Unfortunately, however, the righting effect is not proportional to the difference between the right and left H.E.'s.
R, Direction of reaction of wing indicated.
R R, Resultant direction of reaction of both wings.
M, Horizontal (sideway) component of reaction.
L, Vertical component of reaction (lift).
In the case of A, the resultant direction of the reaction of both wings is opposed to the direction of gravity or weight. The two forces R R and gravity are then evenly balanced, and the surface is in a state of equilibrium.
In the case of B, you will note that the R R is not directly opposed to gravity. This results in the appearance of M, and so the resultant direction of motion of the aeroplane is no longer directly forward, but is along a line the resultant of the Thrust and M. In other words, it is, while flying forward, at the same time moving sideways in the direction M.
In moving sideways, the keel-surface receives, of course, a pressure from the air equal and opposite to M. Since such surface is greatest in effect towards the tail, then the latter must be pushed sideways. That causes the aeroplane to turn; and, the highest wing being on the outside of the turn, it has a greater velocity than the lower wing. That produces greater lift, and tends to tilt the aeroplane over still more. Such tilting tendency is, however, opposed by the difference in the H.E.'s of the two wings.
It then follows that, for the lateral dihedral angle to be effective, such angle must be large enough to produce, when the aeroplane tilts, a difference in the H.E.'s of the two wings, which difference must be sufficient to not only oppose the tilting tendency due to the aeroplane turning, but sufficient to also force the aeroplane back to its original position of equilibrium.
It is now, I hope, clear to the reader that the lateral dihedral is not quite so effective as would appear at first sight. Some designers, indeed, prefer not to use it, since its effect is not very great, and since it must be paid for in loss of H.E. and consequently loss of lift, thus decreasing the lift-drift ratio, i.e., the efficiency. Also, it is sometimes advanced that the lateral dihedral increases the "spill" of air from the wing-tips and that this adversely affects the lift-drift ratio.