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On the Unsteady Motion of a Slender Body through a Compressible Fluid

Published online by Cambridge University Press:  07 June 2016

L. E. Fraenkel
L. E. Fraenkel*
Affiliation:
Department of Aeronautics, Imperial College*
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Summary

Ward's slender-body theory is extended to examine the unsteady motion of a slender body through a fluid at rest. The cross-sectional area and shape of the body, its forward velocity and its lateral motion are all arbitrary functions of time, but are subject to the restrictions of small disturbances. The length of the body is fixed. An approximate velocity potential is obtained by the joint use of two integral transforms, and the accuracy of this potential is discussed in some detail. General expressions for the aerodynamic forces acting on the body are derived in terms of a co-ordinate system which moves forward with the body in the mean direction of motion, but is fixed laterally. These expressions are then transformed, for the particular case of an oscillating rigid body moving forward with variable velocity, to expressions in terms of co-ordinates referred to the body axes. (The former co-ordinate system makes possible a fairly compact general treatment, whereas the latter is more convenient if the solution of a particular rigid-body problem is required.) Finally, arguments are advanced to justify the application of the slender-body theory to wings of slender plan form whose trailing edges are perpendicular to the direction of motion, and results are given for an oscillating wing moving forward with variable velocity.

Type
Research Article
Information
Aeronautical Quarterly , Volume 6 , Issue 1 , February 1955 , pp. 59 - 80
Copyright
Copyright © Royal Aeronautical Society. 1955

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References

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