Winged keels lift calc

[willfox]

I am currently designing a keel with wingletts and have looked at certain designs from the 11th chesapeake symposium. They give the dimensions of the keel sections under test which include 2 keels with winglets. They give graphs of lift coefficient v's angle of attack.

Obviously to find lift it is 0.5 x dencity x plan form area x v^2 x Cl. Am I correct in thinking that if I simply scaled the keel down to a desired size, the lift coefficient would be the same? The tests were done in a wind tunnel so i presume to obtain the lift force I would use dencity of water?

Also I am aware that winglets also increase effective draft. Does anyone know how this is calculated?

[HJS]

The aspect ratio has to be corrected to AR eff


hjs

[tspeer]

Originally Posted by willfox

I am currently designing a keel with wingletts and have looked at certain designs from the 11th chesapeake symposium. They give the dimensions of the keel sections under test which include 2 keels with winglets. They give graphs of lift coefficient v's angle of attack.

Obviously to find lift it is 0.5 x dencity x plan form area x v^2 x Cl. Am I correct in thinking that if I simply scaled the keel down to a desired size, the lift coefficient would be the same?

Approximately, yes. That is the point of using nondimensional coefficients.

Unfortunately, fluid mechanics is "the science of the non-constant constant." You should also pay attention to the Reynolds number (chord * speed / kinematic viscosity) at which the tests were conducted. There are scale effects that have to be reckoned with. If you are operating at a higher Reynolds number that the tests, the coefficients will probably be conservative. If you are operating a a substantially lower Reynolds number (say, the better part of an order of magnitude less), then the maximum lift will probably less than the test data, drag will be higher, etc.

The tests were done in a wind tunnel so i presume to obtain the lift force I would use dencity of water?

Yes.

Also I am aware that winglets also increase effective draft. Does anyone know how this is calculated?

The effective draft is based on the idea that the drag due to lift ("induced drag") is inversely proportional to the square of the depth, and proportional to the square of the lift. If you plot the drag coefficient vs the square of the lift coefficient, you will get an approximately straight line. The slope of that line is due to the induced drag - the flatter the better. The effective depth, d_e, will be the square root of the area divided by slope of the line (dCD/d(CL^2)) times pi:

d_e = sqrt( area / (pi * dCD/d(CL^2)) )

Winglets reduce the induced drag, making the line above flatter. You can get the same effect without winglets by making the keel deeper, and you can do it with less wetted area than the winglets. So it really comes down to the constraints on keel depth. If you have a reason why the keel can't be made physically deeper, like sailing in shoal waters or class rules, then winglets make sense. If you have the freedom to increase the depth, the performance will be better if you go with a longer straight keel.

[willfox]

Thanks so much Tom, all my pondering have been answered! Your website looks very interesting. I'll be sure to take a deeper look.

For my design, the performance is secondary to drarf requirement so I am very happy going down this route. Thanks again Tom,

Will Fox

[willfox]

Sorry Tom, Also i am guessing that The keel area is just the plan form area? As winglets are involved these are not taken into account as the plan form area view make little difference?