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Note on the Evaluation of the Integral

Published online by Cambridge University Press:  28 July 2016

N. A. Routledge ,
W. T. Lord  and
E. Eminton
N. A. Routledge
Affiliation:
Royal Aircraft Establishment
W. T. Lord
Affiliation:
Royal Aircraft Establishment
E. Eminton
Affiliation:
Royal Aircraft Establishment
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Extract

The Integral I occurs frequently in aerodynamics. To cite a particular case, Ward has shown that if S(x) is the cross-sectional area distribution of a slender body its wave drag D is given to a first approxition by D = qI/(2π), where q is the kinetic pressure. In this case, S(x) is often defined numerically, and the direct evaluation of I is then complicated by the presence of the logarithmic singularity. Several methods may be employed to avoid this complication. Legendre has recently suggested rewriting I in a non-singular form, which unfortunately is not well suited to numerical work. Here, a method for the evaluation of the unmodified integral is presented.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 58 , Issue 527 , November 1954 , pp. 787 - 788
Copyright
Copyright © Royal Aeronautical Society 1954

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References

1. Ward,, G. N. (1949). Supersonic Flow Past Slender Pointed Bodies. Quarterly Journal of Mechanics and Applied Mathematics, Vol. II, Pt. I, pp. 75–97, March 1949.CrossRefGoogle Scholar
2. Legendre,, R. (1953). Limite Sonique de la Resistance d'ondes d'un Aeronef. Comptes Rendus. Tome 236. No. 26, pp. 2,479-2,480, June 1953.Google Scholar
3. Eminton,, E. and Lord,, W. T. Some Special Slender Bodies of Minimum Drag. (Unpublished Royal Aircraft Establishment Technical Note.)Google Scholar
4. Routledge,, N. A. Evaluating the Supersonic Drag Integral using .Fourier Series. (Unpublished Royal Aircraft Establishment Technical Note.)Google Scholar
5. Lord,, W. T. and Eminton,, E. (1954). Slender Bodies of Minimum Wave Drag. (Unpublished Royal Aircraft Establishment Technical Note; abstract in Journal of the Aeronautical Sciences, Vol. 21, No. 8, August 1954).Google Scholar
6. Whittaker,, E. and Robinson,, G. (1944). The Calculus of Observations. Blackie, 4th Edition, 1944, p. 264.Google Scholar