834 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 77.14 



of the Taylor quotient r„ less than 2.0. This is 

 below the planing range for most motorboats. 



C. E. Werback has developed still another 

 dimensional relation, derived originally by G. F. 

 Crouch, of the following form: 



7(kt) = C 



i 



(ft) 

 TF(lb) 

 Ps (horses) 



(77.ii) 



Transposed for deriving the shaft power in terms 

 of the other quantities it becomes 



Fs (horses) 



W (lb) 7' (kt) 



CVL;,^ (ft) 



(77.iia) 



Analysis of this method indicates that a family 

 of curves for various displacement-length quo- 

 tients TF/(0.010L)^ is required for taking off 

 .proper values of the coefficient C. However, on 

 the basis that displacement-length quotients for 

 good planing craft are of the order of 200 or 

 slightly less, Fig. 77. F gives a graph for selecting 



This is on Approximate Meonline. 

 Only. There Should Be Q Fomlly- 

 of Curves for Various DisplQce-_ 

 ment-Lenqth Quotients 



Taylor Quotierrt Tq= t^ 



' ill liinlnnl L 



50 



1.0 



3.0 



J.O 



Fig. 77.F Crouch- Werback Formula and Graph 



FOR Relating Shaft Power to Length, Speed, 



AND Weight 



C at Tj values greater than 2.5 and not exceeding 

 6.0. 



D. PhiUips-Birt gives a dimensional formula 

 exactly the same as K. C. Barnaby's (Eq. 77.i) 

 for relating the brake power P^ , the total 

 weight W, and the speed Y ["The Design of 

 Seagoing Planing Boats," The Motor Boat and 

 Yachting, Jan 1954, p. 29]. This takes the alter- 

 native forms 



where the coefficient K^ is taken from a table 

 given by PhilUps-Birt, reproduced here as 

 Table 77.e. 



N. L. Skene uses a formula almost exactly 

 the same as Eqs. (77.i) and (77.iii), with the 

 alternative forms 



F(kt) = i^.^/f^^^^ 



/ W (long tons) 



Pb (horses) = 





(77.iii) 



(77.iiia) 



^^ 



F (lb) 



Y (mph) \Pb (horses) 

 P. (horses) =^(M_5imph) 



(77.iv) 



(77.iva) 



The values of Skene's coefficient C range from: 



(a) 180 to 185 for high-speed runabouts 



(b) 190 to 205 for multiple-step or shingled 

 hydroplanes 



(c) 210 for single-step hydroplanes of good design 



(d) 220 for small sea sleds to 270 for the largest 

 and most efficient sleds 



(e) 240 to 250 for small, three-point hydroplanes 

 ["Elements of Yacht Design," New York, 1944, 

 p. 222]. 



A value of C = 185 appears appropriate for the 

 ABC tender. 



Five of the methods listed give first approxi- 

 mations to the shaft power as follows, based upon 

 an estimated weight, at this stage, of 19,000 lb 

 or 8.482 tons, a speed of 24 kt, a waterline 

 length hy,!^ of 35 ft, a T, of 4.056, and an P„ of 

 1.208: 



I. Method of K. C. Barnaby, Table 77.d. With a 

 boat of the Y-chine, stepless type, 35 ft long, and 

 YlVh = 4.056, K^ is 3.4. Then 



P^ = A ^ = 8.482 -^^ = 422.6 horses. 



II. Method of P. Du Cane, Fig. 77.E. The ratio 

 of (IF in lb)/(PB in horses) is estimated conserva- 

 tively at 43. Then 



Pb = (IF in lb)/43 = 19,000/43 = 442 horses. 



III. Method of Crouch-Werback, where C is 

 taken as 72 from Fig. 77.F, and Eq. (77.iia) is 



Ps (horses) = 



F (lb) F^ (let) 

 C'VL^^ (ft) 



19,000(24)' 

 (72)'V35 



= 356.9. 



From this the brake power Pb is estimated as 

 356.9/0.95 or 375.7 horses. 



