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Breakdown of the Modified Point Mass Model for High Elevation Trajectories

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Technical memo.

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Murphy has shown that for a sufficiently high angle of fire the quasi-steady state assumption breaks down near apogee, where conditions change most rapidly. When this occurs precession or the slow mode of the epicyclic motion is excited and transient motion persists on the downleg. As a result trajectory predictions with the modified point mass model show significant range errors for some high angle trajectories. Murphy suggested in reference 2 that a further modification could be incorporated in the modified point mass model to correct this problem. The idea has not been followed up, principally because the gun elevations which produce such behaviour are not used a great deal in practice. However, the break down of the quasi-steady assumption does have implications for the calibration of the modified point mass trajectory model for shell fire control purposes. The modern Mach number fitting technique for calibration of shell fire control models ref. 3, using data from Range and Accuracy trials, relies on the overall accuracy of the trajectory model. This brief report summarises the results in reference 2 and looks at the magnitude of the transient motion induced by the rapidly changing conditions near apogee and the relation between that motion and gun elevation. Results are given for a variety of shells of interest to the Australian Army. Finally some conclusions are drawn about the relevance of the effect to practical trajectory calculation, with particular emphasis on model calibration and Range and Accuracy trials.

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  • Armor
  • Fire Control and Bombing Systems

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