95 



The roots of [29a] can be represented as functions of the parameter 



\- 



When the critical velocity F, = 1 is reached m h becomes zero and 

 remains zero for Fj,^^ >1 . Thus for the whole supercritical range ra = 0. The 

 integral (2b) can be put into various shapes when performing actual 

 computations. 



D. The Wave Resistance of Ships in Rectangular Canals 



The rather complicated formula for this case has been derived by 

 Sedov and Keldysh and Sretensky.^^ '^® 



jjcosh mj^(z+h) sinj/^^^tanh m, h x<7(x,z)dxdz 



P, is a similar expression with the cosine instead of the sin and represents 

 the influence of odd terms of the surface equation, k is an integer while b is 

 the width of the canal. 



The values of m, are the roots of the equations 



where 



y^m^ - ^ tanh mh = ttK 



APPENDIX 3 

 THE VISCOUS PRESSURE RESISTANCE 



Observations and some measurements of the velocity distribution at 

 the stern indicate that with normal models the chief reason for the viscous 

 pressure resistance is, contrary to earlier opinions, not the separation but 

 the pressure defect due to increase of boundary layer thickness. 



Two methods have been proposed to deal with this problem in a quan- 

 titative way: 



