336 LOGARITHMIC SPEED-POWER DIAGRAM. 



The fact that both the exponent and coefficient of friction vary in the 

 formula for frictional resistance makes it impossible to introduce this term 

 directly in the laws of comparison. Detail calculation shows that if fric- 

 tional horse-power be calculated for two similar surfaces at corresponding 

 speeds, the ratio of horse-power is very closely approximated by the 6.735 

 power of the speed-ratio, or the 3.3675 power of the length-ratio. (See 

 appendix.) 



This relation holds most closely for surfaces above 50 feet in length, but 

 is a good approximation even as low as 10 or 15 feet in length. 



Since friction power of the ship varies nearly as the 6.735 power and 

 residual power as the 7th power of the speed for similar hulls at corresponding 

 speeds, it may be expected that their sum, or effective horse-power, will vary 

 as some power of the speed between 6.735 ^^^ 7- It is somewhat variable, 

 dependent upon the ratio between frictional and total resistance or power, 

 as indicated approximately below : — 



Ratio 



In common practice, the power consumed in surface friction is from 50 

 to 60 per cent of the effective power, as low as 40 per cent only in very high- 

 speed craft, and dropping possibly to 10 per cent in hydroplanes or rising to 

 90 per cent at low speeds for long cargo vessels. It may be stated that for 

 normal designs, from full boats of low speed to fine forms of high speed, there 

 is not much error in assuming the exponent of reduction to be about 6.866. 



Errors due to this assumption are discussed in the appendix. 



Proceeding to the application of the logarithmetic diagram to these 

 calculations; on the "Foundation Sheet," Plate 129, is a set of logarithmic 

 co-ordinates so drawn as to cover a convenient range for calculation. The 

 main variable which is used as abscissa in all cases is arbitrarily chosen to be 

 speed, V, in knots (see bottom of diagram). The scale of ordinates is marked 

 "Horse-power" but is also used for reading displacement, length, beam, 

 draught, wetted surface, or other dimensional quantities. 



