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The prediction of the drag of aerofoils and wings at high subsonic speeds*

Published online by Cambridge University Press:  04 July 2016

R. C. Lock
R. C. Lock*
Affiliation:
RAE, Farnborough, Hants
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Summary

After a brief discussion of alternative ways in which the drag of an aircraft wing can be derived theoretically, attention is focused on a technique whereby the separate ‘far-field’ components of drag — viscous, trailing-vortex (induced) and wave — are calculated separately. In particular, a new approximate method is described for estimating the wave drag. Based on an exact two-dimensional analysis involving the flow conditions just upstream of the shock wave, a simple formula is derived which, to first order, involves only a knowledge of the Mach number distribution on the surface of the aerofoil ahead of the shock and of the surface geometry at its foot. The accuracy of this formula is assessed for aerofoils by comparison with more exact theoretical results and with experiment. A ‘strip theory’ extension to swept wings is proposed and illustrated by applying it to a particular transport-type wing body combination. Using experimental pressure measurements as input, all three components of drag are estimated theoretically, and by adding their sum to separate balance measurements of the body drag comparisons between ‘theory’ and experiment for the overall drag can be made. These show a satisfactory standard of accuracy, the error varying between —5% and — 1% of the total drag over a wide range of Mach number and lift coefficient.

Type
Research Article
Information
The Aeronautical Journal , Volume 90 , Issue 896 , July 1986 , pp. 207 - 226
Copyright
Copyright © Royal Aeronautical Society 1986 

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Footnotes

†

Now Visiting Professor of Aerodynamics, The City University, London.

*

Paper based on lecture given at the Royal Aeronautical Society's Symposium on ‘The prediction and reduction of aircraft drag’, 2nd March 1983. Revised November 1984.

References

1.Computation of viscous-inviscid interactions. AGARD-CP-291 (particularly Papers 1, 2 and 10), 1981.Google Scholar
2. Lock, R. C. and Firmin, M. C. P. Survey of techniques for estimating viscous effects in external aerodynamics. Numerical methods in aeronautical fluid dynamics, ed Roe, P. L., Academic Press, 1982.Google Scholar
3. Oswatitsch, K. Gas dynamics. (English version by Kuerti, G.), Academic Press, New York, 1956, 209.Google Scholar
4. van der vooren, J. and Slooff, J. W. On inviscid isentropic flow models used for finite difference calculations of two-dimensional transonic flows with embedded shocks about aerofoils, 1973, NLR MP73024 (U).Google Scholar
5. Bocci, A. and Billing, C. Unpublished work at ARAGoogle Scholar
6. Garabedian, P. R. and Korn, D. G. Analysis of transonic aerofoils, 1971, 24, 841.Google Scholar
7. Lock, R. C. Unpublished work at RAE.Google Scholar
8. Lock, R. C. A modification to the method of Garabedian and Korn. Numerical methods for the computation of transonic flows with shock waves, (GAMM Workshop). Friedr Vieweg und Sohn, Braunschweig, 1980.Google Scholar
9. Lock, R. C. An assessment of methods for calculating the wave drag of aerofoils using an Euler program. RAE Technical Memorandum Aero 1958, 1984.Google Scholar
10. Jameson, A., Schmidt, W. and Turkel, E. Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes. AIAA Paper 81–1259, 1981.Google Scholar
11. Collyer, M. R. and Lock, R. C. Prediction of viscous effects in steady transonic flow past an aerofoil. Aero Qu., 1979, 30, 485.Google Scholar
12. Green, J. E., Weeks, D. J. and Brooman, J. W. F. Prediction of turbulent of boundary layers and wakes in compressible flow by a lag-entrainment method. ARC R&M 3791, 1973.Google Scholar
13. Ashill, P. R., Weeks, D. J. and Wood, R. F. Unpublished RAE work. 1984.Google Scholar
14. Cook, P. H., Mcdonald, M. A. and Firmin, M. C. P. Aerofoil RAE 2822: pressure distributions and boundary layer and wake measurements. AGARD AR 138, Paper A6, 1979.Google Scholar
15. Ashill, P. R. and Weeks, D. J. Unpublished RAE work.Google Scholar
16. Ashill, P. R. and Weeks, D. J. A method for determining wall-interference corrections in solid-wall tunnels from measurements of static pressure at the walls. AGARD CP-335, Paper 1, 1982.Google Scholar
17. Arthur, M. T. A method for calculating subsonic and transonic flow over the wings of a wing-fuselage combination with allowance for viscous effects. AIAA Paper 84-0428, 1984.Google Scholar
18. Ashill, P. R. and Smith, P. D. An integral method for calculating the effects on turbulent boundary layer development of sweep and taper. RAE Technical Report 83053, 1983.Google Scholar
19. Squire, H. B. and Young, A. D. The calculation of the profile drag of aerofoils. ARC R&M 1838, 1937.Google Scholar
20. Cook, T. A. Measurements of the boundary layer and wake of two aerofoil sections at high Reynolds numbers and high subsonic Mach numbers. ARC R&M 3722, 1973.Google Scholar
21. Cooke, J. C. The drag of infinite swept wings. ARC Current Paper 1040, 1969.Google Scholar
22. Hodges, M. D., Ashill, P. R., Cozens, P. D. and Lock, R. C. Application to a particular model of an approximate theory for determining the spanwise distribution of and total wave drag on a swept wing. MOD(PE) S&T Memorandum 1–84, 1984.Google Scholar
23. Firmin, M. C. P. and Cook, P. H. Disturbances from ventilated tunnel walls in aerofoil testing. AGARD CP 348, Paper 8, 1983.Google Scholar
24. Maskell, E. C. Progress towards a method for the measurement of the components of the drag of a wing of finite span. RAF. Technical Report 77732, 1972.Google Scholar