Banked Turn

This is a steady motion in a horizontal circle with the plane ofsymmetry inclined to the vertical, as shown in Figure 10.10. The direction of motion is longitudinal and there is no side-force.

If ф is the angle of bank and r is the radius of the turn, then:

L cos ф = W

W V2

L sin ф =———-

g r V2

tan ф = —.

gr

If the differences due to the difference in speed at the outer and inner wing tips are ignored, then:

L = W sec ф w sec ф

CL =

and therefore, as in Figure 10.8, the stalling speed V’S is determined by the intersection of the curves CL V2 versus V with CLmax versus V graph. From the relation:

it appears that banking increases the stalling speed, and if we treat CLmax as a constant, the increase is in the ratio: