PASSAGE THROUGH RESONANCE OF ROLLING FINNED PROJECTILES WITH CENTER-OF-MASS OFFSET

Abstract

Finned projectiles that are meant to be unspun could acquire small roll rates in flight due to slight configurational asymmetries. If the roll rate matches the natural yawing frequency of the projectile, a resonance phenomenon takes place resulting in yaw amplification, and possible loss of stability. To avoid this, finned projectiles are deliberately spun to a roll rate well beyond the resonance value. This gives rise to a passage-through-resonance phenomenon in the flight of finned projectiles. Finned projectiles passing through resonance are known to exhibit the phenomena of roll lock-in, transient resonance, and catastrophic yaw. Projectiles locked in at the resonance condition experience large yaw and are likely to lose the desired flight path. On the other hand, transient resonance is a milder phenomenon where the projectile locks in at resonance briefly before continuing to build-up to the design value. However, the yaw amplification during the brief period of resonance may be sufficient to destabilize the projectile. The problem of passage through resonance of finned projectiles with a center-of-mass offset is considered in this paper. Roll lock-in and transient resonance at normal and reverse resonance is shown. It is observed that the yaw amplification at transient resonance is much lower than that at lock-in. The lack of yaw amplification can be understood based on the bifurcation analysis and numerical simulations reported in this paper.