# The Myth of Aspect Ratio

Discussion in 'Hydrodynamics and Aerodynamics' started by DCockey, Feb 20, 2011.

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### Leo LazauskasSenior Member

Sorry, Slavi, but it will be nothing like that. It is a simple (DOS) program for planar wings of arbitrary aspect ratio (but not too small ). I might release code for cambered surfaces at some later stage. Thickness effects and multiple surfaces are not all that interesting to me at present, and I don't have time yet.

The linear results in XFLR are exactly what I am interested in. More published experimental results would be nice too, as I no longer have access to academic journals.

My code produces the different components (potential lift, LE suction, SE suction etc) so we can compare results from different codes fairly easily.
For example, what C_L and C_Di does XFLR predict for rectangular, delta, and elliptical planforms without LE suction effects?
How are XFLR predictions affected by aspect ratio?

I am trying to develop accurate pressure distributions to include in Flotilla 3.x so I can predict the wave resistance and wave patterns of lifting surfaces in water.
(See, for example, the pictures in the thread www.boatdesign.net/forums/design-software/flotilla-hovercraft-hydrodynamics-36344.html)
At very high speeds the wave resistance of these travelling pressure distributions is given by a formula identical to that for the induced drag of a lifting surface. In that case, of course, an elliptical pressure distribution in the y-direction is optimal. In the x-direction there will be a square root like singularity at the leading-edge, and a Kutta condition at the "stern".

Having accurate results for simple lifting surfaces is a good way of verifying calculations along the way, and aspect ratio effects are important too. (It means we can do surfboards as well as other planing-like bodies) It's slow to do it this way, but we Rainmen need that sort of certainty

Leo.

Last edited: Mar 1, 2011
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### DCockeySenior Member

Perhaps discussions of hydrodynamics and analysis methods need a home (if Jeff is agreeable) rather than being scattered in the Boat Design, Sailboats and Powerboats as well as other forums. Threads such as this one are somewhat odd companions to ones on converting a surfboard to a windsurfer. Stability and presumably other hydrostatics already have their own forum. Several possibilities come to mind:
1) A new Analysis and Hydrostatics forum.
2) Expand the Software forum to Software.
3) Expand the Stability forum to Stability and Analysis.

Folks following this thread would be some of the ones who would presumably are interested in the more technical discussions relating to analysis and theory.

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### Leo LazauskasSenior Member

They sound like reasonable suggestions, DCockey.

Sorry that I wandered off-topic for a while, but I hope the short note I attached has brought it back towards consideration of aspect ratios.

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### daiquiriEngineering and Design

I agree. A forum called "Hydrodynamics" or similar could be useful.

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### daiquiriEngineering and Design

Oh-oh! That's quite a task, Leo!
Unless it's flying pretty deep underwater, you'll have to cope with a hydrofoil bending the free surface above it, which in turn will change the pressure distribution and flow pattern around the foil, which in turn will influence the free surface above it, which in turn...
I have seen some papers around which deal with that issue. When (or if) I find them, I'll see to pass them to you.

P.S.
DCockey - for a moment, don't worry about the thread continuing to drift. As soon as Jeff creates a new sub-forum, he'll be able to move all the off-topic messages into some new thread. Isn't it so, Jeff?

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### Leo LazauskasSenior Member

Sorry, I'm still not making myself clear.

The travelling pressure is above the water, just like a hovercraft cushion. To solve the planing problem for a given hull with equation z = Z(x,y), we just have to find a pressure distribution that causes the free-surface to have the same shape z = Z(x,y) underneath the pressure distribution. It's a lot simpler to say that than to solve it

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### DCockeySenior Member

Leo, could the type of analysis you are trying to do for lifting bodies be called a "flat ship" analysis? Is there a derivation available? Would a match asymptotic expansion approach be useful? (I've used that before but a long time ago.)

Perhaps it needs its own thread.

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### DCockeySenior Member

Leo's modified results assume vortex separation form the leading edge and/or side-edge/tip. For wings with attached flow at the leading edge and side-edge/tip his potential flow solution would presumably be closer to a "real" wing. The experimental results he uses for comparisons are from surfaces with sharp edges, at least for the rectangular wings.

Anyone know of experimental observations of the flow characteristis for sailboat keels and rudders of low aspect ratio and/or highly swept leading edges? How common is vortex generation from leading edges. The Delft keel series includes one of low aspect ratio, "232.3". The information I have from Fossati gives an AR of 0.28 but this appears to be the aspect ratio based on the keel draft and area. An equivalent wing AR (assuming for the keel the bottom of the canoe hull acts as a hydrodynamic mirror surface) would be 0.56. Unfortunately I don't have any specific performance data on the Delft keels.

Leo's charts of CL, etc go to 32 degrees. This is well beyond the normal operating range for keels and rudders except possibly when manuevering.

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### DCockeySenior Member

Perhaps "Hydrodynamics and Aerodynamics" since there is likely to be discussion of sails at some point.

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### Leo LazauskasSenior Member

It is a flat-ship type of analysis, but I have found a few tricks that help with the difficult numerics that bedevil some methods.

Here are some references to start you off.

Tuck, E.O. "Low-aspect-ratio flat-ship theory", J. Hydronautics, Vol. 9, 1975, pp. 3-12.

Tuck, E.O. and Dixon, A. "Surf skimmer planing hydrodynamics", J. Fluid Mechanics, Vol. 205, 1989, pp. 581-592.

Tuck, E.O. "The planing splash", 9th Int. Workshop on Water Waves and Floating Bodies, Kuju, Japan, 17-20 Apr. 1994, pp. 217-220.

Tuck, E.O. and Lazauskas, L., "Free-surface pressure distributions with minimum wave resistance", ANZIAM Journal, 43, 2001, E75-E101.

Tuck, E.O., Scullen, D.C. and Lazauskas, L., "Wave patterns and minimum wave resistance for high-speed vessels", 24th Symposium on Naval Hydrodynamics, Fukuoka, Japan, 8-13 July, 2002.

Tuck, E.O. " Slender planing surfaces", J. Engineering Mathematics, Vol. 58, 2007 pp. 289-299.

Also see the work of Lawrence J. Doctors, and by Cheng and Wellicome in the references cited in the above.

Good luck!
Leo.

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### Leo LazauskasSenior Member

Jen:
In addition to the above reply, see also Section 5.9 of the attached rough excerpt from "Applied Computational Aerodynamics" by W. H. Mason.

I'm not sure how you interpolate between the zero suction and 100% suction results for real airfoils as shown in Fig. 5-24. Maybe some of the practical people here can give us a clue.

Good luck!
Leo.

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### DCockeySenior Member

Leo,

My understanding of the use of "leading edge suction" (LES) in the calculation of lift and drag for wings with leading edge separation is very limited and perhaps faulty. I'm confused by the use of the LES which appears to be calculated without accounting for the effect of the leading edge vortex and/or separation bubble on the potential flow from which the LES is derived.

My look at several references has been very cursory but it seems like some of these models are of the type where the modifications are ultimately based on empirical adjustments which improve agreement with experimental results, and the link to fundamental physics my be rather tenuous beyond curves have similar shapes.

This isn't to say that such methods don't have appropriate uses, but rather that trying to use them to explain physical phenomena is frequently fundamentally backwards.

The above is not meant as a criticism of any of your work, just trying to better understand this area. Any thoughts you have would be welcomed.

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### DCockeySenior Member

From page 5-37 of the attachment Leo provided above (bolding was added by me):

"Of course, a very thin flat plate will realize almost none of the suction force, and hence will have a drag component. However, an airfoil section (even a fairly thin one) with a smooth round nose may in fact achieve nearly all of the suction force, at least at small angles of attack. If the airfoil section in the wing does not achieve the full suction performance, the resulting drag must be added to the induced drag."

"The drag due to lift is thus broken up into induced drag and additional profile drag. As described previously, the induced drag is a function of the wing spanload only, and is independent of the details of the particular airfoil used in the wing. The additional profile drag is associated with the airfoil used in the wing. At low lift coefficients this drag should be small, only becoming important as flow separation starts to develop on the airfoil section. The additional profile drag becomes large as wing stall is approached."

The last sentence of the first paragraph says to consider the added profile drag as if it was induced drag. But then the beginning of the second paragraph explains that the profile drag is different than induced drag. This is typical of the confusion in aerodynamics and hydrodynamics about induced drag. Not every drag increase due to lift production is induced drag.

Last edited: Mar 7, 2011
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### Leo LazauskasSenior Member

I agree with you, David, and I mention in the compendium that the LESA can be criticised on several points. That's why I have included the various components in the output. Users can choose whether the suction analogy is appropriate for their particular application. If so, they can see how each of the components in the LESA contributes to the total: if not, they can just use the potential values.

There are many other factors that should be considered, e.g. vortex contact, vortex bursting and asymmetry on low aspect ratio wings, and 2D bubble bursting on high aspect ratio wings. But, in truth, my only interest is in the solution of the lifting-surface equation. All else is just annoying "real" engineering.

Leo.

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### Mikko BrummerSenior Member

Strictly speaking, the keel or rudder can be considered "mirrored" only when the boat is standing still. As soon as the the boat gets moving, free surface effects should not be ignored: The effective depth (or aspect ratio) of a keel depends on Froude number. So, at speed the effective aspect ratio of the keel can be nearly halved (?) when the mirror effect fades and consequently induced drag will increase considerably. Whether you consider this effect as induced drag, or keel wave making drag can be questioned.

I know that some people maintain (but I don't know) that the relevant Fn for the keel (or rudder) is based on its own chord length, not the vessel LWL, so the keel Fn will rise very high very soon as the boat gets into speed. In this respect, there would be a difference in the induced drag of a short chord keel and a long chord one, at equal depth.

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