Free surface effect: NASA Report 1232

Updated December 19, 2021

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The goal of this study is to benchmark flow5's prediction in the case of a free surface at infinite Froude number against the test cases described in NASA Report 1232 "A THEORETICAL AND EXPERIMENTAL INVESTIGATION OF THE LIFT AND DRAG CHARACTERISTICS OF HYDROFOILS AT SUBCRITICAL AND SUPERCRITICAL SPEEDS", By KENNETH L. WAD LIN, CHARLES L. SHUFORD, Jr., and JOHN R. McGEHEE, 1955.

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The project file used to perform the comparisons can be downloaded here: NASA1232_v7.21.fl5.


The two hydrofoils with aspect ratio equal to 4 and 10 have been modelled.

The method used for the benchmark is the uniform triangular panel method with thick surfaces. This is the preferred method in flow5 for its robustness and versatility. The other methods lead to very similar results.

The polars are of type 1. Since there is no surface downstream of the hydrofoil, the use of a T6 polar with a VPW is not necessary.

Test cases

The test cases selected for the benchmark are the measurements performed

It is to be noted that the experiments were performed in two different tanks, and that the temperature and therefore the kinematic viscosity varied between measurements. The fluid properties in the flow5 analyses were set to reflect those conditions as understood from the explanations given in the report.

The bottom and lateral surfaces of the water tanks are ignored in the analyses.



Comparisons to results of Fig. 6a at depth = 0.59 chords

Comparisons to results of Fig. 6e at depth = 4.09 chords


Comparisons to results of Fig. 5a at depth = 0.84 chords

Comparisons to results of Fig. 5b at depth = 3.84 chords

The predictions tend to get more accurate as the distance to the free surface increases and as the aspect ratio increases.

Influence of depth

AR4 - Predicted influence of depth
AR10 - Predicted influence of depth

The influence of the free surface is no longer felt at depths equal to 4 chords.

Influence of the panel method

The results of all methods are close and within the error margin of the analyses.

Conclusion and recommendations

The free surface effect is not felt when the hydrofoil operates at depths greater than a few chords.