Sec. 54.2 



AIR AND WIND RESISTANCE OF SHIPS 



275 



considered logical and is used as the reference in 

 this book. 



The ship designer, naval architect, and ship 

 operator then need a curve or table of multiples, 

 to compare the wind velocity at other heights 

 with that at 6 ft. The necessary data can be 

 and have been derived from (1) theoretical con- 

 siderations and from (2) observed simultaneous 

 wind velocities at several heights above a reason- 

 ably level water surface. 



Making use of boundary-layer theory it is 

 possible to develop a simple formula which shows 

 that the ratio of the wind velocities at two 

 different heights above a solid, level surface 

 should vary as the fifth root of the ratio of the 

 heights [Experiment Tank Comm., Japan, "Ab- 

 stract Notes and Data," 6th ICSTS, 1951, pp. 

 71-92]. Taking hi and h^ as these heights, and 

 TTi and W2 as the wind velocities at these heights. 



W2 _ Wind velocity at height h^ 

 Wi Wind velocity at height hi 



(54.i) 



A discussion by D. Brunt, also based upon 

 boundary-layer theory but making use of experi- 

 mental observations to some extent, is given in 

 his book "Physical and Dynamical Meteorology" 

 [Cambridge (England), University Press, 1944, 

 pp. 247-255]. Brunt is inclined to use a seventh- 

 root velocity variation rather than a fifth-root 

 variation, based upon the distribution in the 

 1/7-power velocity profile illustrated in the right- 

 hand diagram of Fig. 5.K. It is apparent, from 

 the discussion presented by Brunt, that the rate 

 of wind variation with height is complex, depend- 

 ing upon a number of variables which could be 

 evaluated only with difficulty in actual practice. 



It is not a simple matter to find reliable experi- 

 mental data known to have been taken over the 

 water. Furthermore, the exact vertical location of 

 the "Surface" observations used for reference are 

 rarely stated. Presumably they are at least as 

 high as a man sitting in a small boat. The low 

 heights of interest to the ship designer, say 

 several hundred feet, are in the category of 

 micro-heights in the field of meteorology. 



The only careful, systematic investigations 

 made over the sea appear to be those of J. S. Hay, 

 published in Porton Technical Paper 428 (un- 

 classified) of 24 June 1954, issued by the Chemical 

 Defense Experimental Estabhshment of the 

 Ministry of Supply of Great Britain (copy in 

 TMB library) . Unfortunately, however, the obser- 

 vations covered a range of only 0.5 to 8 meters 



(1.64 ft to 26.248 ft) above the sea. Hay found 

 that the local velocity U at any height h above 

 the quiet water surface (represented by the 

 symbol z in the paper) varied generally in accord- 

 ance with the logarithmic formula 



U 



C/:.o 



lioh -{■ h 



(54. ii) 



where C/1.0 is the velocity at the reference height 

 of 1 meter (3.28 ft), and a and h are numerical 

 values tabulated by Hay for different wind and 

 sea conditions. 



The roughness of the sea surface, increasing 

 with the wind velocity at the reference height, 

 changes the type of viscous flow somewhat and 

 with it the numbers a and h. Hay lists 8 references 

 on page 16 of the report. 



Because of the diminished relative roughness 

 of the average water surface as compared to the 

 average land surface, the speed of the wind for a 

 given atmospheric disturbance is greater over 

 water than over land. Likewise, the reduction in 

 wind speed as the height is diminished, due to the 

 increased wind friction over the land, is greater 

 than over the water [Curry, M., "Yacht 

 Racing," Scribner's, New York, 1948, p. 130]. 

 For this reason, velocity observations made over 

 land should not necessarily be taken as applying 

 over water. However, even though it is known 

 that they do not apply, it has been necessary 

 to make some use of data taken over the land. 



Based on available sources, Hsted in the next 

 paragraph, the graphs of Fig. 54.A have been 

 prepared. Briefly: 



I. The solid-line graph A is based upon a com- 

 bination of data from references (c) and (e) of 

 the list which follows 



II. The short-dash graph B at the left represents 

 values derived from Eq. (54.1), based upon a 

 wind velocity of 1 (unity) at 6 ft above the water 

 level. It appears to represent the probable rate 

 of variation over a reasonably smooth water 

 surface as well, if not better, than most of the 

 experimental data. 



III. The long-dash graph C at the right of the 

 figure represents the mean of the data from (b) of 

 the following list, indicated by the small open 

 circles. 



The references consulted were: 



(a) Schoeneich, "Der Windwiderstand bei Seeschififen 

 (The Wind Resistance of Oceangoing Ships)," 

 Schiffbau, 22 Nov 1911, Vol. XIII, pp. 121-129. 



