Dagan and Tulin 



t = ea2, b^ ^""^^^ , d,. =0, dg. = (41) 



and both inner and outer solutions are uniquely determined. 



Our estimates of t and b are confirmed, Eq. (41) showing 

 that t = O(e^) and b = ©(e^*^^) . The nonlinear character of the prob- 

 lem is manifest in the inner expansion. 



We have now a uniform solution which can be written by- 

 adding the inner and outer solutions and subtracting their comnnon 

 part. 



(c) The Bow Drag 



The horizontal force acting on the bow is found by the pressure 

 integration in the inner zone (Fig. 4f) 



D=r 5dy=4lmr (1 + w^) dz =ilm r (l+w)(l--^) 



.J . r»J . r»0 



, d^ 



(42) 



Since w is analytical in the lower t, half plane the integra- 

 tion along BJ may be replaced by integration at infinity (at H) and 

 around the origin J. After expanding l/w^ -^ w^ at infinity and near 

 the origin, we get for D 



2 



D = 1|- (1 + cos P/tt) (43) 



The same result, excepting the cos P/ir term, may be 

 obtained directly from the first order outer expansion. 



To roughly compare the result of Eq. (43), with Baba's 

 findings, lets assume that the bow is completely blunt with (3 = tt/Z 

 and a = 1. For e = l/Fr^- » 0.34 we have 



C^= 2D = 0,34 (44) 



which is roughly four times larger than the value estimated by Baba. 



At this stage it is difficult to find which of the following 

 factors explain this discrepancy: The asymptotic character of the 

 solution, the lack of details on the bow shape or, may be the most 

 important, the crude representation by Baba of a three-dimensional 

 flow by a two-dimensional equivalent (Fig. la). Future experiments 



620 



