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On the equations of motion for an aircraft with an internal moving load which is then dropped

Published online by Cambridge University Press:  04 July 2016

L. Bernstein
L. Bernstein*
Affiliation:
Department of Engineering , Queen Mary & Westfield College , University of London , London, UK
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Abstract

Equations of motion have been developed for the situation in which a substantial load, carried internally by an aircraft, is drawn along a ramp by an extraction parachute and is then dropped. The motion of the load is assumed to remain in the plane of symmetry. The perturbations to the aircraft motion are assumed to be small so that the equations can be linearised following the representation of the aerodynamic out-of-balance forces using conventional aerodynamic derivatives. The resulting system of six ordinary differential equations consists of the four normally associated with the longitudinally-perturbed motion of the aircraft (slightly modified by the reaction forces due to the load), together with two describing the motion of the load.

Numerical solutions are presented for a generic aircraft, the investigation examining the effects of a number of different parameters such as the ratio of the mass of the load to that of the aircraft, the length and angle of the ramp, the friction between the load and the ramp and the direction of the parachute extraction force. In addition the effects of employing various control strategies to limit the disturbed motion have also been computed.

It was found that the acceleration of the load, relative to the aircraft, was sensibly constant. In the absence of any resetting of the controls (elevators and throttle), the disturbances computed exceeded those for which the linearisation is justified. When the controls were reset, either as the load began to move or as it was jettisoned, to the trim values appropriate to the unloaded aircraft flying at the same speed, the disturbances were reduced, but remained large, the phugoid mode being dominant. The incorporation of various kinds of feedback from the disturbance variables to the elevator was also investigated and a successful control strategy was identified, that limited the perturbations and minimised the steady-state errors in airspeed and angle of climb.

Type
Research Article
Information
The Aeronautical Journal , Volume 102 , Issue 1011 , January 1998 , pp. 9 - 24
Copyright
Copyright © Royal Aeronautical Society 1998 

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References

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