850 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 77.27 



tender is 197.8 and the T„ at designed speed is 

 4.057. From the referenced graph the minimum 

 resistance per pound of weight for a displacement- 

 length quotient of 160 to ISO is 0.123 lb, cor- 

 responding to a resistance of 2,377 lb for a dis- 

 placement of 19,000 lb. From Fig. 77.0 the 

 minimum resistance predicted, at a trim angle d 

 of 3.25 deg, is 2,320 lb. 



The LCB of the boat at rest is found, by routine 

 methods, to be approximately 0.594L„.l abaft the 

 FP. By Table 77.f, the center of the projected 

 chine area is found to be 0.532L,rL abaft the FP. 

 The CB thus lies at slightly more than 6 per 

 cent of LwL abaft the centroid of the chine area. 

 This is close to an average value as indicated by 

 E. P. Clement ["Hull Form of Stepless Planing 

 Boats," SNAME, Ches. Sect., 12 Jan 1955, PL 9]. 



It may be assumed that the CG of the boat 

 laid out in Figs. 77. B and 77. K lies directly above 

 the center of bu oyancy CB when the craft is at 

 rest. Then LCG = 0.594L,rL = 0.594(35) = 20.79 

 ft abaft the FP, or 14.21 ft forward of the AP at 

 the transom. To run at a steady trim the CP 

 position on the bottom must lie approximately 

 under the CG position in the hull. From the 

 upper graph of Fig. 77.0, the running trim for 

 this CG position is found to be about 4.9 deg by 

 the stern. At this trim the total resistance Rr 

 from the lower set of graphs of that figure is 

 2,500 lb. 



The resistance data given by Murray take no 

 account of the still-air drag of the hull and upper 

 works above the DWL. To predict this value for 

 the ABC tender, it is necessary to estimate the 

 transverse projected area above water. A rough 

 calculation from Fig. 77. B gives 60.2 ft^. For the 

 still-air drag the designer may use the dunensional 

 formula Dsa = 0.0044^7' [S and P, 1943, p. 52], 

 where D is in lb and V is in kt. Substituting, 

 Dsa = 0.004 (60.2) (24)' = 138.7 lb. Other 

 coefficients for this formula are given in Sec. 54.7. 



Based upon the rule given by H. F. Nordstrom 

 [SSPA Rep. 19, 1951, p. 15], the resistance of well 

 streamlined appendages for a twin-screw motor- 

 boat need not exceed 7 per cent of the bare-hull 

 total resistance. An estimated value is then 

 0.07(2,500) = 175 lb. Still-air drag and wind 

 resistance for motorboats are discussed further in 

 Sec. 77.37. 



The total resistance Rt + Dsa + ^app = 

 2,500 -I- 138.7 -I- 175 = 2,813.7 lb. The effective 

 power is then 2,813.7(24)1.0889/550, or about 

 207 horses. Assuming a propulsive coefficient t/^ 



of 0.50 in the absence of a better value, the shaft 

 power P.5 (or better, the propeller power Pp) is 

 Pe/vp = 207/0.50 = 414 horses. With a trans- 

 mission loss of say 5 per cent in the shafting and 

 bearings, the brake power Pb required to be 

 delivered by the engines is 414/0.95 = 436 horses. 



This independent estimate compares well with 

 the first approximations to the shaft power in 

 Sec. 77.14, where it was found that two engines, 

 each delivering a brake power of 225 horses, 

 would be adequate for the purpose. 



K. C. Barnaby gives a few average values of 

 the propulsive coefficient j/p as applying to craft 

 in the category being considered here [INA, 1943, 

 Appx. 1, p. 126]: 



(a) 25-ft motorboats, average t]p is about 0.58 



(b) 50-ft motorboats, average tjp is about 0.59. 



Barnaby's book "Basic Naval Architecture" 

 [1954, Art. 191, Fig. 100, p. 306] contains a graph 

 of average tjp values which indicates a propulsive 

 coefficient of only about 0.45 for single-screw 

 craft 50 ft long. Since this graph extends to 

 lengths of 1,000 ft it may not be intended to 

 cover motorboats. 



77.27 Running Attitude and Fore-and-Aft Po- 

 sition of the Heavy Weights. To visualize the 

 situation at this stage relative to the probable 

 position of the proposed craft with reference to 

 the surrounding water and its running attitude 

 when planing, the designer proceeds to predict 

 certain features. Among these are the change in 

 elevation of the center of gravity CG with speed, 

 the fore-and-aft position of the center of pressure 

 CP and of the CG, the dimensions and shape of 

 the wetted bottom surface, the position of the 

 probable impact area in waves, and the best 

 positions for the heavy weights in the boat. 



There are at least two methods of determining 

 the vertical position of the boat when underway 

 at full speed with respect to the level of the sur- 

 rounding undisturbed water. One is to make use 

 of a diagram such as that given by A. B. Murray 

 in Fig. 2 on page 658 of his referenced paper, or in 

 Fig. 29. D of Volume I of the present book, for a 

 full-planing craft of about the same size and 

 shape. Although Murray's diagram referenced in 

 this case is for 40-ft V-bottom motorboats it 

 should serve reasonably well for the ABC tender, 

 which is 35 ft on the waterhne and 38 ft overall. 

 At the designed speed of 24 kt, equivalent to 

 27.6 mph, tlie rise of the center of gravity above 

 its at-rest position is approximately 0.7 ft, or 



