TRIANGULAR 

 .15 



TRIANGULAR AND 

 RECTANGULAR 



RECT. 

 d| = 0.88 



C Dc = l.33 



TRIANG. 

 Qj = 1.0 



= 0.67 



8 16 24 



TRIM, T, DEG 



Figure 10. Effects of plan form, deadrise 0°, /,,,/b = 3.0. 



32 



and the crossflow component at two-thirds the wetted length. Going to a triangular 

 plan form does not change the lift coefficient appreciably, and shifts the center-of- 

 pressure forward by an approximately constant amount. 



Resistance. — The drag associated with planing surfaces is partly skin friction and 

 depends on boundary-layer conditions which are influenced by pressure gradients and 

 Reynolds number. In the case of prismatic surfaces, the induced drag is assumed to 

 be simply the load times the tangent of the trim angle, and the boundary layer to be 

 fully turbulent. Analyses of model measurements have largely substantiated the validity 

 of these assumptions for engineering estimates. It is then preferable to calculate the 

 resistance of full-size elements, using the wetted area-lift coefficient relationship derived 

 from tank model tests rather than extrapolating model resistance values. 



The relative planing efficiency for various cross sections (refs. [14 to -8]) is 

 shown in Figure 11. This is the hydrodynamic lift-drag ratio from model data plotted 

 against trim for a mean wetted length-beam ratio of 3.0. The peaks of the curves for 

 various cross sections occur at trims of from 5° to 9° depending on the dead rise. 

 At high trims, the curves tend to approach the cot T boundary curve representing the 

 induced lift-drag ratio. It has been noted that at high trims and low length-beam 

 ratios, measured lift-drag ratios for a flat plate actually lie a little above this boundary 

 because of forward flow in the spray root ahead of the stagnation line. 



The L/D is reduced as the dead rise is increased throughout the range of trim 

 shown as would be expected. As shown previously the addition of horizontal chine 

 flare or vertical chine strips increases the lift of the dead rise surfaces. These addi- 

 tions also increase the lift-drag ratios by a useful amount in the best trim range in the 

 same manner as a decrease in the effective angle of dead rise. There is little to choose 

 between the two forms of chine with regard to their beneficial effect on the efficiency 

 of either the 20° or 40° surfaces. 



194 



