CALCULATIONS ILLUSTRATING THE EFFECT OF BOUNDARY LAYER ON WAVE RESISTANCE 
O20 
0-15 
O10 
SCALE OF 
O10 020 
SCALE OF f 
With the full end leading we have 
1 
reise |(—2¢ eet 
2277, 253 
+ |\ 384 + ag 
—2 
cs 
and with the fine end leading we have 
1 
rise |(—j-2e+e)ersae 
== 
glereae . (42) 
-t 
3771 419 
‘a ie + 48 
ry 
Jersae (43) 
We shall examine only the difference in resistance 
between the two cases. Forming I? ap J? from (42) and 
(43) and using the difference we obtain eventually 
f2 
sn ae ipeny e 
Be wy Ke a) 3 3 ¥ 
23 «56\ . /15 169 15 ) 
+ (5+ 3) (87) — spe 7 
7) SD (fly 253 N7/ 
+(%-p)sn(s) + epe(e7 
479 1 56. /1 
+ ae () + pes (jr) Joos oa0 
(44) 
alias tile 
el i sl a lo ea ee ea 
aie 
bl a 
als val 
40 
O50 
O 
aE 
O30 
Fic. 3 
535 
These integrals have been computed and the curve is 
shown in Fig. 3; the ordinates in this curve are the 
corresponding difference in © values for this model. 
This curve may be compared with results from experi- 
ments with unsymmetrical models, for instance in work 
at the N.P.L. by Wigley.!° The curve has the same 
general character and the right order of magnitude, 
except that in the experimental models the difference in 
resistance diminishes to zero at about f=0-5. The 
agreement could probably have been improved in the 
calculations by taking the point of departure of the new 
curve at different points for the full end and the fine end. 
However, there is little to guide one meantime in making 
these assumptions, and moreover, in dealing with actual 
ship models boundary layer structure is still more 
difficult to unravel in its dependence upon form. 
References 
(1) T. H. Havetock: Proc. Roy. Soc., A, 110, p. 233 (1926). 
(2) T. H. Havetock: Proc. Roy. Soc., A, 149, p. 417 (1935). 
(3) W. C. S. WicLey: Trans. Inst. Eng. Ship. (Scotland), 81, 
p. 187 (1938). 
(4) G. S. BAKER: Trans. N.E. Coast Inst., 46, p. 83 (1929). 
(5) T. H. HAvELockK: Proc. Roy. Soc., A, 138, p. 339 (1932). 
(6) W. G. A. PERRING: Trans. I.N.A., 67, p. 95 (1925). 
(7) K. SCHOENHERR: Trans. Soc. Nav. Arch. and Mar. Eng. 
(New York), 40, p. 279 (1932). 
(8) W. C. S. Wictey: Trans. I.N.A., 59, p. 193 (1927), 
(9) F. H. Topp: Trans. Inst. Mar. Eng., 57, p. 1 (1945). 
(10) W. C. S. WiGLEY: Trans. I.N.A., 86, p. 41 (1944). 
(11) Cong. Intl. Dir. Bassins (Paris), p. 201 (1935). 
(12) T. H. HAvELocK: Proc. Roy. Soc., A, 108, p. 582 (1925). 
(13) S. GoLDSTEIN: Modern Developments in Fluid Dy- 
namics, Vol. I, p. 123. 
