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22 | MARINE REVIEW. [July 25, $$. LIMIT OF ECONOMICAL SPEED. ONE PER CENT. INCREASE OF SPEED BEYOND THE ECONOMICAL LIMIT IN ORDINARY VESSELS MEANS FIVE PER CENT. INCREASE IN HORSE 'POWER--SOME VALUABLE DEDUCTIONS. Mr. E. Tennyson D'Eyncourt read a paper at the last meeting of the Institution of Naval Architects upon the subject "The Limits of Economical Speed of Ships." As it is a subject of vital interest at present it is herewith reproduced: oe A wish has frequently been expressed at meetings of this institution that members would give results of their experience derived from the actual performance of vessels on progressive trials and the methods they adopt in estimating the power necessary for driving ships at given speeds; more especially was this the case when Mr. James Hamilton read his paper on "Horse Power Deduced from Progressive Trials," three years ago. I have therefore endeavored to bring into line the data obtained from a large number of progressive trials of ships of different forms and to derive certain broad practical rules from these data, which may, I trust, be of interest and may possibly elicit the results of their experience from others who have made a study of the question. I think it has, perhaps, been too common a practice in fixing the speed for a vessel, and in estimating the necessary indicated horse power for that speed, to over- look the question of what speed is appropriate to the form of vessel* under consideration. and to go upon the broad basis of allowing plenty of margin of horse power, with the result that often too high a speed has been aimed at and too much power has been allowed. As a necessary consequence, the weight and cost of the excess has been a continual burden upon the earning capacity of the ship. This was, perhaps, very well when competition was not so keen, but nowadays when cost has to -be cut down to a minimum in every direction, not only by the ship builder but also by the ship owner, the question of giving a ship enough, -and not too much, power and speed has become one of first importance. It is necessary to bear in mind the fact that every ship has an appro- priate limit of speed beyond which it is not economical to attempt to drive her; or, in other words, any increase of speed beyond this limit requires an undue increase of power. It has therefore been my object to arrive at a method of defining this limiting speed for ships of different sizes and different forms. To attempt to arrive at a general solution 'to meet all cases is, I need hardly say, an impossibility; but I venture to think that a fair approximation to the suitable power and speed may be F ig. i, Gurve LL gives values for Limiting asa percentage of VF for different block PPgives corresponding as pere. e of pee ated $0 Fig. 2. nee! Curves of Herse-Power. -- by skan friction. Coefficient of fineness. Fig. 3. * Ci Qurve of values of PH' at umnuting speed Ce ih wy Fegan HP. ec 300) . s = wave H.F Cicer I 8 a aoe ae oe | C2 | a Bey oe |e Ci 2 Te wal s F ti i Shap 100 200 ~ 300 400 - 500 609 700 yt Bi ie 0 On WL. Ue ae Scale of Speed. Limiting Speed Unity. arrived at by a consideration of the general principles governing the relation between the dimensions and form of ships on the one hand and the appropriate speed and power on the other. To obtain accurate values it is, of course, necessary to consider each case individually upon its own merits; to have the exact form of the under-water body and a record of the performance of a similar ship or of model experiments. In analyz- ing the trial results which I have had at my disposal I have not attempted to divide the indicated horse power absorbed into all the heads, which, in making an exhaustive analysis would perhaps be necessary; but I have for the sake of ease in comparing the performances of different vessels always assumed the effective horse power to be half the indicated horse power. This is a somewhat crude method, perhaps, but I think as good as any other where so many unknown or at least doubtful quantities are involved. I think, also, this is a fair average value to assume for the propulsive coefficient with modern triple or quadruple expansion ma- chinery and suitable propellers at the higher speeds which I am consider- ing. Having, therefore, made this assumption I have proceeded to calcu- late the horse power absorbed by skin friction on the basis given by the late Mr. Froude and now universally adopted; and all the difference after deducting the skin horse power from the effective horse power at any speed, gives the power necessary to overcome the so-called residuary resistance, which at the higher speeds is principally caused by wave- making. For brevity's sake this may be termed the wave horse power The different values of the wave horse power obtained by this method for similar ships, and in some cases for sister ships, show up the variations in the value of the propulsive coefficient \ of propeller AA Curve of Fffective Horse-Powr BB . . Horse-Power absorbed .CC.. . Horse-Powerabsorbed by wave making &c. efficiency, etc., actually occurring in practice; but the merit. of the method lies in the fact that it gives a definite comparison between the performances of different ships. The naval architect must make allowance for the efficiency. of machinery, etc, ds experience dictates. Having obtained curves in the manner indicated for many ships of varying dimensions, forms and degrees of fineness, | have been able to deduce the general results shown in the table below. This gives the coefficient of fineness and the amount of parallel body which may be associated with that coefficient, and the corresponding limiting economical speed, expressed as a percentage of the square root of the length of the ship in feet on the water-line. Parallel body as Limiting economical Coefficient of percentage of total speed in knots as fineness. nee : ele gs vl 6 . 14 86 a 30 68 8 49 48 Diagram I, shows these values in curves P P and L_L. The former gives the appropriate length of parallel body, which is equivalent to giving the combined lengths of entrance and run; and it will be seen that the percentage values of WL for the limiting economical speed are prac- tically the same as the percentage values of the combined length of entrance and run, This agrees with the value which has been given previously for vessels with no parallel body, but gives a smaller eco- nomical speed for vessels with parallel body, the previous rule having been that the economical speed is equal to the square root of the sum of the lengths of entrance and run, and it seems to show that a penalty must be paid for introducing parallel body. Bee Taking actual trial results, I find that the indicated horse power at the limiting speed, as defined above, is varying as the fourth power of the speed, and varies, in increasing ratio, till at about 12 per cent. above the limiting speed it is varying as the seventh power of the speed; whilst the wave horse power varies as vz' at the limiting speed, and as y!0, or sometimes as a higher power of y, at 12 per cent. above the limiting speed; and that at this point, viz., about 12 per cent. above the limiting speed, the wave horse power is approximately equal to the skin horse power, and then rises above it, the skin horse power, of course, always varying as y2-83, Diagram II gives a typical curve of horse power, A A being the curve of effective horse power, with 100 as its value at the limiting or unit speed. Curve B B gives the skin horse power, and curve C C the wave horse power. I have not taken the curves below .6 of the limiting speed, as it is not neces- sary to do so for my present purpose. The ratio of wave horse power to skin horse power at the limiting speed depends, of course, upon the form of entrance and run and the mean girth of the vessel up to the water line; but % seems to be a fair average value for vessels--of fine entrance and run and full midship section. If the midship section is fined, and the wetted surface thereby reduced for the same block co- efficient, it naturally follows that the entrance, or run, or both, must be filled out, with the effect that the skin resistance is reduced, and the wave-making increased, bringing the curves of skin horse power and wave horse power more closely together, as indicated by the dotted curves on the diagram, and bringing the point where skin horse power is equal to wave horse power to a lower speed. It is therefore impossible to lay down gen- eral rules to meet all cases, as the variations which may occur are almost infinite in number, and so only an indication of the kind of thing that may be expected can be given. Considera- tions of stability, involving beam; or fulness of water line, or of girth, which affects weight of hull, more especially if the vessel is to be built to Lloyd's rules, or the question of docking facill- ties, are merely examples of what the designer has to take account of, and they often hamper him in. adopting what he knows would be a better form, or more suitable dimensions for the speed than those he is compelled to take. The results I have obtained are from the : trials of vessels of good form for the coeffi- cients of fineness they possess. But there are many ships whose performances are not so good as I have indicated, and_ there are others, again, with better performances; the latter, however, generally speaking, appear to have had rather better propulsive coefficients than the 50 per cent. I have assumed; one or two examples apparently having values of 57 to 58 per cent. The values of the admiralty constant, caDHr* 1a e. at the limiting speed, as found above, are fairly uniform, varying, how- ever, with the size of ship as given by the table below: Length of ship on water line. ve re Value of C at Value of C when skin NG: Limiting speed, H-P.=wave. Her. 200 225 188 300 256 207 400 278 234 500 295 2at 600 310 246 __ These values of C are less for the smaller ships, on account of the higher coefficient of friction for the shorter length of vessel, and also on account of the error in the assumption of the general truth of the law of comparison when applied to the whole resistance. These two causes are not, however, sufficient of themselves to account. for the decrease in the value of C. I think this decrease is partly due to eddy-making,