where p = density of fluid (Slugs/ft^) 



V = velocity of flow (ft/sec) 



m = coefficient of viscosity (lb-sec/ 

 ft^) 



V = m/p = kinematic viscosity (ft^/ 



sec) 

 1 = a characteristic length of the 

 body (ft) 



The Reynolds number can also be obtained 

 from the nomogram in Figure 8.25. 



An additional factor is roughness of the 

 body surface which will increase frictional 

 drag. Naval architects generally add a 

 roughness-drag coefficient to the friction- 

 drag coefficient value for average conditions. 



Because a submersible rarely travels at 

 constant speed, forces must be considered 

 that arise from the acceleration of a mass of 

 fluid entrained by the body or fairings. The 

 added mass is determined by the mass den- 

 sity of the fluid and size, shape and motion of 

 the body. Likewise, there is a moment of 

 inertia accompanying angular acceleration 

 which is also added (16). Both the former 

 force (called virtual or induced mass) and the 

 latter, moment of inertia, are treated under 

 unsteady flow in hydrodynamic considera- 

 tions. 



While such considerations are of extreme 

 importance to the military submarine — 

 where high speed, among other factors, is 

 desired — they are less important to submers- 

 ibles where 2 or 3 knots generally will suf- 

 fice. More important than the shape of a 

 submersible are considerations of pressure 

 hull size, component arrangement, maneu- 

 verability, weight saving and surface sea- 

 keeping. Furthermore, while a particular 

 hull shape may be hydrodynamically satisfy- 

 ing, the external instruments and equipment 

 attached from dive to dive will frustrate any 

 attempts by the hydrodynamicist to main- 

 tain a low drag coefficient. A number of the 

 large corporations and academic institutions 

 have derived the drag forces operating on 

 their vehicle. One such case is ALVIN, for 

 which Mavor et al. (8) present a moderately 

 detailed but fully referenced account of the 

 procedures and results. Resistance data for 

 bodies of ALVIN's shape (described as ocu- 

 lina) were not available at the time of its 

 design; consequently, a one-twelfth scale 

 model was constructed at the Massachusetts 



Institute of Technology and towed by a 

 pusher sting dynamometer. A drag coeffi- 

 cient of 0.027 based on its wetted-surface 

 area was indicated. A second test on a one- 

 quarter scale model at the Illinois Institute 

 of Technology confirmed the 0.027 drag coef- 

 ficient. For comparison purposes, a total 

 drag coefficient for the ALB ACORE -type hull 

 was calculated at 0.0033. While ALVIN is not 

 the most streamlined of submersibles, it is 

 not the worst, and it might serve as a gen- 

 eral comparison for the drag coefficient of 

 contemporary submersibles (with a spherical 

 bow) against a streamlined body of revolu- 

 tion. Interestingly, ALVIIS's resistance is ap- 

 proximately equal to that of a sphere having 

 the same cross-sectional diameter as the 

 hull, and the hull shape in this range of 

 fineness ratio may not have important ef- 

 fects on resistance. 



PROPULSION POWER 

 REQUIREMENTS 



To derive the horsepower required of a 

 submersible's motor two factors must be de- 

 cided: What is the desired speed, and what 

 resistance must be overcome? In most cases 

 the designer will have fairly firm notions 

 concerning speed, but the resistance or drag 

 of the vehicle is not always known. 



Model testing and the engineering talents 

 required for drag and dimensional analyses, 

 such as those performed on ALVIN, are ex- 

 pensive and far beyond the resources of the 

 so-called "backyard builder." Furthermore, if 

 the model tests were to show an optimum 

 horsepower which was not available off-the- 

 shelf, few, if any, of the smaller builders 

 would be able to afford the cost of a specially 

 built motor. The approach taken by the small 

 builder to motor selection is based, in the 

 final analysis, on availability and trial and 

 error. 



An example of the above approach is found 

 in the NEKTON vehicles. According to Mr. 

 Douglas Privitt of General Oceanographies, 

 the procedure followed in selecting a propul- 

 sion motor for those vehicles was based on 

 the following constraints: The motor had to 

 be DC, series wound, small and light weight. 

 It had to provide a speed of 2 knots at an 

 economical current drain and be available 



395 



