264 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 53.3 



(15) Ratio of the chine beam Be to the mean 

 wetted length L^s , or the aspect ratio 



(16) Planing number Rt/W. Its reciprocal may- 

 be used if it is an advantage to do so. 



(17) Ratio of the distance designated as [CP 

 from trailing edge of planing surface] to the mean 

 chine beam Be 



(18) Speed coefficient Cy o r beam-Froude num- 

 ber, where Cv = V/-vgBc 



(19) Load coefficient, where Ca or Cw , sym- 

 bolized preferably as Cld, = W/{wBc) 



(20) Dynamic-lift coefficient, C^l = W/(qBc) = 

 2iC,n)/C^ 



(21) Resistance or drag coefficient Cpianins r = 

 Rr/(wB^). 



The marme architect, seeing this list for the 

 first time, is amazed at its length and complexity, 

 as compared to that for a surface ship of the dis- 

 placement type. It is perhaps satisfying, but not 

 always comforting for this architect to realize 

 that his amazement is fully justified. The problem 

 of estimating and predicting planing-craft per- 

 formance is indeed more intricate and involved 

 than that for a normal type of surface ship. 



53.3 Principal Forces and Moments on a Plan- 

 ing Craft. As an aid in presenting, in systematic 

 fashion, the quantitative data relating to pre- 

 diction of planing-craft performance. Fig. 53. A is 



drawn to supplement Fig. 13. C in Sec. 13.3 on 

 page 206 of Volume I. The accompanying figure 

 shows the principal forces acting on a craft 

 during planing. The propulsive force and its 

 component, not shown in Fig. 13. C, are indicated 

 here, as are the buoyancy force (assumed finite 

 and not negligible), the relative-wind forces, and 

 the drag of the appendages. The relative-wind 

 drag is in this case assumed equal to the stUl-air 

 resistance. The thrust-deduction force is assumed 

 as zero, although in practice this is probably 

 never the case. In the diagram of Fig. 53. A there 

 would be a thrust-deduction force exerted on the 

 strut and rudder assembly abaft the propeller 

 and on the exposed shaft ahead of it, if not on the 

 hull proper. 



There are forces due to the formation of spray 

 roots and the generation of spray, indicated 

 on the diagrams of Figs. 13. B and 13. D, but 

 their positions and vector directions are not well 

 known. 



53.4 Determination of Dynamic Lift. There 

 is no liquid circulation as such about an inclined 

 fiat plate skimming along the water surface, or 

 about any planing craft in the manner described 

 for the hydrofoils of Chap. 14 of Volume I. It is 

 found possible, nevertheless, to estimate the 

 dynamic lift of such a plate reasonably well by 

 calculating the lift due to circulation, as if the 



Woterline Lern^th L^ 



Croft Qt Rest 

 Lift Force L 



Wetted Le ngth at 5peed V 



Pressure Draq Dpft^ 

 of Appendoaes 



Direction of Flow 

 Under Bottom 



Thrust-Deduction Force AT is Assumed Zero 

 Buo\;Qnc\j Force B is That Due to Water 



Displaced b\j Afterbodvj 

 Force DE 13 Ltane3*(lnduced Droq Di)sece 



^ (Slope Draq)sec0 

 Force CD is Force Dp;., times sec 9 

 Force AC is Bottom-Friction Force Dp times sec 6 



- NOTE: — Not shown here, to avoid confusion, 



Weight is the vertical force (or upward force normal to 



Force W the shaft axis) exerted by the propeller because 



' of the non-axial flow in which it is operating. 



This is the force mentioned in the second para- 

 graph of Sec. 53.6 on page 268. It is developed 

 by the action explained in Sees. 17.7 and 33.5 

 of Volume I, and illustrated in Figs. 17. C, 17. D, 

 and 33.1 on pages 264, 265, and 485, respectively, 

 of that volume. 



Fig. 53. a Definition Diagram op Forces on a Planing Boat 



