# Looking to find out at what height WiG effect stops

Discussion in 'Boat Design' started by RipSlider, Jul 17, 2008.

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### RipSliderJunior Member

Hello all.

Just a very quick question. I'm interested in being able to work out a way to calculate where the WiG ( Wing in Ground ) effect breaks down at a hieght.

hmmm... that's not a very clear sentence.

if I have a tri-hulled boat which I want to go very fast, the out-rigging arms will produce X amount of lift for a given speed, Y.

<<Note - trimarine is not very good example, as WiG will be VERY low, but bear with me >>

If I keep the speed constant, and simply raise the height of the outriggers, at some point the WiG effect will break down and no dymanic lift will be produced.

My question is therefore: How do I calculate that height?

I'm guessing that there is one or more partial differential equation(s) which links speed, lifting area, height above surface and a number of other factors. I just can't find it.

If anyone can offer any advice/guidance, I would greatly appreciate it.

Thanks

Steve

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### FAST FREDSenior Member

For most aircraft the effect drops off very rapidly at an altitude of over 50% of the wingspan .

100ft wing span , it needs the power of an aircraft not a WIG to go over 50ft.

Swopping speed for altitude IS possible , so If a need rose it would be fine to "pop up" to 100 ft , but the air speed would decay rapidly , so it would only be to clear an object for a few seconds.

FF

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### Leo LazauskasSenior Member

There is a lot of work around on ground effect, but not all of it is easy going.
There is a nice section on ground effect in Truckenbrodt's book on aerodynamics, but I haven't got it here with me, otherwise I'd scan some of the diagrams. (If I still had a memory, I'd even remember the title of the book!)

Here are a few references if you are really, really keen on the theory...

TUCK, E.O. "Unsteady small-gap ground effects",
California Institute of Technology, Engineering Science Report 78-1, 1978.

TUCK, E.O. "A non-linear unsteady one-dimensional theory for wings in
extreme ground effect", Journal of Fluid Mechanics, 98 (1980) 33-47.

TUCK, E.O. "Steady flow and static stability of airfoils in extreme
ground effect", Journal of Engineering Mathematics, 15 (1981) 89-102.

TUCK, E.O. "Nonlinear extreme ground effect on thin wings of arbitrary
aspect ratio", Journal of Fluid Mechanics, 136 (1983) 73-84.

STANDINGFORD , D.W.F. and TUCK, E.O. "Lifting surfaces in ground effect",
Workshop on Ekranoplans and Very Fast Craft, University of NSW, 5-6 December 1996.
Proceedings ed. L.J. Prandolini, Inst. Mar. Engrs. NSW, pp. 230-243.

Have fun!
Leo.

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### marshmatSenior Member

Hi Steve,

So you know how to deal with partial differential equations.... you're probably good to figure out all that physics/math garbledegook Leo mentions
(I can safely make jokes like that, being in engineering physics myself and having spent way too much time around quantum wave equations....)

But as our venerable Fred points out, the rule of thumb that ground effect is irrelevant at altitudes above 1/2 wingspan is a good, reliable and generally pretty accurate guideline.

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### kach22iArchitect

Just don't fly over 50 feet in the air or the FAA will be all over you.

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### eponodyneSenior Member

Effeciency of WIG effect also increases the closer one gets to the surface. At distances less than 10% span the effect is quite pronounced (or thats what my reading tells me, I don't do empirical data on my own). I know the Soviets found that if the underside of the wing has a slight 'S' shape, it also improves matters.

Hope this helps.

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### RipSliderJunior Member

Partial diff's are easy. You try to work them out in the convential manner, get stuck, swear a lot, and then throw them into a Genetic Algorithm package and wait a coupl of minutes for everything to be worked out for you!

Thanks for the responses everybody. "1/2 the wingspan" is good enough for me - I think - it's for a model boat rather than a full sized one, so if it sinks, no one drowns.

Steve

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### tspeerSenior Member

That's not true. Dynamic lift will be produced at any height if the outriggers are acting like wings. There will be more lift at low altitude, but there will still be lift at high altitude. The biggest difference will be the drop in induced drag, which will, in principle, drop to zero when the wing is right at the surface. As a practical matter, the drop in drag is significant, but doesn't go to zero.

The induced drag is approximately

Di = Lift^2 / (pi * b^2 * 1/2 * density * velocity^2 * efficiency_factor)

Di = induced drag
Lift = dynamic lift produced by the surface
b = span of lifting surface (tip to tip)
density = fluid density
velocity = free-stream velocity of the fluid
efficiency_factor = factor to account for effect of planform shape, interference with the ground, etc.

The efficiency_factor is a function of height. The top line in this graph is what simple theory says is the manner in which it varies:

There's a big difference for very small gaps, and the efficiency factor gradually approaches 1 as the distance from the surface increases. Strictly speaking, this graph is for different designs, in which each design is optimized for the particular distance above the ground. That's not really the same as changing the distance from the surface for a given design, but it gives you an idea of what the effect of height is like.

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