The following text may have been generated by Optical Character Recognition, with varying degrees of accuracy. Reader beware!

[January 11, RESIST The editor of the Marine Review submits to me from Mr. 8B. L. Smith of the Institute of Naval Architects, London, a communication re- ferring to my article in the Review of Nov. 9, 1899, on the Admiralty Co-efficient with Some Facts Gleaned from Torpedo Boat Steam Trials. Mr. Smith says: “If the writer of this article will be kind enough to answer a few questions, it will give me and others the means of judging the value of his conclusions. Suppose we have three ships—200 feet long, 400 feet long, 800 feet long; their beams one-tenth of their length their draught 6 feet, 12 feet and 24 feet, respectively. What speed would the 800-foot vessel go without wave resistance? Would the rate of speed be increased by reducing the beam and to what extent? What would be the most economical rates for the vessel, 3,000 or 6,000 miles voyages? What would be the best beam? Would the other ships be a guide and to what extent? Any other information that Mr. Fairburn may furnish ill be gladly accepted.” : iy article on ae “Admiralty Co-efficient” was not intended to be a general treatise on the resistance and powering of ships. The first three lines of the final paragraph of the article, which | will here quote: “‘It follows, therefore, that the larger the boat the higher will be the admiralty co-efficient, provided the rising speed is not reached, but if this speed be exceeded, the larger the boat the smaller will be this co-efficient,” can be considered the conclusions reached in the article under question. TI de 6. cS) OO wl a < BS 00 100 E.H.Pe. SCALE. FOR WAVE MAKING RESISTANCE. % le U DC) 18) i 4) - 40 a: Fic.1. 120 not see how Mr. Smith’s questions have any bearing on the article, and I also fail to see how any answers which I may make to the questions asked should influence anyone in accepting the conclusions reached in the article before mentioned. I do not intend to enter into a newspaper controversy over this matter, but I will reply to Mr. Smith’s questions out of courtesy to the writer and the institution in whose rooms the letter was penned. é The length; beam and draught of three vessels which we will term a, b, and.c, ane stated: - a b Cc Weeneti sre ae ee as 200 feet 400 feet 800 feet Vea a ok cbs wes 20 feet 40 feet 80 feet POI as oss oes was 6 feet 12 feet 24 feet We will assume a block co-efficient of .5, which will give a displacement of 340 tons for vessel “a.” The wetted surface of the same vessel will be 4,100 square feet. As the wetted surface varies as the square of the ratio of the linear dimensions and the displacement as the cube of the same, the following figures are easily determined for the three visionary vessels: a b Cc Displacement <=... 055... 840 tons 2,720 tons 21,760 tons Wetted surface: .23.30...5 4,100 sq ft 16,400 sq ft 65,600 sq ft Replying to the first question, ““What speed would the 800-foot vessel go without wave resistance’? will say that wave making resistance is a part of the total resistance of any ship at the lowest speeds. The amount f this wave making resistance increases with the fullness and speed of the ship. Although at low speeds it is very small and can at times be almost neglected, nevertheless it exists and should be considered when a vessel is powered from the known performance of a similar vessel. A gunboat 226 feet long at a speed of about 7 knots per hour has wave making resistance equal to 17 per cent. of the total resistance. The same ratio exists in the case of a smaller, faster gunboat 190 feet long at a speed of 8 knots per hour. The former vessel at a speed of 10 knots and the latter at a speed of 10% knots experiences wave making resistance equal to 25 per cent. of the total resistance. Vessels of this class as a rule at a speed, V=./1 when L=length on the water line, have wave making resistance equal to the skin frictional resistance or 50 per cent. of the total resistance. At any speed that would make any proposed or built ship today a commercial success, wave making resistance would be in evidence and to such an extent that it would demand consideration. Replying to the second question, ‘Would the rate of speed be in- creased by reducing the beam, and to what extent”? will say that a re- duction of beam would decrease the wave making resistance at any speed and raise the speed at which wave making resistance becomes particularly noticeable, assuming, of course, that the block co-efficient and character of lines remain the same, and if a constant displacement is desired it is obtained by increasing the draught. If we assume that all the resistance is due to surface friction or that wave making resistance is only a very small percentage of the total resistance, then it is obvious that any change of dimensions that will decrease wetted surface without increasing wave making resistance will decrease the E. H. P. necessary to overcome the resistance of the ship. If the length, draught and block co-efficient remains the same, any decrease of beam will lessen the amount of wetted surface and accordingly decrease the resistance of the ship and the power to overcome the same. Continuing this subject and replying to the third question, “What would be the most economical ratio for the vessel, 3,000 to 6,000 mile voyages, and what would be the best beam”? will say that with a stated length, co-efficient of fineness and displacement, the question of determin- ing the best beam is a very complicated and difficult matter. Draught of ANCE O “WM. A. FATI F SHIPS. water is quite often limited, and stability and strength have usually: much more to do with the determination of the beam of a vessel than propulsive efficiency. We will assume, however, that the latter is all important, the influence of the former qualities being neglected; also that the vessel is large and of very low speed, the wave making resistance being so small that it can be neglected. Under such conditions the best beam is the one that gives niinimum wetted surface on any stated length; block co-effi- cient and displacement, the draught being the second variable. Let us consider a case first of maximum beam, the draught being reduced to a minimum of say 1 foot. The length, co-efficient of fineness and displace- ment being constant, the wetted surface would be increased from 65,600 square feet (see table vessel “c’’) to about 1,142,400 square feet. Let us now consider a case of minimum beam of say 1 foot with maximum draught. Here the wetted surface would be still further increased to about 2,985,500 square feet. If the water lines and cross sections of the vessel were rectangles, the block co-efficient being 1:0, minimum wetted _ surface would be obtained with a beam of 61.968 feet and a draught of 30.984 feet, or a ratio beam do draught of 2 to 1. If the water lines were rectangles and the sections triangles or areas bounded by arcs, minimum wetted surface for.a constant displacement would occur where the beam of the vessel is equal to twice the draught. As the water lines of a vessel are not rectangles, but areas bounded by curved lines, the fullness of which depends on the block co-efficient, we can determine the dimen- sions to give minimum wetted surface on a stated length, co-efficient of fineness and displacement with a close degree of aceuracy, by making the mean width of the water line equal to twice the draught. If the co-effi- cient of fineness of the load water plane is--75, the ratio of beam to draught is 2°66. If Cw= 8, ratio B to d=2-50.. When Cw=°9 ratio B to d=2-22. If economy of propulsion should be the only quality worthy of consideration when determining the most suitable dimensions for a modern cargo steamship 800 feet long, then the draught of such a vessel 32°5 feet, the maximum of today, would give the vessel a beam of 72 to 73 feet. The last question, “Would the other ships be a guide and to what extent”? referring to powering vessel ‘“‘c’” from the known performances of vessels “a’’ and “b,” is probably intended to show the fallacy of the admiralty co-efficient method of powering similar ships when of low speed. But the imperfections of the co-efficients Cp and C, were ex- plained at length in some cases, and in others briefly mentioned in the article relative to the admiralty co-efficient and the rising speed, and none 400 A. “5H +§HE sO 300 | ——— EHP. = 60 200 rae ee : ek = EHR, = 135 100 | if 2 2.5 3 3.5 RATIO OF LINEAR DIMENSIONS. ric. 2. of these imperfections seriously affect the conclusions stated in the article in question. If the resistance of a ship is composed wholly of that due to surface friction, then it is a simple matter to estimate the E. H. P. necessary to overcome this resistance. Rt=C. S. V1‘88. Where Rt= resistance in pounds due‘to friction, C is a co-efficient of friction: S is the area of wetted surface in square feet and V is speed in knots. Now a resistance of one pound at a speed of one knot absorbs .0,030,707 H. P. (Taylor); then E. H. P.=.0,030,707 V. Re=CXS.0,030,707 V2"83. The co-efficient of friction C varies with the extent and natufe of the surface. A vessel 200 feet long with a steel, clean, well-painted bottom will have a co-efficient of friction of .00945. A 400-foot vessel will have a co-effi- cient of .00910, and-an 800-foot vessel will have a co-efficient of about 00895. At a speed of 12 knots per hour the power, E. H. Pf, to over- come the frictional resistance of these vessels, a, b and c, would be 135 ae P., 519 H. P. and 2,042 H. P. respectively. The ratio is as 1:3.85:15.12. If the co-efficient of friction is constant the ratio would be as 1:4:16. The corresponding speeds of these vessels would be in the ratio of the square root of the ratio of the linear dimensions, or as 1:1.414:2. There- fore if 185 H. P. is required to overcome the resistance of vessel “a” at 1% knots, vessel “b” at the corresponding speed of 16.968 knots will re- quire 1,883 H. P. and vessel ‘“‘c” at the corresponding speed of 24 knots will require 14,520 H. P. Suppose the trials of vessel “a” proved that at a speed of 6 knots per hour the frictional resistance was 98 per cent. of the total resistance experienced by the vessel. The E. H. P. required to overcome this Rt would be 18.94 H. P. and the total E. H. P. required to overcome. Rt-+Rw would be 19.33 H. P., Rw being 21.17 pounds and E. H. Pw, being .89 H. P. This small amount of wave making resistance would require 50 E. H. P. to overcome it when vessel “c” is propelled at her corresponding speed of 12 knots. When the resistance of a ship is composed wholly of frictional resistance, the admiralty co-efficient can- not be accurately applied at corresponding speeds, and the larger the ratio of linear dimensions the greater will the discrepancy be. Vessel “a” :