CALCULATIONS OF SHIP TRIM AT HIGH SPEEDS 
and 
r @ 2 2 
M = -5 il i we ( -=)(u a, =) Pw, 2) dede (9) 
SUG) 
Carrying out the integrations and, for convenience in computation, 
changing the variable from @ to u with sec 6 = cosh wu, we obtain 
the result 
{oo} 
649pb? 
u- “or X,(B)X (8) X4(0) sech? udu, (10) 
OS “0 
eh B=«x,dcosh*u; a= k )/coshu; 
z ZU fh AON Os 
4 8 Q\ 4 3 
Xa= Zr get (1-ae)singa+ (4-2) con20, 
4 42 96 64 192\ . 
+ Gy4— — — — —_ 4 Je erg sin 2a + 
16 150 96 
+ = —3, +t =, ]Cosi2ia> + 
a a 
“a 
2f 2 3 96 720 74 768 1440\ . 
+ a, {ats eo a ae) aeweaes sin2 a+ 
12) 291 1344 720 9 
aP Toes cra ar ae a aro COS zZQ>. 
The moment M given by (10) will, if positive, tend to give a trim of 
angle @ which is positive with bow up and stern down. In comparing 
with model results, we note that the model is towed, the point of 
attachment of the tow-line being at the water level in the midship 
section; if R is the total resistance, we have therefore a reverse 
moment Rd’, where d' is some fraction of the draft d of the model. 
The effective positive moment is M ~ Rd’. 
We have also the restoring moment due to the hydrostatic pressure 
and for this we take, as a sufficient approximation for the present 
purpose, gpAk?0, where Ak? is the moment of inertia of the area of 
the water plane section about Oy. For the models defined by (7), 
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