T. H. HAVELOCK 
Ahk? = wi'(z es a,). (11) 
With these assumptions we turn the calculated moment into an equiv- 
alent trim @ given by 
M — Rd’ 
OS area ae 
gp Ak 
calculating values from (10) and (11), and using the measured total 
resistance for R and an estimated value of d’; the actual value of d' 
is not important as in any case Rd’ is found to be a small fraction of 
the value of M. 
(12) 
4. Numerical calculations were made in the first place for two 
Teddington models of this type, with extreme values of the parameter 
a: namely 
Model 1805A, with a, = -0.6 
Model 1846A, with a, = 0.6 
For each model we have 
length = L = 27 = 16 ft; 
beam = 26 =1.5 ft; 
draft =d=1 ft. 
Further details of the models, and measured values of the trim are 
given by Wigley [8]. 
For these models d‘ was taken to be 5 inches. The integral in 
(10) was computed by quadrature, the value of the integrand being 
calculated for values of wu differing by 0.1; it was not generally neces- 
sary to go beyond about 3.6 for the upper limit of wu. This process 
was carried out for six values of the Froude speed ratio f in the 
range 0.32 to 0.54, f being equal to v//(gL). Finally the results 
were expressed as trim by the stern in inches for the 16-foot model, 
that is by 1920 the experimental results for these models ‘being 
recorded in that form. 
As an example of numerical values, at a speed ratio f = 0.5, the 
calculated trim for model 1805A is 6.45 inches, while the measured 
value was 6.0 inches; of the calculated value, the moment M of (10) 
gave 6.72 inches and the term — Rd’ reduced this by 0.27 inches. 
Similarly for Model 1846A at f = 0.5, the calculated trim is 4.82 
inches, the measured value being 4.7 inches. 
The results for the two models are shown in Fig. 1. The full 
curves are the measured values, and the broken curves show the 
values obtained from the present calculations. 
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