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Coning in Forward Flight
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An expression for the steady portion of blade flapping, or coning, <?0, may be derived in forward flight using the same procedure as was used in hover—that is, setting all of the blade bending moments to zero at the hinge. Figure 3.33 shows a rotor blade with aerodynamic, weight, inertial, and centrifugal forces acting on a blade element. At the flapping hinge—which for this analysis will be assumed to be at the center of rotation—the net moment must be zero since a hinge cannot support a moment. The equations for the four moments are:
, R2
mg rar — —mg —
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Since only the steady portion of the flapping is being derived, only those terms that do not contain sin j/, cos j/, sin 2 j/, or cos 2 j/ need be retained. When MA is expanded and the trignometric identity
The constant portion of the weight equation is simply:
mgR2
Note that this is identical to the equation for coning derived for the hovering rotor with ideal twist. Although this equation has been derived for a rotor with flapping hinges, it is a good assumption even for two-bladed teetering rotors and for rigid rotors, since the aerodynamic and centrifugal forces overpower whatever structural stiffness the blades may have.
