322 



HYDRODYNAMICS IN SHIP DESIGN 



Snr. 57.11 



slope drag Dg (or thrust Ts) in lb for a ship 

 weight W of 1 long ton, covering a range of water- 

 level drops per 100 ft horizontal distance varying 

 from 0.02 to 10.0 ft. These correspond to a range 

 of d from 0.01 deg to 5.7 deg. The values so 

 derived may then be related directly to the values 

 of total resistance Rt per ton of weight displace- 

 ment A, mentioned in the sections preceding. For 

 example, the 100-ft version of the 944-t barge on 

 SNAME RD sheet 141 has a value of fir/A of 

 2.414 lb per ton at a speed V of 4.03 kt. If drifting 

 down a river having a surface slope of about 

 0.12 ft per 100 ft, the slope thrust is sufficient to 

 overcome the hydrodynamic drag for a 4.03-kt 

 speed through the water. If steered properly the 

 barge would go at least 4 kt downstream through 

 the water. If the current velocity in way of the 

 barge were say 3.5 kt, its speed past the banks or 

 over the bed would be about 7.5 kt. 



For the ABC ship of Part 4, ascending the 

 river to Port Correo, it may be assumed that 

 under certain flood conditions, with a river 

 current of 4 kt in that portion of the channel 

 section occupied by the ship, the drop in surface 

 level is 0.1 ft per 100 ft. The corresponding slope 

 drag from Table 57. d is 2.24 lb per long ton of 

 weight displacement. Assuming a W value of 

 16,000 t at this stage of the voyage, the calculated 

 slope drag is 35,840 lb. This is to be added to the 

 ship's hydrodynamic drag. At the same time the 

 current speed is subtracted from the ship's speed 

 through the water, say 15 kt, to give a speed of 

 11 kt made good over the ground. 



57.11 Ship Still-Air and Wind Resistance from 

 Chapter 54. To all the resistances derived or 

 mentioned in Sees. 57.5, 57.6, 57.9, and 57.10, 

 where appropriate, there should be added the still- 

 air or the wind resistance of the abovewater hull, 

 of upper works, and of all projections from both. 

 The ship creates a relative-wind speed Wr equal 

 to its own trial speed V, even though there is 

 no natural wind blowing over the trial course. 



The significance of still-air resistance, wind 

 drag, and wind resistance is described in Sec. 

 26.15 and illustrated in Figs. 26.G and 26.H. The 

 methods of estimating and calculating them are 

 described in Chap. 54. 



57.12 Calculating the Overall Wetted Surface 

 and Bulk Volume of a Submerged Object. A 

 prediction of the pressure and friction drag of 

 any submerged object, by any one of several 

 methods, requires first a calculation of the 

 overall wetted surface Sb and of the bulk volume 



Vb . The area (Sb of a submarine is that of the 

 outer hull, or of the pressure hull with outer 

 tanks, plus that of the superstructure, deck 

 erections, fairwaters, and all appendages except 

 those in the "short" category defined in Sec. 

 45.12. The area Sb of a submerged object in 

 general is the area bounding the portion which 

 pushes the water aside as the object is self- 

 propelled or dragged along. 



The bulk volume V^ is the entire volume within 

 the wetted boundary, whether all of that volume 

 is buoyant and weight-supporting or not. Any 

 Hquid in free-flooding spaces lying within the 

 overall boundary is considered as solidified or 

 frozen in place, so far as resistance to motion is 

 concerned. For instance, the bulk volume of a 

 whale with a mouth full of water includes the 

 volume of that water because, for this example 

 at least, it moves along with the animal. However, 

 the overall wetted surface does not include that 

 of the inside of its mouth, because there is no 

 friction drag on that surface affecting the body 

 motion. 



The 0-diml bulk fatness ratio is defined as the 

 ratio of the bulk volume Vb or Vs to the quantity 

 (O.lOLo^)^, where Lqa is the overall external 

 length of the hull when submerged. Values of bulk 

 fatness ratio, for submersibles and submarines of 

 varied type and service, range from about 3.4 to 

 5.4, with values rising to 8.5 for craft intended 

 for .special .service. 



The overall maximum-section area ^4.y of a 

 submerged body or submarine, as projected on 

 the y-z plane, is measured to the same external 

 boundary as the bulk volume. It is customary to 

 take this area as the maximum transverse pro- 

 jected area or frontal area, even though the deck 

 erections and fairwaters forming a part of this 

 area lie in a different transverse plane than that 

 of the maximum section of the main hull. 



57.13 Drag Coefficients and Data for Sub- 

 merged Bodies. There are many technical papers 

 and reports in existence giving resistances, drag 

 coefficients, and similar data for fully submerged 

 bodies, most of them bodies of revolution intended 

 to serve as basic shapes for airship hulls. Un- 

 fortunately, the validity of many of these data 

 are questionable, because of: 



(a) A practice of the 1900's, 1910's, and 1920's of 

 testing models in wind tunnels at Reynolds 

 numbers too small to produce flows that were 

 dynamically similar to those expected on the 



