356 F. H. Todd 
0-5 
R IN POUNDS 
VIN KNOTS 
0-4 
ae 10 
300 209 fete) (eo) 
DEPTH OF SUBMERSION IN FEET, 
MEASURED TO CENTRE LINE OF SUBMARINE 
Fig. 7. Effect of depth of submergence on a 
submarine of 80,000-ton displacement, L/D 
= 7.0 (from Ref. 3) 
run at a considerable depth below the surface. From these same model experiments Mr. Crago 
has shown that if the submarine is running in shallow water there can be a serious bottom 
effect also. For the same submarine of 80,000-ton displacement, for example, at 50 knots in 
water 300 feet deep, the resistance is some four times as great as in deep water when deeply 
immersed. For a ship of this size this figure is somewhat academic, as no one could ever 
contemplate driving such a ship at 50 knots in such a depth of water! But the results serve 
to indicate the problems that are likely to be met with when a large submarine is approaching 
shallow water on the continental shelf or when coming into estuaries. In fact, for a vessel of 
this size we must revise our ideas of what we mean by shallow water. 
Before leaving this question of resistance, it is worth while pointing out that in a sub- 
marine of this type the resistance would be almost wholly frictional, and to obtain the full 
benefit in power reduction it would be essential to keep the hull clean at all times, since 
any penalty due to roughness and fouling would be considerably greater than in the corre- 
sponding surface ship. This points to the need for frequent dockings, and as we shall see 
when discussing the operation of such a ship, this poses considerable problems. For a ves- 
sel of this type running deeply submerged in the comparatively calm conditions a long way 
below the surface of the sea, it is interesting to consider the possibility of maintaining 
laminar flow over the hull to a greater or lesser extent. The benefits to be derived from 
such a possibility are, of course, great. For a submarine 650 feet in length with a dis- 
placement of 75,000 tons running at a speed of 20 knots, the corresponding Reynolds number 
is 1.7 x 10°. The values of Cp for turbulent and laminar flow are 0.00144 and 0.00010 
respectively, and if we assume that the laminar flow hull is perfectly smooth and omit the AC, 
allowance of +0.0004 in this case, but add 20 percent in each for conning tower, etc., then 
the ratio of total resistance for laminar and turbulent flow is 0.25. This is an ideal condi- 
tion, of course, for a number of reasons. To encourage laminar flow over the hull, the shape 
