Turbulent Skin Friction Coefficient

The variation in turbulent flat plate skin friction coefficient with Reynolds number is calculated below. This is used when compiling an estimation of aircraft parasitic drag as described in the tutorial on the Drag Polar. The skin friction is graph originally published in USAF Stability and Control Datcom [1] and reproduced in Roskam Part VI Chapter 4.2 [2]. The calculator provides an estimation of the skin-friction coefficient based on a curve fit; the methodology is described below the graph.

The Reynolds number input can be determined using the AeroToolbox Reynolds Number Calculator.

Select Nearest Mach:

Reynolds Number:

Skin Friction Coefficient:

Turbulent Mean Skin Friction Coefficient (extract from Roskam)

Calculation Methodology

The skin friction coefficient calculator makes use of a power curve fit for each of the Mach numbers shown on the graph. The resulting \( C_{f} \) my therefore differ slightly from the value obtained directly from the graph. It is left to the user to determine whether the curve fit is appropriately accurate for use (see the disclaimer below).

A curve fit is determined at each Mach number in the form:

$$y = A {x}^{B} \Rightarrow C_{f} = A \cdot {R_{e}}^{B} $$

\( A \) and \( B \) are given the values shown in the table below. The \( R^{2} \) term is published to give the user an indication of the quality of the curve fit.

Mach A B R 2
0.0 0.0391 -0.157 0.9967
0.3 0.0399 -0.159 0.9976
0.7 0.0392 -0.16 0.9971
0.9 0.0376 -0.159 0.9965
1.0 0.0381 -0.161 0.9970
1.5 0.0371 -0.164 0.9966
2.0 0.0329 -0.162 0.9941
2.5 0.0286 -0.161 0.9944
3.0 0.0261 -0.161 0.9936

[1] Hoak, D.E, et al, USAF Stability and Control Datcom, Flight Control Division, Air Force Flight Dynamics Laboratory, WPAFB, Ohio, 45433-0000, 1978, (approved for public release). Link to document.

[2] Roskam, J, Airplane Design Part VI: Preliminary Calculation of Aerodynamic, Thrust and Power Characteristics, Roskam Aviation and Engineering Corporation, 1987.

Disclaimer (the simple version):

I have made every effort to ensure that all the calculations that form part of this tool are correct and accurate, I have back-tested it and validated it against the original graph published. HOWEVER, I cannot and do not guarantee that the results output from the calculator are correct. You should always double check the results being output – especially if you are using the results for engineering calculations. Finally, if you do discover any bugs in the calculations I would really appreciate it if you would drop me an email at hello@aerotoolbox.net and let me know so I can make the correction.

Disclaimer (the legal version):

Aerotoolbox.net has made this skin friction calculator freely available to use by accessing it from the aerotoolbox.net/skin-friction address. Be aware that the content on this site is copyrighted and redistribution or copying of this content is prohibited. The release of this calculator does not and cannot warrant that any functions contained within are accurate or error free. The use of this software comes with NO WARRANTY or LIABILITY of any kind. The entire risk as to the software applicability, performance and quality lies solely with you as the user and not Aerotoolbox.net. It is the responsibility of the user to ensure that the correct values have been selected at all times and to cross-reference the results with those contained in the cited references. In no circumstance or event shall Aerotoolbox.net, or the domain owner associated with the website, be liable for any damages, whether direct or indirect, incidental, special, or consequential arising out the use of or any defect inherent in the software. By using this calculator, you as the user expressly agree to the terms of this disclaimer in full.