Induced drag of surface-piercing foils

Hi,

if you look at the modern attempts to foil-assisted monohulls, like this:
http://www.boatdesign.net/forums/attachments/sailboats/97363d1421531704-2015-imoca-60-foil-assist-imoca-60-test-boat.jpg
you can see foils with tips stretching out of the water (in the picture above, both tips actually).

What is the induced drag of such a foil? There are no fully formed tip vortices, but the waves and splashes instead. How to estimate the drag?

regards

krzys

 

The foil doesn't need an actual tip in order to have an induced drag - just a spanwise variation in the loading.

Lifting-line or lifting-surface codes can calculate lift, pitching moment & induced drag (using reflected images) for the limiting cases of zero or infinite Froude Number.

 

Yes, if you consider the surface as a stiff one, you can use reflected images. What's interesting, the induced drag can be zero then (e.g. for a half ring with a uniform lift distribution).

Unfortunately, the stiff surface limit is not very interesting. It works for very small speed, when the lift of the foil is insignificant, or for very large speed, when the induced drag is insiginifcant...

regards

krzys

 

Myszek, welcome to the front line of the modern hydrofoil research - how to set correct boundary conditions at the air-water surface interface of a hydrofoil and how to account for cavitation and ventilation.

You won't find many people able to give an answer from the first-hand experience, but there are some technical papers in internet which could help you. This one gives an IMO very clear overview of the problem and on how to set the CFD simulation: http://www.marinepropulsors.com/proceedings/2013/1A.1.pdf and could be a good starting point for your study.

The attached paper by Brizzolara and Villa might also be of help.

Cheers

 

I can't give you any numbers right now, but I believe that relatively modest boatspeeds (where induced drag is not insignificant) correspond to large enough Froude numbers (based on the chord of the foil) to justify using the high-speed limit.

 

Tom Speer has given a good summary of this subject in a previous thread
(Posts # 2, 4 & 14) :

http://www.boatdesign.net/forums/boat-design/hydrofoil-questions-17688.html

 

Thank you. That was a really good summary of facts by Mr. Speer.

 

From a 2007 thread http://www.boatdesign.net/forums/boat-design/hydrofoil-questions-17688.html post #2 by Tom Speer:

Looks like a disagreement on whether the foil operating near the free surface has higher or lower drag. My thought (without any analysis) is that Tom Speer is correct and the induced drag is approximately doubled.

 

The foil has lower drag in the low-speed limit (which is analogous to ground effect) & higher drag in the high-speed limit (which uses image singularities of opposite sign).

The doubling of the induced drag is only applicable to a horizontal foil, where the entire span is very near the surface. For a slanted foil, or a V, much of the span is much deeper, so the factor can be considerably less than 2. Also, when deeply immersed, the induced drag for a V foil or other foil of nonplanar shape, can be much less than it is for a horizontal foil of the same span. So, the net induced drag of a surface-piercing foil isn't as high as you might think.

 

Thank you, that's what I needed. And special thanks for Tom Speer, of course.
First, he proved that I misunderstood the mirror image method
Then, he showed the very simple "biplane" estimation.

The result, that the induced drag is doubled by the surface interference, is very intuitive.
And the idea appears immediately: it's well known, that the annular biplane wing has a half of the induced drag of the planar one. Imagine a half-ring hydrofoil with the appropriate lift distribution. Together with the mirror image, it forms an annular wing. So, the effective induced drag will be the same as a planar foil far from the surface. Am I right?

Thanks again

krzys

 

I'm afraid that there are several issues that you are still confused about.

However, rather than getting bogged down trying to straighten them out, I would like to point out that your foil would only have a 1/2 ring shape at one particular depth & incidence angle.

So your observation (which I do not agree with) would be only a theoretical peculiarity, probably not something of any practical use on a surface piercing foil, which is in-effect constantly changing
shape.