Posted By: Rolf_Nilsen
Good explanation on planform and twist - 10/26/09 08:34 AM
I dont hang out much on Sailing Anarchy, but Petes posts about F-40 Adrenaline have made me check the multihull forum there more often. Yesterday this little gem was posted by Tom Speer, a professional aeorodynamist. Since it is quiet here (even if the Alter Cup have just been sailed on F16 Vipers! Come on guys, give us the inside scoop.) I thought this might be food for thought for those who are interested in sailing and aeorodynamics.
First of all, the vortices shed at the head and the foot are not the whole story when it comes to the induced drag due to lift. The induced drag really comes from the fact that the entire wake has a finite span. You can think of the rig basically displacing a whole block block of air to windward, and that has to be made up by air flowing in from leeward. It's just like the flow behind a canoe paddle. You see a strong vortex at both edges of the paddle as the water flows in behind it, and the edges are just a part of the picture. Likewise, the ends of a rig are only part of the picture. Shaping the planform is all about leaving behind the right kind of wake.
For the same luff length, the minimum induced drag comes from having a uniform crosswind velocity in the wake. You can think of the wake coming off the leech as a rigid sheet, with no wrinkles or distortions in it. This may not sound like a very useful criterion, but in fact it's possible to calculate the planform shape, or the twist for a given planform, once the wake is specified and it only takes a spreadsheet to do it. The result looks a lot like the classical elliptical planform, but is distorted by interference from the water's surface.
Once you become limited by the boat's stability so that you have to start sheeting out to keep it upright, what matters is no longer the minimum drag for the luff length, but the minimum drag for a given heeling moment. Now the optimum wake no longer has a uniform crosswind velocity imparted to it, but instead the velocity distribution should drop off linearly from the foot to the head. This is like the wake coming off in a rigid sheet that is also rotating so that it comes off faster at the foot than at the head. The resulting planform is a lot more egg-shaped, like a sailboard rig. When you include the fore-triangle in the total planform, what's left for the mainsail gets to be a lot more rectangular in shape.
A fat-head main can shift gears between these two extremes by controlling the twist. In light winds, it can do a better approximation of the uniform crossflow wake than a more pointed planform, and in heavier winds it can twist off to maintain the same heeling moment. Since a taller rig has less induced drag, it's possible to get less drag from a taller tapered planform than from the shorter planform that has the minimum drag for its size, while maintaining the same heeling moment as the shorter rig.
The ideal shape for a rigid wing would be tapered toward both the foot and the head, but more tapered toward the head. It's also important to have a way of changing the aerodynamic twist, like Cogito did when it won the C-Class Challenge Trophy. Twist allows the heeling moment to be controlled, and it also allows the rig to adapt to the different amounts of shear in the wind.
However, there may be other considerations at play than just minimizing the induced drag. On a C-class cat, it's important to be able to fly a hull, so having some extra area up top to get the hull out sooner may make it worthwhile, even if it has to be twisted off afterward.
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..My question is - is it better to have a smaller chorded tip than root( tapered profile) or is a non tapered wing good enough? The use of the wing is for hard sail purposes not a keel.
First of all, the vortices shed at the head and the foot are not the whole story when it comes to the induced drag due to lift. The induced drag really comes from the fact that the entire wake has a finite span. You can think of the rig basically displacing a whole block block of air to windward, and that has to be made up by air flowing in from leeward. It's just like the flow behind a canoe paddle. You see a strong vortex at both edges of the paddle as the water flows in behind it, and the edges are just a part of the picture. Likewise, the ends of a rig are only part of the picture. Shaping the planform is all about leaving behind the right kind of wake.
For the same luff length, the minimum induced drag comes from having a uniform crosswind velocity in the wake. You can think of the wake coming off the leech as a rigid sheet, with no wrinkles or distortions in it. This may not sound like a very useful criterion, but in fact it's possible to calculate the planform shape, or the twist for a given planform, once the wake is specified and it only takes a spreadsheet to do it. The result looks a lot like the classical elliptical planform, but is distorted by interference from the water's surface.
Once you become limited by the boat's stability so that you have to start sheeting out to keep it upright, what matters is no longer the minimum drag for the luff length, but the minimum drag for a given heeling moment. Now the optimum wake no longer has a uniform crosswind velocity imparted to it, but instead the velocity distribution should drop off linearly from the foot to the head. This is like the wake coming off in a rigid sheet that is also rotating so that it comes off faster at the foot than at the head. The resulting planform is a lot more egg-shaped, like a sailboard rig. When you include the fore-triangle in the total planform, what's left for the mainsail gets to be a lot more rectangular in shape.
A fat-head main can shift gears between these two extremes by controlling the twist. In light winds, it can do a better approximation of the uniform crossflow wake than a more pointed planform, and in heavier winds it can twist off to maintain the same heeling moment. Since a taller rig has less induced drag, it's possible to get less drag from a taller tapered planform than from the shorter planform that has the minimum drag for its size, while maintaining the same heeling moment as the shorter rig.
The ideal shape for a rigid wing would be tapered toward both the foot and the head, but more tapered toward the head. It's also important to have a way of changing the aerodynamic twist, like Cogito did when it won the C-Class Challenge Trophy. Twist allows the heeling moment to be controlled, and it also allows the rig to adapt to the different amounts of shear in the wind.
However, there may be other considerations at play than just minimizing the induced drag. On a C-class cat, it's important to be able to fly a hull, so having some extra area up top to get the hull out sooner may make it worthwhile, even if it has to be twisted off afterward.