Studies in Wave Resistance. 579 
5129 pb?l 
a m (1-4 6)? p3 
Tf a Oe ie 1( 1 
05 EES = Ba fea go LL 
21a me” Mame)! algae e tm |e 
Loy eyo | ai =U 
+58 aD Yo 
9 oh 
“2 \aoaiee : ot) p+ sh 1 ye OO 
1 16 1 512 & 16384 64 
= (1—1. 82 + —9 (14. 292-1 gt) L912 & | 16384 6 
[5 Coo 15 (E 5 at 35 pt 315 pe 
1620 IT 2W YEH 
+35 PI —go) ee hy, 
+51 (co-ats ®t pay eg (Id ora 8 9), 
Higa tag), tgs Ba) 2 + BES) (29) 
This, with p=gL/c?, gives the wave resistance as a function of thé 
velocity. 
For large values of p it is simpler to calculate directly from an asymptotic 
expansion. This may be obtained directly from the integral expression for 
R, or by substituting in (29) the asymptotic expansions of Yo, Y; and Youl. 
The latter method gives a check for the coefficients in (29), since the positive 
powers of p must disappear from the expansion ; in this way the first few 
terms of the expansion are found to be 
5129p 671 
$e 
Le? SC a oh *) sin (p—7) 
=) { (5 3° +755 aa A 
1S) ET os. 1 _@ 
al ago ag 8) = 008 (p aa @) 
We shall consider now four cases numerically. 
ae 1 A, SEHD 16 21 94 i 
R [5c 3 8)+ 72 (1+28 19) 
Calculations for Four Models, 
7. In model A we take 8=0; so that the level lines of the ship are the 
parabolic curves 
= b(1—2?//?), 
The expression for the wave resistance reduces to 
see Lea oe 1 Als 
Rises 3/1522 \60” ti”) % 
w/t oo 5) z(2 Sale 2) } 31 
terse Eo \ eg? tg? hip) ay CD) 
207 
