52 



SMITHSONIAN foNTHIBUTIONS TO KNOWLEDGE 



VOL. 



27 



that it is too heavy in front and, therefore, wish to move the center of pressure forward an amount, 

 say 6, without affecting the crater of gravity, we can calculate the proper relative positions of the 

 front and rear wings in the following manner. While the aerodrome as a whole is halanced at the 

 poinl CO,, the weight of the wings is not balanced around this point, for the rear wing, owing to 

 its decreased lifting effect, is proportionately farther from CP, than the front wing. In order, there- 

 fore, to avoid moving the center of gravity of the machine as a whole, any movement of the wings 

 must be made in such a way as to cause the difference between the weight of the rear wing multi- 

 plied by its distance from CO, and the weight of the front wing multiplied by its distance from CO, 

 to equal a constant: that is, 



w(m + a) — w (0.66m — a) = constant, 

 and 



O.SZwm + 2wa = constant. 



If now the wings he moved so that CP, is moved forward a distance 6. we may indicate the distance 

 from CO, to the new CP rw by z, and equating the difference between the weight of the rear wing 



Fig. 7. 



-£l-.6u(z*b)— ^ 



k«r- 



§2-*^-.fcb(Vb3 



VCG, 



Fig. 8. 



Fig. 9. 



Figs. 7-9. Diagrams illustrating formula? for moving C. P. without disturbing C. G. 



multiplied by its new distance from CO, and the weight of the front wing multiplied by its new 

 distance from CO,, and making this difference equal to the constant difference, we can calculate z 

 in terms of m and 6, as follows: 

 Fig. 8, 



■w(a + z) — «)(0.66(z + 6) + 6 — a) = 0.33icjb + 2wa. 



.'. z = m + 5b. 



Knowing z, we readily find that the new distance from CPf W to CG, equals: 



O.GG(z + 6) + 6 = 0.66m + 56. 



In a similar manner we may calculate the proper relative positions of the front and rear wings 

 when we wish to move the center of pressure backward a distance, 6, from the original CP, without 

 changing the position of CO,. From Fig. 7, we have as before: 



w(m + a) — w( 0.66m — a) = constant, 

 O.ZZwm + 2wa — constant. 

 Fig. 9, 



w(z, + a) — ■io(0.66(» l — 6) —6— a) =0.33M?m + 2wa. 



.'. z, = m — 56. 

 Similarly we have for the new distance from CPf W to CO,: 



0.66 (z, — 6) — 6 = O.GG?n — 56. 



