46 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



We first reduce to the orig^in Oj about which [> and T^are 

 measured, which is / inches vertically above o.,. 



Denote by primes forces and moments in pounds and pound-inches 

 on the model for 30 miles per hour wind velocity referred to axes 

 through the point o.,- Then : 



L'=V rcos — Mz sin 0, 

 M'=Vr, 

 N'=Vjis'mO + Mzcose, 



X'=- Vf sin ^ + ^ Md cos xp-McS,\nxp-V p\ — — , 



F' = 



Vr— Mc cos i/' — MjD sin tp 



I 



sin 6 



Z'=J^ rcos 6 + ^ Mn cos ip — Mc s'm\l/—J'''p\- 



If the center of gravity of the aeroplane (model) be arranged to 

 have the y coordinate zero, and its x and s coordinates a and b (in 

 inches) referred to o-^, we have for the axes passing through the 

 center of gravity : 



X, = X', 



■ i\=y', 



L^^L'-^rcY', 



M^ = M'-cX' + aZ', 



N, = N'-aY', 



where A\, F^, Z^, L^, M^, N^ are the quantities expressed in pounds 

 and inch-pounds on the model at 30 miles per hour. Converting to 

 full-speed full-scale and to units of pounds and pounds-feet per unit 

 mass, we obtain the required .Y, Y, Z, L, M, N . 



The model was first set at an angle of wing chord to wind of 

 0° corresponding to high speed. Measurements were then made 

 as above for angles of yaw of ±25°, ±15°, ±10°, ±5°, 0°, keeping 

 the incidence constant. In reducing the observations, values for left- 

 and right-hand angles of yaw were averaged to eliminate errors due 

 to lack of symmetry in the model. In the first test the angle of pitch 

 is zero, and the axis of x horizontal. The test was repeated with the 

 model at angles of incidence of 6° and 12°, corresponding to the 

 intermediate and slow speed conditions. Here, again, 9 in the 

 formulae of reduction is zero, since each new axis of x is also 

 horizontal. 



It is apparent that the labor involved in the complete solution for 

 X, Y , Z, etc., is considerable and, im fortunately, the method requires 



