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Wing Paddle Papers

Written by Al Bowers

Thursday, 07 September 2006

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Wing Paddle Papers
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Performance Prediction for Olympic Kayaks

P. S. Jackson Journal of Sports Sciences, 1995, 13, 239-245.

This paper sets out the effects of the various factors which determine the speed of racing kayaks and canoes, with the aim of identifying the areas most likely to lead to improvements. The friction, wave, and aerodynamic components of hull drag are first described in terms of the hull parameters, in order to provide accurate predictions of propulsive power as a function of hull speed. The generation of thrust by paddling is described via the mechanics of vortex-ring wakes, in oredr to determine the propulsive efficiency in terms of the parameters describing the blade and stroke. Equating the thrust and drag then leads to a predictive model for hull speed in terms of all the parameters describing hull and blade performance. This is used to determine the sensitivity of hull speed to small changes in each parameter, enabling the most important factors to be identified. The paper concludes with a discussion of various improvements to kayaks that have actually appeared in recent years, and uses earlier analysis to explain and predict the resulting speed changes.

Sketches of the vortex ring formed at each paddle stroke for the drag blade (a) and the wing blade (b).

Planform and section of (a) drag blade, (b) wing blade, and (c) fingered blade.

Editorial Comments: Sander's two papers appear to point out that the key parameters for improved performance with wing paddles are 1/ high stroke rate (at least 90 strokes/min) and 2/ large lateral motion (at least 50 cm). The high stroke rate may be due to the early design wing paddles used in these studies (from the early 1990s), modern blades may not require such rates. Some of the "slip" in Sanders paper is due to the removal of the paddle from the water (a part of the exit) and may actually contribute to the "braking" on each stroke because the paddle is not still being pulled aft at the exit of each stroke). This may be a possible place for improvement. The hand motion data is also useful as it shows the upper hand crossing over the centerline being advantageous in nearly all cases, which establishes the paddle blade being placed in the water as close to vertical as reasonable.

Based on that data, and measuring a wing paddle, the Reynolds number is about 320,000 and about 2.5 to 3.0 lift coefficient. These are reasonable numbers as long as the stroke rate keeps the blade above the crtical Strouhal number (critical Strouhal is about 0.21, it is the rate below which the vortex flow breaks down and allows stalling and separation of the flow across the paddle blade). This critical stroke rate is about 70-80/min for most wing paddles. 1-D simulation shows these assumptions are reasonable and fall into the expected performance envelope of sprint kayakers.

Jackson believes that "fingered" blades could lead to improvement in efficiency. There is probably little or no improvement in efficiency. Slotted airfoils like this usually result in increased lift coefficient at the large expense of drag and a general decrease in efficiency (lift-to-drag ratio or L/D) compared to a solid blade. Given that the power output of humans is fairly limited (see below), efficiency (L/Dmax) is probably a more important driver to maximum speed than maximum lift coefficient (CLmax); the implication is that solid wing blades will remain more effective for kayak and surfski racing than slotted ("fingered") blades will. This may not necessarily be the case for the shortest race distances in sprint kayak (of 1 minute or less), where power outputs are higher and anerobic output may account for improved performance far more than aerobic performance. Note: the chart shows legs alone and total output. the difference between these curves is the added output for arms alone. However, the legs and torso are used in surfski and sprint kayak, so the output is above the difference between the curves, though how much is subject to some conjecture.

[Note: Selina Kendal, the student who worked with Dr Ross Sanders on the first two papers, has had her name appear on recent results sheets for the Molokai race, a gratifying case of theory and reality meeting by one of the foremost minds in wing paddles. -AHB]