Single finned surfboards: how about asymmetrically foiled fins?

Asymmetrically foiled fins are the norm for rail mounted 'side fins' on multi finned surfboards, and have been for at least the past 40 years. The principle used is that during a turn, the fins on one side of the surfboard are dominant, so the foil can be optimised for the positive angle of attack which they are experiencing... when the angle of attack becomes negative for those fins when turning in the other direction,it doesn't matter as they will often be lifted out of the water as the board rolls.

With single finned surfboards it has always been assumed that the foil must be symmetrical, as the same fin has to do all the work whether the board is turning left or right.

I was recently shaping the asymmetrical '371' single finned surfboard shown below. The board is designed for 'left handers' i.e waves which break to the left when viewd from behind. Thyat'swhy the planshape has less curve on the inside rail ( the rail which will be engaged when the board is trimming left). I want that rail to be fast and low drag. , and am not concerned about the turn radius, in fact I'd prefer the turn radii to be greater for high speed adjustments to the line. The reduced outline curve on the left will help to achieve this.

When 'cutting back'it would be nice to have more planshape curve in order to turn more tightly. In addition using the narrow outline from the left handed railon both sides would make the board very narrow, requiring greater thickness to get the necessary volume... something I'm keen to avoid as it tends to make the board less stable. So, the right hand side of the board can use more curve and width, as shown.

Supermarine 371

The design is 11 feet long by 22.25" wide. If the left hand rail were used only i.e.on both sides, then the board would only be 18 inches wide. If the right hand rail were used on both sides she'd be 27 inches wide. Both theoretical widths are within the practical range,

While shaping, it occurred to me that since the surfboard will be using the left hand rail ( effectively 'turning left') most of the time, especially in fast breaking waves, there's a potential advantage to be gained by foiling the single fin asymmetrically. Provided that the efficiency gain due to the asymmetrical fin being flown 'right side up' while going left is greater than that lost by flying it 'upside down' when going right, there should be a net gain. Because the surfboard will be going left most of the time (and arguably requires greater efficiency when doing so as it needs more speed to race the curl than when 'cutting back')  then the asymmetrical foil should win.

Of course not all asymmetrical airfoils will be suitable. Many are only designed for 'right way up' flying, and perform so badly inverted that they would be worse than useless when turning right.

Here's one such foil:

E174

The lift/drag graph below shows that when the wing is inverted ( or rather the effective angle of attack becomes negative i.e. lift is less than zero)  the lift/drag ratio declines rapidly and the wing enters the stall.

Instead we choose a foil section which performs well 'inverted'. The chosen foil is less markedly asymmetrical but it has a nice low drag bucket at up to four degrees angle of attack, and approximately a third less drag in this zone than at minus four degrees angle of attack.

As luck or good design would have it this foil section is the same one which we used for the surfboard planshape.

Lift vs drag graph

The graph below shows that lift vs angle of attack is more or less constant throughout the range from negative 10 degrees to positive ten degrees angle of attack. So the fin will feel very similar to a symmetrically foiled fin when in use. That's good.

It's worth noting that the graph also shows that effective zero angle of attack ( where the fin produces zerolift) will be at approximately minus 1.2 degrees,so the fin should be offset from the 'centreline' of the board by that much, all else being equal.

Consistent rate of lift production through negative and positive aoa values.

Here we can see the low drag advantage flying the foil upright vs inverted, as angle of attack changes. What this foil should deliver is an advantage over similar symmetrical foils throughout the full range of angles of attack, and throughout a typical range of surfing speeds.

|Speed is represented here by the coloured lines... red is a reynolds number of 500,000 or 9mph in water of 10 degrees C, gold is a reynolds number of 1,000,000 or 22 mph.

Water temperature is also relevant, as changing the water temperature from 0 degrees to 20 degrees C increases the reynolds number by 65%. This means that for some foils a fin with substantially shorter chord can be used in summer or in warmer water generally. It's not an issue in this case as the low and high reynolds numbers give similar results in the required speed range. Going faster than the modest 22 mph which the airfoil tools plotter allows us will obviously not be an issue.

Drag vs angle of attack showing the low drag bucket from minus one to four degrees angle of attack.

Yes,as you have probably guessed, we are Supermarine Spitfire crazy, and are using the 371 Supermarine Spitfire foil for both the surfboard planshape  and its fin foil, in addition to a Spitfire wing inspired elliptical planform for the fin.

Hence the board will be the 'Supermarine 371' model.

Many thanks to the creators of airfoiltools.com

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