BMW Oracle Wing

Not so. Two elliptical wings of the same area and different span will have very different induced drags. And the induced drag will dwarf the profile drag at the lift coefficients useful for sailing.

This spreadsheet may help you calculate the induced drag. It will also calculate the planform shape with minimum induced drag, including the effect of interference with the water's surface. But won't take into consideration a nonuniform wind or rake (yet).

 

Sorry... (better) One has to be in the mind of the talker. A scary place.

I was just referring to the simplistic results of the analysis. So... Lift to Drag as it gets rotated into Heel/Thrust. I don't have the spread sheet with me at the moment, but both were at 24 degrees between apparent wind and course sailed.

Racing Sail was: heel=3720 lbs, thrust=634 lbs => 5.9:1
NACA0012 was: 2.3:1.

 

Excellent spreadsheet, Tom!

 

Ooooh... did not see tspeer's second post till your (daiquiri) post notified me. Got to get back to my computer with Excel on it.

Just to simplify the variables to satisfy my curiosity... assuming we ignore surface conditions, aspect ratio, etc... IOW... the plain 2D case theoretical text book case.

A simple NACA 0012 at 12 degrees AOA has a lift to drag of about 62:1

What would a sail be... say one with a round cross section mast and with an optimum but realistic shape. And I'm not saying a hard number needs to be analyzed for... just a educated guess. Does it approach the wing... say 50:1 or is it really down in the 20:1 range?

 

Here are some results from the spreadsheet you can check. This one shows the way induced drag varies with geometry for a uniform downwash. With no gap, this is what is produced by the classical semi-elliptical planform. You can see that doubling the span drops the induced drag by 75%. It also doubles the height of the center of effort, as you'd expect because the planforms are similar in shape.



There is a limited comparison with experimental data in this figure:

I don't know to what extent that comparison can be generalized to other cases. If anyone has more data I'd certainly like to see them.

I think you're missing the distinction between section L/D and complete wing L/D. For moderate to high aspect ratios, operated in the linear lift range (no flow separation), the section characteristics and the induced drag are two completely independent problems. This illustration shows what's going on.

The induced drag (and the 3D effects on the lift curve) are due to general flow pattern corresponding to deflecting the air over a finite span to produce the lift. (Ideally) it doesn't matter how the lift at a given spanwise station is produced. So all section shapes are equal so long as they are oriented to produce the same lift.

The induced drag comes from the fact that the sail operates in a header of its own making. The typical lift-drag bookkeeping makes the effect of this header look like a drag force.

The section shape problem is all about the boundary layer on the surface. The change in drag due to lift for a section is due to the changes in local velocity affecting the skin friction and the boundary layer thickness effectively changing the shape of the section. There is also a change in the lift curve due to the boundary layer affecting the conditions at the trailing edge. This is different from a change in the local angle of attack due to the wake changing the lift.

You have to sum the drag from the profile data with induced drag calculated from the planform geometry. You can combine any profile with any planform shape.