sq. ft. tons. Estimated Displacement, Horse-power, etc., of Steamvessels of Various Sizes. Displace ment. Wetted Surface LBDX CL(1.7D + BC) 35 1.5 .55 1.13 64 2 .65 2.38 96 1.5 .55 1.41 80 2 .65 2.97 120 3.5 1.5 .55 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 Curing one revolu tion, 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 Ppitch 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, V v = 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 v1 eration, viz.: F = M = or Fv1, when t = 1 second, v, being g the acceleration. Thrust of screw in pounds = W g 64 AV −(V − v) = 2AV(V — v). 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 13.4 66 66 66 1.42 .57 1.48 screw having blades projecting backward. Ferryboat " Bergen, with or- at speed of 12.09 stat. miles per hour. 1.53 dinary true-pitch screw Steamer Homer Ramsdell," with ordinary true-pitch screw........... 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): P = pitch of propeller in feet = R = = speed in knots, revolutions per minute, and x = percentage of apparent slip. For a slip of 10%, pitch 10133S in which S 112.6S R I.H.P. D= diameter of propeller = K (PXR) 3' 100 K being a coefficient given I.H.P. in the table below. If K = 20, D = 20000 (PXR)3° shaft in inches, n = number of blades, b = breadth of blade in inches where it joins the boss, measured parallel to the shaft axis; k = 4 for cast iron, 1.5 for cast steel, 2 for gun-metal, 1.5 for high-class bronze. Thickness of blade at tip: Cast iron .04D+.4 in.; cast steel .03D+.4 in.; gun-metal .03D + .2 in.; high-class bronze .02D+.3 in., where D = diameter of propeller in feet. C. I., cast iron; G. M., gun-metal; B., bronze; S., steel; F. S., forged steel. 4 21 -22.5 10.5-9 66 64 66 66 66 3 22 -23.5 8.5-7 66 66 3 25 7-6 B. or F. S. If P 1.4D and R = 100, then D145.8 × I.H.P. = 2.71 VI.H.P. From these two formulæ the figures for diameter of screw in the table on page 1009 have been calculated. They may be used as rough approximations to the correct diameter of screw for any given horse-power, for a speed of 10 knots and 100 revolutions per minute. For any other number of revolutions per minute multiply the figures in the table by 100 and divide by the given number of revolutions. For any other speed than 10 knots, since the I.H.P. varies approximately as the cube of the speed, and the diameter of the screw as the 5th root of the I.H.P., multiply the diameter given for 10 knots by the 5th root of the cube of one tenth of the given speed. Or, multiply by the following factors: 5 6 7 8 9 11 12 13 14 15 16 = .577 .660 .736 .807 .875 .939 1.059 1.116 1.170 1.224 1.275 1.327 Speed: (8+10) 17 18 19 20 21 22 23 24 25 26 27 28 = 1.875 1.423 1.470 1.515 1.561 1.605 1.648 1.691 1.733 1.774 1.815 1.855 For more accurate determinations of diameter and pitch of screw, the formulæ and coefficients given by Seaton, quoted above, should be used. Efficiency of the Propeller.-According to Rankine, if the slip of the water bes, its weight W, the resistance R, and the speed of the ship v, This impelling action must, to secure maximum efficiency of propeller, be effected by an instrument which takes hold of the fluid without shock or disturbance of the surrounding mass, and, by a steady acceleration, gives it the required final velocity of discharge. The velocity of the propeller over. coming the resistance R would then be the first of the last two terms being useful, the second the minimum lost work; the latter being the wasted energy of the water thrown backward. The efficiency is E=v÷ (v+ 1); and this is the limit attainable with a perfect propelling instrument, which limit is approached the more nearly as the conditions above prescribed are the more nearly fulfilled. The efficiency of the propelling instrument is probably rarely much above 0.60, and never above 0.80. In designing the screw-propeller, as was shown by Dr. Froude, the best angle for the surface is that of 45° with the plane of the disk; but as all parts of the blade cannot be given the same angle, it should, where practicable, be so proportioned that the "pitch-angle at the centre of effort" should be made 45°. The maximum possible efficiency is then, according to Froude, 77%. In order that the water should be taken on without shock and discharged with maximum backward velocity, the screw must have an axially increasing pitch. The true screw is by far the more usual form of propeller, in all steamers, both merchant and naval. (Thurston, Manual of the Steam-engine, part ii., p. 176.) The combined efficiency of screw, shaft, engine, etc., is generelly taken at 50%. In some cases it may reach 60% or 65%. Rankine takes the effective H.P. to equal the I.H.P. ÷ 1.63. Pitch-ratio and Slip for Screws of Standard Form. Results of Recent Researches on the efficiency of screw-propel lers are summarized by S. W. Barnaby, in a paper read before section G of the Engineering Congress, Chicago, 1893. He states that the following general principles have been established: (a) There is a definite amount of real slip at which, and at which only, maximum efficiency can be obtained with a screw of any given type, and this amount varies with the pitch-ratio. The slip-ratio proper to a given ratio of pitch to diameter has been discovered and tabulated for a screw of a standard type, as below (see table on page 1012): (b) Screws of large pitch-ratio, besides being less efficient in themselves, add to the resistance of the hull by an amount bearing some proportion to their distance from it, and to the amount of rotation left in the race. (c) The best pitch-ratio lies probably between 1.1 and 1.5. (d) The fuller the lines of the vessel, the less the pitch-ratio should be. (e) Coarse-pitched screws should be placed further from the stern than fine-pitched ones. (f) Apparent negative slip is a natural result of abnormal proportions of propellers. (g) Three blades are to be preferred for high-speed vessels, but when the diameter is unduly restricted, four or even more may be advantageously employed. (h) An efficient form of blade is an ellipse having a minor axis equal to four tenths the major axis. (i) The pitch of wide-bladed screws should increase from forward to aft, but a uniform pitch gives satisfactory results when the blades are narrow, and the amount of the pitch variation should be a function of the width of the blade. (j) A considerable inclination of screw-shaft produces vibration, and with right-handed twin-screws turning outwards, if the shafts are inclined at all, it should be upwards and outwards from the propellers. For results of experiments with screw-propellers, see F. C. Marshall, Proc. Inst. M. E. 1881; R. E. Froude, Trans. Institution of Naval Architects, 1886; G. A. Calvert, Trans. Institution of Naval Architects 1887; and S. W. Barnaby, Proc. Inst. Civil Eng'rs 1890, vol. cii. One of the most important results deduced from experiments on model screws is that they appear to have practically equal efficiencies throughout a wide range both in pitch-ratio and in surface-ratio; so that great latitude is left to the designer in regard to the form of the propeller. Another important feature is that, although these experiments are not a direct guide to the selection of the most efficient propeller for a particular ship, they supply the means of analyzing the performances of screws fitted to vessels, and of thus indirectly determining what are likely to be the best dimensions of screw for a vessel of a class whose results are known. Thus a great advance has been made on the old method of trial upon the ship itself, which was the origin of almost every conceivable erroneous view respecting the screw-propeller. (Proc. Inst. M. E., July, 1891.) THE PADDLE-WHEEL. Paddle-wheels with Radial Floats. (Seaton's Marine Engineering.) The effective diameter of a radial wheel is usually taken from the centres of opposite floats; but it is difficult to say what is absolutely that diameter, as much depends on the form of float, the amount of dip, and the waves set in motion by the wheel. The slip of a radial wheel is from 15 to 30 per cent, depending on the size of float. D is the effective diameter in feet, and C is a multiplier, varying from 0.25 in tugs to 0.175 in fast-running light steamers. The breadth of the float is usually about 4 its length, and its thickness about its breadth. The number of floats varies directly with the diameter, and there should be one float for every foot of diameter. (For a discussion of the action of the radial wheel, see Thurston, Manual of the Steam-engine, part ii., p, 182.) Feathering Paddle-wheels. (Seaton.) The diameter of a feathering-wheel is found as follows: The amount of slip varies from 12 to 20 per cent, although when the floats are small or the resistance great it |