Vessels, showing the method adopted for calculating the indicated horse power required for propelling vessels of different types at any desired speed; by means of Tables and Rules he had, some years previously, prepared for his own use. The reason for preparing those Tables and Rules was, that in consequence of the great variation in the types of both vessels and engines which at that time had recently taken place, the formula that were sufficient for calculating the resistance of screw pro- pellers when applied to one type of vessel, and driven by one type of engines, had practically become obsolete ; or required to be supplemented by formula having a wider range, that should embrace the various types of both vessels and engines. It will be observed, therefore, that in the treatise on the Power and Speed of Steam Vessels, provision is made for calculat- ing the indicated horse-power required for vessels of different types, when propelled by engines also of different types. The further object the writer then had in view, in preparing those Tables and Rules, was to facilitate as far as practicable the accurate calculation of the power required by screw propellers when applied to vessels of different proportions ; by ascertaining VI INTRODUCTION. the variation produced in the ratios of the several proportions of a vessel, due to variations in the proportions of different vessels ; and thereby to obtain a proportional quantity for each vessel, to which the resistance of the vessel should be correctly referrible ; this proportional of vessel being so calculated, that it is considered to afford a relatively true measure of the amount of work to be done in propelling different vessels at any sjDeed ; the proportion- ate resistance of each vessel varying with each difference in the proportions of the vessels. By means of this proportional of vessel, the relative resistance of screw propellers of different proportions when applied to the same or different vessels can be correctly compared ; and the difference in their efficiency, or the relative amount of power re- quired to propel different vessels of any proportions at any speed, when fitted with screw propellers of whatever proportions, can be clearly ascertained. It will be found by the formulae given in this treatise that the efficiency of screw propellers depends principally on the amount of surface adopted for the blades, and that the main problem remaining to be solved by experience is the minimum amount of surface that should be adopted, due regard being had to the pro- portion of the slip of the screw ; it will also be made evident by the examples given, that in cases where the amount of surface in the blades is even twice the average quantity, the propelling power of the screw does not increase in any similar proportion ; for the reduction in the proportion of the slip of the screw (which gives the increase in the amount of work done) is infinitesimal, as com- pared with the increased amount of power required ; hence the necessity for determining, as accurately as possible, the minimum INTEODUGTION. Vll amount of surface that should be adopted for the blades of screw propellers. As the minimum amount of effective horse-power required for the efficient propulsion of vessels — the proportion of the effective to the indicated horse-power — also the proportion of the slip of the screw — all of which form important factors in the formulae given for calculating the resistance of screw propellers, require to be more correctly determined than at present by further experi- ence ; it is considered that these formulae will materially assist in elucidating the necessary information on these points, whereby the efficiency of screw propellers may be increased ; for it is confidently claimed that these formulas affi)rd the means of very approximately calculating the power required by screw propellers of whatever proportions ; and in the Tables given for the pro- portions will be found the best proportions adopted at the present time. THE RESISTANCE AND THE PROPORTIONS SCKEW PEOPELLEKS. oK«o The problems involved in calculating the resistance of screw propellers, and in the right determination of the best proportions thereof, are very interesting, although complex ; they are also of the utmost importance, as on the correct solution of these problems depends the efficiency of the screw propeller as the propelling medium for vessels, and on the efficiency depends the economy of the results obtained. The problems as stated being complex, it is evident that all the conditions involved in their solution should be clearly com- prehended, and that they should be embodied in any formula for making the necessary calculations to ascertain the resistance of screw propellers, in order to determine on the suitability of a pro- posed screw propeller to any proposed vessel — or in any formula for determining the best proportions of screw propellers ; it is likewise essential that the formula for resistance should show results corresponding with the results obtained in practice, with screw propellers of whatever proportions, when applied to vessels of any type. ^ RESISTANCE AND PROPORTIONS OP SCREW PROPELLERS. The writer having devoted considerable attention to the solution of these problems, and having prepared the requisite formulae for calculating the resistance of screw propellers — also for determining the best proportions of screw propellers — as applied to vessels of different types ; they are now submitted to the consideration of those who may be interested in the subject, in the hoj)e that they will be received as an endeavour to attain the desired end of providing the means by which theory and practice may, with reference to screw propellers, go hand in hand together : for by determining theoretically the results that may be expected from screw propellers of any proportions, it prevents disappointment in the results obtained practically on trial ; and avoids the delay and expense consequent on having to provide other screw propellers of different proportions. Moreover, as it may safely be affirmed that without the correc- tive influence of theory, practice may not be guided in the right path ; so on the other hand, theory unless corroborated by practice is valueless : this treatise will therefore contain various examples in practice which embrace a wide difference in the pro- portions of the screw propellers, and which will doubtless be deemed sufficient to establish the practical accuracy of the formulae herein given for calculating the resistance of screw propellers, whatever their proportions ; whether applied to the same or to different vessels. The object of the present treatise will consequently be to explain in the first instance the formula by which the resistance of screw propellers may be very approximately calculated, with the view of comparing the calculated power required by the screw propeller with the calculated power required by the vessel, CONDITIONS. <> in order to decide on the suitability of the screw to the vessel : and subsequently to explain the formuloe adopted for determining the proportions of screw propellers : as it is considered that the reasons for adopting these proportions will be better appieciated after the formulas for calculating the resistance have bten fully discussed. In preparing the formulee for calculating the resistance of screw propellers, it was essential to remember that there are three main conditions involved in the correct solution of any problem in connection with marine propulsion ; that each condition requires to be treated separately ; and finally, that all the three conditions require to be compared in conjunction. The three conditions are as follows : — Condition 1. — That the effective horse-power required to over- come the resistance of the vessel at the desired speed (as a measure of the amount of work to be done) will vary with the type of the vessel ; and that the effective horse-power required should be found as accurately as possible by calculation ; and should be a minimum in accordance with the best examples in practice. Condition 2. — That the effective horse-power developed by the engines at the required number of revolutions per minute for the desired speed of vessel should by calculation be found equal to the minimum effective horse-power required for the vessel. Condition 3. — That the effective horse-power required to overcome the resistance of the propelling medium at the necessary velocity for the desired speed of vessel should by calculation be found equal to the minimum effective horse-power required for the vessel, n 2 4 RESISTANCE AND TEOPORTIONS OF SCREW PROPELLERS. The above three conditions, as defined, prove that each one of them is relatively equal to the other, which must of necessity be the case if the effective horse-power is to be equal to the amount of work to be done, neither more nor less ; which is the result which should be attained in all instances of the application of power : and it is obvious that in the propulsion of vessels — the resistance of the vessel being as stated above the measure of the amount of work to be done — it is also the measure of the effective horse-power that should be developed by the engines to overcome the resistance of the screw propeller at the required velocity. It is therefore manifestly correct that in all cases of the appli- cation of power the amount of work to be done should be ascertained as accurately as possible, to insure that the means adopted shall be suited to the desired end, without on the one hand entailing a waste of power by reason of the means adopted being in excess of the requirements ; or, on the other hand, failing to realise the desired results by reason of the insufficiency of the means adopted. In the application of power to the propulsion of vessels, it is evident that unless the effective horse-power necessary to propel the vessel at the desired speed be first calculated and determined, so that the results attained shall be in accordance with the best examples, it will be impossible, from want of the means of com- parison, to conclude, even after calculating the resistance of the screw propeller, whether the proportions of the screw propeller are those best suited to fulfil the requirements of the greatest efiSciency and consequent economy : as these requirements are best fulfilled when the power required for the vessel does not exceed the minimum power required by the best examples. EFFECTIVE HORSE-POWER FOR VESSEL. .Consequently, by calculating the minimum effective horse- power that should be required for the vessel, also the effective horse-power required by the screw propeller, a very necessary check is afforded on the proportions proposed for any screw propeller ; for should the calculated power required for the screw propeller, on comparison with the calculated power required for the vessel, be found to be greater or less, the necessity for a corre- sponding variation being made in the proposed proportions of a screw propeller will at once become apparent. Condition 1 . — The Effective Horse-power required for the Vessel. The importance of ascertaining as accurately as possible the effective horse-power that should be required to propel any vessel at the desired speed being allowed, the method of calculating the same will be explained. To accomplish this as accurately as possible was one object the writer had in view in preparing the Tables given in the treatise on the ' Power and Speed of Steam Vessels ' ; and by means of Tables 1, 2, 3, 4, 5, which are given in this treatise, a pro- portional quantity for each vessel can be readily obtained, to which the proportionate resistance of the vessel shall be correctly referrible ; the proportionate resistance of each vessel varying with each difference in the proportions of the vessels. This proportional of vessel is a quantity that should therefore combine the variations in the different ratios due to the variations that occur in the several proportions of different vessels ; and this proportional of vessel, for a vessel of any type, will be found thus : — Find the proportion of displacement of the vessel to the O.M. tonnage, by dividing the displacement by the O.M, tonnage ; 6 EESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. then find the proportion of draught to beam by dividing the draught by the beam. With these two proportions refer to Table 1, and decide thereby on the comparative fulness of the lines of the vessel. Having decided on the fulness of the lines of the vessel, multiply the maximum area in square feet of the midship section of the vessel by the ratio of displacement given in Table 2, to allow for the difference in the fulness of the fore and aft lines of the vessel — multiply this product by the ratio of power required for the draught of water given in TaBle 3 ; multiply this product by the ratio given in Table 4 for the vv^et surface due to the pro- ]3ortion of length to beam of vessel ; and this quantity will be the proportional of vessel required. Note. — A further modification of this proportional should be made when the power required per 0. M. tonnage and per A. M. S. has been calculated according to the treatise on the power and speed of vessels, and found not to be equal : then the proportional found as above should be multiplied by the mean of the ratios of the power per 0. M. tonnage and per A. M. S., taking the power per A. M. S. as unity. To obtain this modification, reference must be made to that treatise. When the vessel is tried at a less draught of water than the maximum, the corresponding proportional of vessel will be found by multiplying the above proportional for the maximum draught of water by the diminished area of the midship section on trial, and dividing the product by the maximum area of the midship section ; or in other words, the proportional of vessel at the diminished draught of water will be directly in proportion to the diminished area of the midship section. EFFECTIVE HORSE-POWEE FOR VESSEL. 7 The minimum effective horse-power required for any vessel should then be determined in relation to this proportional of vesselj in accordance with the results obtained from the best examples in practice. In the treatise on the ' Power and Speed of Steam Vessels,' the power required for the vessel (shown by the Tables) is an average of the best examples that were then submitted to calcula- tion, and the effective horse-power (derived from the indicated horse-power), as calculated by those Tables for any type of engines, will be found to amount to one half the proportional of any vessel, at a speed of eight knots per hour ; and for other speeds, the effective horse-power required for any proportional of vessel will vary in proportion to the ratios of power given in Table 5. The effective horse-power thus found for the vessel being the average of the best of numerous examples then analysed by the writer, it is clear that the power mentioned above should be taken as a maximum, and consequently should never be exceeded. In the present treatise examples are given of vessels fitted with screw propellers of very different proportions of surface in the blades, compared with the proportional of vessel and the desired speed per hour ; and it will be found that in cases where a large amount of surface has been adopted for the blades the power required for the vessel is in excess of the above average : and that in other cases, where the surface of the blades is small the power required for the vessels is less than the above averao-e. As the amount of power required for the vessel is found to vary very materially with the proportion of surface adopted for the blades of the screw propeller, it becomes necessary so to 8 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. proportion the surface of the blades, that the effective horse-power required shall not exceed that shown to be sufficient by the best examples in practice : for, although the formulae herein given for calculating the resistance of screw propellers will determine most approximately the power required by any screw propeller, whether the power required for the vessel be in excess, or below the average, they do not determine the amount of power that should be required for the vessel, except by inference. Inferentially, however, it may be concluded by means of the best examples in practice — showing the smallest amount of power required in relation to the vessel, at the desired speed — that in other examples, where a greater amount of power is required in relation to the vessel, the amount of surface in the blades of the screw is in excess : this will be made evident when the relative resistance of screw propellers is considered. The proportions given in this treatise for the surface of the blades of screw propellers are therefore intended to produce results agreeing with the best practical examples; they will consequently require the smallest amount of effective horse- power to propel the vessel at the desired speed ; and the amount of effective horse-power that should be required for the vessel, with these proportions of surface — when the effective horse-power of the engines is calculated according to the proportions given in Table 6 — may be readily ascertained for any speed of vessel, as will be fully explained hereafter, when the proportions of screw propellers are under consideration. Note. — Examples being given of some vessels requiring a greater, and of others a less amount of effective horse-power in relation to the proportional of vessel than that given above — EFFECTIVE HOESE-POWER OF ENGINES. 9 viz. one half the proportional of vessel at a speed of eight knots per hour, and varying for other speeds in proportion to the ratios of power given in Table 5 — it will be convenient in this treatise to refer to this amount of power as the normal effective horse- power; it being also the maximum effective horse-power that should never be exceeded. Condition 2. — The Effective Horse-power of the Engines. It is the custom of engineers to refer to the indicated horse- power in all cases, when calculating the power for steam vessels ; but, owing to the important difference between the proportion of the effective horse-power and the indicated horse-power in different types of engines, the indicated horse-power cannot be accepted as a true measure of the amount of work to be done unless regard be had to the type of engines fitted in the vessel. This subject was thus briefly referred to in the treatise on the ' Power and Speed of Steam Vessels ' : — " As the indicated horse-power obtained from the engines on board a vessel is generally taken as the measure of the resistance of the vessel, and as the power obtained is always stated to be the total indicated horse-power calculated from the diagrams taken off the engines ; it is essential to bear in mind that as different types of engines are of varying efficiency, through greater friction of the parts and the power absorbed in working the various pumps, &c., the type of engine in each case must be considered, in deciding on the proportion of indicated horse-power required for the vessel." It will also be observed in that treatise, that provision is made in Tables 6 and 9 for calculating the proportion of indi- 10 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. cated horse-power required for O.M. tonnage, and per area of midship section, for four various types of engines ; by naeans of which, allowance is made for the average diiference in the pro- portion of the effective horse-power to the indicated horse-power in these various types, which include all the types of the present time. In the present treatise it is necessary that the subject should be submitted to closer investigation, the object in view being to arrive at conclusions as accurate as possible respecting the varying proportions of the effective to the indicated horse-power in dif- ferent types of engines, for the purpose not only of showing that allowance must necessarily be made for this variation in cal- culating the indicated horse-power required for the vessel; but for ascertaining as clearly as possible that the effective horse- power developed by the engines shall be equal to the minimum effective horse-power required for the vessel : also that the effective pounds pressure on the pistons of the engines, when driving the screw propeller, may be compared with the calculated resistance in pounds pressure of the screw propeller at the required velocity ; for, by adopting this method of comparison in cases of actual practice, a good test is afforded of the accuracy of the formulae herein given for calculating the resistance of screw propellers, it being clear that the effective horse-power of the engines must always be balanced by the resistance of the screw propeller. The question of the correct proportion of the effective horse- power as compared with the indicated horse-power, according to the type of engines, has never yet been authoritatively deter- mined ; therefore, in these investigations the writer has relied on EFFECTIVE HOESE-POWEE OP ENGINES. 11 his own experience; and has prepared Table 6, showing the proportions adopted for various types of engines, after very careful consideration of the subject, and after submitting the differeM proportions to the test of comparing the calculated results obtained by these proportions with the results realised in practice. Table 6 is, however, not submitted as being final on the subject, although calculations made with these proportions agree very approximately with the results obtained in practice ; for it may well be that different engineers will entertain different views on the subject of these proportions : consequently, it is desirable to point out that the only modification that will be necessary in the following formulee, to meet any variation deemed advisable in the proportions given in Table 6, will be readily made by making a proportionate alteration in the con- stant required to be employed in the formulae. This constant is derived from Table 9. The proportions given in Table 6 show the great difference existing in the proportions of the effective horse-power as com- pared with the indicated horse-power, according to the various types of engines ; and thereby the necessity is proved of adopting the effective horse-power in all cases where a true measure is required of the amount of work done : and in this treatise, where the effective horse-power is referred to, it must be understood that it is intended to be obtained in accordance with the propor- tions given in Table 6. By means of Table 6, or any proposed variations in the same, it will be easy to eliminate the proportion of the effective horse-power according to the type of engines from any calcula- tions made for ascertaining the indicated horse-power required ; 12 RESISTANCE AND PROPORTIONS OP SCREW PROPELLERS. or from the indicated horse-power calculated from the diagrams taken ofif the engines, with the view of determining the effective horse-power developed by the engines as a relatively true measure of the amount of work done ; the effective horse-power being found by multiplying the indicated horse-power by the proportion given in Table 6, according to the type of engines and the maximum pressure of steam used. It will thus be seen that the indicated horse-power, as at present obtained, serves the very useful purpose of forming the basis from which the effective horse-power is derived ; and it should likewise be noted that the amount of effective horse-power required to do the same amount of work is the same with any type of engines, whatever may be the difference in the amount of the indicated horse-power. The proportion of effective to indicated horse-power will doubtless vary slightly with any difference in the size of the engines, but very careful experiments would be needed to deter- mine this point with any accuracy; it is, however, considered not to be of great importance in a practical sense, but attention is directed to this variation as a possible cause of a slight dis- crepancy in the calculated results when compared with the results in practice ; and allowance can be made for this, as experience may suggest, if found of sufficient importance. Condition 3. — The Effective Horse-power Required for Screw Propellers. The effective horse-power required to overcome the resistance of screw propellers at the necessary velocity for the desired speed of vessel should be equal to the minimum effective horse-power EFFECTIVE HORSE-POWER REQUIRED. 1 3 that should be required for the vessel, in accordance with the best examples in practice : consequently, the first problem that has to be solved in connection with screw propellers consists in finding by calculation, as approximately as possible, the resistance of screw propellers — due to their proportions, and the velocity at which they have to be driven, when propelling a vessel at the desired speed per hour. In studying the resistance of screw propellers, the subject may be advantageously divided under two heads — viz. the Positive Resistance and the Relative Resistance. 1. The Positive Resistance of screw propellers is intended to show the resistance in pounds pressure of any screw propeller, due to the proportions of the screw, the velocity of the screw, and the consequent force of impact of the blades with the water, when applied to a vessel of any proportions ; to enable the resist- ance thus calculated to be compared with the effective pounds pressure on the pistons of the engines, as these two quantities should be equal : also to ascertain that the amount of effective horse-power required for the screw shall not exceed the minimum effective horse-power that should be required for the vessel. 2. The Relative Resistance of screw propellers is intended to show the relative amount of effective horse-power required by different screw propellers of whatever proportions, when travelling at any velocity, whether applied to the same or to different vessels, to enable their comparative efficiency to be clearly deter- mined, and thereby to decide on the correct proportions that should be adopted for any screw propeller. 14 resistance and proportions op screw propellers. 1. — The Positive Eesistance of Screw Propellers. Previous to proceeding to discuss in detail the various points comprised in the subject of the resistance of, or the power required by, screw propellers, it is desirable to explain the basis on which the whole subject has been treated. It may therefore be briefly stated that the resistance of screw propellers has, in this treatise, been taken to be in proportion to the force of impact of the blades with the water, due to the area of the vertical surface of the blades transversely, and the circum- ferential velocity with which the blades strike the water : modified by the different proportions of the screws ; modified further in relation to the proportions of the vessel to which the screw propeller is applied ; also to the forward motion of the vessel through the water. It will thus be observed that the resistance of screw pro- pellers is referred entirely to the transverse resistance of the blades of the screw whilst rotating in a direction transversely, or at right angles to the direction of the progress of the vessel through the water : the reason for this may be explained thus : That the screw propeller is carried by the vessel which is in motion, and that when the slip of the screw is nil, the direct resistance of the screw fore and aft may also be said to be nil ; it is consequently manifest that the resistance of the screw is pro- duced by the transverse rotation of the blades through the water, modified by the angular velocity of the blades due to the propor- tion of the j^itch to the diameter of the screw, modified also by the other proportions of the screw, and the proportions of the vessel. Having thus explained the view taken of the resistance of POSITIVE RESISTANCE. 15 screw propellers as a whole, it becomes necessary to state in detail the various points which are considered to constitute the positive resistance of screw propellers. The positive resistance of screw propellers will be found to vary in relation to the following proportions. 1. The vertical transverse surface of the blades of the screw. 2. The square of the circumferential velocity in feet per second at the mean velocity diameter. 3. The pressure on the vertical transverse surface due to the force of impact of the blades with the water. 4. The proportions of the screw propeller, due to variations in the diameter, the pitch, the slip, the surface and the form of the blades, and the size of the boss — modified in relation to the proportions of the vessel ; taking also into consideration that the vessel is in motion. This may be termed the coefficient of resistance. 5. The circumferential distance travelled by the screw at the mean velocity diameter per revolution, divided by the distance travelled by the piston per revolution of the engines. This proportion may be termed the leverage, or the multiple of stroke. The following explanations are offered with reference to the above proportions. Proportion 1. — By the vertical surface of the blades trans- versely is meant the surface contained within vertical lines drawn from the edges of the blades, at right angles to the axis of the screw ; or the surface as seen at the side view of the screw. Proportion 2. — The circumferential velocity is measured at a diameter of the screw, which may be termed the mean velocity 16 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. diameter, being the mean of the diameter at the centre of the length of the blades, and the diameter at the centre of pressure of the vertical transverse surface. Proportion 3. — The pressure on the vertical transverse surface of the blades is due to the force of impact of the blades of the screw propeller with the water ; and the view taken is, that the resistance offered by the surface of the blades, when the screw is rotating at the required velocity to propel the vessel at a given speed, must be equal in pounds pressure to the effective pounds pressure on the pistons of the engines. For it is clear that the resistance of the screw must always be balanced by the effective power of the engines. The force of impact of the blades of the screw propeller with the water has therefore to be calculated on the well-known law of the resistance to bodies passing through water — i, e. it will be in proportion to the weight of the height of a column of water equal to the distance a body must fall to acquire the circumferential velocity in feet per second at the mean velocity diameter of the screw propeller. The law of falling bodies shows that a body will fall through a distance of 16 '08 feet per second, and will have acquired a velocity of 32*16 feet per second ; also that the distance fallen by a body will be in proportion to the square of the velocity acquired : consequently the proportion will stand thus : — 32-16' : 16-08 :: velocity : height of fall. , <. 1 16-08 X velocity' , . , „ „ ,, or by tormula W^T¥ ~ height of fall. By means of this formula the impact of the vertical trans- verse surface of the blades will be readily calculated, but POSITIVE RESISTANCE. 17 important modifications will be necessary in the amount of the impact thus found, due to variations in the proportions of screw- propellers, in the proportions of the vessels to which the screws are to be applied, also to the forward motion of the vessel : these modifications will be discussed under Proportion 4 Note. — The amount of impact calculated for the blades by means of the above formula would be correct, supposing the blades of the screw to have no angle, and that the vessel was not in motion ; this amount may therefore for reference be termed the maximum impact : and the amount of impact, when modified as stated above, may be termed the true impact. Proportion 4. — This is termed the coefficient of resistance, and is of a very comprehensive character : it therefore forms a very important factor in calculating the positive resistance of screw propellers ; including as it does, all the modifications stated to be necessary in the calculated force of impact of the blades with the water, when the impact has been calculated as explained in Proportion 3. These modifications are rendered necessary, by variations in the proportions of the screw propellers, by variations in the proportions of the vessels to which the screws are to be applied, also by the forward motion of the vessels: and the method of deciding on the requisite modifications to meet these several variations has been arrived at by means of calculations very carefully made, of numerous examples of screw propellers of very different proportions, applied to vessels likewise of very different proportions ; and with vessels propelled at very different speeds per hour. In deciding on the requisite modifications due to variations 18 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. in the proportions of screw propellers, it will be seen, on consideration of the subject, that the effect produced by any variation in the proportion of the extreme diameter of the screw to the mean pitch, will be also to vary the proportion of the slip of the screw; also to vary the diameter of mean velocity, consequently to vary the proportion of the pitch to the circum- fereotial distance travelled at the diameter of mean velocity ; also to vary the proportion of the vertical transverse surface of the blades that will be required. These variations in the different proportions of a screw propeller will produce a corresponding variation in the amount of resistance due to each ; therefore each variation in the pro- portions of the screw must be taken into account in the calculations necessary to ascertain the positive resistance of any screw propeller : and the variations occurring in screw propellers that have to be taken into account in the calculations to obtain the coefficient of resistance are the following. 1. Proportion of mean pitch to extreme diameter. 2. „ of slip. 3. „ of mean pitch to circumference of mean velocity diameter. 4. Area of the vertical transverse surface of the blades. 5. The form of the blades and the size of the boss. Factors 1, 2, and 3 require to be treated together to obtain a quantity which is termed the proportional of pitch. Factor 4 requires to be treated with the requisite modification due to variations in the proportions of the vessel, to obtain a quantity Avhich is termed the proportional of surface. Factor 5 requires to be treated with the requisite modifica- POSITIVE RESISTANCE. 19 tion due to the forward motion of the vessel, to obtain a quantity which is termed the constant. It will be observed that the proportional of pitch includes the variations in the diameter, the pitch, and the slip ; as experience shows that the proportion of slip depends greatly on the pro- portion of the pitch to the diameter of the screw, which will be seen on reference to Table 10, where the decimal quantities of the ratios therein given represent the proportion of slip that may be expected with screw propellers of different proportions of pitch to diameter, and with different proportions of surface in the blades. The column in Table 10 showing the propor- tion of surface = 1 ' represents the proportion of surface that would require the normal amount of effective horse-power (see Note, page 8), when the proportion of slip agrees with the proportions given in Table 10. To obtain the proportional of pitch, the following calculations are necessary. When the pitch is equal to or less than the diameter, divide the mean pitch by the extreme diameter ; or by formula, -zr-. -— = E P. •^ diameter When the pitch exceeds the diameter, and when the slip agrees with the proportions given by the decimal quantities in Table 10, divide the pitch by the diameter, and take the cube root of the quotient ; or by formula, \/ ^. :— = EP'- '' V diameter When the proportion of slip differs from the proportions given by the decimal quantities in Table 10, deduct the actual pro- 3 20 RESISTANCE AND PROPORTIONS OP SCREW PROPELLERS. portion of slip from the ratio in Table 10, and square the remainder to obtain the ratio of a multiplier which must be multiplied into R P or E P' ; and the product will be R P or R P' corrected for slip. To allow for the variation in the proportion of the mean pitch to the circumference of the mean velocity diameter, divide the pitch by this circumference ; or by formula, —. — ^—5 = E C ; •^ circumierence then multiply R P or R P' by R 0, and the product will be the proportional of pitch. Note.^ — R P or R P' must if necessary be corrected for slip. The proportional of surface requires to be obtained to allow for the variations in the proportion of the vertical transverse surface of the blades, also to allow for the variations in the pro- portions of the vessels •, for experience shows that the resistance of screw propellers is very materially affected by the proportion adopted for the vertical transverse surface of the blades, in relation to the proportions of the vessel to which the screw propeller is to be applied. To allow for the variations in the different proportions of the vessel, it is necessary to obtain the proportional of vessel by the method explained at page 5 ; and it will then be found that the proportion of the positive resistance of screw propellers, due to the proportion of the vertical transverse surface of the blades in square feet, in relation to the proportional of vessel, can be calculated thus : Divide the proportional of vessel by the vertical transverse surface of the blades in square feet, and take the cube root of the POSITIVE EESISTANCE. 21 quotient ; multiply this quantity by the vertical transverse surface of the blades in square feet, and the product will be the proportionate resistance of the screw ; or by formula, \J - — VT"S X V T S = proportionate resistance of screw. But for the purpose of obtaining the proportional of surface required for the co-efficient of resistance, the necessary calculation will be as follows : — Divide the proportional of vessel by the vertical transverse surface of the blades in square feet, and take the cube root of the quotient ; this quantity will be the proportional of surface ; or by formula, ^ Proportional ^of v jg ^ ^,,^^,,^^^^1 ^f ,^^^,,_ The constant required to allow for the forward motion of the vessel is found to vary inversely in proportion to the square of (the mean velocity diameter of the screw -4- the extreme diameter), as shown in Table 9 ; and as one eifect produced by different forms of blades, also by different proportions of size of the boss, consists in altering the proportion of the mean velocity diameter to the extreme diameter of the screw, it is evident that this variation, caused by the form of the blades and the size of the boss, will be provided for in this constant. Table 9 has been prepared to show the constants required for screw propellers of different diameters having the same form of blade, which in Table 9 is taken to be the form shown in the drawing given of the screw of Example A 3 (Fig. 2), and having the boss of a normal size, or about one-seventh of the extreme diameter of the screw. 22 EBSISTANCE AND PEOPOETIONS OF SCREW PROPELLERS. But witli different forms of blades and size of boss, the proportion of the mean velocity diameter to the extreme diameter will vary as already stated ; and the constant required to provide for this variation will be found in Table 9, opposite the quotient obtained by dividing the velocity diameter by the extreme diameter. The mean velocity diameter must in all cases be found very exactly from the drawing of the screw jDropeller. Should the quotient obtained by dividing the velocity diameter by the extreme diameter not be found in Table 9, the correct constant can be easily found by the following proportion : — (velocity diameterV —, ^-T. — ) : -230 :: -6' : constant, extreme diameter/ Having thus obtained the proportional of pitch, the pro- portional of surface, and the constant, Let P P = proportional of pitch. „ P S = proportional of surface. „ C = constant. Then PPxPSxC = coefficient of resistance. Proportion 5 — requires no explanation. Keferring to the foregoing explanations given of the five pro- portions on which the positive resistance of screw propellers is said to depend, the reasoning on which the formula for calcu- lating the positive resistance have been framed may be summed up as follows : — The positive resistance of screw propellers is considered to be in proportion to the area of the vertical transverse surface of the POSITIVE RESISTANCE. 23 blades, to tlie pressure on that surface due to the force of impact of the blades with the water, consequent on the circumferential velocity at the mean velocity diameter, modified by the co-efficient of resistance, to allow for the difference in the proportions of different screw propellers, and the forward motion of the vessel through the water ; also to the proportion of the multiple of stroke ; or the proportion of the circumference of the mean velocity diameter compared with the travel of the piston per revolution of the engines. The following are the data, in a tabulated form, that are required of the vessel, the engines and the screw propeller, for use in the formula for calculating the positive resistance of screw propellers : — 1. Data required of the vessel, for obtaining the proportional of vessel, that the indicated and the effective horse-power required for the vessel, at the desired speed per hour, may be calculated and compared with the calculated resistance of the screw propeller ; Length between perpendiculars. Beam extreme. Draught of water — mean maximum — or mean on trial. Displacement — maximum — or on trial. Area of midship section — maximum — or on trial. Speed per hour — desired — or on trial. 2. Data required of the engines, for calculating the indicated and the effective horse-power developed by the engines at the required velocity : Type of the engines. Number of cylinders. Diameter of the cylinders — respectively when compound. 24 EESISTANCE AND PROPORTIONS OP SCREW PROPELLERS. Length of stroke. Pressure of steam, maxiraum. Proportion of stroke at which steam is cut off. Revolutions per minute — desired — or on trial. Note. — When the vessel is fitted with twin screws, the number of the cylinders, and their respective diameters when compound, as applied to each screw, should be given. 3. Data required of the screw propeller, for calculating the positive resistance thereof, that the same may be compared with the calculated power that should be required for the vessel : Number of screw propellers. Number of blades in each screw propeller. Diameter, extreme. Pitch, mean. Proportion of shp per cent — on trial — or to be expected. Area of the vertical transverse surface in the blades of each screw. ^sfoTE. — For the purpose of ascertaining correctly the positive resistance of screw propellers, or for the accurate comparison of the relative resistance of screw propellers of different proportions, it is essential that the measurement of the surface of the blades should be taken very correctly ; and that it should only include the surface contained in the straight part of the length of the blades : the surface of the curve at the boss not being considered effective. See dotted lines shown at top of curve in Drawing. From the drawing of the screw propeller, showing the exact form of the blades, it will be necessary to obtain the following particulars : — The diameter of the centre of the length of the blades. POSITIVE EESISTANCE. 25 The diameter of the centre of pressure of the vertical trans- verse surface of the blades. Note. — The mean of these two diameters will be the mean velocity diameter of the blades of the screw. With the foregoing data determined, the following explana- tion is offered of the formulae for calculating the positive resist- ance of screw propellers. By referring to page 15, it will be seen that the positive resistance of a screw propeller varies in relation to five propor- tions, each of which has to be embodied or taken into con- sideration in the formula ; and it will be observed that the formulae are so framed as to give effect to this condition : and the form in which the problem is proposed to be solved is to show the method adopted for calculating the positive resistance of a screw propeller when rotating at the requisite velocity to give the speed attained on the trial of the vessel,' and then to compare the calculated resistance or the effective horse-power required by the screw with the effective horse-power given out by the engines on the trial ; thus affording a good test of the correctness of the formulse. The method adopted in the formulse for calculating the positive resistance of screw propellers, applied to vessels which have already been tried, or not, is therefore as follows : — 1. From the data of the vessel, find the proportional of vessel ; and decide therefrom on the minimum effective horse-power that should be required for the vessel, at the desired speed per hour. See pages 5, 6, and 7. 2. From the data of the engines, find the effective horse- power developed by the engines, that the same may be compared 26 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. witli the minimum effective horse-power required for the vessel : find also the effective pounds pressure on the pistons of the engines, that the same may be compared with the resistance in pounds pressure of the screw propeller at the requisite velocity for the speed of the vessel. 3. From the drawing of the screw propeller, find the mean velocity diameter ; which is the mean of the diameter at the centre of length of the blades, and of the diameter at the centre of pressure of the vertical transverse surface of the blades. 4. Find the circumference in feet of the mean velocity diameter, and multiply the same by the revolutions per minute obtained on trial (or by the revolutions decided on for the desired speed of vessel), and divide the product by 60 : the quotient will be the circumferential velocity of the mean velocity diameter, in feet per second. 5. Multiply the square of the circumferential velocity in feet per second by 16 • 08^ and divide the product by 32 • 16^ (or 1035) ; the quotient will be the height of the column of water in feet. 6. Divide the height of the column of water in feet by 2 • 3, and the quotient will be the pressure in pounds per square inch ; due to the velocity of the blades through the water. 7. Multiply the pressure in pounds per square inch by the area in square inches of the vertical transverse surface of the blades, and multiply the product by the co-efficient of resistance ; the product will be the force of impact of the blades with the water in pounds pressure. Note. — For the co-efficient of resistance, see explanation of Proportion 4 of the Positive Resistance of Screw Propellers. POSITIVE EESISTANCE. 27 8. Divide the circumference of the mean velocity diameter in feet by the distance travelled in feet by the piston per revolution of the engines, and the quotient will be the leverage — or multiple of stroke. Multiply this proportion into the force of impact of the blades in pounds pressure, and the product will be the positive resistance of the screw propeller in pounds pressure. The following are the above formula, in a tabulated form, for calculating the positive resistance of screw propellers : — Circumference of mean velocity diameter X revolutions per minute go = velocity in feet per second. (Velocity in feet per second)^ X 16-08 , . , Q2-iQ^ ~ height of column of water in feet. Height of column of water in feet nTg = pounds pressure per square inch. Pounds pressure X vertical surface in square inches x coefficient = force of impact. Force of impact X multiple of stroke = positive resistance of screw propeller in pounds pressure. The positive resistance of the screw propeller in pounds pressure thus found by the formulse, is intended to give a very close approximation to perfect accuracy, which however can be obtained only when the minimum amount of effective horse- power required for the eificient propulsion of vessels — the pro- portion of the effective to the indicated horse-power — also the proportion of the slip of the screw — are more exactly determined than at present, by further experience ; but on comparing the results obtained by these formulae with the results obtained practically on 28 RESISTANCE AND PROPORTIONS OP SCREW PROPELLERS. the trials of diiFerent vessels, the results obtained by these formula may be deemed sufficiently correct for the solution of practical problems. See Table of Comparative Results, p. 90. Having found by calculation the resistance of the screw propeller in pounds pressure, it should be compared with the effective pounds pressure on the pistons of the engines, as these two quantities should be equal; the effective horse-power required by the screw should then be calculated and compared with the effective horse-power required for the vessel. The effective horse-power required by the screw propeller will be calculated thus : Multiply the resistance in pounds pressure found for the screw, by the velocity of the piston in feet per minute at the required number of revolutions for the speed of vessel, and divide the product by 33,000 ; the quotient will be the effective horse-power required by the screw ; , . , Eesistance in pounds of screw x velocity of piston per or by formula, ^^^^^^^^ £ f— = eifective horse-power for tlie screw. minute 33000 ' ' When the effective horse-power thus found for the screw propeller does not agree with the minimum effective horse-power that should be required for the vessel at the desired speed per hour, the proportions of the screw propeller should be modified until the effective horse-power for the screw shall agree with the effective horse-power for the vessel. The indicated horse-power required can be obtained from the effective horse-power thus calculated, by dividing the effective POSITIVE RESISTANCE. 29 horse-power by the proportion given in Table 6, according to the type of engines and the maximum pressure of steam. Various examples are given of these formula worked out in extenso, that the results obtained by calculation and on trial may be compared. The foregoing formula are arranged for calculating the resistance of screw propellers fitted to vessels that have been tried, and the number of revolutions of the screw per minute practically ascertained — or in cases where the number of revo- lutions of the screw have been determined on, as suitable for the desired speed of the vessel ; it is, however, considered that it would be desirable (as it will be found convenient in practice) to give the arrangement of the formulae for calculating the number of revolutions per minute to be expected from a screw propeller of any proposed proportions, to enable the number of revolutions of the screw, so found by calculation, to be compared with the number of revolutions required of the engines when giving out the required effective horse-power. All the data being determined of the vessel, the engines and the screw propeller, that are stated to be necessary for use in the formulae for calculating the positive resistance of screw pro- pellers ; the proportional of vessel, the effective horse-power of the engines, the effective pounds pressure on the pistons of the engines, and the coefficient of resistance will have to be found by calculations as previously explained ; the mean velocity diameter will likewise have to be found from the drawing of the screw propeller. The following are the formula, in a tabulated form, so arranged 30 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. that the number of revolutions per minute to be expected from a screw propeller of any proposed proportions may be found by calculation : Effective pounds on piston „ „ . - , , ■■ ■■■- ,.. , — ^-T — r = force of impact of blades. Multiple 01 stroke ^ Force of impact of blades , . , i^ — ^^—. — 7 r- — r 1 -■ '■ — = pounds pressure per square inch. Coefficient x vertical surface m square ms. r t- r ~x Pounds pressure per square incb X 2 • 3 = height of column of water in feet. Height of column of water in feet x 32 '16^ ,■,-,.,., — „ ,,„ = (velocity in feet per second)'. Note. — Extract the square root — then, Velocity in feet per second x 60 ■, ,■ n TTi 7 —i ^ — -. — T^ 7 — : — J—, = revolutions ot screw per mm. Circumierence oi mean velocity diameter in leet ^ When the number of revolutions of the screw thus found do not agree with the number of revolutions determined on for the engines, it will at once be apparent that the proportions proposed for the screw propeller must be modified, until the revolutions calculated for the screw shall agree with the revolutions deter- mined on for the engines. 2. — The Eelative Eesistance of Screw Propellers. The relative resistance of screw propellers is intended, as stated at page 13, to show the relative amount of efiective horse- power required by screw propellers of different proportions, to enable their relative efficiency to be determined, and thereby to decide on the best proportions for any screw propeller. It will of course be understood that the basis of the reasoning RELATIVE RESISTANCE. 31 adopted in framing the formulge for calculating the positive resistance is applicable also to the framing of the formulae for calculating the relative resistance : i. e. it depends on the area of the vertical transverse surface of the blades, on the velocity of that surface, on the multiple of stroke at the mean velocity diameter, on the variations in the different proportions of the screw propellers ; also on the variations in the proportions of the vessels to which the screws are to be applied, and the motion of the vessel through the water. The same data of the vessel, the engines and the screw propeller required for calculating the positive resistance, will be required for calculating the relative resistance. The method adopted for determining the relative resistance of screw propellers is to decide on the proportions of a screw propeller — which is termed the standard screw propeller — which will propel a given proportional of vessel at a given speed, with a given amount of effective horse-power ; and to compare the multiple of the ratios of the proportions of other screw propellers with the multiple of the ratios of the proportions of the standard screw propeller, which are taken as unity. The following are the proportions decided on for the standard screw propeller : Diameter, extreme = 10' 1". Pitch, mean = 10' 1". Mean velocity diameter in feet = 5 • 9. Eevolutions per minute = 83. Multiple of stroke = 4. Velocity of piston per minute = 385. y (Pitch -^ diameter) = 1. Pitch -^ circumference of velocity diameter = -544. Constant = "242. Area in square feet of vertical transverse surface =18. Proportional of vessel = 400. Speed of vessel in knots per hour = 8. Proportion of effective horse-power to proportional of vessel = -5. 32 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. It will be observed that the proportions adopted for the standard screw propeller require the amount of efi'ective horse- power in relation to the proportional of vessel when propelled at a speed of eight knots an hour, that is described in the Note, page 8, as the normal effective horse-power. The reasons for adopting these proportions are, that the relative resistance of screw propellers may be calculated and compared vpith the resistance of a screw propeller requiring a normal amount of effective horse-power ; as examples are given where the effective horse-power required is in some cases greater, and in others less, than this normal amount. The resistance of the vessel being in proportion to the propor- tional found for each vessel by the method explained at page 5, the surface in the blades of the screw should be so proportioned to this proportional (which is the relative measure of the amount of work to be done), that the effective horse-power required for the vessel shall in no case exceed one-half the proportional of vessel, at a speed of eight knots per hour : this proportion of effective horse-power must, however, as previously stated, be taken as a maximum, for recent examples show that this amount of effective horse-power may be reduced to less than three-eighths when the speed of the vessel is not great. The recent examples given in this treatise will show clearly that the relative amount of effective horse-power required to propel a vessel at any given speed depends greatly on the pro- portion of surface adopted for the blades of the screw propeller, and that the greatest efficiency is obtained in cases where the amount of surface is relatively small : consequently, by calcu- lating the relative resistance of different screw propellers applied RELATIVE RESISTANCE. 33 to different proportionals of vessels, and then comparing their eflSciency with the standard screw propeller, a sure method is afforded of coming to a correct conclusion as to the best amount of surface that should be adopted for screw propellers applied to any vessel, in order that the effective horse-power required for the vessel shall not exceed that shown to be sufficient by the best of these recent Examples : and these proportions of effective horse-power and of surface will be found in Table 8. The relative resistance in all cases will be found to be in proportion to the following factors, when the proportion of slip agrees with Table 10 : — 1. The square of the ratio of the mean velocity diameter in feet. 2. The square of the ratio of the number of revolutions per minute. 3. The ratio of the multiple of stroke. 4. The ratio of the velocity of piston per minute. 5. The ratio of ^ (mean pitch -^ extreme diameter) when pitch exceeds diameter. 6. The ratio of (mean pitch -^ circumference in feet of mean velocity diameter). 7. The ratio of the constant. Note 1. — When the proportion of slip differs from the pro- portions given by the decimal quantities in Table 10, deduct the actual proportion of slip from the ratio in Table 10, and square the remainder, to obtain the ratio of a multiplier which must be multiplied into factor 5, and the product will be factor .5 corrected for slip. Note 2. — When the pitch is less than the diameter, factor 6 will be the ratio of (mean pitch -r- extreme diameter). When the screw propellers are to be applied to the same vessel, to be propelled at the same or a different speed ; the 34 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. relative resistance will then further be in proportion to the following factor, in which Y T S = the area in square feet of the vertical transverse surface of the blades : — 8. The ratio of V' ^^^.^j^^g X ratio ofVTS. When the screw propellers are applied to different vessels, to be propelled at the same, or a different speed ; the relative resistance will then further be in proportion to the following factor : — . _,, , . „ a' / ratio of proportional of vessel . „ „ 9. The ratio of V ratio of Y T S ^ '^ of V T S. The ratios of the various proportions of different screw pro- pellers, or the various factors specified above, are obtained by dividing one set of proportions of one screw propeller by the corresponding proportions of the other screw propeller ; the ratios of the proportions that serve as the divisors being taken as unity : and the proportions given of the standard screw pro- peller are intended to serve as the divisors, consequently the ratios of these several proportions will be unity. It is therefore necessary to determine all the proportions for any screw propeller, of which it is proposed to calculate the relative resistance, corresponding with those given for the standard screw propeller, and then to divide those respective proportions by the respective proportions of the standard screw propeller : the quotients will be the ratios required. Having thus obtained the ratios of the proportions of any screw propeller, compared with the ratios of the proportions of the standard screw propeller, the necessary calculations to obtain EELATIVE RESIST AKCE. 35 the relative resistance of any two screw propellers may be explained as follows : — Multiply in both cases the first seven factors together, and then multiply their product either by factor 8, if the screw pro- pellers are to be applied to the same vessel, to be propelled at the same or a different speed ; or by factor 9, if the screw propellers are applied to different vessels, propelled at the same or a different speed : the respective products thus obtained will be the relative resistance of the respective screw propellers. The proportions of the standard screw propeller being the divisors, the ratios of each of the proportions, or factors, is taken as unity, as already explained ; consequently, the multiple of all the ratios for the standard screw propeller will still be unity : with which the multiple of all the ratios of the proportions of any other screw propeller can be readily compared, and the proportion of their relative resistance will be seen at a glance. Examples are given showing the application of this method of calculating the relative resistance of screw propellers. The relative amount of effective horse-power required for different screw propellers will, of course, be equal to their relative resistance. The relative efficiency of different screw propellers will be found thus : — 1, For the same vessel at the same speed, the relative effi- ciency will be in proportion to the relative effective horse-power. 2. For different vessels at the same speed, the relative efficiency will be in proportion to the relative effective horse- power required for each vessel, divided respectively by the respective ratios of the proportionals of vessels. D 2 36 RESISTANCE AND PROPOETIONS OF SCREW PROPELLERS. 3. For different vessels at different speeds, tlie relative efficiency will be found by dividing the respective relative efficiency found for each vessel — according to either 1 or 2, as above — by the respective ratios of power required for the speed of each vessel, as given by Table 5. The object gained by thus obtaining the relative efficiency of different screw propellers is, that allowance is thereby made for any difference in the proportions of the vessels, also for any difference in the speed at which the vessels are propelled ; con- sequently bringing them all to the equal test, which is propor- tional to the amount of work done. The real amount of effective horse-power required for any screw propeller, of which the relative amount of effective horse- power has been ascertained from the standard screw propeller, will be found by calculation thus :■ — - Divide the proportional of vessel (to which the Standard Screw is applied) by 2, and multiply the quotient by the relative effective horse-power already found ; the product will be the real effective horse-power required : . , Proportional of vessel , , . «. , . , or by formula, ^ X relative effective horse-power = real effective horse-power. It is, however, considered desirable that the real effective horse-power thus found for any screw propeller should be verified by calculating the positive resistance of the same screw propeller ; in accordance with the formulse previously given herein : as the result obtained by the calculations for the positive resistance will be a check on the results obtained by the calcula- tions for the relative resistance. RELATIVE RESISTANCE. 37 The area of the vertical transverse surface of the blades, suitable to the proportions of any screw propeller, that shall require the normal amount of effective horse-power in relation to the propor- tional of vessel and the desired speed of vessel per hour ; and of which the relative efficiency shall be equal to the relative efficiency of the standard screw propeller, will be found by calculation thus : Decide on the different proportions of the seven factors for the proposed screw propeller similar to the first seven factors given for the standard screw propeller ; then, by dividing each of these proportions of the proposed screw by the corresponding proportion of the standard screw, the ratios of the proposed screw will be obtained ; the ratios of the proportions of the standard screw being taken as unity. The ratios of the proposed screw must then be multiplied together, and their product divided into the ratio of power given in Table 5 for the desired speed per hour of the vessel ; the quotient will be the difference in the ratio of power required by theseven factors of the proposed screw, as compared with the seven factors of the standard screw ; and this difference in the ratio of power of the proposed screw will necessitate a corresponding alteration in the ratio of the vertical transverse surface of the blades of the proposed screw, which can be determined by Table 7, or by the diagram which is given for this purpose. Table 7 and the diagram for determining the ratios of power compared with the ratios of the vertical transverse surface of the blades, are based on the following formula : — .^/Proportional of vessel „„„ i- j. A/ YTS X V T a = proportion of power. The explanation of this formula is given at page 20. 38 RESISTANCE AND PROPORTIONS OP SCREW PROPELLERS. Having determined on the difference in the ratio of surface of the blades for the proposed screw, compared with the standard screw, the ratio of surface must be multiplied by "045 (the multiplier for surface given in Table 8, as requiring the normal amount of effective horse-power, equal to one-half the proportional of vessel) — and the product multiplied by the proportional of vessel, will give the area in square feet of the vertical transverse surface of the blades of the proposed screw propeller ; when the form of the blades is similar to that shown for A 3, Fig. 2. It is, however, expedient to note that the relative resistance and consequent efficiency of screw propellers is affected by the form adopted for the blades of the screw, likewise by the diameter given to the boss of the screw ; and as the effects produced in the relative resistance of screw propellers by variations in these two proportions are identical, they may be considered in unison. It will be observed that the effects produced by any difference in the form of the blades, or the proportion of the diameter of the boss of the screw, will be to alter the proportion of the mean velocity diameter to the extreme diameter ; consequently to alter the proportions of the four following factors, which constitute part of the factors by which the calculations are made for ascertaining the relative resistance of screw propellers. The factors affected will be the following : — 1 . The square of the ratio of the mean velocity diameter in feet. 3. The ratio of the multiple of stroke. 6. The ratio of (mean pitch -i- circumference of mean velocity diameter. 7. The ratio of the constant. By allowing the number of revolutions of the screw, the PROPORTIONS. 39 velocity of the piston, the proportion of pitch to diameter, and the area of the vertical transverse surface to remain without alteration, the calculations necessary for ascertaining the difference produced in the relative resistance by the variations in the above proportions will consist only of the factors that are necessarily affected, and the effect produced will be more clearly ascertained. The proportions given for the standard screw propeller are for a form of blade similar to that shown on the drawing for Example A 3, Fig. 2 ; and the Tables 7, 8, and 9 are intended to give results in accordance with that form. The difference in the efficiency of screw propellers, due to variations in the form of the blades, and in the diameter of the boss, can be readily calculated by obtaining from the drawings of the different forms of blades proposed for any screw propeller the proportions of the four factors given above ; then multiply together the four ratios of the proportions for each screw respec- tively, and divide one multiple of the ratios by the other ; the quotient will show the difference of efficiency required. The Proportions of Screw Propellers. It is most important that the proportions of screw propellers should be determined on correct principles, or, in other words, that they should be in accordance with the amount of work to be done. Consequently, as the propulsion of a given vessel at a given speed forms the measure of the work to be done by the screw propeller, it is obvious that part of the problem consists in ascertaining as approximately as possible the resistance of vessels in relation to the difference in their proportions. 40 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. The method adopted for finding a proportional quantity for each vessel, to which the resistance of a vessel of any proportions shall be correctly referrible, is explained at page 5 ; and this proportional quantity is termed the proportional of vessel. The proportions of screw propellers should therefore be determined partly in relation to this proportional of vessel and partly in relation to the maximum desired speed of the vessel. The proportional of vessel requires to be calculated at the maximum draught of water of the vessel. The proportions of a screw propeller that have to be determined are the following : — 1. The extreme diameter. 2. The mean pitch. 3. The proportion of slip. 4. The area of the vertical transverse surface of the blades. 6. The form of the blades. 6. The diameter of the boss. The Extreme Diameter. — This proportion may be correctly determined in relation to the proportional of vessel and the maximum desired speed per hour of the vessel in knots, when the vessel is fitted with a single screw, thus : — Divide the speed of the vessel per hour in knots by 40, and multiply the quotient into the proportional of vessel ; the product will be the area of the disc of the screw propeller ; , . , „ . , Speed of vessel in knots . , „ or by formula lor a single screw, — ^t^ X proportional of yessel = area of disc. When the vessel is fitted with twin screws, divide the speed of the vessel per hour in knots by 40, and multiply the quotient PEOPORTIONS. 41 into (the proportional of vessel -r- 2) ; tlie product will be the area of the disc of each screw ; , . , „ , . Speed of vessel in knots proportional of vessel or by formula for twin screws, — -rz x - — 3 = area of each disc. From the area of the disc, the extreme diameter can be readily found. The diameter of the screw found by the above formulae is considered to be the average diameter that should be adopted. It can, however, be varied as experience may suggest to be desirable ; but the above formulae are very simple, and the results agree with practice. When the draught of water of the vessel admits of an increase (which may be considered desirable) in the extreme diameter of the screw, as found by the above formula, the pitch of the screw will require to be modified in accordance with the reduced proportion of slip to be expected consequent on the alteration in the proportion of the pitch to the diameter ; the area of the vertical transverse surface of the blades will likewise require to be modified, consequent on the increased circum- ferential velocity of the blades and the alterations produced in the other proportions of the screw propeller. With these necessary modifications, the extreme diameter of the screw may be varied as experience may suggest to be desirable, which will probably occur in cases of vessels with shallow draught of water, when the proportion of the pitch to the diameter becomes coarse. Pitch, — This proportion is determined in relation to the three following conditions, viz. : the number of revolutions per minute 42 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. required of the engines to give out tte requisite amount of power found for the vessels, the maximum speed of vessel desired, and the proportion of slip to be expected of the screw. It is considered desirable that the proportion of the pitch should not exceed twice the extreme diameter. In cases where this proportion would be exceeded, the extreme diameter may be increased, or the number of revolutions per minute may be increased, making the requisite alteration in the diameter of the cylinders of the engines. Proportion of Slip. — This proportion is not very readily deter- mined in a perfectly accurate manner, the law regulating the same not being very clear. Table 10 has, however, been pre- pared from experience and tested by numerous examples, to show the ratios of the proportion of slip that may be expected with screw propellers of different proportions of pitch to diameter, and with different proportions of the vertical transverse surface of the blades. Experience shows that the proportion of slip depends mainly on the proportion of the pitch to ' the diameter, and varies but slightly in relation to the proportion of surface in the blades. It will also be observed in Table 10 that the ratios of the proportion of slip vary very approximately in proportion to the cube root of (the pitch -T- the diameter), the ratio of the proportion of slip when nil being taken as unity ; but further experience is considered desirable to determine the proportion of slip with perfect accuracy. In Table 10, the column showing the proportion of surface = 1 • represents the proportion of the vertical transverse surface of the blades that would require the normal amount of effective PROPORTIONS, 43 horse-power and the ratios of the proportion of slip to be expected with that proportion of surface. The decimal quantities of the ratios will be the proportion of slip. The other columns of Table 10 give the ratios of the proportion of slip to be expected with different proportions of surface, comparing the proportion of surface in the blades with the proportion of surface = 1. It may be desirable here to remark that a reduction in the proportion of slip does not necessarily imply a gain in the amount of power required, for it is clear that if the same number of revolutions per minute be required with engines of the same type and size, to propel the same vessel at the same speed, with screw propellers of different proportions, the proportion of the slip is immaterial ; and the power given out by the engines will be the same. The area of the Vertical Transverse Surface of the Blades. — The right determination of this proportion is deemed to be of the greatest importance, for, unlike the proportions of the diameter and of the pitch, which, if made of greater proportions than necessary, do not involve a waste of power, but, by overpowering the engines, simply reduce the speed of the engines, which is an obvious disadvantage ; the consumption of steam being, however, less in proportion, no waste of power is involved. But when the area of the vertical transverse surface of the blades is increased beyond a due proportion to the proportional of vessel and the maximum speed of vessel desired, a positive waste of power occurs, which is made clearly evident on a careful examination of the various examples given in the Table showing the comparative results obtained from different screw propellers on trial. The examples given in that Table show that where the pro- -ii RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. portion of the vertical transverse surface of the blades is small, when compared with the proportional of vessel and the speed required, a smaller proportion of effective horse-power is sufficient to propel the vessel at the desired speed, than when the proportion of surface is greater. The vertical transverse surface of the blades of any screw propeller consequently requires to be so proportioned to the proportional of vessel and the maximum speed per hour desired of the vessel, that the proportion of the effective horse-power required shall not exceed that shown to be sufficient by the best practical examples. Note. — When the vessel is fitted with twin screws, each screw should have one-half the required surface. At page 37, the method of calculating the area of the vertical transverse surface of the blades for any screw propeller that shall require the normal amount of effective horse-power in relation to the proportional of vessel and the desired speed per hour, is explained. The same method is applicable for calculating the area of the vertical transverse surface that shall require a different amount of effective horse-power to the normal amount^ by adopting a slight modification. It will be observed that in the method as explained at page 38, the ratio of the surface of the blades, when found by the necessary calculations, has to be multiplied by • 045 to give the corrected multiplier by which the proportional of vessel has to be multiplied to obtain the ai'ea in square feet of the vertical transverse surface of the blades for any screw propeller that shall require the normal amount of effective horse-power. PROPORTIONS. 45 In Table 8 are given the different multipliers that require to be multiplied into the ratio of the surface of the blades (found as above described), to give the corrected multiplier by which the proportional of vessel has to be multiplied, to obtain the area in square feet of the vertical transverse surface of the blades for any screw propeller that shall require a proportion of effective horse- power, compared with the normal effective horse-power, as shown by the proportion of effective horse-power given in the last column of Table 8, opposite the various multipliers given in the second column of the same Table. It has already been stated in the Note, page 8, that the normal effective horse-power is also the maximum effective horse- power that should be required ; consequently it will be observed that the multiplier '045 for surface (in the second column of Table 8) which requires the normal or maximum effective horse- power is placed opposite the proportion '5 of effective horse- power (in the last column), which, as already explained, is the normal or maximum horse-power that should be required in relation to any proportional of vessel, when the vessel is pro- pelled at a speed of 8 knots per hour. Consequently, by adopting any of the multipliers for surface in the second column of Table 8 as the multiplier, to be multiplied into the ratio of the surface as explained above, the proportion of effective horse-power in relation to the proportional of vessel, at a speed of vessel of 8 knots per hour^ will be found in the last column of the same Table, opposite the multiplier that may be adopted. It will thus be seen that Table 8 serves a very useful purpose, in showing at a glance the proportion of effective horse- 46 RESISTANCE AND PROPORTIONS OP SCREW PROPELLERS. power required, by adopting the different multipliers ; and this proportion of effective horse-power can be readily compared with the normal effective horse-power of "5, when the multiplier adopted is "045. The relative efficiency obtained by the different multipliers will be in inverse proportion to the proportion of the effective horse-power given in the last column of Table 8. Examples are given showing the application of this method of calculating the area of the vertical transverse surface of the blades for screw propellers. It may be noted that the multipliers for the surface of blades given in the second column of Table 8 are the multipliers that give the area of the vertical transverse surface of the blades of screw propellers, which agrees with the area adopted in the screw propellers that show the best results in the examples herein given. They may consequently be safely relied on ; but by working out the results obtained from the best of other examples — by the aid of the formula for calculating the relative resistance or efficiency of screw propellers — additional experience will be brought to bear on the subject, which may show that the higher multipliers given for the higher speeds of vessel may with advantage be reduced. If the method adopted for calculating the proportional of vessel be correct, and the proportional of vessel together with the speed of the vessel being the measure of the work to be done, it is to be expected that the multipliers in Table 8 for the higher speeds may, with additional experience, be made to approximate more closely to the multipliers for the lower speeds, and thereby add to the eflSciency of screw propellers at the higher speeds of vessel. OBSERVATIONS. 47 It is therefore in the direction of reducing the surface of the blades of screw propellers to a safe minimum, due regard being had to the proportion of slip, that improvement may be expected in the efficiency of screw propellers. Form of Blade and size of Boss. — These proportions have been fully treated whilst explaining the formula for calculating the relative resistance of screw propellers ; and from the method explained for calculating the effect produced on the relative resistance, by variations in these proportions, it is obvious that it is important to adopt that form of blade, and that proportion of boss, whereby the efficiency of the screw propeller becomes the greatest. The form of blade recommended is that shown on the drawing for Example A 4, Fig. 3 ; and it is recommended that the diameter of the boss should be kept as small as possible, compatible with the diameter of the shaft and the strength of boss required. Observations on the following Examples, showing the Calculated Eesistance of Screw Propellers. The calculated indicated horse-power is obtained by means of the Tables in the ' Treatise on the Power and Speed of Steam Vessels,' for the purpose of ascertaining the mean of the ratios of power per O.M. and per A. M.S. ; which is then available for calculating the proportional of vessel as explained. It will doubtless be observed that the calculated indicated horse-power does not agree with the normal indicated horse- power. This arises from the calculated indicated horse-power being 48 EBSISTANCE AND PROPORTIONS OF SCREW PROPELLERS. derived from an average effective liorse-power for eacli type of engine ; whereas the normal indicated horse-power is derived from an effective horse-power in which allowance is made for different pressures of steam as well as for different types of engines. It will also doubtless be observed that the calculated resistance in pounds pressure of the screw propeller is generally less than the effective pounds pressure on the pistons of the engines. This may be explained by the presumption that the eflSciency of the engines on the trial trip is reduced by the increase of friction, and that the friction will diminish when the engines have been some time at work. In comparing the relative efficiency of the different examples it should carefully be remembered that the effective horse-power affords the only true measure of comparison ; and by comparing the effective horse-power on trial with the calculated normal effective horse-power on trial, the relative efficiency of the different examples can be readily ascertained ; thus : — , , E.H.P. on trial 5552 , „ Example A 1. ^ ^ ^ - =1-7. E.H.P. normal 3273 ^ E.H.P. on trial 654 Example D. ^ „ .„ = — — = -8. E.H.P. normal 820 1-7 Then —^ = 2 • 125, showing the ef&ciency of Example D to be 2 • 125 times the ' o efficiency of Example A 1. This is accounted for by the difference in the proportion of the vertical transverse surface in the blades of the screw pro- pellers to the proportionals of the vessels : in Example A 1 the OBSERVATIONS. 49 proportion of the vertical transverse surface being considerably above the proportion that would be given by the normal mul- tiplier "045, and in Example D the proportion of the vertical transverse surface being below the proportion that would be given by the same normal multiplier : and, further, to the dif- ference in the relative efficiency of the forms of the blades of Fig. 1 for Example A 1, and Fig. 2 for Example D. See drawing of Forms of Blades. Again, Example D was tried at the maximum draught of water of the vessel, whereas Example A was tried at a less draught of water than the maximum : this should be carefully noted in all cases of comparison, for it is evident that the surface of the blades of the screw propeller being proportioned for the maximum draught, the surface will be in excess when the vessel is tried at a less draught of water ; and the difference in the relative efficiency due to this cause can be readily ascertained by means of factor 9, p. 34. The normal effective horse-power given in the Examples shows the effective horse-power that should be required when the surface of the blades of the screw propeller is proportioned to the proportional of vessel. Note. — The method shown in the examples, of correcting the coefficient for slip, amounts to the same in principle as correcting the proportional of pitch for that purpose ; as explained in the text under Proportion 4 of the Positive Kesistance of Screw Pro- pellers : therefore either method may be adopted, as found most convenient. Examples A 1, A 2, A 3, and A 4 are given to show the results obtained from screw propellers of four different proportions E 50 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. applied to the same vessel, tried under similar conditions : they are therefore considered to be particularly instructive. Example B is fitted with the same type of engines, working with the same pressure of steam as Examples A ; the results obtained by calculations made on the same basis can therefore be fairly compared. Examples C, D, and E are vessels of full displacement which attained different speeds on trial, with engines of a similar type ; and will therefore be found instructive for the purpose of comparison. Examples F 1 and G are also considered useful for the same purpose. Examples A 5 and A 6, also F 2 and F 3, are given to show proposed Examples worked out, so that the speed of vessel desired shall be attained with the normal amount of effective horse-power. In concluding these investigations of the problems set forth in this treatise — viz. the Resistance and the Proportions of Screw Propellers, in which the writer considers the subject has been treated in the only possible manner by which the problems can be correctly solved ; and which consists in treating in combina- tion the subject as a whole, and in detail with reference to the type of the vessels, the type of the engines, and all the possible variations in the screw propellers produced by difference in the proportions and the form of the blades, all of which have been fully provided for in the tables and formulse herein given : the writer desires to observe that the most important inference to be drawn therefrom appears to be, that the greatest efficiency to be obtained from any screw propeller will be realised by adopting the minimum amount of surface for the blades in accordance OBSERVATIONS. 51 with the best examples in practice, as clearly shown in Table 8 ; for by this table the proportion of effective horse-power required in relation to the multiplier for surface, that experience may show can be safely adopted for the required speed of vessel, will be readily seen. It is therefore, as already stated, in the direction of minimising the surface of the blades as far as practicable, without unduly increasing the proportion of slip, that improvement may be looked for in the efficiency of screw propellers : moreover, the important difference in the relative efficiency due to variations in the forms of the blades, as herein explained, must not be overlooked. E 2 52 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. Abbeeviations in Examples fob Eesistanob or Screw Peopbllbes. For Vessel. O.M. = Old measurement tonnage. D.T. = Displacement in tons. A.M.S. = Area of midship section in square feet. B. = Beam extreme in feet. D. = Draught mean in feet. L. = Length between perpendiculars in feet. L.B. = Proportion of length to beam. D.B. = Proportion of draught to beam. D.O. = Proportion of displacemeut to old measurement tonnage. W.S. = Wet surface. P.V. = Proportional of vessel. S.K. = Speed in knots per hour. For Engines. I.H.P. = Indicated horse-power. E.H.P. = Eifective horse-power. S. = Pressure of steam in boilers in pounds per square inch. P.E.P. = Proportion of eifective to indicated horse-power. E. = Revolutions per minute. T.P. = Travel of piston in feet per revolution of the engines. V. = Velocity of piston in feet per minute. For Screw Propeller. D.E. = Diameter extreme in feet. D.M.V. = Diameter of mean velocity in feet. P. = Pitch mean in feet. C. = Circumference of diameter of mean velocity in feet. M.S. = Multiple of stroke. V.T.S. = Area of vertical transverse surface of blades in square feet. S.C. = Proportion of slip. P.D. = Proportion of mean pitch to extreme diameter. P.O. = Proportion of mean pitch to circumference of mean velocity diameter. D.V.E. = Proportion of mean velocity diameter to extreme diameter. P.P. = Proportional of pitch. P.S. = Proportional of surface. 53 TABLES FOR THE BESISTANOE AND THE PROPORTIONS OF SCREW PROPELLERS. Table 1. — Proportion of Displacement to O.M. Tonnage, to decide on the comparative fulness of the Lines of different Vessels. Draught to Beam. Very Fine Lines. Medium Fine LineB. Fine Lines. Medium Full Lines. Full Lines. Very FuU Lines. ■6 ■55 -5 -45 -4 -375 -33 -3 -25 -2 ■166 ■125 ■28 •2 •11 •05 •95 •92 ■82 •76 ■67 •55 •48 •37 •44 •35 •25 •18 ■07 ■03 ■92 •86 •75 ■62 •54 ■41 -6 1^76 •5 1-65 -39 1-53 ■31 1^44 -19 1^31 -15 1-26 -02 1-12 •96 105 •84 ■92 •69 •76 •6 •66 •46 •5 1'92 1-8 1-66 1'57 1-43 r38 1^22 1^15 1- ■82 -72 -55 08 95 8 7 55 49 32 24 09 9 78 6 Table 2. — Ratio of Displacement in re- lation to the fulness of the fore and aft lines of the vessel. Table 3. — Ratio of Power in relation to the Draught of Water of the Vessel. Table. 4. — Ratio of Wet Surface in re- lation to the pro- portion of the length to the beam of the Vessel. Table 5. — Ratio of the Power required for different speeds per hour. Lines of Vessel. Ratio of Displace- ment. Draught to Beam. Eatio of Power. Length to Beam. Ratio of Wet Surface. Knots per Hour. Ratio of Power. Very fine . . Medium fine Fiue .. .. Medium full Full .. .. Very full .. -9 ■95 !■ 105 1^1 115 ■6 ■55 ■5 ■45 ■4 ■375 •33 •3 ■25 ■2 ■166 ■125 ■91 ■96 1^ 1^079 1^132 1.165 1^219 1^331 1^44 1612 1^788 2^04 10 times 9 „ 8 „ 7 „ ei„ 6 „ 51 „ 5 „ 4i„ i ,. 3J., 3 „ 1^108 1-074 1-041 1- ■981 ■96 ■94 ■92 ■895 •87 •85 •82 7 I* 9 10 11 12 13 14 15 16 17 18 •67 •823 1^ 1^42 193 2-6 337 4-29 5-35 66 8^ 9^6 11 39 1 54 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. Table 6. — Proportion of Effective Horee-power to the Indicated Horse-power in relation to the maximum pressure of Steam, for various types of Engines. Ordinary Condensing Engines. Compounc Maximum Enginea. Compound Engines with separate Circulating. Ordinary Non-condensing Engines. 1 Maximum Proportion Proportion Maximum ' Proportion Maximum Proportion Steam in of Effective Steam in of Effective Steam in , of Effective Steam in of Effective Lbs. H.P. Lbs. HJ. Lbs. 1 H.P. Lbs. HP. 10 -58 50 •68 50 -73 50 ■63 15 59 60 69 60 74 60 64 20 6 70 7 70 75 70 65 25 61 80 71 80 j 76 80 66 30 j 62 90 72 90 1 77 90 67 Table 7. — Katio of Power compared with the Ratio of the Vertical Trans- verse surface of the Blades. liatio of Surface. 666 7 75 s 85 9 95 05 1 125 25 375 5 625 75 875 •2 -25 ilatio uf Power. 75 7826 815 852 888 926 963 0328 0655 0813 1625 2369 31 3828 4525 521 58 7 Table 8. — MultipUers for use in the Formula for calculating the proportion of the Vertical Transverse surface of the Blades, in relation to the Proportional of Vessel at different speeds. Showing also the proportion of Effective Horse-power required, in relation to the Proportional of Vessel, at a speed of Vessel of 8 knots per hour, with the different Multipliers. Speed of Vessel in Knots. 7 S 9 10 11 12 13 14 15 16 17 18 Multipliers for Surface of •024 •026 •028 •03 •032 •034 •036 •038 •04 •042 •044 •045 Ilatio of Surface. Ptatio of Power. 533 577 622 666 711 755 8 844 888 933 977 1^ 654 686 72 75 786 818 852 884 918 95 982 1- Proportion of Effective H.P. to Proportional of Vessel at 8 Knots. •327 •343 •36 •375 393 •409 •426 •442 •459 •475 •491 •5 ^oTsfre^w^'} = P^Portional of Vessel x (Single Screw.) Speed of Vessel in knots 40 TABLES. 55 Table 9. — Constants for Screw Propellers of different Diameters, with the average form of Blades — Fig. 2 — in inverse proportion to (Diameter of Mean Velocity -i- Extreme , Diameter)^. Kxtreme Diameter of Screw in Feet. Velocity Diameter. Extreme Diameter. ®'' red. constant. Extreme Diameter Velocity Diameter. Ditto r.„„=t.„f ofS^crewin Extreme Diameter. Squared. Constant. 5 •6 36 230 16 567 321 258 6 ■597 356 232 17 564 318 260 7 •594 352 235 18 561 314 263 8 ■591 349 237 19 558 311 266 9 •588 345 240 20 555 308 269 10 •585 342 242 21 552 304 272 11 •582 338 245 22 549 301 275 12 •579 335 247 23 546 298 278 13 •576 331 250 24 543 294 281 14 •573 328 253 25 54 291 284 15 ■57 325 255 Table 10. — Eatio of Slip in relation to the proportion of Pitch to the Diameter of the Screw, and to the Proportion of the Vertical Transverse Surface of the Blades to the Proportion found by Table 8, taking the Multiplier ^045 as Proportion = 1. Pitcli to Diameter. Proportion of V.T.S. = 2. Proportion of V.T.S. = l-IS. Proportion of V.T.S. = 1-5. Proportion of V.T.S. = 1-26. Proportion of V.T.S. = 1-. Proportion of V.T.S. = -75. 1^ 1- 01 02 1-03 04 1-05 1-1 1^026 036 046 1-056 066 1-076 1-2 1^052 062 072 1-082 092 1-102 1-3 1-078 088 098 1-108 118 1-128 1^4 1-104 114 124 1-134 144 1-154 1^5 1-13 14 15 1-16 17 1-18 1-6 1^156 166 176 1-186 196 1-206 1^7 1-182 192 202 1-212 222 1-2.82 1-8 1-208 218 228 1-238 248 1-258 1^9 1^234 244 254 1^264 274 1-284 2- 1^26 27 28 1^29 3 1-31 UoTE. Eatio of Slip = 'v'P -;- D approximately. The Ratio of slip when Xil is taken as unity. 56 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. EXAMPLE A 1. Vessel. lingines. Screw Propeller. CM. = 3065 Type : Compound with separate Number of screws, 2 D.T. = 3750 Maximum circulating Nnmber of blades in each, 4 ,^ = 3300 On trial Number of sets of Engines, 2 D.E. = 18' 6J" A.M.S = 777 Maximum LH.P. = 7503- total on trial DM.V. = 11 „ = 700 On trial E.H.P. = 5552- P. = 18 U B. = 46' 1" S. = 65- C. = 34-55 D. = 19 9 Maximum P.E.P. = -74 M.S. = 5-76 ,, = 18 U On trial E. = 91 • V.T.S. = 88-5 total L. = 300 T.P. = 6- = ^^-^K'^ef} L.B. = 6-52 V. = 546- » D.B. D.O. = '43 Maximum = 1 '22 IHP -4900-/^°™''' \ hti.f. - 4yuu Imj^ximum/ s.c. = 6372 sq. ins. = Nil. P.V. = 815- E.H.P. = 3630- P.D. = -98 s.'k. = 734- On trial = 16-6 „ LH.P. = 4423-{^°™f "°} P.O. D.V.E. = -524 = -594 E.H.P. = 3273- Constan P.P. P.S. = -235 = -5135 = 2-024 Calculated I.H.P. b OR Vessel at Maximum Calculated I.H.P. fob De AL'GHT. Vessel on Trial. O.M. : 3065- ■264 lines A.M.S. = 777- - 666 lines 809-16 1-04 L.B. 841-36 -926 D.B. 778-766 -693 W.S.O.M. 539-154 -981 W.S.L.B. 528-759 LH.P. at 8 knots. 517-482 1-1 D.B. A.M.S. maximum. A.M.S. on trial. 777 : 4843 : : 700 7W)^ 777)3390100 568-7 -981 W.S.L.B. 557-208 LH.P., A.M.S. 528-759 „ O.M. 2)l086- 543- I.H.P. mean at 8-92 8 knots. 4843- I.H.P. mean at 16-6 knots. 4363 LH.P. at 16-6 knots on trial. Actual I.H.P. on trial = 7503. EXAMPLES. 57 EXAMPLE A 1. Pkopoktional of Vessel Maximtim. I.H.P., A.M.S. 557) 528 I.H.P., O.M. at 8 knots. Peoportional op Vessel on Trial. A.M.S. maximum. A.M.S. on trial. 777 : 815 :: 700 A.M.S. •948 Eatio of power 1- O.M. A.M.S. mean. Normal E.H.P. maximum, 2)815 P.V. maximum. 407 E.H.P. at 8 knots. 8^92 at 16 '6 knots. ■74)3630 E.H.P. /uu 777)570500 2)1-948 734 P.V. on trial. •974 Eatio of power = 777 1 Eatio D.T. Normal B H.P. on trial. 2)734 P.V. on trial. 777 IID.B. 367 E.H.P. at 8 knots. 8-92 at 16-6 knots. 854-7 •98 W.S.jL.B. •74)3273 E.H.P. 4900 I.H.P. 1. 4423 I.H.P. 837 • 6 • 974 Eatio of power mean. 815^92 P.V. maximum EFFEOTrvB Pressure in Pounds on the Pistons op each set op Engines. 2)7503 • Total I.H.P. on trial. 3751 -5 I.H.P. of each set of Engines. •74 P.B.P. Eesistance in Pounds Pressure op the Blades OP each Screw Propeller. D.M.V. = 11' 0" C. = 34-55 91 • E. T,P. C. 6^)34^55 5^76M.S. 2776^11E.H.P. 33000 60)3144 • 05 546)91608000 167,782 lbs. eifective pressure on Pistons. 52^4* = 2745^76 16-08 1035)44151 • 82 2-3)42-65 P.D. = -98 P.O. = -524 18^5 lbs. 6372- sq. ins. V.T.S, •5135 P.P. V.T.S. 88^5)734 P.V. 8^3 ^ = 2-024 P.S. ■5135 P.P. 117882 •244 Coefficient. 1-0393 -235 Constant. 28763-2 5-76 M.S. -24416 Coefficient. 166,674-88 lbs, Eesistance of Screw Propeller. 58 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. EXAMPLE A 2. Vessel. Engines. Screw Propeller. O.M. = 3065 Type : Compound with separate Number of screws, 2 D.T. = 3750 Maximum circulating Number of blades in each, 2 j^ = 3300 Oq trial Number of sets of Engines, 2 D.E. = 18' 6J" A.M.S. = 777 Maximum I.H.P. - 4368- total on trial D.M.V. = 11 = 700 Oq trial E.H.P. = 3232- P. = 18 IJ B. = 46' 1" S. = 65- C. = 34-55 D. = 19 9 Maximum P.B.P. = -74 M.S. = 5-76 ,^ = 18 IJ Oq trial E. = 89- V.T.S. = 44-25 total L. L.B. = 300 = 6-52 T.P. = 6- V. = .534- )> _ 99.,9c/in each) - ^^ ^^^ \ screw / D.B. D.O. = '43 Maximum = 1-22 LH.P.=4158-{^^ormal^} s.c. = 3186 sq. ins. = -028 P.V. = 815- B.H.P. = 3076- „ P.D. = -98 s.k. = 734- Oq trial = 15-7 LH.P.=3749-{^31-} P.O. D.V.E. = -524 = -594 E.H.P. = 2774- „ „ Constan P.P. P.S. = -235 = -5135 = 2-5506 Calculated I.H.P. fob Vessel at Maximum Db aught. Calculated I.H.P. mean at 8 knots for A 1 = 543 7-56 4105 I.H.P. mean at 15-7 knots. Calculated I.H.P. foe Vessel oif Trial. A.M.S. maximum. A.M.S. on trial. 777 : 4105 :: 700 700 777)2873500 3698 I.H.P. at 15-7 knots on — — trial. Actual I.H.P. on trial = 4368. EXAMPLES. 59 EXAMPLE A 2. Proportional of Vfssel Maximum. I.H.P.. A.M.S. 557) 528 LH.P., O.M. at 8 knota •948 Eatio of power O.M. 1- „ „ A.M.S. Peopobtional op Vessel on Tbial. A.M.S. maximum. A.M.S. on trial. 777 : 815 :: 700 700 777)570500 2^1-948 •974 Batio of power mean. A.M.S. = 777 1 Eatio D.T. 777 1-1 D.B. Normal E.H.P. maximum. 2)815 P.V. maximum. 407 7-56 854-7 -98 W.S, L.B. 837-6 - 974 Ratio of power mean. 815 -92 P.V. maximum. •74)3076-92 E.H.P. 4158 LH.P. 734 P.V. OB trial. E.H.P. at 8 knots, at 15-7 knots. Normal E.H.P. on trial. 2)734 P.V. on trial. 367 E.H.P. at 8 knots. 7-56 at 15-7 knots. -74)2774 B.H.P. 3749 I.H J>. Bffeotivb Pressure in Pounds on the Pistons of each set of Engines. Ebsistanoe in Pounds Pressube op the Blades of each Screw Propeller. 2)4368 Total I.H.P. on trial. 2184 I.H.P. of each set of Engines. -74 P.E.P. 1616-16 E.H.P 33000 V. 534)53333280 99,875 lbs. effective pressure on ^^■^^— Pistons. D.M.V. = 11' 0" 0. = 34-55 89- E. V.T.S. ient. Besisi T.P. C. 6-)34-55 5-76 M.S. 60)3074-95 P.D. = -98 P.O. = -524 51-24^ = 2626-56 16-08 ■5135 P.P. 1035)42235-03 2-3)40-8 17-7 lbs. 3186. sq. ins. V.T.S. 44-25)734 P.V. 16-6 4/ = 2-5506 P.S. -5135 P.P. 56392-2 •307 CoefiBc 1-3097 -235 Constant. 17312 -34 5^76 M.S ■ 3076I Coefficient. 99,717-12 lbs. ;ance of Screw Propeller. 60 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. EXAMPLE A 3. Vessel. Eugioes. Screw Propeller. CM. = 3065 Type : Compound with separate Number of screws, 2 D.T. = 3750 Maximum circulating Number of blades in each, 4 ?» = 3300 On trial Number of sets of Engines, 2 D.E. = 16' 3r' A.M.S. = 777 Maximum I.H.P. = 7714- total on trial D.M.V. = 96 ,^ = 700 Ou trial E.H.P. = 5708- ,, P. = 20 B. = 46' 1" S. = 65- C. = 29-84 D. = 19 9 Maximum P.E.P. = -74 M.S. = 4-97 IT = 18 1 J On trial R. = 97- V.T.S. = 78 -5 total L. L.B. = 300 = 6-52 T.P. = 6- V. = 582- S» = 39 -251'° """"H \ screw / D.B. D.O. = -43 Maximum = 1-22 LH.P. = 6798-/^°™^M ' \maximum/ B.C. = 5652 sq. ins. = -046 P.V. = 815- E.H.P. = 5030- P.D. = 1-23 S.K. = 734 • On trial = 18-5 „ I.H.P. = 6130-.[^°™^J°'^} P.O. D.V.B. = -670 = -584 E.H.P.= 4536- "!, Constant P.P. P.S. = -243 = -7088 = 2-106 calonlated i.h.p. fok vessel at maximum Dkatjght. Calculated I.H.P. mean at 8 knots for A 1 = 543 12-36 6721 I.H.P. mean at 18-5 knots. Calculated I.H.P. foe Vessel on Trial. A.M.S. maximum. A.M.S. on trial. 777 : 6721 :: 700 700 777)4704700 6055 I.H.P. at 18-5 knots on trial. Actual I.H.P. on trial = 7714 EXAMPLES. 61 EXAMPLE A 3. Propoktional of Vessel Maxqiusi. I.H.P., A.M.S. 557) 528 I.H.P., O.M. at 8 knots. •948 Batio of power O.M. 1- „ „ A.M.S. Peopoktional of Vessbx on Trial. A.M.S. maximum. A.M.S. on trial. 700 777 815 : 700 777)570500 2)1-948 • 974 Ratio of power i mean. Normal E.H.P. maximum. 2)815 P.V. maximum. 407 E.H.P. at 8 knots. 12.36 at 18.5 knots. -74)5030-5 E.H.P. 734 P.V. on trial. A.M.S. = 777 1 Eatio D.T. Normal E.H. P. on trial. 2)734 P.V. on trial. 777 1-1 D.B. 367 E.H.P. at 8 knots. 12-36 at 18-5 knots. 854-7 •98 W.S., L.B. -74)4536 E.H.P. 6798 I.H.P. 6130 IHP 837-6 •974 Eatio of power 815-92 P.V. maximum. Effective Pressure w Pounds on the Pistons of each set of Engines. Eesistanoe in Pounds Pressure op the Blades of each Screw Propeller. 2)7714 3857 -74 Total I.H.P. on trial. I.H.P. of each Set of Engines. P.E.P. D.M.V. = 9' 6" C. = 29-84 97- E. T.P. C. 6-)29-84 2854-18 E.H.P 33000 60)2894-48 4-97 M.S. 582)94187940 161 , 835 lbs. effective pressure on Pistons. 48 -24^ = 2328- 16-08 yP.D:= 1-058 P.C. = -670 1085)37434-24 2-3)36- 158 •7088 P.P. V.T.S. 78-5) 734 P.V. 15-72 lbs. 5652- sq. ins. V.T.S. r- 9-35 = 2-106 P.S. -7088 P.P. 88849-44 •3627 Coefficient. 1-4927 -243 Constant. 32225-53 4-97 M.S. -3627 Coefficient. 160,158-25 lbs. Eesistanoe of Screw Propeller. 62 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. EXAMPLE A 4. Vessel, ■ Engines. Screw Propeller. CM. = 3065 Type : Compound with separate Number of screws, 2 D.T. = 3750 Maximum circulating Number of blades in each, 2 ^, = 3300 On trial Number of sets of Engines, 2 T.H.P. = 7556- total on trial D.E. = 18' IJ" A.M.S. = 777 Maximum D.M.V. = 10 2J „ = 700 On trial E.H.P. = 5591 • „ P. = 21 3 B. = 46' 1" S. = 65- C. = 32-125 D. = 19 9 Maximum P.E.P. = -74 M.S. = 5-354 „ = 18 1 J On trial K. = 93- V.T.S. = 62-5 total L. L.B. = 300 = 6-52 T.P. = 6- V. = 558- J? ^31.25 fin each) \ screw D.B. D.O. = • 43 Maximum = 1-22 „ LH.P. =6798-1 ^°™*1 ) 1 maximum/ S.C. = 4500 sq. ins. = -063 P.V. = 815- E.H.P. = 5030- „ P.D. = 1-17 S.K. = 734- On trial = 18-5 TTTTJ cian./N'ormal on\ I.H.P. = 6130 1 j^j^j 1 P.O. D.V.E. = -661 = -563 E.H.P. = 45.36- „ „ ConstanI P.P. P.S. = -261 = -689 = 2-272 Calculated I.H.P. fob Vessel at Maximum Dkaught. Calculated I.H.P. mean at 8 knots for A 1 = 543 12-36 Calculated I.H.P. fob Vessel on Trlal. A.M.S. maximum. A.M.S. on trial. 777 : 6721 :: 700 700 6721 I.H.P. mean at 18-5 knots. 777)4704700 6055 I.H.p. at 18-5 knots on trial. Actual LH.P. on trial = 7556 EXAMPLES. 63 EXAMPLE A 4. PKOrOKTIONAL OF VESSEL MaXBIUM. I.H.P., A.M.S. 557) 528 I.H.P., O.M. at 8 knots. • 948 Batio of power O.M. Proportional of Vessel on Trial. A.M.S. maximum. A.M.S. on triaL 777 : 815 :: 700 700 1- 2)1-948 A.M.S. 777)570500 •947 Eatio of power mean. A.M.S = 777 1 Eatio D.T. 777 1-lD.B. Normal E.H.P. maximum. 2)815 P.V. maximum. 407 E.H.P. at 8 knots. 12-36 at 18-5 knots. 854-7 ■98 W.S.. L.B. 837-6 •974 Eatio of power mean. 815-92 P.V. maximum. •74)5030-5 E.H.P. 6798 LH.P. 734 P.V. on trial. Normal E.H.P. on trial. 2)734 P.V. on triaL 367 E.H.P. at 8 knots. 12-36 at 18-5 knots. •74)4536 E.H.P. 6130 LH.P. Effective Pressure in Pounds on the Pistons op each set of Engines. 2)7556 Total LH.P. on trial. 3778 LH.P. of each set of Engines. •74 P.E.P. 2795-72 E.H.P. „ „ 33000 558)92258760 165,338 lbs. effective pressure on Pistons. Eesistance in Pounds Pressure of the Blades OF EACH Screw Propeller. D.M.V. = 10' 2J" 0. = 32-125 93- E. T.P. C. 6)32-125 5 -354 M.S. 60)2987- 62 49-8= = 2480- 16-08 1035)39878-40 2-3)38-53 16-75 lbs. 4500- sq. ins. V.T.S. ^V.D. = 1-043 P.O. = -661 •6894 P.P. V.T.S. 62 • 5) 734 P.V. _ 11^74 ^ = 2-2723 P.S. -689 P.P. 76175-00 ■4086Coeflaoient. 1-5656 •261 Constant. 31125-105 5-354 M.S. •4086 Coefficient. 166,643-25 lbs. Eesistance of Screw Propeller. 64 RESISTANCE AND PROPORTIONS OP SCREW PROPELLERS. EXAMPLE B. Vessel. Engines. Screw Propeller. DM. = 4610 Type : Compound with separate Number of screws, 1 D.T. = 8500 Maximum circulating Number of blades, 4 „ = Number of sets of Engines, 1 D.E. = 23' 6" A.M.S. = 926 Maximum I.H.P. = 4900- Mean D.M.V. = 12 lOJ 5» fMeanonj 1 voyage / E.H.P. = 3626- „ S. = 65- P. C. = 31 6 = 40-416 B. = 45' 2" PEP. = -74 M.S. = 4-04 D. = 23 7 Maximum R. = 52-3 V.T.S. = 74- 57 = 22 oP"''" °°1 \ voyage / T.P. = 10- V. = 523- S.C. = 10356 sq. ins. = -09 L. L.B. = 455 = 10- LH.P. = 5467- 1 ^™™''^ ] \maximumj P.D. P.O. = 1-34 = -78 DB. = • 522 Maximum E.H.P. = 4045 • D.V.E. = -547 D.O. P.V. = 1-84 = 1226- Maximum I.H.P. = 5066-f— 1} Oonstani P.P. = -277 = -842 ,j = 1136- Mean E.P.P. =3748- „ P.S. = 2-4849 S.K. = 15- „ Calculated I.H.P. fok Vessel at Maximum Draught. CM. 4610 •303 lines A.M.S. 1396-83 •914 L.B. 1275-94 1-02 D.B. 1300-5 •6 W.S., CM. 780-0 1-108 W.S., L.B. 864-24 LH.P. at8 knots 926 •766 lines 709-31 •98 D.B. 694-82 2-108 W.S., L.B. Calculated I.H.P. fok Vessel Mean. A. M.S. maximum. A.M.S. mean. 926 : 5388 :: 858 858 926)4622904 769-95 I.H.P., A.M.S. 864-24 „ CM. 2)1633- 5000 IH.P. at 15 knots on voyage. Actual I.H.P. on voyage = 4900. 816-5 I.H.P. mean at 8 knots. 6-6 5388-9 I.H.P. mean at 15 knots. EXAMPLES. 65 EXAMPLE B. Peopoetional op Vessel Maxtmtjm. I.H.P., A.M.S. 768) 864 I.H.P., O.M. at 8 knots. 1-125 Ratio of power O.M. 1- „ „ A.M.S. 212-125 Peopoetional of Vessel Mean. A.M.S. Maximum. A.M.S. mean. 926 : 1226 :: 858 858 926) 1051908 1136 P.V. mean on voyage. 1 - 0625 Ratio of power mean. A.M.S. 926 1-15 Ratio D.T. 1064-9 •98 D.B. Normal E.H.P. Maximum. 2)1226 P.V. Maximum. 613 E.H.P. at 8 knots. 6-6 at 15 knots. Norma] E.H.P. mean. 2)1136 P.V. mean. 568 E,H,P. at 8 knots. 6-6 at 15 knots. 1042-72 1-108 W.S., L.B. 1154-5 1-0625 Ratio of power mean. •74)4045-8 E.H.P. 5467 I.H.P. •74)3748-8 E.H.P. 5066 LH.P. 1226- 12 P.V. Maximum. Resistance in Pounds PsEssrEE op the Blades OP THE SoEEW PeOPELLEE. Eppeotite Peessure in Pounds on THE Pistons of the Englnes. D.M.V._12'10J" C. = 40-416 52-3 E. T.P. C. 10-)40-416 4-04 M.S. 60)2113-75 4900 Total I.H.P. on voyage. -74P.E.P. 35-229^ = 1241- 16-08 ^t:d;= 1-08 3626 E.H.P. on voyage. 33000 P.0.= -78 •842 P.P. V.T.S. 74 •) 1136 P.V. mean. 15-35 y = 2-4849 P.S. - 842 P.P. V. 523)119658000 228,791 lbs. effective pressure 1035)19955-28 2-3)19-28 on Pistons. 8-38 lbs. 10656 sq. ins. V.T.S. Coefficient corrected foe Slip. Ratio of slip = 1-13 89297-28 -6266 Coefficient. 2-0922 •277 Constant. Actual „ = -09 55963-5 4-04 M.S. •5794 Coefficient. 1-04^ = 1-0816 •5794 Coefficient. 226,090-5 lbs. Resistance of Screw Propeller. icient. • 62G6 Corrected coefE 66 RESISTANCE AND PROPORTIONS OP SCREW PROPELLERS. EXAMPLE C. Vessel. Engines. Screw Propeller. O.M. = 2480 Type: Compound Number of screws, 1 D.T. = Maximum Number of sets of Engines, 1 Number of blades, 4 = 4490 On trial I.H.P. = 1717 • On trial D.E. = 17' 0" A.M.S = 724 Maximum E.H.P. = 1219- D.M.V. = 9 9J = 615 On trial S. = 80- P. = 20 3 B. = 39' 0" P.E.P. = -71 C. = 30-75 D. = 21 Maximum E. = 60- M.S. = 3-84 = 18 3 On trial T.P. = 8- V.T.S. =42-5 L. = 330 V. = 480- = 6120 sq. ins. L.B. D.B. = 8-46 = • 54 Maximum I.H.P.=2270-^--l^} S.C. = Nil. P.D. =1-19 D.O. = 2-1 E.H.P. = 1611- P.O. = -66 P.V. = 908- = 771- LH.P.,= 1927-{^°-f-} D.V.E. = -576 Constant = -25 S.K. = 12-2 On trial E.H.P. = 1368- P.P. = -6916 P.S. =2-6273 Calculated I.H.P. foe Vessel at Maximum Draught. Calculated I.H.P. foe Vessel ON Teial. O.M. = 24^ •324 lines A.M.S. = 724- •818 lines 803 • 52 1-025 L.B. 823^075 107 D.B. 880-61 •735 W.S., O.M. 646-80 1-057 W.S., L.B. 682-82 I.H.P. at 8 knots. 592-23 -96 D.B. A.M.S. maximum. A.M.S. on trial. 724 : 2277 :: 615 615 568-32 1-057 W.S.,L.B. 600-37 LH.P., A.M.S. 682-82 ,, O.M. 2)1283- 724)1400355 1934 I.H.P. at 12-2 knots on trial. Actual I.H.P. on trial = 1717. 641-5 I.H.P. mean at 8 knots. 3-55 2277-3 I.H.P. mean at 12-2 knots. EXAMPLES. 67 EXAMPLE 0. Peoportional of Vessel Maximum. I.H.P., A.M.S. 60 0) 682 LH.P., O.M. at 8 knots. 1-153 Ratio of power O.M. 1" .. „ A.M.S. 2^2-153 1 • 076 Ratio of power mean. Pkopoetional of Vessel ov Trlil. A.M.S. Maximum. A.M.S. on trial. 724 : 908 :: eis 615 724)558420 ' 771 P.V. on trial. A.M.S. = 724 1-15 Ratio D.T. 832-6 •96 D.B. Normal E.H.P. Maximum. 2)908 P.V. Maximum. 454 E.H.P. at 8 knots. 3-55 at 12-2 knots. 799-29 1-057 W.S., L.B. -71)1611-7 E.H.P. 844-54 1 - 076 Ratio of power mean. 2270 I.H.P. Normal E.H.P. on trial. 2)771 P.V. on trial. 385-5 E.H.P. at 8 knots. 3-55 at 12-2 knots. -71)1368-5 E.H.P. 1927 LH.P. 908-14 P.V. Maximum. Resistance in Pounds Pressure of the Blades OP THE SoBEw Propeller. Effective Pressure in Pounds on THE Pistons op the Engines. 1717 Total I.H.P. on trial. •71 P.E.P. D.M.V.= 9' 9 J" C. = 30-75 60- R. 60 )1845 1219-07 E.H.P. 33000 30-75^ - 945-56 16-08 T.P. C. 8-)30-75 3-84 M.S. v'pS: =1-048 P.O. = -66 480)40227000 83,806 lbs. effective pressure on Pistons. Coefficient corrected for Slip. Ratio of slip = 1^1 1035)15204 • 60 2-3)14-69 6-387 lbs. 6120 sq. ins. V.T.S. V.T.S. 42-5)771 •6916 P.P. P.V. 18-14 4^"^ 2-6273 P.S. ■6916 P.P. Actual - -0 1-V = 1^21 •4542 Coefficient. 39088^44 •5495 Coefficient. 21478^85 3^84 M.S. 1^8170 • 25 Constant. •4542 Coefficient. • 5495 Corrected coefficient. 82,475 lbs. Resistance of Screw Propeller. F 2 68 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. EXAMPLE D. Vessel. Engines. Screw Propeller. CM. = 1815 Type : Compound Number of screws, 1 D.T. = 4565 Maximum Number of seta of En = 1108 •48 Coefficient. 1^898 •253 Constant. 13540-9 3-98 M.S. -4801 Coefficient. •5322 Corrected Coefficient. 52 ,889-2 lbs. Resistance of Screw Propeller. 70 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. EXAMPLE E. Vessel. Engines. Screw Propeller. O.M. = 2241 Type : Compound Number of screws, 1 D.T. = 5600 Maximum Number of sets of Engines, 1 Number of blades, 4 = 5585 On trial I.H.P. = 1460 On trial D.E. = 16' 0" A.M.S = 780 Maximum E,H.P. = 1044 1 D.M.V. = 92 = 777 On trial S. = 85 P. = 17 li. = ■AT 0" P.E.P. = 715 C. = 28-75 D. = 23 Maximum E. = 70 25 M.S. = 3-59 = 22 11 On trial T.P. = 8 V.T.S. =35-5 L. = 330 V. = 562 „ = 5112 sq. ins. L.B. = 9- I.H.P. = 1634 Normal S.C. = -07 D.B. = -62 Maximum E.H.P. = 1168 P.D. =1-06 U.O. = 2-5 P.O. = -585 P.V. = 899- D.V.E. = '572 S.K. = 11-076 On trial Constant = -254 P.P. = -5937 P.S. =2-9362 Calculated I.H.P. for Vessel at Maximum Draught. O.M. = 2241- •324 lines 726-08 •99 L.B. 718-74 1-13 D.B. 811-34 •763 W.S., O.M. 618-79 1-074 W.S., L.B. A.M.S. 663-73 LH.P. at 8 knots. ;780- •818 lines 638-04 •9 D.B. 574-2 1-074 W.S., L.B. Actual LH.P. on trial = 1460. 616-47 LH.P., A.M.S. at 8 knots. 663-73 „ O.M. „ 2)1280- 640 • I.H.P. mean at 8 knots. 2-6 1664 I.H.P. mean at 11 knots. EXAMPLES. 71 EXAMPLE E. Propoetional op Vessel Maximum. I.H.P., A.M.S. 616) 663 I.H.P., O.M. at 8 knots. 1-076 Eatio of power O.M. 1- „ „ A.M.S. 2)2 -076 1 • 038 Eatio of power mean. A.M.S. = 780 l-15EatioofD.T. 897 •9 D.B. 807-3 1-074 W.S.,L.B. 866-7 1 - 038 Eatio of power mean. -9 P.V. Maximum. NoBMAi E.H.P. Maximtim. 2)899 P. V. MaximuD. 449-5 E.H.P. at 8 knots. 2-6 at 11 knots. ■715)1168.7 E.H.P. on trial. 1634 I.H.P. Eesistance in Pounds Peessuee op the Blades OP THE SOEEW PeOPBLLEK. EppBonvB Prbssueb in Pounds on THE Pistons op the Engines, 1460 Total I.H.P. on trial. •715P.E.P. 1043-9 E.H.P. 33300 562)34448700 61,296 lbs. effective pressure — — on Pistons. D.M.V. = 9' 2" C. = 28-75 70-25 E. T.P. C. 9) 28-75 60)2019-68 3-59 M.S. 33 -66^ = 1132-89 16-08 4/p.D. = 1-015 P.C. = -585 •5937 P.P. V.T.S. 35-5)899 P.V. 25-32 4/'^2-9362P.S. - 5937 P P 1035)18216-87 2-3)17-6 7-65 lbs. 5112 sq. ins. V.T.S. 39106-80 -4427Coe£aoient. 1-7432 •9n4 Cnnsfiant 17312-22 3-59 M.S. -4427Coefficif 62,150-8 lbs. Resistance of Screw Propeller. RESISTANCE AND PROrORTIONS OP SCREW PROPELLERS. EXAMPLE PI. Veeaels. Engines. Screw Propeller. CM. = 1039 Type : Compound Number of screws, 2 D.T. = 1248 Maximum Number of seta of Engines, 2 Number of blades in each, 2 = 1230 On trial LH.P. = 2887- total on trial D.E. = 13' 2" A.MS = 334 Maximum E.H.P. = 2078- „ D.M.V. = 75 = 330 On trial. S. = 92- P. = 15 8 B. = 32' 0" P.E.P. = -72 0. = 23-17 D. = 14 3 Maximum E. = 113- M.S. = 3-86 = 14 li On trial T.P. = 6- V.T.S. = 34- total L. = 210 V. = 678- _ ,„. /in each " ■" \ screw „ = 2448- sq. ins. L.B. D.B. = 6-56 = -445 Maximum IHP -2192- / Normal \ l.M.f. _ /19^ \maximum/ D.O. = 1-201 E.H.P. = 1578- S.C. = -067 P.V. = 360- P.D. = 1-19 S.K. = 16-49 On trial P.O. = -675 D.V.E. = -563 Constant = -261 P.P. = -7073 P.S. = 2-195 Oaloulatbd I.H.P. fob Vessel at Maximum Deaught. A.M.S. = 334- -695 lines .M. = 1039- -275 lines 285-725 1-02 L.B. 290-7 ■95 D.B. 275-5 1- W.S., O.M. 275-5 -98 W.S., L.B. 269-5 LH.P. at 8 knots. 232-13 1-08 D.B. 250-56 -98 W.S., L.B. Actual I.H.P. on trial = 2887. 245- I.H.P., A.M.S. at 8 knots. 269-5 „ O.M. 2)5 14- 257 - I.H.P. mean at 8 knots. 8-77 2253-89 LH.P. at 16-5 knots. EXAMPLES. 73 EXAMPLE P 1. Peopoetional of Vessel Maximtim. I.H.P., A.M.S. 245) 269-5 I.H.P., O.M. at 8 knots. A.M.S. 1 - 1 Eatio of power 2)2-1 1 - 05 Eatio of power O.M. A.M.S. mean. NoBMAL E.H.P. Maximum. 2)360 P.V. Maximum. = 334 -975 Eatio of D.T. 180 E.H.P. at 8 knots. 8-77 at 16-5 knots. -72)1578-6 E.H.P. 325-65 1 -08 D.B. 2192 I.H.P. 351 •98 W.S., L.B. 343-98 1 - 05 Eatio of power mean. 360-15 P,V. Maximum. Eesistancb in Pounds Pressuee op the Blades OF EACH SOEEW PeOPELLEE. Effective Peessuee in Pounds on the Pistons of each set of Engines. 2)2887 Total I.H.P. on trial. 1443-5 I.H.P. of each set of •72 P.E.P. [Engines. V. 1039-32 E.H.P. of each set of 33000 [Engines. 678)34297560 50,586 lbs. effective pressure on Pistons. D.M.V. = 7' 5" 0. =23-17 113 E. V.T.S. Hcient. T.P. C. 6)23-17 3-86 = M.S. ^PJ). = 1-048 P.O. = -675 '' 60)2618-21 43-637^ = 1905- 16-08 •7073 P.P. 1035)30632-40 V.T.S. 34)360 P.V. 2-3)29-6 12-9 lbs. 2448 sq. ins. 10-6 il~= 2-195 P.S. -7073 P.P. 31579-2 -4052 Coei 1-5528 -261 Constant. 12795-81 3-86 M.S, -4052 Coefficient. 49,388-7 lbs, Eesistance of Screw Propeller. 74 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. EXAMPLE G. Vessel. Engines. Screw Propeller. O.M. = 63-3 Type : Compound Number of ecre"ws, 1 D.T. = 95- Maximum Number of sets of Engines, 1 Number of blades, 4 „ = „ On trial I.H.P. = 76- On trial D.E. = 5' 0" A.M.S = 66-27 Maximum E.H.P. = 53-2 „ D.M.V. = 30 ,, = „ On trial S. = 70- P. = 10 B. = 14' 0" P.B.P. = -7 C. = 9-424 D. = 56 Maximum E. = 125- M.S. = 3-77 = „ On trial T.P. = 2-5 V.T.S. = 5-4 L. = 72 V. = 312-5 „ = 776- sq. ins. L.B. D.B. = 5-14 = -4 i-H-p-=^^-«Uxrut} S.C. = -3 P.D. = 2- D.O. P.V. = 1-43 = 76-6 E-H-P-= S^-3Urum} P.C. = 1-06 D.V.E. = -6 S.K. = 9- On trial Constant = -23 P.P. = 1-335 P.S. = 2-42 Calculated I.H.P. fob Vessel at Maximum Draught. O.M. = 66-3 -31 lines. A.M.S. 20-553 1-355 L.B. O.M. .at 8 27-10 -89 D.B. 24-03 2-28 W.S. + L.B 54-72 I.H.P knots. 66-27 -783 lines. 51-678 1-132 D.B. 57-732 •92 W.S., L.B. 53-084 I.H.P., A.M.S. at 8 knots. 54-72 I.H.P. O.M. at 8 knots. 5)107-8 53-9 I.H.M. mean at 8 knots. 1-42 76-5 I.H.P. mean at 9 knots. EXAMPLES. 75 EXAMPLE G. Pbopobtional op Vessel Maxutom. LH.P., A.M.S. 53-08) 54-72 LH.P., O.M. at 8 knots. 1 ■ 03 Eatio of power O.M. 1- „ „ A.M.S. 2)2 -03 1-015 Eatio of power mean. A.M.S. = 66 1-1 Eatio of D.T. 72-6 1-132 D.B. NoKMAL E.H.P. Maximtim. 2)76-6 P. V. Maximum. 38-3 E.H.P. at 8 knots. 1-42 at 9 knots. ■7)54-38 E.H.P. on trial. 77-6 LH.P. ontriaL 82-18 •92 W.S., L.B. 75-5 1-015 Eatio of power mean. 76-6 P. V. Maximum.. Eesistance in Pounds Pbessuee ov the Blades OP THE SOEEW PbOPBLLEB. D.M.V. = 3' 0" C. = 9-424 125- E. T.P. C. 2-5)9-424 Eppbotitb Pbessuee in Pottnds on THE Pistons op the Enqines 76 = Total I.H.P. on trial. •7 P.E.P. 53-2 E.H.P. on trial. 33000 V. 60)1178-0 19- 63--' = 385-336 16-08 3-77 M.S. 5P.D. = 1-26 P.O. = 1-06 312-5)1755600 1035)6196-202 2-3)5-986 2-6 lbs. 776- sq. ins. V.T.S. 1-335 P.P. V.T.S. 5-4)76-6 P. V. _14-2 ^ = 2-42 P.S. 1-335 P.P. 5618 lbs. effective pressure — — on Pistons. 2017.6 •743 Coefficient. 3-2307 - 23 Constant. 1498-63 3-77 M.S. -74306 Coefficient. 5648-4 lbs. Eesistance of Screw Propeller. 76 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. EXAMPLE A 5. — Proposed Screw Propellers. Vessel. Engines. Screw Propeller. Type : Compound with separate Number of screws, 2 circulating Number of blades in each, 4 Number of sets of Engines, 2 D.E. = 18' 6" CM. = 3065 I.H.P. = 5685- total calculated D.M.V. = 10 4 D.T. = 3750 Maximum E.H.P. = 4206- „ P. = 20 6 A.M.S = 777 S. = 65- C. = 32 5 B. = 46' 1" P.E.P. = -74 M.S. 5 416 D. = 19 9 Maximum E. = 92- V.T.S. = 42 14 total L. L.B. = 300 = 6-52 T.P. = 6- V. = 552- )) = 21 Q_ fin each ' \ screw, P.B. D.O. = • 43 Maximum = 1-22 I.H.P. = 5758- ( ^°™^* 1 \maxmium/ s.'b. = 3034 sq. ins. 066 P.V. = 815- E.H.P. =4261- „ P.D. 1 1 S.K. = 17-5 Intended P.O. = 63 D.V.E. =z 56 Constant = 264 P.P. z= 646 P.S. = 2-684 Calculated I.H.P. for Vessel at Maximum Draught. Calculated I.H.P. mean at 8 knots for Al = 543- 10-47 5685 - I.H.P. mean at 17 - 5 knots. EXAMPLES. 77 EXAMPLE A 5, — Proposed Screw Propellers. Proportional of Vessel Maximum. LH.P., A.M.S. 557) 528 I.H.P., O.M. at 8 knots. •948 Eatio of power O.M. 1- „ „ A.M.S. 2) 1-948 •974 Ratio of power mean. A.M.S. = 777 1 Eatio D.T. 777 1-1 D.B. 854-7 •98 W.S., L.B. 837-6 - 974 Eatio of power mean Xormal E.H.P. Maximum. 2)815- P.V. Maximum 407-5 E.H.P. at 8 knots 10-47 at 17-5 knots 74)4261- E.H.P. total normal 5758- I.H.P. „ 815-92 P.V. Maximum Eesistance in PorxBs Pressure op the Blades OF each Screw Propeller. Effective Pressure in Pounds on the Pistons of each set of Engines. 2)5758- LH.P. total normal 2879 I.H.P. of each set of Engines. -74 P.E.P. 2130- E.H.P. 33000 552)70290000 • 127 , 337 lbs. effective pressure on Pistons. •.M.V. = 10' 4'' C = 32-5 92- R. ins. fflo Rt T.P. C. 6-)32-5 5-416 M.S. 60)2990-0 49-83= = 2483- ,;yP.D. = 1-026 P.O. = -63 16-08 -6463 P.P. 1035)39926-86 V.T.S. 42-14)815- P.V. 2-3)38-57 16-77 lbs, 3034- sq. i 19-34 ^y/ = 2-t;.^4 P.S. V.T.S. -646 p.p. 50880-18 •4575 Coe 1-7338 ient. ■ 264 Constant. 2.3277-6 5-416 M.S. ■4575 Coefficient, 126,068-2 lbs. :'sistance of Screw Propeller. 78 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. EXAMPLE A 6. — Proposed Screw Peopellees. Vessel. Engines. Screw Propeller. Type : Compound with separate Number of screws, 2 circulating Number of blades in each, 4 Number of seta of Engines, 2 D.E. = 15' 3" O.M. = 3065 I.H.P. = 5685- total calculated D.M.V. = 88 D.T. = 3750 Maximum E.H.P. = 4206- P. = 23 A.M.S = 777 S. = 65- C. = 27-25 B. = 46' 1" PE.P. = -74 M.S. = 4-54 D. = 19 9 Maximum E. 92- V.T.S. = 55- total L. L.B. = 300 = 6-52 T.P. 6- V. 552- n-.E /in each' - ^' ° \ screw / D.B. DO. = -43 Maximum = 1-22 LH.P. 5758-/ N°™^^ ] l^maximum/ = 3960- sq. ins. S.C. = -17 P.V. = 815- E.H.P. 4261- P.D. = 1-5 S.K. = 17-5 Intended P.C. = -84 D.V.B. = -569 Constant = -256 P.P. = -949 P.S. = 2-4558 Caloulated I.H.P. FOK Vessel at Maximum Draught. Calculated I.H.P. mean at 8 knots, for A 1 = 543 10-47 5685- I.H.P. mean at 17 '5 knots. EXAMPLES. 79 EXAMPLE A 6. — Proposed Scbew Peopelleks. Proportional op Vessel Maxhtom. I.H.P., A.M.S. 557) 528 LH.P., O.M. at 8 knots. • 948 Eatio of power O.M. 1- „ „ A.M.S. 2)1-948 A.M.S. ■974 Eatio of power mean. 777 1 Eatio D.T. 777 1-1 D.B. Normal E.H.P. Maximum. 2)815 P.V. Maximum. 407-5 E.H.P. at 8 knots.- 10-47 at 17-5 knots. -74)4261- E.H.P. total normal. 5758- LH.P. 854-7 •98 W.S., L.B. 837-6 -974 Eatio of power mean. 815-92 P.V. Maximum. Eesistance dt Pounds Pressceb on the Blades of each Borew Propeller. D.M.V. = 8' 8" C. =27-25 92 E. T.P. C. 6)27-25 4-54 M.S. Eftectivb Pressure in Pounds on THE Pistons of each set of Engines. 2)5758 LH.P. total normal. 2879 LH.P. of each set of -74P.E.P. [Engines. 60)2507-0 i/P.D. = 1-13 P.O. = -84 V. 2130 E.H.P. of each set of 33000 [Engines. 1035)28091-76 2-3)27-14 552)70290000 11-8 lbs. 3960 sq. ins. V.T.S. •9492 P.P. V.T.S. 55)815 P.V. 14-83 .^"^2-4558 P.S. -949 P.P. 127,737 lbs. effective pressure on Pistons. 46728 -596 Coefficient. 2-3305 •256 Constant. 27849-8 5-54 M.S. -5964 Coefficient. 126,434 lbs. Eesistance of Screw Propeller. 80 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. EXAMPLE F 2. — Peoposed Soeew Pkopelleks. Vessel. Engines. Screw Propeller. Type : Compound Number of screws, 2 Number of sets of Engines, 2 Number of blades in each, 4 O.M. = 1039 LH.P. = 2253- total calculated D.E. = 13' 2" D.T. = 1248 Maximum E.H.P. = 1622- „ „ D,M.V. = 7 7 A.M.S. = 334 „ S. = 92- P. :r: 16 6 B. = 32' 0" P.E.P. = -72 0. = 23-96 D. = 14 3 Maximum K. = 113- M.S. = 4- L. = 210 T.P. = 6- V.T.S. = 20-16 total L.B. D.B. D.O. = 6-5G = - 445 Maximum = 1-201 „ V. = 878- LH.P. =2192-1^°™^! ] \maximumj )» = 10-08 f° """"H \ screw J 1451- sq. ina. P.V. = 360- E.H.P. = 1578-1 ^°"™^1 ] \maximum/ sic. = •115 S.K. = 16-5 On trial P.D. r= 1-25 P.O. = ■688 D.V.E. = -576 Constant = •25 P.P. = •731 P.S. = 2-6132 Calculated LH.P. eoe Vessel at Maximum Deaught. A.M.S. = 334- -695 lines .M. = 1039- -275 lines 285-725 1-02 L.B. 290-7 •95 D.B. 275-5 1- W.S., O.M. 275-5 -98 W.S., 269-5 LH.P L.B. . at 8 knots 232-13 1-08 D.B. 250-56 -98 W.S., L.B. 245- LH.P., A.M.S. at 8 knots. 269 -5 „ O.M. 2)514- 257- LH.P. mean at 8 knots. 8-77 2253-89 LH.P. mean at 16-5 knots. EXAMPLES. EXAMPLE F 2.— Proposed Screw Pbopellbrs. Proportional op Vessel Maxisiuji. LH.P., A.M.S. 242) 269 ■ 5 I.H.P., O.M. at 8 knots. 1 - 1 Ratio of power O.M. 1- „ „ A.M.S. 2)2-1 A.M.S. 1 "05 Ratio of power mean. 334 •975 Ratio of D.T. 325-63 1-08 D.B. 351 -98 W.S., L.B. 343-98 1 - 05 Ratio of power mean. 360-15 P.V. Maximum. Normal E.H.P. Maximum. 2)360 P.V. Maximum. 180 E.H.P. at 8 knots. 8-77 at 16-5 knots. -72)1578-6 E.H.P. total normal. 2192 LH.P. „ Resistance in Pounds Pressure op the Blades or each Screw Propeller. Eppectite Pressure in Pounds on the Pistons of bach set op Engines, 2)2192 1096 LH.P. total normal. LH.P. of each set of 72 P.E.P. [Engines. V. 789-12 E.H.P. of each set of 33000 [Engines. 678)26037000 38,402 lbs. effective pressure on Pistons. D.M.V. = 7' 7" C. = 23-96 113 E. V.T.S. ent. T.P. C. 6)23-96 4- MS 60)2707-48 45-125^ = 2036- 4'F.D. = 1-0625 P.O. = -688 16-08 1035)32738-88 2-3)32-63 13-75 lbs. 1451 sq. ins. -731 P.P. V.T.S. 20-16)360 P.V. 17-85 4/ = 2-6132 P.S. -731 P.P. 19951 •4775Coeffici 1-9101 -25 Constant. 9526-6 4- M.S. -4775Coefecient. 38,104 lbs. Resistance of Screw Propeller. G 82 RESISTANCE AND PROPORTIONS OP SCREW PROPELLERS. EXAMPLE F 3. — Peoposed Sobew Peopelleks. Vessels. Engines. Screw Propeller. Type : Compound Number of screws, 2 Number of sets of Engines, 2 Number of blades in each, 4 CM. = 1039 I.H.P. = 2253- totalcalculated D.E. = 10' 0" D.T. = 1248 Maximum E.H.P. = 1622- „ D.M.V. = 5 10 A.M.S. = 334 S. = 92- P. =20 B. = 32' 0" P.E.P. = -72 0. = 18-33 D. — 14 3 Maximum E. = 118- M.S. = 3-05 L. = 210 T.P. = 6- V.T.S. = 22-66 Total L.B. D.B. DO. = 6-56 -445 Maximum 1-201 V. = 708- LH.P. = 2192- ( ^°y™^l \maximum n . QQ /in each' = 1631- so. in 3. P.V. — -360 E.H.P. = 1578- S.C. = -3 S.K. 16-5 On trial P.D. = 2- P.C. = 1-091 D.V.E. = -585 Constant = -242 P.P. = 1-3746 P.S. = 2-5408 CALO0LATED I.H.P. EOK VESSEL AT MAXIMUM DkACQHT. A.M.S. = 334- -695 lines O.M. = 1039- •275 lines. 285-725 1-02 L.B. 290-7 -95 D.B. 275-5 1- W.S., O.M. 275-5 •98 W.S., L.B. 269-5 I.H.P. at 8 knots 232 13 1-08 D.B. 250-56 •98 W.S., L.B. 245- I.H.P., A.M.S. at 8 knots. 269-5 „ O.M. 2): i514- 257- I.H.P. mean at 8 knots. 8-77 2253-89 LH.P. 16-5 knots. EXAMPLES. 83 EXAMPLE F 3.— Peoposed Scbew Peopellees. Peopobtional of Vessel Maximum. LH.P., A.M.S. 245) 269-5 LH.P., O.M. at 8 knots. 1 • 1 Eatio of power O.M. 1- „ „ A.M.S. 2)2 1 1 • 05 Eatio ef power mean. Noemal E.H.P. Maximxim. 2)360 P. V. Maximum. 180 E.H.P. at 8 knots. 8-77 at 16-5 knots. A.M.S. = 334 •975 Eatio of D.T. 325-65 1-08 D.B. •72)1578-6 E.H.P. total normal. 2192- LH.P. •351 W.S., L.B. 343-98 1 • 05 Eatio of power mean. 360-15 P.V. Maximum. Eesistanoe in Pounds Peessuee op the Blades OP EACH SOEBW PeOPELLEE. Effective Peessuee in Pounds on the rstons op bach set op engines. 2)2192 LH.P. total normal. 1096 I.H.P. of each set of •72 P.E.P. [Engines. 789-12 E.H.P. 33000 708)26037000 36,775 lbs. effeotiye pressure on Pistons. D.M.V.= 5' 10" 0. =18-33 118 E. T.P. C. 6-)18-33 3-05 M.S. 60)2162-94 36-042- ^P.D. = 1-26 P.O. =1-091 1296- 16-08 1-3746 P.P. V.T.S. 1035)20839 -68 2-3)20-13 8-75 lbs. 1631-sq.ins.V.T.S 22 • 66)360 • P.V. 16-41 4^^ 2 -5408 P.S. 1-3746 P.P. 3-4914 -242 Constant. 14271-25 - 845 CoefGcient, ■8449 Coefficient. 12058-9 3-05 M.S. 36,776 lbs. Eesistance of Screw Propeller. 84 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. EXAMPLE SHOWING METHOD OF CALCULATING THE SURFACE OP THE BLADES. Standaed Sceew Peopellek 2 Proposed Scee-w Peopellees, A 5. D.E. P. S.K. = 10' 1" = 10 1 = 8. D.E. = 18' 6" P. = 20 6 S.K. = 17-5 intended. Phopoetions. Eatios Peopoetions. Eatios. D.M.V. = 5-9 E. = 83- M.S. = 4- V. = 385- 9-;= 1- D.M.V. = 10-83 1-75 1 _ j.gg , _ 3. E, = 92- 1-108/ - 1 y^y -^ ^^y M.S. = 5-41 1-352 V. =552- 1-433 4/^.0.= 1- P.O. = -544 Constant = -242 \/F.T>. = 1-026 1-026 P.O. = -63 1-158 Constant = -264 1-091 Multiple of ratios 1- Multiple of ratios 9-515 Eatio of power per S.K !• Eatio of power per S.K. 10-466 Normal V.T.S. per P.V. - Multiplier = • 045 Normal V.T.S. per P.V. - Multiplier = • 045 9-515"il0-466 5) 1-1 Eatio of power 1 „ t^' 1-15 VTSf See Diagram. ■ 045 Normal multiplier. •05175 815- P.V. Maximum same as A 1. 2)42-135 total V.T.S. 21 -067 V.T.S. of each screw. EXAMPLES. 85 EXAMPLE SHOWING METHOD OF CALCULATING THE SUEFACE OF THE BLADES. Standard Soeew Pbopeller. D.E. = 10' 1" P. = 10 1 S.K. = 8- Pbopoetions, D.M.V. = E. M.S. = V. = 4/P.D. = P.O. = Constant = 5 83 4 385 1 Eatios. 544 242 Multiple of ratios Eatio of power per S.K Normal V.T.S. per P. V.— Multiplier = 2 Peoposed Scee-w Peopellees, a 6. D.E. - 15' 3" P. = 23 S.K. = 17-5 intended. Peopoetions. D.M.V. E. M.S. V. V'PD. P.O. = 8-66 = 92- = 4-54 = 552- = 113 •84 4671 ■108} Constant = •256 Eatios. 1-625'= = 2-6406 .. .. 1-135 .. .. 1-433 .. .. 1-13 .. .. 1-544 .. .. 1-057 Multiple of ratios 8-024 Eatio of power per S.K 10-466 045 Normal V.T.S. per P.V.— Multiplier = -045 8^024)10-466 1-304 Eatio of power. \ g r)ia»ram 1-5 „ of V.T.S. / °®® '^S"^*"- - 045 Normal multiplier. -0675 815 • P. V. Maximum same as A 1. 2)55-01 total V.T.S. 27 ■ 5 V.T.S. of each screw. 86 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. EXAMPLE SHOWING METHOD OP CALCULATING THE SURFACE OP THE BLADES. Standard Sokew Propeller. D.E. = 10' P. = 10 S.K. = 8' Proportions. D.M.V. E. M.S. V. 4/ P.D. P.O. = 5-9 = 83- = 4- = 385- = 1- •544 Ratios. }:} = 1-^ = 1 Constant = •242 Multiple of ratios Ratio of power per S.K Normal V.T.S. per P. V.— Multiplier = 2 Proposed Screw Propellers, F 2. D.E. = 13' 2" P. = 16 6 S.K. = 16-5 on trial. Proportions. Ratios. D.M.V. E. M.S. V. ^P.D. ■p.c. Constant = 7 = 113 = 4 = 678 = 1 583 0625 688 25 285\ _ 361/ ~ 1^747^ = 3^052 .. .. 1- .. .. 1^761 .. .. 1^062 .. .. 1-264 .. .. 1-033 Multiple of ratios 7-549 Ratio of power per S.K 8-77 045 Normal V.T.S. per P. V.— Multiplier = '045 7-549)8-770 1-16 Ratio of power.) CI -rv- 1-25 „ ofV.T.S.|^<=®^'^g'''*"- ■ 045 Normal multiplier. -05625 360- P.V. Maximum same as F 1. 2)20-160 total V.T.S. 10-08 V.T.S. of each screw. EXAMPLES. 87 EXAMPLE SHOWING METHOD OF OALCULATING THE SURFACE OF THE BLADES. Standard Scbew Pbopeller. D.E. = 10' 1" P. = 10 1 S.K. = 8' 2 Pkoposed Soebw Pbopellers, F 3. D.E. = 10' 0" P. = 20 S.K. = 16-5 on trial. Proportions. D.M.V. = 5-9 E. = 83- M.S. = 4- . V^ =385- v'l-'.D. = 1- . P.O. = -544: Constant = -242 Ratios. Multiple of ratios Ratio of power per S.K. Normal V.T.S. per P. V.— Multiplier : Proportions. D.M.V. B. M.S. V. ^P.D. P.O. = 5-833 = 118- = 3-05.. = 708- .. = 1-26 = 1-091 Constant = -242 -988" 1-421 Ratios. = 1-404^ Multiple of ratios 7 Ratio of power per S.K 8 045 Normal V.T.S. per P. V.— Multiplier = 971 762 839 26 77 045 7-)8-77 1-253 Ratio of power.) q„„ -n-™™™™ 1-4 „ of V.T.S. r'^'^^^'Sram. ■045 Normal multiplier. •0630 360- P. V. Maximum same as F 1. 2)22-680 total V.T.S. 11-348 V.T.S. of each screw. 88 RESISTANCE AND PROPORTIONS OF SCREW PROPELLERS. EXAMPLES SHOWING THE CALCULATED RELATIVE RESISTANCE OP SCREW PROPELLERS. A 5. Peopoktion. V.T.S. = 21-07 y Ratio SfPTvT _ V Ratio of V.T.S. ~ Multiple of ratios as per example for surface of blades Ratios. 1- ^/v- 9-515 A 6. Peopoktion. V.T.S. = 27-5 ^ ^Ratio of P.V. Ratio of V.T.S. Multiple of ratios as per example for surface of Ratios. 1-3 .= -917 8-024 Total multiple of ratios . . .. .. 9-515 Total multiple of ratios . E 3. Peopoetion. V.T.S. = 11-33 9-564 E 2. Peopoetion. V.T.S. = 10-08 Ratios. .. .. 7-549 .. .. 7-549 Ratios. 1-11 7 Ratio of P.V. V Ratio of V.T.S. Multiple of ratios as per j example for surface of blades Total multiple of ratios . . "/ Ratio of P.V. \/ Ratio of V.T.S. ~ Multiple of ratios as per 1 example for surface of ) blades ) Total multiple of ratios \7l.ll= ■''' .. .. 7- .. .. 7-497 Note. — The Relative resistance of Screw Propellers being in proportion to the Total multiple of the ratios, it will be observed that the Relative resistance of Examples A 5 and A 6, also P 2 and E 3, are respectively equal ; consequently the Effective Horse-power required by the above examples would also be respectively equal. EXAMPLES. 89 EXAMPLES SHOWING THE CALCULATED RELATIVE RESISTANCE OF SCREW PROPELLERS COMPARED WITH THE STANDARD SCREW PROPELLER. Stanbabd Soeew. Pkopobtions. P.V. = 400- . V.T.S. = 18- . Ratios. 1- 1- A 5. Peopoktions. P.V. = 815- .. Total V.T.S. = 42-14 .. Ratios. 2-0375 2-341 ^-, Ratio of P.V. Ratio of V.T.S. Ratio of V.T.S =1 Multiple of ratios as per example"! _ y 1; _ 3/ Ratio of P7vr _ ^2^ V 1 ■ ~ " V Ratio of V.T.S. ~ V 2^ for surface of blades Relative E.H.P. P.V. _ 400 ~2~ ~ T " 1- : 200- RealE.H.P =200- Standaed Screw. Peopobtions. P.V. = 400- V.T.S. = 18- Ratios. 1- 1- V^ Ratio of P.V, :s: = V r - Ratio of V.T.i Ratio of V.T.S. Multiple of ratios as per example) for surface of blades / Relative E.H.P. P.V. _ 400 ~~2r ~ "2" ■■ = 1- = 200- RealRH.P =200- Ratio of V.' Ratio of V.T.S. Multiple of ratios as per example\ _ for surface of blades ~ •)- -955 2-341 9-515 Relative E.H.P =21-266 200- Real E.H.P. F 2. Propoetions. P.V. = 360- .. Total V.T.S. = 20-16 : 4253-200 Ratios. -9 1-12 V'i Ratio of P.V. VI?I = V 112 .qa Ratio of V.T.S. /v / , -„ - Ratio of V.T.S =1-12 Multiple of ratios as per example! _ 7.(540 for surface of blades / ~ Relative E.H.P. 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