Sec. 54.4 



AIR AND WIND RESISTANCE OF SHIPS 



277 



where /^wud is tlie wind resistance, exerted m the 

 direction of ship motion, ^^ is the abovewater 

 silhouette area of the ship (defined in Sec. 26.15), 

 as viewed from astern, and Wg is the relative 

 wind velocity, derived from the vectorial addition 

 of the ship speed V and the true-wind velocity Wt- 

 For what was supposed to be the worst case, the 

 true mnd was in those years assumed to be 

 always from ahead. 



The necessity for using data derived from 

 aeronautical studies, many of them in \vind 

 tunnels, as well as data formerly expressed in 

 other units of measurement, called definitely for 

 non-dimensional wind-drag and wind-resistance 

 formulas. On the basis that substantially all the 

 drag of a ship hull and its upper works is a pressure 

 effect, due to deflection and separation drags, the 

 general equations for the wind drag D,^ , with the 

 latter always measured in the same direction as the 

 relative wind-velocity vector W ^ , are 



(>DCAir) — 



D, 



Dw = Cfl(A,„|4p,„iF«^ 



= Cnui.^ 7, A^W^ 



(54. iv) 



A^W^ 



(54 .v) 



Here the mass density p(rho) is, from Sec. 

 X3.8 m Appendix 3, taken as 0.002378 slugs per 

 ft^, for "standard" air conditions at a temperature 

 of 59 deg F, 15 deg C, and a sea-level pressure of 

 14.696 lb per in' or 2,116.2 lb per ft'. 



The area Ap^^j or A^ is that of the abovewater 

 silhouette of the hull or structure in question, 

 when projected on a vertical plane normal to the 

 direction of the relative wind. The velocity of that 

 wind is W^ .For rough calculations it is assumed 

 constant over the whole vertical span of the 

 abovewater structure being blown upon. 



For more refined estimates the structure should 

 probably be considered as composed of two or 

 more vertical layers, each \vith its own relative- 

 wind velocity, dependent upon its average height 

 above the water surface, employing the wind- 

 velocity multiples of Fig. 54. A. In addition, each 

 layer should be composed of a typical kind of 

 structure, such as (1) hull, (2) upper works, and 

 (3) spars and rigging, so that if appropriate a 

 separate drag coefficient as well as a separate 

 average relative-wind velocity W^ may be used 



Fig. 54. B Typical Wind-Resistance Model 



