206 Dr. T. H. Havelock. [June 7, 
the model. The latter is frequently specified by various coefficients of 
fineness, which of course give only an approximate estimate of form, and 
in any case do not make a set of independent variables; no attempt is 
made here beyond giving all the available data for each model. With the 
results given above and in the previous paper, one can find an approximate 
estimate of the leading coefficient 8, at least for forms similar to those already 
examined. It was noticed that, other things being equal, 8 was proportional 
to the displacement-length coefficient; also for given values of the latter 
8 appears to be approximately proportional to the ratio of beam to draft. 
This seems reasonable, since wave-making is largely a surface effect ; that is, 
for a disturbance travelling below the surface the wave-making falls off 
rapidly with its depth. In several of the cases already examined, it 
happens that @ is numerically only slightly larger than the product of the 
two ratios mentioned, that is, @ is a little greater than (B/H) x D/(L/100)*, 
with all the quantities in the units specified above. This result is used now 
to make an approximate estimate of total effective horse-power for a 
certain ship, as it affords opportunity for introducing other points of 
interest. The data for the ship are those of the “Turbinia,” as far as 
they are available from the published record of trials.* 
Turbinia.—Displacement = 444 tons; length = 100 feet; beam = 9 feet; 
draft = 3 feet; cylindrical coefficient = 0:66; speed = 31 knots. 
The displacement-length coefficient is 445, while the ratio of beam to 
draft is 3; since the cylindrical coefficient is less than those already 
examined, we take 8 as about 5 per cent. greater than the product of these 
two ratios, that is, @ = 140. Following out the indications of the previous 
cases, m should be nearly 3; as we shall calculate quantities for ¢ = 3-1 
the exponential e~”/’ only varies slowly with m, so that m = 3, with suffi- 
cient approximation. Under the same conditions we take »/c? = 60° and 
y = 0:15, also a= 2. Calculating from formula (2) with these values, we 
obtain an estimate of 410 for the effective horse-power of the ship at 31 knots 
due to wave-making, 
any of the usual approximate formule, with simple powers of the speed, when 
with the possibility of this being slightly in defect ; 
extended to this high value of ¢ give possibly twice this estimate, a result 
which is much too high. If we take the area of wetted surface (S) as 
970 square feet and the frictional coefficient (7) as 0°0095, we may calculate 
the frictional effective horse-power from the expression 0:00307/SV**®; it is 
470 at 31 knots. We obtain thus an approximate estimate of 880 for the 
total effective horse-power of the ship at 31 knots. It is stated in the record 
referred to above that the total effective horse-power at 31 knots is 946, 
* C. A. Parsons, ‘Trans. Inst. Nav. Arch.,’ 1897, vol. 38, p. 232. 
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