Resistance of a Ship among Waves 301 
gives the variation of R’ with the ratio of the length of the model to the 
wave-length. It is obvious that the greatest positive values of R’ will occur 
when there is a crest near the bow and a trough near the stern, and con- 
versely for negative values of R’. The stationary values of (9) give the 
corresponding values of k,l, or 27l/A; one such value gives A/2l = 0-55 
approximately, and for this velocity R’ is negative if = 0 and positive if 
ji—ie 
4—For numerical calculations we shall consider a model for which theo- 
retical and experimental values of the wave resistance in still water are 
known; this is Model 1302 investigated by Wigley at the National Physical 
Laboratory, the results being given in these Proceedings (Wigley 1934). 
The form of the model is given by the following: 
From z = 0 to z = —id, 
y = b{1—(x+a)2/7}, y=b, y = b{1—(«—a)?/P} 
for x ranging from —l—ato —a, —atoa, atol+a respectively; 
From z = —4d to z = —d, 
y = 30(1—2?/d*) {1—(e@+a)?/P},  y = 3b(1—27/d?), 
y = $0(1 -24/d2) {1 —(@—a)/P} 
for the respective ranges for x of 
—l—ato —a, —atoa, atol+a. (10) 
The dimensions, all in feet, were a = 0:5, b = 0-484, 1 = 7-5 and d = 2. 
Carrying out the integrations of (6) over the longitudinal section of the 
model, we obtain 
,  Spbe*h(, 4/1 Nave 3( 1 1 ~tl 
Ee R02 alert ani ue Kod | Kod i 
x {sin Ko(/ + @) — Kol cos Ky(J +a) —sin kya} cosf. (11) 
We shall take # = 0 so as to obtain maximum effects as far as the position 
of the model relative to the waves is concerned. In the following table values 
of R’/c?h are shown for several different velocities, R’ being in lb. with c in 
ft./sec. and h in ft. The column R,/c? gives the corresponding theoretical 
values for the wave resistance in still water, taken from fig. 6 of Wigley’s 
paper. 
R, has maxima and minima according to the interference of bow and 
stern waves; while R’ oscillates between positive and negative values in 
431 
