When the ship is exceptionally well-proportioned, the bottom quite clean, and the efficiency of the machinery high, as low a rate as 4 I.H.P. per 100 feet of wetted skin of block model may be allowed The gross indicated horse-power includes the power necessary to overcome the friction and other resistance of the engine itself and the shafting, and also the power lost in the propellor. In other words, I.H.P. is no measure of the resistance of the ship, and can only be relied on as a means of deciding the size of engines for speed, so long as the efficiency of the engine and propellor is known definitely, or so long as similar engines and propellers are employed in ships to be compared. The former is difficult to obtain, and it is nearly impossible in practice to know how much of the power shown in the cylinders is employed usefully in overcoming the resistance of the ship. The following example is given to show the variation in the efficiency of propellers: H.M.S." Amazon," with a 4-bladed screw, gave.. H.M.S." Amazon," with a 2-bladed screw, increased pitch, H.M.S. "Iris," with 2-bladed screw, increased pitch, less Relative Horse-power Required for Different Speeds of Vessels. (Horse-power for 10 knots 1.)-The horse-power is taken usually to vary as the cube of the speed, but in different vessels and at different speeds it may vary from the 2.8 power to the 3.5 power, depending upor the lines of the vessel and upon the efficiency of the engines, the propeller, etc. HPC 4 6 8 10 12 14 16 18 20 22 24 S2 8.0769.239.535 1.1.666 2.565 3.729 5.185 6.964 9.095 11.60 14.52 17.87 21.67 S2.9.0701.227.524 1. 1.697 2.653 3.908 5.499 7.464 9.841 12.67 15.97 19.80 24.19 S3 .0640.216.512 1.1.728 2.744 4.096 5.832 8. 10.65 13.82 17.58 21.95 27. S3.1 .0584.205.501 1.1.760 2.838 4.293 6.185 8.574 11.52 15.09 19.34 24.33 30.14 $3.2 .0533.195.490 1.1.792 2.935 4.500 6.559 9.189 12.47 16.47 21.28 26.97 33.63 S3.3.0486.185.479 1.1.825 3.036 4.716 6.957 9.849 13.49 17.98 23.41 29.90 37.54 S3 4.0444.176.468 1.1.859 3.139 4.943 7.378 10.56 14.60 19.62 25.76 33.14 41.90 S3-5.0405.167.458 1.1.893 3.247 5.181 7.82411.31 15.79 21.4228.34 36.73 46.77 EXAMPLE IN USE OF THE TABLE.-A certain vessel makes 14 knots speed with 587 1.H.P. and 16 knots with 900 I.H.P. What I.H.P. will be required at 18 knots, the rate of increase of horse-power with increase of speed remaining constant? The first step is to find the rate of increase, thus: 14*: 16* :: 587: 900. whence x (the exponent of S in formula H.P. S) = 3.2. From the table, for S3-2 and 16 knots, the I H.P. is 4.5 times the I.H.P. at 10 knots, .. H.P. at 10 knots 900 ÷ 4.5 = 200. From the table, for S3-2 and 18 knots, the I.H.P. is 6.559 times the I.H.P. at 10 knots; .. H.P. at 18 knots = 200 × 6.559 1312 H.P. Resistance per Horse-power for Different Speeds. (One horse-power == 33.000 lbs. resistance overcome through 1 ft. in 1 min.)-The resistances per horse-power for various speeds are as follows: For a speed of 1 knot, or 6080 feet per hour = 101 ft. per min., 33,000 1011% 325.658 lbs. per horse-power; and for any other speed 325.658 lbs. divided by the speed in knots; or for = 1 knot 325.66 lbs. 6 knots 54.28 lbs. 11 knots 29.61 lbs. 16 knots 20.35 lbs. The figures for I.H.P. are "round." The "Medusa's" figures for 20 knots are from trial on Stokes Bay, and show the retarding effect of shallow water. The figures for the other ships for 20 knots are estimated for deep water. More accurate methods than those above given for estimating the horse-power required for any proposed ship are: 1. Estimations calculated from the results of trials of similar" vessels driven at "corresponding" speeds; "similar" vessels being those that have the same ratio of length to breadth and to draught, and the same coefficient of fineness, and "corresponding" speeds those which are proportional to the square roots of the lengths of the respective vessels. Froude found that the resistances of such vessels varied almost exactly as wetted surface X (speed)2. 2. The method employed by the British Admiralty and by some Clyde shipbuilders, viz., ascertaining the resistance of a model of the vessel, 12 to 20 ft. long, in a tank, and calculating the power from the results obtained. Speed on Canals.-A great loss of speed occurs when a steam-vessel passes from open water into a more or less restricted channel. The average speed of vessels in the Suez Canal in 1882 was only 5% statute miles per hour. (Eng'g. Feb. 15, 1884, p. 139.) Estimated Displacement, Horse-power, etc.-The table on the next page, calculated by the author, will be found convenient for mak ing approximate estimates. The figures in 7th column are calculated by the formula H.P. = S3 D3 ÷ c, in which c = 200 for vessels under 200 ft. long when C.65, and 210 when C.55; c = 200 for vessels 200 to 400 ft. long when C = .75, 220 when C.65, 240 when C = .55; c = 230 for vessels over 400 ft. long when C = .75, 250 when C.65, 260 when C = .55. The figures in the 8th column are based on 5 H.P. per 100 sq. ft. of wetted surface. The diameters of screw in the 9th column are from formula D= 3.31 I.H.P., and in the 10th column from formula D = 2.71 †/I.H.P. To find the diameter of screw for any other speed than 10 knots, revolu tions being 100 per minute, multiply the diameter given in the table by the 5th root of the cube of the given speed 10. For any other revolutions per minute than 100, divide by the revolutions and multiply by 100. To find the approximate horse-power for any other speed than 10 knots, multiply the horse-power given in the table by the cube of the ratio of the given speed to 10, or by the relative figure from table on p. 1006. THE SCREW-PROPELLER. The "pitch " of a propeller is the distance which any point in a blade, describing a helix, will travel in the direction of the axis during one revolution, the point being assumed to move around the axis. The pitch of a propeller with a uniform pitch is equal to the distance a propeller will advance during one revolution, provided there is no slip. In a case of this kind, the term "pitch" is analogous to the term "pitch of the thread" of an ordinary single-threaded screw. Let P= pitch of screw in feet, R = number of revolutions per second, V = velocity of stream from the propeller = P × R, v = velocity of the ship in feet per second, Vv slip, A = area in square feet of section of stream from the screw, approximately the area of a circle of the same diameter, AX V = volume of water projected astern from the ship in cubic feet per second. Taking the weight of a cubic foot of sea-water at 64 lbs., and the force of gravity at 32, we have from the common formula for force of accelW eration, viz.: F= M or F1, when t = 1 second, v1 being the acceleration. W v g t g 64 AV -(V − v) = 2AV(V — v). Thrust of screw in pounds = Rankine (Rules, Tables, and Data, p. 275) gives the following: To calculate the thrust of a propelling instrument (jet, paddle, or screw) in pounds, multiply together the transverse sectional area, in square feet, of the stream driven astern by the propeller; the speed of the stream relatively to the ship in knots; the real slip, or part of that speed which is impressed on that stream by the propeller, also in knots; and the constant 5.66 for sea-water, or 5.5 for fresh water. If S = speed of the screw in knots, s = speed of ship in knots, A = area of the stream in square feet (of sea-water), Thrust in pounds: =AX S(Ss) X 5.66. The real slip is the velocity (relative to water at rest) of the water projected sternward; the apparent slip is the difference between the speed of the ship and the speed of the screw; i.e., the product of the pitch of the screw by the number of revolutions. This apparent slip is sometimes negative, due to the working of the screw in disturbed water which has a forward velocity, following the ship. Negative apparent slip is an indication that the propeller is not suited to the ship. The apparent slip should generally be about 8% to 10% at full speed in wellformed vessels with moderately fine lines; in bluff cargo boats it rarely exceeds 5%. The effective area of a screw is the sectional area of the stream of water laid hold of by the propeller, and is generally, if not always, greater than the actual area, in a ratio which in good ordinary examples is 1.2 or thereabouts, and is sometimes as high as 1.4; a fact probably due to the stiffness of the water, which communicates motion laterally amongst its particles. (Rankine's Shipbuilding, p. 89.) Prof. D. S. Jacobus, Trans. A. S. M. E., xi. 1028, found the ratio of the effective to the actual disk area of the screws of different vessels to be as follows: Tug-boat, with ordinary true-pitch screw. 66 1.42 .57 screw having blades projecting backward.. Ferryboat" Bergen," with or- at speed of 12.09 stat. miles per hour. 1.53 dinary true-pitch screw 13.4 Steamer Homer Ramsdell," with ordinary true-pitch screw...... 66 66 66 1.48 1.20 Size of Screw.-Seaton says: The size of a screw depends on so many things that it is very difficult to lay down any rule for guidance, and much must always be left to the experience of the designer, to allow for all the circumstances of each particular case. The following rules are given for ordinary cases. (Seaton and Rounthwaite's Pocket-book): 10133S P = - pitch of propeller in feet = in which S = speed in knots, R(100-x)' Rrevolutions per minute, and x = percentage of apparent slip. 112.6S |