Elsevier

Progress in Aerospace Sciences

Volume 63, November 2013, Pages 67-83
Progress in Aerospace Sciences

Catastrophic yaw. Why, what, how?

https://doi.org/10.1016/j.paerosci.2013.06.002Get rights and content

Abstract

Flight dynamics problems in tail stabilized missiles and bombs appear when failing to achieve their design steady-state motion because the rolling velocity occasionally locks to the pitch frequency giving rise to wobbling motions that can reach the quality of catastrophic. The flight condition attained when the coincidence between the roll and the pitch frequency persists is called roll lock-in and the large amplitude oscillation regime, catastrophic yaw. This event can occur at subsonic and supersonic velocities and invariably leads to catastrophic failure of the flight. The purpose of this paper is to give a visual explanation of the mechanism conducive to roll lock-in and catastrophic yaw and relieving means by answering the three questions: Why does the wobbling motion appear?, What is it that makes the wobbling grow to very large amplitudes? and How can catastrophic yaw be prevented?

Introduction

Finned missiles and bombs sometimes display an anomalous comportment when failing to achieve their intended steady-state spin that remains locked to the pitch frequency by the action of nonlinear induced roll moments. This sustained resonant flight condition exhibits pitch–yaw angular oscillations of moderate amplitude by amplification of the non-rolling trim angle of attack. The roll lock-in oscillation occasionally progresses to the very large amplitude motion characteristic of catastrophic yaw by the action of the roll orientation-dependent side moment.

Linear aeroballistics theory, assuming linear aerodynamics and constant rolling velocity, predicts the occurrence of roll resonance and the resulting amplification of the trim angle due to slight asymmetries when the roll rate is close to the pitch frequency. However missile lock-in requires the performance of an additional character, the nonlinear induced roll moment that cancels the roll moment due to deliberate fin cant plus the roll moment due to damping. The induced roll moment, at the enlarged angle of attack due to trim amplification, is caused by the cyclic fin loading on finned missiles and by the coupling of a center of mass offset with the lateral forces. Under certain conditions, the missile in persistent resonance becomes severely unstable by the action of the nonlinear induced side moment.

The roll–yaw resonance phenomenon acted on by slight asymmetries, due to manufacturing tolerance or unexpected damage at launch, was first presented by Nicolaides, who also introduced the induced roll moment due to cyclic loading to explain roll lock-in and assigned to the induced side moment the occasionally large multiplying factors for the trim angle [1], [2], [3], [4]. This type of behavior was named catastrophic yaw and described as a propeller-like flight by Nicolaides Video 1. Over the years, from the middle 50s, a number of authors have developed analytic models of increasing complexity to demonstrate the existence of free flight steady-state resonance at large amplitudes. Glover [5] showed the effect of mass asymmetries on the origin of an induced roll moment. Price [6], in a detailed explanation of roll lock-in mechanism, presented the larger effect of the induced roll moment caused by a center of mass offset compared to that due to cyclic loading. Pepitone [7] showed the effects of the roll orientation-dependent pitch and yaw moments on the angular motion of the missile. A particularly relevant contribution by Murphy [8] developed an analytical model of persistent resonance combining linear transverse aerodynamics and a nonlinear roll moment due to center of gravity offset. Morote [9] presented the amplitude response of the pitch–yaw motion caused by the roll orientation-dependent side moment and the numerical determination of the large amplitude equilibrium points. Murphy and Mermagen [10] showed that the nonlinearity introduced in the system by the side moment, makes possible the occurrence of lock-in even in the absence of the trim angle originated by small aerodynamic asymmetries. Morote et al. [11], [12] departing from a conservative cubic model of motion, presented the minimum roll deflection for a given boundary value of the center of mass offset to avoid catastrophic yaw.

The following is the Supplementary material related to this article Video 1.

.

This paper is intended to give a graphic insight into the missile dynamics to improve the understanding of the mechanism leading to catastrophic yaw and possible remedies by answering the three questions: Why does the wobbling motion appear?, What is it that makes the wobbling grow to very large amplitudes? and How can catastrophic yaw be prevented?

Section snippets

Trim angle of attack and fin cant

A non-rolling cruciform tailed missile (Fig. 1a) that, for example, has a manufacturing fault consisting of a slight tail-down symmetric deflection of the two horizontal panels (Fig. 1b) cannot fly aligned with the impinging flow because the downward tail force (Fig. 1c) due to the small symmetric deflection, gives rise to a pitch moment at the center of gravity (Fig. 1d) that rotates the missile around the y axis to a trim angle (Fig. 1e) at which the normal forces generated at nose and tail

Non-linear induced side moment

It has been shown that the action of induced rolling moments combined with an unfortunate selection of δT can give rise to wobbling motions at lock-in but only of moderate amplitude unless unrealistically large asymmetry figures (r^, CM0) or negligible damping (h^) are considered. Very large multiplying factors for the trim angle, under usual conditions, require the performance of an additional feature of the system; the non-linear induced side moment. This moment derives from a characteristic

Minimum fin cant

As might have been suggested by the previous section, one may think that being the large trim amplitudes anchored in the proximities of ω^e=1, say between 0 and 3, an expeditious means for avoiding intersections other than the point of very low amplitude, is the use of a large value of ω^e to move the roll surface far away to the right. This move may work as long as the value of ω^e reached is not large enough to make the low amplitude point at the foot of the roll surface unstable due to

Conclusion

This paper offers a detailed explanation of the mechanism conducive to roll lock-in and catastrophic yaw. The paper also presents the minimum design roll deflection for avoiding equilibrium points other than the equilibrium point of very low amplitude for a given boundary value of the center of mass offset. The recommended minimum fin cant expressions are based on conservative, cubic or linear, force and moment expansions at the “+” position that equal or surpass the normal force and the

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