wetted length. T is the trim angle, and /? is the effective angle of dead rise from keel 

 to chine. The introduction of a constant crossflow drag coefficient in the second term 

 correlates the experimental data from different sources, and for different cross sections 

 and plan forms over a very wide range of the independent variables; for example, 

 speeds up to 80 feet per second, trims up to 30°, and length-beam ratios up to 8.0. 



Center of pressure. — The center-of-pressure ratio derives from corresponding 

 ratios for the lifting-line and crossflow lift terms, a x and a 2 . These ratios remain con- 

 stant for either rectangular or triangular plan forms throughout the range of available 

 data. The two equations are therefore generally representative of the recent research 

 on pure planing, and numerical solutions of them provide a convenient summary of 

 the significant results. 



Chine rounding. — The variation of lift coefficient and center-of-pressure ratio 

 of a sharp-edged flat plate with trim for a typical wetted length-beam ratio of 3.0 is 

 shown in Figure 6. The curves fit recent experimental data from metal models best 



C 

 SHARP 1.33 

 R = l/64" 1.20 

 R=l/16" 1.15 



d|=0.88 



a 2 =o.50 







8 



16 

 TRIM, T, DEG 



24 



32 



Figure 6. Effects of chine rounding, deadrise 0°, l m /b = 3.0. 



using a crossflow drag coefficient of 4/3. A small amount of chine rounding (% 4 

 inch in a 4-inch beam) such as might be found on a sanded wooden model appreciably 

 reduced the lift coefficient and the apparent value of C D which might account for 



some of the observed discrepancies among data from various sources. With a given 

 load, this effect would be expected to increase the wetted area, frictional resistance, 

 and total resistance at low trim angles. At high trims where the frictional resistance is 

 small, the effect on planing efficiency is negligible. 



For rectangular-plan-form flat plates, the center of pressure of the lifting-line 

 component of lift apparently remains at V& of the mean wetted length, and of the 

 crossflow component at V2 the mean wetted length. The total center-of-pressure ratio 

 moves from approximately 0.80 at low trims to % at the high trim of 30°. Chine 

 rounding has only a small effect on the position of the center of pressure. 



191 



