Effect of Leeway on lift/drag of a hydrofoil

[Doug Lord]

I need some expert help. Please see the rough sketch below. I'm trying to understand how leeway would affect the lift and drag of a hydrofoil. The foil would be a 63412 section operating at a CL of about .4 (within the dragbucket of the section).
It is a foil to be used to lift a small trimaran's main hull early before it would lift due only to heel.
Any analysis or comment would be gratefully received!

[DCockey]

By "main foil" do you mean the cross piece at the bottom?

[Doug Lord]

Originally Posted by DCockey

By "main foil" do you mean the cross piece at the bottom?

----
Yes. Also, I was interrupted before I could post the second image which is there now-my apologies.

[Tim B]

You have a foil flying at an effective pitch and sideslip. You can work out these angles by doing some vector analysis. There has been plenty of research done on wings at sideslip, so you might want to try google for "effect of sideslip on wings". The NACA papers are also likely to have lots of good stuff in them.

Grammatical Rant: By the way, one could say that the sideslip affects the lift and drag of the wing, but we are interested in the effect of sideslip on lift and drag. Remember "cause and effect" if in doubt.

Tim B.

[Doug Lord]

Originally Posted by Tim B

You have a foil flying at an effective pitch and sideslip. You can work out these angles by doing some vector analysis. There has been plenty of research done on wings at sideslip, so you might want to try google for "effect of sideslip on wings". The NACA papers are also likely to have lots of good stuff in them.

Grammatical Rant: By the way, one could say that the sideslip affects the lift and drag of the wing, but we are interested in the effect of sideslip on lift and drag. Remember "cause and effect" if in doubt.Tim B.

---------------------------
Thanks ,Tim-I always screw that up-maybe I'll remember now.
---

[tspeer]

Handbook methods may be misleading for cases like this. There is a considerable difference between an isolated foil and a foil attached to a strut when it comes to the effects of leeway. Here are some results from a lifting line analysis, which is the simplest method of estimating the induced drag of such a configuration.

The geometry I used has a foil with a taper ratio of 0.4 and a strut with uniform chord. The foil is one semi-span below the surface, and a linearized free-surface approximation (infinite Froude number) is used.

The first case shows the loading and downwash along the span of the foil at zero leeway. The Oswald efficiency factor for each individual foil panel is 1.82 compared to what the panel's drag would be if the panel were isolated. because the span is doubled. For the whole span, the efficiency factor is 0.91. The lift curve slope is 56% of the 2D lift curve slope.

When the strut is operating with a lift coefficient of 0.2, the leeward foil panel lift decreases from a lift coefficient of 0.4 to a lift coefficient of 0.34, and the induced drag coefficient goes from 0.0195 to 0.0197, dropping the efficiency factor for that panel to 1.33. The windward panel lift increases from a lift coefficient of 0.4 to 0.56, the induced drag coefficient goes from 0.0195 to 0.0181, and the efficiency factor for that panel is 2.58. The strut's induced drag coefficient is 0.0108 and its efficiency factor is 1.17.

The attached plots show the lift distribution and the downwash distribution along the span of each panel. With no leeway, the downwash on the foil is almost uniform - a uniform downwash would produce the minimum induced drag for the foil's span. With leeway, the lift distributions look nothing like the nearly-elliptical distribution of the first case. The downwash distributions are far from uniform.

There is also a heeling moment due to asymmetrical lift on the foil in addition to that of the strut.

Obviously, these results wil change with depth of immersion, foil &strut geometry, etc. When you start analyzing complex foil geometries, the lift distributions can be very strange due to the interaction between the surfaces.

[Doug Lord]

Thanks very much, Tom!

[Doug Lord]

I learned something recently about the effect of leeway on the lift/drag of a hydrofoil that was a trully fascinating learning experience.
I had been familiar with Hugh Welbournes DSS system which is a retractable hydrofoil that slides horizontally to leeward. The idea is to create vertical lift and increase righting moment. I had always thought that the biggest problem with that system might be keeping it underwater far enough. When I discovered that V3 in the Barcelona World Race was using curved lifting foils pioneered by the 60' tri's it sparked my imagination and I came up with what I thought was a great solution for monohull dinghies: a curved lifting foil that went outboard instead of inboard. That way it would produce vertical lift that would also result in increased RM like the DSS system.( See rough sketches 1 & 2 below) I was pretty excited. I started looking very carefully at the idea-see rough sketch # 3 below that shows the foil viewed from forward(just the leading and trailing edges). Some of the rosy glow began to fade when I realised that an outboard curved foil would have both high pressure and low pressure on the same side.
I decided to contact some friends and acquaintances to get a better idea of the problem. It occurred to me that the best answer might come from Greg Ketterman whose foilers are legendary(Long Shot among others). I asked him why his foils were pointed inboard-here is what he said:

Originally Posted by Doug Lord

This is an e-mail I got from Greg Ketterman in response to the question:"Is there any special reason the trifoiler foils point inward?". It occurred to me that the Trifoiler case was similar to the reverse curve foils and since Greg has been very helpful to me I asked him. It should be noted that Greg actually tried outboard foils and sent pictures of them. I have his permission to post this here. Greg is also a member of the boatdesign.net community. I urge anyone with an interest in hydrofoil design and development to read the enclosed paper-page 14 and Figure 14a&b on page 32 are directly related to this discussion. For those interested in model hydrofoils there are details of his model throughout this paper including sail area, foil area and improvements warranted by testing. I'm grateful to Greg for taking the time to put this together and for his help:

(emphasis by DL)

Hi Doug,

Forgive me if I am too condescending but I am amazed at how many people do not get this. ***** argues that it would provide more righting moment. Imagine how ineffective a curved daggerboard would be if it curved out. I would have expected you to understand.
The boat in the attached photo did not perform well at all.

My senior project report explains it here; http://picasaweb.google.com/gketterm...57835053693858

A simpler way to look at it is the aspect ratio of the horizontal foil adds to the aspect ratio of the vertical foil when the foil points in. Aspect ratio is everything with hydrofoil sailboats.

All the best;
Greg Ketterman

VP Engineering Hobie Cat Co.
------------------------------------
Hobie Trifoiler specs: http://www.hcana.hobieclass.com/site...ifications.htm
------------------------------------

=============
Rough Sketches, left to right: 1) first conception of the outboard pointing curved foils, 2) shows approx. additional righting arm, 3) rough sketch of leading and trailing edges with lifting portion of foil at approx. +3 degrees angle of incidence and lateral resistance portion of foil toed in approx. 3 degrees and showing zero degree point. Foil is NOT twisted. This is when I realized that all was not well with this idea. 4) from Greg Ketterman's paper showing high and low pressure areas on "L" foils and on "T" foils. Note that on the "L" foils the pressures were correct as long as the windward foil pulled down. In lighter conditions, with the windward foil lifting up there would appear to be high and low pressure on the same side substantially reducing aspect ratio according to Greg-same problem with my original idea and caused by leeway:

click on image- Note that on my rough sketches the lee side is the right side of the picture; on Gregs sketch the lee side is the left side of the picture:

[tspeer]

Your third sketch shows the crossover point where lift is zero and asks, "no induced drag?" Quite the opposite is the case - there is tremendous induced drag produced there.

The vorticity shed into the wake is proportional to the rate of change of the lift - the slope of the spanwise lift distribution. At the point where the lift goes to zero, there is a very large change in lift going on between the sideways lift of the upper part of the foil and the vertical lift of the bottom portion. It is like the span of the two segments of the foil is terminated there. After all, the lift also has to go to zero at the physical tip of a hydrofoil, so you could slice the foil in two at that point and you'd have no change.

In fact, the effective span will be worse than chopping each segment there because you still have the trailing vortex from the lift on the one segment that is contributing to the induced drag of the other, compared to what you'd have if they were widely separated.

Perhaps a better way of visualizing this is to draw the "downwash" distribution, or the velocity imparted by the foil to the water. The upper segment has lift to windward, so it is deflecting the water to leeward. The bottom segment is lifting up, so it is deflecting the water downward. This is exactly what you would have if you had a vortex trailing from the point of zero lift, because the water would be swirling in a clockwise direction around the vortex. And, in fact, this is what you would see in the wake, too - a very strong vortex shed there with a weaker vortex in the opposite direction at the tip and hull junction (depending on how much lift is transferred over to the hull).

With a J foil, you can envision a uniform distribution of the wash in the wake wrapping around the foil, and this would minimize the induced drag.

[Doug Lord]

Thanks, Tom. It seemed to me that Greg said that the "J" foil pointed outboard would behave like the "reverse curve foil" pointed outboard. He used an example saying that the aspect ratio of a "J" foil pointing outboard (or reverse curve foil pointing outboard) would be halved as compared to the foil pointing inboard. Is that a viable way to explain it? Am I understanding that correctly?
I can see that when there is high and low pressure on the same side of either foil there is a great deal of drag. Thanks again for your help.