Sec. 57.15 



TOTAL RESISTANCE OF BODY OR SHIP 



323 



prototypes [Wuinblum, G. P., TMB Rep. 758, 

 May 1951, p. 1] 



(b) Uncertainties as to the interference effects of 

 supporting struts attached to the sides of the 

 bodies, with their axes normal (or nearly so) to 

 the body axis 



(c) Towing models in water at inadequate sub- 

 mergence, and picking up wavemaking drag 

 when the latter was supposed to be absent. 



S. F. Hoerner abstracts most of the modern 

 (1940-1950) drag data for streamlined bodies on 

 pages 67-72 of his book "Aerodynamic Drag," 

 pubhshed in 1951. Both Hoerner and W. S. Diehl 

 give extensive drag data on a great variety of 

 fuselage and hull shapes and components in the 

 references listed in Sec. 55.5. 



It is necessary in all these cases to differentiate 

 clearly between published Co values for total 

 drag, including friction, and the Co values for 

 pressure drag only, often called "form drag" in 

 the literature. Induced drag becomes a factor 

 when the submerged bodies run at yaw or pitch 

 angles and develop circulation around them- 

 selves because of this effective angle of attack. 



57.14 Pressure Resistance of Submerged 

 Bodies as a Function of Depth. Sees. 10.16 and 

 10.18 of Volume I emphasize that pressure resist- 

 ance due to wavemaking remains a factor in the 

 motion of a submerged body or simple ship, often 

 of considerable importance, until the submergence 

 is great enough to produce a flow pattern sub- 

 stantially similar to that at infinite depth. It is 

 not possible to establish an arbitrary limit for 

 this depth of submergence h, reckoned to the 

 body axis, without taking into account the sub- 

 mergence-Froude number of Sec. 10.17, the ratio 

 h/Lw , the L/D ratio, the form of the body or 

 ship, and other factors. A square-bowed body 

 obviously needs more depth to eliminate surface 

 wavemaking than one with a tapering bow. A 

 body or ship of normal L/D ratio, reasonably well 

 streamlined and having a transverse section not 

 drastically different from that of a circle, with no 

 topside appendages or protuberances, is reason- 

 ably free of pressure drag due to wavemaking at 

 a submergence, to its top, of three times its 

 vertical diameter. 



G. P. Weinblum tackles this problem for stream- 

 Uned bodies of revolution in TMB Report 758, of 

 May 1951, on an analytical and mathematical 

 basis corresponding to that described in Chap. 50. 



Sec. 7.2 points out that pressure drag due to 



separation decreases with depth because more 

 external pressure is available to create a pressure 

 gradient which will turn the water to follow the 

 body slopes in the run. Of the quantitative nature 

 of this effect around streamlined submerged 

 bodies not much is known, except that at infinite 

 depth there is sufficient pressure to turn the water 

 around any corner, however sharp. This is on the 

 basis that, if the water did not so turn in any 

 region, a cavity or void would be left, in which the 

 pressure would be substantially the vapor pressure 

 of water. The decreasing-pressure gradient toward 

 this cavity would then be very large, and would 

 immediately generate sufficient lateral force to 

 deflect the water and cause it to follow the surface. 

 Although in practice there appears to be no 

 actual void, the turning effect nevertheless 

 remains. 



A third factor enters here, primarily because it 

 is necessary to rely upon model tests in air or 

 water for practically all pressure-drag data. This 

 is the interference effect of the struts or supports 

 necessary to hold the model in the wind tunnel, 

 in the water tunnel or channel, or in the model 

 basin. If attached to the top, bottom, or sides of 

 the body, the struts interfere with the flow 

 pattern and change the velocity and pressure 

 fields. If attached at the stern, a single longi- 

 tudinal support or "sting" interferes with any 

 separation zone that may exist there. 



It is unfortunate that many of the published 

 drag data on submerged bodies are to be taken 

 with caution, because in these cases: 



(1) The type, nature, shape, and position of the 

 supporting struts are not described or shown in 

 the test reports 



(2) The depth of submergence of bodies tested 

 in water is not known, nor are there any data of 

 record concerning visible or measured wavemaking 

 on the surface. 



57.15 Resistance Due to Flow of Water 

 Through Free-Flooding Spaces. The flow of 

 water through the free-flooding spaces of both 

 surface ships and submarines in straight-ahead 

 motion is discussed in Sec. 20.9 of Volume I. 

 There it is mentioned that free-flooding spaces 

 which extend for a considerable distance forward 

 and aft, so far that openings through the shell 

 at the forward end lie in a. +Ap region while 

 those at the after end are in a — Ap region, 

 may be expected to have longitudinal flow 



