where z, is the specific gravity of the eimbient fluid. 



Exajnples of the calculations leading to these expressions are: 



2 ■■ 2 2 



(a) Since v = - u v,mv = moj v « (m/A t) * 1; this is = z\ if 



3 

 m = TeX . I is obtained similarly. 

 6 



(b) To make (c^ + BS) v « cX, where v « (jv « l/Cx/T), it is 

 necessary that (c, + BS) « eX /T. This is most simply secured by making 



c » BS cc ex^ /r~. 



2 2 2 2 



(c) To make BS 9 <^ eX, let BS = eX . Dividing this by BS <r eX /t 



gives S a l/ZT, and dividing S « l/F into BS = eX /T gives B « teX . 



(d) If Theodorsen's values for the lift are used, 



^b + e = C/B«X; -b+e= >'^~7b « X 

 2 2 L 



whence 



b = C/B - /E /B <x X ; e = (C/B) - (3/2) b = X 

 ij 



Also, pJl-. = B/(iTb) a tgX. Write p = CP,,) C being the specific gravity of 



the fluid bathing the foil and p the density of p\ire water. Then, p 



o o 



being the same for all foils, I « reX/i;. 



As a special case, if the systems actually differ only in scale, all 



linear dimensions varying as X, then e = t = 1 and the similitude Just 



3 5 2 1+ 2 



described reqioires that m<=cX,I. °^X,c =X,CoaX,L<=cX,Ba:X, 



fc) 1 "i 



3 li , . 



C a X , E^ o: X (or b a e « £„ « X) , with S and ^ remaining constant for 



all systems. Also, u = l/X. 



69 



