Rotor H-force. Prouty defines rotor H -force as the "horizontal force perpendicular to the rotor shaft." We will use a slightly different (and I think more consistent) definition. We will define H -force as the "component of rotor aerodynamic force generated in the tip-path plane and generally opposite to the direction of motion." The situation can be considered as follows: the rotor generates an aerodynamic force that is a combination of all lifts and drags on the rotor blade. This is a vector quantity, and thus has three components. Define a coordinate system aligned with the tip-path plane. Two coordinate directions are in the plane (one generally in the direction of the tail boom and the other out the right side of the helicopter), and the other is perpendicular to the tip-path plane pointing upwards. The component of the rotor aerodynamic force that points along the upward coordinate is what we call thrust ( T). The component of the rotor aerodynamic force that points toward the tail boom is what we will call horizontal or H-force. The H -force is also known as rotor drag.

Though choice of reference coordinate system is arbitrary, if one chooses to mix systems (as Prouty does), it is very important to make sure one doesn't "double dip" when accounting for all forces acting. This is why we will use the tip-path plane as a reference. However, this decision means we will have to rederive the expression for the H -force. (Note that figure 3.36 on page 177 is not only confusing, but wrong according to Prouty's text!)

Using a figure similar to figure 3.35 on page 174, derive an expression for dH (or DH) in terms of dL and dD_pr. Be sure to point out the differences between your expression (in tip-path plane coordinates) and Prouty's (in shaft-plane coordinates). See if you can do the integration to come up with an expression for C_H/s. Please do not spend too much time on this! It may be easier to do the azimuthal integration first so you can eliminate the y-terms that integrate to zero.