Design of Low-Resistance Hull Forms 



Cdw = Cp (1 + 1.5t^/2 + 7 ^3) * 



Hence, for motion at speed v through a fluid of density / and viscosity /x, the 

 drag D is given by 



1 , V2/3t 



D = -4r pV^ (2.168 + 0.946 t 2) (1 + 1.5 t^^^ + 7 t^) C^. . 



^ o.syst'*/^ *^ 



where Cp is a function of the Reynolds number 



R„ = 



pVL _ 1.318 pVV^/ 3 



Most of the standard turbulent friction formulations imply that Cp varies 

 something like R" '^^ . Hence, for minimum drag with a given speed V and vol- 

 ume V the factor 



n = (2.168 + 0.946 t 2) (1 + 1.5 t^^^ + j ^.3^ ^- i/s 



must be a minimum. It can be seen from Fig. 2 that n has a fairly flat mini- 

 mum in the region of t = 0.15, and that n does not differ much from this mini- 

 mum value for t in the range 0.1 to 0.25. This covers the range of beam-to- 

 length ratios encountered in ships. 



Setting t =0.15 we obtain the minimum value of D, 



min '^ r ^ n ' ' 



(2) 



Fig. 2 - Factor n proportional to the 

 drag of the streamlined form 



*Hoerner uses the Schoenherr line for Cp. The ITTC formula (Eq. (5) below) 

 approxinnates quite closely to this for Reynolds numbers greater than 10 . 



707 



