# Drivers for the "sqare top" width?

Discussion in 'Hydrodynamics and Aerodynamics' started by jmf11, Dec 23, 2021.

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### SkyakSenior Member

Well Phil, I beg to differ.
You are just adding sail area to achieve a lift profile, then claiming superiority.
By "sweep of the rig" do you mean height of the tip off the water? If so Cos(-heel)=Cos(heel).
Induced drag is just one drag component, and it is not always a negative -when the wind is aft of beam it can contribute to thrust. My way puts more sail cord (and area) in more wind. Sail area always costs in rating so the boat that gets more wind/area wins.
This can be demonstrated creating four models of plane wings with the combinations of anhedral 12 deg or dihedral 12 deg combinations with narrow end and wide end.

Induced drag is a concept for accounting for pressure being lost out the ends of a finite span. The ellipse optimum is to accelerate the fluid evenly. Lets consider the (edit) 2D coefficient of lift to be constant so that planform points to the winner. In the case of a flat wing, planform is an ellipse. In the case of regular heel, or dihedral, the free stream fluid momentum is already contributing to flow off the ends even before considering acceleration due to lift, so it takes more cord toward the ends, not less. In the case of reverse heel, or anhedral, the free stream momentum has a component from the ends toward the center, so the ends don't need as much cord (lift is closer to the 2D infinite profile) and the center can support more cord. The span of the anhedral and dihedral examples are equal, and for the sake of this analysis, all wings have equal area.

Last edited: Mar 29, 2022
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### ErwanSenior Member

While it makes sense to optimize tapper ratio for induced drag minimization, I wonder if paying attention to the bottom of the sail could be rewarding too:
1-The more you have sail area or lift at the bottom of the sail, the more you have circulation and downwash.
2-If the downwash angle decreases the apparent wind angle, then it decreases it, where the apparent wind shear is the most pronouced, at the footsail, in other words, where we would need the opposite: more apparent wind angle.
3-If the above-mentionned remarks are appropriate, then the question could be how t0 shape the circulation along the span,
in order to create a kink in the downwash line, somewhere a little above the deck, starting where the apparent wind angle starts to narrowing faster.
Hope it can be understood

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### Doug HalseySenior Member

Paying attention to the bottom of the sail is what deck sweepers are all about!

The best thing you can do at the bottom of a sail to reduce its induced drag is to fill up as much of the gap between the sail and the deck as possible. In other words, make the gap as small as possible over as much of the chord as you can.

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### revintageSenior Member

How wide must the ”deck” be to avoid downwash? Thinking of, if adding a horizontal plate on the boom or sail foot on a non-decksweeper could help…

Last edited: Apr 12, 2022
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### Doug HalseySenior Member

The benefits of endplating a boom (if any) are very small - probably slightly less than the amounts shown below (by Hoerner) for single end plates not in the proximity of an actual hull.

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### ErwanSenior Member

In fact I shoud have disclosed my starting point.
My starting point was my candid attempt to make a kind of "reverse engineering" of the C-Cat wing of GroupamaC.
The wing was a deck-sweeper, so that is not the point.
At first, I though the elliptical outline of the wing's leading edge at the bottom was a smart trick to increase AOA.
because apparent wind's AOA is decreasing, going down to the trampoline.
(In other words the leading edge geometry could mitigate if not offsetting the apparent wind shear at the bottom)
In addition this elliptical leading edge is likely to provide a constant downwash, from the point of maximum chord of the wing to the trampoline ( as long as this "elliptical surface distribution" leads to an elliptical lift distribution)
And in this part of the wing, a constant downwash is better than an increasing downwash.

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### Doug HalseySenior Member

You're right that the optimum planforms could be curved like that, even without considering wind shear, but the shapes are more complicated than simple ellipses.

The optimum shapes (using lifting-line theory for flat, untwisted wings in uniform flowfield) morph between full ellipses for very large gaps and half ellipses for very small gaps, giving something like the shape below.

This particular shape is for a wing with aspect ratio of 5, gap / span ratio of 0.001, and constant gap along the entire chord. It is drawn assuming a straight leading edge and a curved trailing edge, but since it is from lifting line theory, it could have been drawn with curvature on either (or both) edges, as long as the chord distribution was preserved.

Of course the effects of partial-chord gaps, sail twist, apparent wind twist due to wind shear, and numerous other factors that vary with the sailing conditions make the problem much more difficult for pros and amateurs alike.

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