The effects of products of inertia on the roll behavior of ballisticre-entry vehicles

TLDR: In this article, a linear quasi-steady theory is developed which demonstrates that inertia asymmetries are: (1) more effective than equivalent mass and aerodynamic imbalance in generating t r im angles over the super-resonant region of reentry flight; (2) equally a s effective at resonance; and (3) less effective over the sub resonant regions.

Abstract: Ballistic reentry vehicles having lateral center-of-gravity offsets (mass asymmetries) exhibit anomalous roll behavior a s a result of tr im angle-generated lateral aerodynamic forces. The t r im angles caused by mass and aerodynamic asymmetries have been thoroughly investigated. However, inertia asymmetries, which result when the principal axes of the vehicle become inclined with respect to the body reference axes, a r e a source of t r im angle which has not been considered. A linear quasi-steady theory is developed which demonstrates that inertia asymmetries are: (1) more effective than equivalent mass and aerodynamic asymmetries in generating t r im angles over the super-resonant region of reentry flight; (2) equally a s effective at resonance; and (3) less effective over the subresonant region. The predictions of this theory a re verified by numerical integrations of the complete equations of motion and by three angular degree-of-freedom wind tunnel experimental results. L, Nomenclature C. g. Center of gravity Axial force coefficient, axial forcelq'S C A Normal force coefficient, normal force/q's CN C Normal force slope coefficient, N a acN/aa. l / r a d Yawing moment coefficient, yawing moment / q'Sd Yawing moment coefficient at p = 0 ' n