Gadd 



where 



_ 4.7 pvg'^' (3) 



Thus, if an overall propulsive efficiency of 70 percent can be assumed, the min- 

 imum horsepower P^- ^ required to propel a body of volume V at speed V is 



Pmin = 1.04X 10-2 ^v3 ^2/ 3 Cp(R^) , (4) 



where p is in slugs/ft^, V in ft/sec, and V in cu ft. 



It is of interest to compare the performances of some of the old airships, 

 whose shapes were quite similar to Fig. 1, with Eq. (4). We assume for air that 

 P = 0.00238 slugs/ft^ and fj./p = 1.564.10-'' ftVsec, and throughout this paper 

 we employ the ITTC formulation for Cp, 



0.075 /_v 



(5) 



(logio Rn-2)- 



In Table 1 the speeds v and actual powers P^ of a few airships are shown to- 

 gether with the estimated values of P^^^, calculated by assuming the displaced 

 volume to be the gas capacity times 1.06 (an average ratio). It can be seen that 

 for the later airships Pa/Pmin ^^^ lower than for the early ones, though it al- 

 ways remained appreciably greater than 1. This is hardly surprising, since the 

 engine nacelles were attached to the hull by struts and bracing wires, whose 

 drag was probably appreciable, and the fabric -covered hulls were probably not 

 completely smooth. 



Table 2 shows a similar comparison for submarines in the submerged con- 

 dition. Here Eq. (4) and Eq. (3) become 



P^in = 1061 V^ A2/3 Cp.(R ) 



mi n r "^ n '^ 



R^ = 2.11 X 10^ VAi/3 



where A is the salt-water displacement in tons (35 cu ft = 1 ton) and V is the 

 speed in knots. Prewar submarines were not primarily designed for high 

 speeds under water and were poorly streamlined, with consequent very high 

 values of p /p . . More modern submarines seem to have performances com- 



a mi n ^ 



parable with those of airships. It has to be borne in mind that the data upon 

 which Tables 1 and 2 are based, and the ship data to be presented below, may not 

 be completely accurate, and that a small error in speed makes an appreciable 

 difference to P„- . 



Surface Ships 



If a body of revolution of the shape shown in Fig. 1 were moved, half im- 

 mersed, through water, with its axis of symmetry in the plane of the undisturbed 



708 



