l6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



drift on this elevator tiap may be over 20 pounds, making- a waste of 

 3.5 propeller horse-pov^er, or about 6 brake horse-powder. 



It is preferable to balance a machine at high speed by placing the 

 center of gravity w^ell forward. Then the 'pilot will have to carry 

 his elevator turned up when flying at low speed. But at low speed, 

 he is most in need of the full elevator motion for control of pitching. 

 We, therefore, conclude that case II, with fixed stabiHzer at —7°, 

 is very much too stable or stiff longitudinally, and case I, with 

 stabilizer at 2? 75, is not stable enough. 



Case III, with stabilizer at —5°, appears to balance longitudinally 

 at +2° incidence, and at + 12° incidence to have (full size) a natural 

 diving moment which could be held by a negative lift on the elevator 

 of only about 44 pounds, corresponding to about 4° elevator angle. 

 Consequently, it was decided to adopt the arrangement of case III 

 for the subsequent stability investigation. 



§6. VECTOR REPRESENTATION 



A clearer conception of longitudinal balance is obtained by repre- 

 senting the resultant forces acting on the model as vectors. Thus, for 

 case II, we observed on the balance the lift L and drift D. The 

 resultant force acting was then of magnitude R=VL^ + D^. This 

 resultant force lay in a direction making an angle 6 given by 

 = ta.n~'^ L/D. The line of action of this resultant was at a per- 

 pendicular distance from the spindle axis given by d = Ms/R, where 

 Ms is the observed pitching moment about the spindle. The re- 

 sultant force, R, is thus defined in magnitude, direction, and line of 

 application, and may be represented graphically as a vector. In 

 figure I, the resultant force vectors for case III are drawn on the 

 side elevation of the model. The model is considered to be fixed and 

 the wind direction to change so that the angle of incidence varies 

 from —1° to -f-8°. The vectors are, therefore, djiawn relative to 

 the aeroplane. 



The vector for 2° passes near the center of gravity. If it were 

 desired to balance the machine at some other attitude, 6° for example, 

 the center of gravity should be located at some point on the vector 

 for 6°. 



Note that on figure i, for angles greater than 2°, the vectors pass 

 to the rear of the center of gravity indicating diving nwments and 

 vice versa. Thus the machine is in stable equilibrium at 2°, and if 

 deviated from this angle, righting moments are at otice created which 

 tend to restore the normal attitude. 



