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The Numerical Evaluation of Curvilinear Integrals and Areas

Part of: 75 year anniversary of Aeronautical Engineering at Glasgow University

Published online by Cambridge University Press:  04 July 2016

T. R. F. Nonweiler
T. R. F. Nonweiler*
Affiliation:
James Watt Engineering Laboratories, Glasgow University
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Extract

We envisage here that it is desired to evaluate (using a digital computer) the integral of a function f (x, y) with respect to x (say), along a curve γ in the xy-plane; the value of the function and of the co-ordinates of the curve being known only at discrete, and possibly irregularly spaced, points of γ. Such a problem frequently arises, especially where γ is a closed curve: as for instance in aerodynamics when it is desired to estimate the force components and pitching moment inferred from an experimentally determined set of pressures taken over an aerofoil; here the function values are related to the pressure measurements and γ is the aerofoil contour.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 72 , Issue 694 , October 1968 , pp. 887 - 888
Copyright
Copyright © Royal Aeronautical Society 1968 

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References

1. Brun, Viggo. A generalisation of the formula of Simpson, for non equidistant ordinates. Nordisk Mat. Tidskr. Vol 1, p 10–15, MR 14, 1019, 1953.Google Scholar
2. Nonweiler, T. The Numerical Evaluation of Curvilinear Integrals denned by Discrete Data. Glasgow University,. Department of Aeronautical Engineering, Report No 6802,. 1968.Google Scholar