280 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 54.8 



0.045 to 0.063 for ship superstructures only [van 

 Lammeren, W. P. A., Troo.st, L., and Koning, 

 J. G., RPSS, 1948, p. 69]. 



On the basis of the foregoing, tests with above- 

 water models towed upside down in basins give 

 a 0-dinil drag coefficient CccAir) of the order of 

 0.85 to 1.2 or more; This agrees well with values 

 for short, blunt-ended, 3-diml bodies [S and P, 

 1943, pp. 52, 159-160; RPSS, 1948, pp. 25, 69]. 



When the deck erections and upper works are 

 not yet laid out, or are known only sketchily, it 

 is possible to approximate the projected area of 

 the abovewater silho\iette, as seen from directly 

 ahead, by E. t. Eggert's formula, Aa= (0.5)B1: . 

 This assumes an average maximum effective 

 height, above the water, of half the beam Bx ■ 

 For the ABC ship of Part 4, mth its tentative 

 beam of 73 ft, the projected area by this rule 

 works out as (0.5) (73)' = 2,665 ft'. For a pas- 

 senger-cargo ship it is probably on the small side. 



The method of using the projected or silhouette 

 area as the basis for the wind-resistance estimate, 

 especially with the relative wind directly ahead, 

 is open to some objection because it takes no 

 account of the fore-and-aft positioii of the parts 

 of this silhouette with respect to each other. A 

 large deckhouse right forward, close to the bow 

 and in the lee of the updrafts from the blunt 

 bow, as on large Great Lakes freighters, probably 

 causes less wind resistance than the same deck- 

 house farther aft. Further, on a large tanker, the 

 forward house may be so far from the forecastle, 

 and the after house so far from the forward 

 house, that the shielding offered by each on the 

 one astern is negligible, even with a relative Avind 

 from right ahead. Vessels with large fore-and-aft 

 gaps or separations between major transverse 

 areas therefore call for the use of coefficients in 



the high portions of the ranges listed previously 

 in this section. 



Table 54. a presents a number of dimensional 

 wind-drag coefficients, taken from the material 

 referenced there. In every case, so far as known, 

 the coefficients given apply to mnd forces 

 generated by a relative wind of incident velocity 

 Wb , blowing from directly ahead, where the 

 relative-wind bearing angle e(theta) is deg. 



When the mass density of the air is taken into 

 account, and consistent units of measurement 

 are used, the dimensional formula and the 

 coefficients listed in Table 54. a give a range of 

 values for Cfl(Air) in the 0-diml formula 



Dnr — ClXAir) cf -^AryR 



(54. iv) 



which vary from 0.974 to 1.505. These are to be 

 compared with the C^'s for flat plates of various 

 aspect ratios, placed normal to the stream, which 

 are fisted in Fig. 55.B. When the coefficient 

 k = 0.004 of the dimensional wind-drag Eq. 

 (54.vii),- employing units as listed at the beginning 

 of this section, is converted for use in the 0-diml 

 Eq. (54. iv), the value of C^xAir) works out as 

 about 1.18. 



54.8 Comments Concerning Wind-Friction Re- 

 sistance of an Abovewater Hull. In Sec. 54.4 

 it is assumed that, because of the irregular shape 

 of the abovewater portion of a ship, its wind drag 

 is all pressure drag, varying as W^ . This is 

 probably true for the general case, where the 

 relative A\dnd may blow from any bearmg relative 

 to the ship. 



With the relative wind nearly ahead, a ship 

 hull proper, excluding the upper works, resembles 

 somewhat a train of streamhned cars behind a 

 streamlined locomotive. In both cases the sur- 



TABLE 54.a — Approximate Wind-Drag Coefficients for Various Types of Ships 



Group I. Dimensional Values of k. 



The values of k pertain to tlie formula R^/iad = kA^W^ , where fiwind is in lb, Aji is in ft^, projected normal to the 

 wind, and Wr is in let. Unless otherwise stated Wr is directly ahead. 



Eggert, E. F. k = 0.004 and Aa , if not known, is taken as (Sx)V2 [EMB Rep. 264, Aug 1930, p. 2] 

 Taylor, D. W. k = 0.004 [S and P, 194.3, pp. 51-52] 

 Chapman, C. F. fc = 0.00454 for an anchored motorboat [SSBH, 1951] 



Chapman, C. F. fc = 0.0051 for an anchored sailboat, measuring Aa to top of deckhouse [SSBH, 1951] 

 Barnaby, K. C. k = 0.004 but A^ is determined by adding to the projected area of the superstructure and upper works 



a diminished projected area of the hull proper, equal to that projected area times 0.45 (Cb) [BNA, 



1948, Art. 163, pp. 192-193] 

 Baker, G. S. fc = 0.0033 for an Atlantic liner and 0.004 for a cargo vessel, combined with a reduction factor which 



calls for using only about 0.3 of the actual projected hull area when computing the overall projected 



area Aa [SEE, 1942, pp. 14-16). 

 Group II. Non-Dimensional Values of 0^,(^1 r) 

 See the text. 



