288 SOME APPLICATIONS OF THE PRINCIPLES OF 
STABILITY. 
As with the ship, the stability of an aeroplane may be considered as 
longitudinal and transverse, both depending on the relation between the 
resultants of the supporting forces, and the position of the center of gravity. 
And like the ship, the aeroplane has metacenters for both directions. 
Let us consider first the longitudinal stability of a rectangular plane 
moving in the air at small angle of incidence. 
If x be distance of the center of pressure from the forward edge we have, 
as with the rudder, 
x =1(0.195-+0.305 sin 7) 
where / is the depth of the plane in the direction of motion and 7 the angle of 
incidence. If a weight be added to the plane so that the center of gravity 
of the whole is at a distance, say 3/, from the leading edge, the plane will 
assume a position of equilibrium at an angle of incidence of approximately 
10 degress, the center of pressure and center of gravity being in coincidence. 
If for any reason the angle of incidence is increased, the center of 
pressure will move farther away from the leading edge and a righting move- 
ment will result, tending to decrease the angle of incidence to 10 degrees, 
similarly, if the angle is decreased below 10 degress an opposite righting 
moment will follow, tending to bring the plane back to its position of 
equilibrium. ‘This condition is readily seen to be similar to that of a ship, 
which, if stable, tends, when inclined from its position of equilibrium, to 
return to that position, the righting moment being, GM sin 7 where GM, 
is the distance between the center of gravity and the metacenter. 
The metacenter of the plane under consideration can be found in the 
following manner: 
The normal pressure P, on the moving plane is given by 
ANY SG 
~ 0.195+0.305 sin 7 
where K is a constant depending on the density of the air, A the area of the 
plane and V its velocity. 
The moment of P about the leading edge is 
Px=KAV’ 1 sin 7. (3) 
; eA: i 
The moment of the total weight W about the same axis is ne cos 7 and 
