FIGS. 7–9. Diagrams Illustrating formulæ for moving C. P. without disturbing C. G.
If now the wings be moved so that CP1 is moved forward a distance b, we may indicate the distance from CG1 to the new CPrw by z, and equating the difference between the weight of the rear wing multiplied by its new distance from CG1 and the weight of the front wing multiplied by its new distance from CG1 and making this difference equal to the constant difference, we can calculate z in terms of m and b, as follows:
Fig. 8,
w(a + z)−w(0.66(z + b) + b−a) = 0.33wm + 2wa,
∴ z = m + 5b.
Knowing z, we readily find that the new distance from CPfw to CG1 equals:
0.66(z + b) + b = 0.66m + 5b.
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, b, from the original CP1 without changing the position of CG1. From Fig. 7, we have as before:
w(m + a)−w(0.66m−a) = constant,
0.33wm + 2wa = constant.