286 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 54.15 



developed by the Bureau of Ships of the U, S. 

 Navy Department. It is 



K = C;c(0.5p).4^/u(cos= ^)Wl (54.ix) 



where Ck is the 0-diml heeling moment coefficient 

 due to wind 



^A is the abovewater area for 5 = 90 deg, 

 projected on the plane of symmetry, with the 

 vessel upright 



hx is the height above the waterplane of the 

 center of the area A a mth the vessel upright 



0(phi) is the angle of heel 



Wjt is the relative-^vind velocity, assumed as 

 directed abeam. 



Model tests give a value of the product 

 Ck(0.5p) of about 0.00147, from which Ck = 

 0.00147/(0.001189) = 1.236. Entering the known 

 or assumed values for a given situation, and 

 assuming successive values of heel angle <^, 

 increasing by 10 deg up to as great a range as 

 desired, a curve of heeling moment on a basis of 

 heel angle is plotted for a given wind velocity. 

 Comparing this with the curve of righting 

 moments in stUl water, the intersection gives the 

 angle to which a ship will heel under the wind 

 effect. Assuming a given maximum or allowable 

 angle of heel, the righting moment for that angle 

 may be set down as X in Eq. (54. ix) and the 

 corresponding wind velocity be found. 



This procedure is in the nature of a rough 

 approximation because, like the example of the 

 preceding section, it assumes a constant wind 

 velocity over the whole lateral abovewater area. 

 Further, it takes no account of second-order 

 effects such as the downwind motion of the ship 

 due to the lateral force exerted by the wind, or 

 the fact that the ship is heeling away from the 

 wind. For a sudden squall, it takes no account of 

 the kinetic rolling energy in the ship when it 

 reaches the nominal angle of equilibrium, which 

 means that the ship would heel beyond the equi- 

 hbrium angle. However, L. Gagnatto, as the 

 result of a more rigorous analysis [ATM A, 1929, 

 Vol. 33, pp. 53-74], finds that the rigorous method 

 gives a maximum angle of heel sensibly less than 

 that derived from the approximate method. A 

 further analysis was carried out by Guntzberger 

 and reported a few years later [ATM A, 1934, 

 Vol. 38, pp. 341-355]. 



E. A. Wright has published a photograph, with 

 accompanying notes, of a destroyer model under- 

 going a wind-resistance test (in a wind tunnel) 

 when heeled [SNAME, 1946, Fig. 25, p. 393]. 



As an indication of the values to be expected 

 under violent beam winds, a model of the World 

 War I Eagle class patrol boats was floated in a 

 shallow pan of water in a wind tunnel, where it 

 was blown upon at various relative-Avind bearings 

 6 from 30 deg (on the bow) to 150 deg (on the 

 quarter). The scale ratio was 48, the weight 

 corresponded to the designed ship W of 480 t, and 

 the full-scale GM simulated in the tests was 

 1.012 ft. This corresponded to (1.012/26.23)5 or 

 0.039S. The dimensions and lines of the vessel 

 are found on SNAME RD sheet 118. 



At a full-scale wind velocity corresponding to 

 100 mph, 86.84 kt, by no means uncommon in 

 hurricanes and typhoons, the maximum angle of 

 heel was over 37 deg. Surprisingly, this occurred 

 with the bow 130 deg away from the wind. The 

 next greatest heel, 35 deg, was encountered with 

 the bow 70 deg from the wind. With the wind 

 abeam, or at bearings of 50 and 110 deg, the heel 

 was less than 33 deg. The smallest heels, 20-22 

 deg, occurred when the bow was either 30 or 

 150 deg from the relative-wind direction [EMB 

 Rep. 15, Jul 1920]. 



An interesting passage from this report is 

 quoted as follows: 



"3. The center of lateral resistance was previously deter- 

 mined by towing a larger but similar model of (an) Eagle 

 boat sidewise and was found to be substantially at the 

 water surface." 



54.15 Estimated Drift and Leeway. It is 

 difficult to estimate, in advance, just how fast a 

 ship, mthout power and under given weather 

 conditions, may be expected to drift under the 

 action of wind alone. This is principally because 

 ships vary in their attitudes to the wind when 

 drifting, so the relative position of the ship axis 

 and the wind direction must generally be assumed. 



Granted that the ship drifts broadside to the 

 wind, and that it is of normal form, a reasonable 

 value of the 0-diml water-drag coefficient of its 

 underwater body is 1.15. This is derived by 

 assuming an actual L/H ratio of 20, but an 

 effective ratio of 10, since at low speeds the ship 

 behaves essentially as would its underwater hull, 

 plus a superposed mirror image, drifting down- 

 wind in infinitely deep water. At these low speeds 

 the effect of waves resulting from the broadside 

 motion can be neglected. The drag coefficient 

 Cd of a flat plate of these proportions is, from 

 Fig. 55.B, about 1.5, but the ship has few sharp 

 edges like the thin plate, especially under the 



