John
Aero/hydro
========
There are 2 forms of drag; a) profile b) induced. They are practically independent of each other.
The foil shape you use affects the profile drag. Profile drag is caused by viscous effects. You need to choose the shape based on the lift coeff and the Reynold's no. Typically CL~0.3 for a centreboard and Re 400k. You can use 2D drag predictions to look at this. eg JavaFoil
If you use a NACA00 section for the rudder, sharpen the leading edge where it goes through the water surface - it will ventilate otherwise. There are lower drag foils (as already advised) which may suit you better.
The induced drag is a 3D phenomena and is the drag that is produced directly a function of lift.
CL=Ao x AR/(AR+2) x aoa where AR=e*span^2/area, Ao is the 2D lift slope of the foil (0.11 CL/deg for most foils) and aoa is the angle of attack and e is the Oswald efficiency factor
The induced drag is given by Cdi=CL^2/(e x pi x AR) .
So you can see that the lift for a given aoa increases as AR increases and as e increases. Similarly the induced drag decreases as a function of AR and e.
So what effects Oswald efficiency?
e is a function of the end terminations of the foils and also what is called the downwash distribution.
When you stick a foil in a fluid and give is an angle of attack of angle A, the flow is angle is increased ahead of the foil by an angle ai and decreased behind the foil by an angle 2*ai. Ai is called the induced angle of attack or upwash and 2*ai is the downwash angle. Upwash from a mainsail makes the wind freer for the the jib. Downwash from the jib makes the wind head for the main. This is why the jib is sheeted at say 10 deg and the main at 0 deg. It is also why when you get a boat ahead and to leeward of you, you fall down. Your boat frees the wind for him, and his boat makes the wind head for you.
Anyway, ai is given by the local section lift CLs/2*pi - A.
A German scientist called Munk worked out that the induced drag was at a minimum when the downwash angle along the foil was uniform. So if CLs is constant along the span, so is ai, and thus so is the downwash angle.
For an untwisted symmetrical foil like a centreboard or rudder, it turns out that to get a uniform ai and the CLs, the planform needs to be an ellipse. If it is anything other than this, eg a triangle, the lift will not be constant along the span - in fact it would theoretically go to infinity at the pointy tip. In consequence ai is not constant and so the induced drag won't be at a minimim.
So, for a completely elliptical foil (like a spitfire wing) e = 1.
Now, if you use 1/2 an ellipse and put it under a boat, the hull forms an end plate and e=2.
But this is not the whole story...
The centre of resistance of a 1/3 ellipse is at a depth of about 42% of the span. But for a triangular tapered foil it is at 33% of the span. For the same AR, the elliptical board will give less induced drag, but more heeling moment. When you're fully powered, what you want is a board shape that gives the best ratio of induced drag to heeling moment. In essense, you can have a longer (and thus higher AR foil) if it is triangular. So there must be some optimum.
Another scientist called Jones was interested in this for gliders - higher AR, less drag, flatter glide slope. But the bending loads at the centre span get get really big. So he wanted to get the minimum drag for a given bending load - just as we want min drag for a given heeling moment. He found that this was achieved the the downwash distribution is tapered linearly. For a centreboard, this is a board shape which is much more tapered than an ellipse.
To cut a long story, you can increase the span by about 15% compared with an elliptical foil and keep the centre of resistance in the same place. If the board shape is such that the downwash tapers linearly to zero at the tip, the induced drag is also some 15% lower than the ellipse. This is what was designed for Will.
There are some detractors. On a centreboard, we can't twist the tip. This means that section lifts at the tip is higher than the root - we have a 'tip staller'. This adds some drag, but should mean the board stalls progressively along its length rather than all at once. You'll have to consult Will to see it it works!
Hope this helps. Try looking at
www.tspeer.com and
www.onemetre.net and
www.desktopaero.comKevin
