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The Limitations of “Ra” to Describe Surface Roughness

[+] Author Affiliations
Martin N. Goodhand, Robert J. Miller

University of Cambridge, Cambridge, UK

Karl Walton, Liam Blunt

University of Huddersfield, Huddersfield, UK

Hang W. Lung, Reg Marsden

Rolls-Royce Plc, Derby, UK

Paper No. GT2015-43329, pp. V05CT16A003; 8 pages
  • ASME Turbo Expo 2015: Turbine Technical Conference and Exposition
  • Volume 5C: Heat Transfer
  • Montreal, Quebec, Canada, June 15–19, 2015
  • Conference Sponsors: International Gas Turbine Institute
  • ISBN: 978-0-7918-5673-4
  • Copyright © 2015 by ASME


Current criteria used to determine whether rough surfaces affect skin friction typically rely on a single amplitude parameter to characterize the roughness. The most commonly used criteria relate the centreline averaged roughness, Ra, to an equivalent sandgrain roughness size, ks. This paper shows that such criteria are oversimplified and that Ra/ks is dependent on the roughness topography, namely the roughness slope defined as the roughness amplitude normalized by the distance between roughness peaks, Ra.

To demonstrate the relationship, wake traverses were undertaken downstream of an aerofoil with various polished surfaces. The admissible roughness Reynolds number (ρ1u1Ra1) at which the drag rose above the smooth blade case, was determined. The results were used to demonstrate a 400% variation in Ra/ks over the roughness topographies tested.

The relationship found held for all cases tested, except those where the roughness first initiated premature transition at the leading edge. In these cases, where the roughness was more typical of eroded aerofoils, the drag was found to rise earlier.

Copyright © 2015 by ASME



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