Sec. 57.10 



TOTAL RESISTANCE OF BODY OR SHIP 



321 



(c) Wisdom, experience, and perhaps intuition 

 to know how to draw a series of parallel extrap- 

 olation lines, in semi-log or any other known 

 type of plotting, when the lines joining the 

 corresponding spots for the different geosims are 

 neither straight nor parallel. 



Although it has been most useful for analysis, 

 the Telfer method manifestly does not lend 

 itself, in its present stage of development, to 

 routine predictions of ship resistance, where the 

 forces must be given in numbers of certain units. 



57.8 Analytical and Mathematical Methods of 

 Predicting Pressure Resistance. The use of pure 

 analytical or mathematical procedures to calculate 

 the pressure resistance of a body or ship due to 

 wavemaking, as of 1955, is described in Chap. 50. 

 This method has not yet progressed to the stage 

 where a quantitative design prediction for a ship 

 of normal form is a practical proposition. Further- 

 more, the pressure resistance due to eddying or 

 separation can only be approximated, and the 

 resistances due to the interactions listed in III 

 of Table 57. a can not as yet be estimated by any 

 known method. 



57.9 An Approximation of Separation Drag. 

 It is explained in Sec. 7.9 of Volume I that separa- 

 tion may occur, and cause added drag, abaft 

 certain discontinuities in the forebody. Although 

 explained, this drag unfortunately can not be 

 estimated with any degree of assurance. 



An estimate of the separation drag on the 

 afterbody or run of a ship requires first an approxi- 

 mate delineation of those hull areas bounding 

 the separation zone. Several methods for making 

 this prediction are described in Sec. 46.3. Means 

 of estimating the drag due to — Ap's in separation 

 zones are discussed in Sec. 46.5. 



Some differential pressures have been observed 

 at selected points on the transoms of certain 

 square-stern models, but at the time of writing 

 the data are incomplete and the results inconclu- 

 sive. 



57.10 Slope Resistance and Thrust. It may 

 be assumed for a calculation of slope drag or 

 thrust on a body or ship, described in Sec. 12.7, 

 that the effective-slope angle in the equation 

 Ds (or Ts) = W sin ^(theta) is that of the con- 

 stant-pressure water subsurface passing through 

 the center of buoyancy CB. If this subsurface is 

 not plane (flat) along the ship length, its slope 

 is measured at the CB position. If the subsurface 

 slope is not known it may be assumed roughly 



equal to the surface slope. If, in turn, the latter 

 can not be determined, the change of trim of the 

 body or ship, reckoned from its attitude in level 

 water at the same loading, may be used for the 

 slope angle B, provided account is taken of the 

 change of trim caused by the ship's speed through 

 the water. 



It is reported that water will flow with a surface 

 slope as small as 0.125 inch (0.0104 ft) to the 

 statute mile. In this case sin 6 is only 2(10~°). 

 The slope drag of a 10,000-ton ship on such a 

 slope is about 45 lb. The slopes of many navigable 

 rivers are of the order of 5 to 8 ft to the statute 

 mile, in which case sin 6 may vary from 0.001 to 

 0.0015 [Durand, W. F., RPS, 1903, p. 119; 

 Nowka, G., "New Knowledge on Ship Propul- 

 sion," 1944, BuShips Transl. 411, pp. 4-5]. The 

 slope thrust on a 1,000-ton barge floating down 

 such a river is from 1 to 1.5 ton, 2,240 to 3,360 lb, 

 sufficient to give it a sizable differential down- 

 stream speed. This may be 3 or 4 kt over and 

 above the river speed in the middle of the channel, 

 sufficient to render it controllable by its own 

 rudders. 



For convenience, Table 57. d gives values (1) of 

 the natural sine of the slope angle d and (2) of the 



TABLE 57. d — Slope Drag and Thrust Data for 

 Varying Water-Surface Slopes 



