Strumpf 



The appendage moment must be zero when a = tk-n, and the product 

 Uw = u^ sin a has this property of symmetry, so it is suitable for estimating the 

 contribution of the appendage to the pitch moment in hovering flight. 



The only experimental results which are available to check the validity of 

 this representation are those obtained at the Davidson Laboratory under spon- 

 sorship of the Lockheed Missile and Space Company (3). The hull was elliptical 

 in cross-section, and the hydrodynamic yaw moment coefficient N' was obtained 

 experimentally as a function of sideslip angle /3 in the range -15° ^ /3 < 90° for 

 the fully appendaged condition. Analogously to Eqs. (5a, b) the yaw moment N 

 due to sideslip velocity v is represented as 



A-t 



N.. uv + N,, Uv 



(6) 



Setting 



in Eq. (6) gives 



u = U cos /3 and v = -U sin /3 



(7) 



N = - I UV^ 



- N; sin 2/3 + N' sin /3 



"i h a 



(8) 



and division by (p/2)A'Cu^ gives the dimensionless equation 



N' = - -^N^ sin 2/3 + N' sin /3 



2 h a 



(9) 



The yaw moment coefficients tabulated in Ref. 3 are based upon ^:^ . These are 

 converted here to the M basis by multiplying the Ref, 3 coefficients by i^'k 

 where A = ttH^ 4 and h is the maximum height of the main hull. The n' data for 

 the full appendage case (3) are curve-fitted to Eq. (9) by a least square analysis 

 and the coefficients are found to be Nv,^ = -0.72 and N(,^ = +0.36. Figure 1 shows 

 the comparison of the curve-fitted theoretical representation 



N' 



0.36 sin 2/3 - 0.36 sin 



(10) 



with the experimental data. The standard deviation of the test data from the 

 theoretical curve is 0.01, which is statistically equal to the standard deviation 

 of the test data among themselves. These results indicate that the theoretical 

 representation of the pitch moment in the equations of motion is accurate over 

 the whole range of angle of attack. 



The hydrodynamic vertical force arising from w is not separated because 

 symmetry conditions dictate that both the hull and appendage forces vanish when 

 a = ±k7T. The representation 



Z = -B„ wU = 4 AU^ Z', sin a 



(11) 



282 



