[Courtesy of Gavin Botha [gbotha "at" mail.arc.nasa.gov], August 1999]
I wrote the text referenced below. I have replied to Brane off line, but though I had better provide some expalaination here on the exchange before the messages start flying.
The text in reference was written about 3 years ago in direct reference to comments being made about higher AR being more "efficient" and providing better performance. That post was followed up by a spreadsheet table listing L/D and sink rates for various AR versions of the theoretical model. Better explainations were also provided regarding the optimization logic. The main objective at that time was to illustrate that there are limits to AR, and that higher AR does not always mean better.
The main logic was that if you started with a wing with fixed span and were optimizing for Max L/D there was a point where a the trade-off between L/D and sink rate becomes evident. Increasing AR beyond this point has minimal L/D improvements, but significant sink rate increases. There is no "real" optimum AR, It is highly dependant on what you are trying to optimize, and what physical constraints you have (ie 60" 2m class etc). If I remember correctly my spread sheet told me that if you were trying to optimize this particular theoretical model for minimum sink (like a floater type model) you would end up with an optimum AR of about 10. If you wanted to optimize for maximum L/D (without sacrificing too much sink rate), then you would end up with a AR of about 14 or 15. This seems to hold true to present designs. The other point being empahsized at the time was the efficiency e (as in Oswalds Efficiency factor) actually decreases as AR increases, so despite higher AR wings having better L/D, the true 'efficiency' is actually lower than a lower AR wing. This is due lift induced viscous drag.
-------- Original Message ---------
Many people have asked for value of the best AR, instead of technical jargon. So I wrote a program that looks at all of the drag components and optimizes AR for a Maximum L/D condition.
NOTE: The optimum AR depends highly on flight condition (High lift, low >lift etc.), so I picked max L/D as a good overall optimization point.
First a quick discussion on the optimization process, (without longequations)
Cd=Cdp+Cd(vortex)+Cd(lift dependent viscous),
Where Cdp is the parasite drag and is a function of (Re#, wing thickness, and skin friction coefficient). Cd (vortex) is the inviscid vortex drag and is a function of (lift coefficient, Aspect Ratio and inviscid wing efficiency (e inv)). The Last term is the lift dependent drag coefficient and is a function of (Cdp and lift coefficient)
For best L/D
Cdp=Cd(vortex)+Cd(lift dependent) (a fact, trust me).
Combining these equations and balancing RE# effects with AR effects, an optimum AR can be determined.
Here are some results. Starting assumptions:
Results: OPTIMUM AR =12.5, corresponds to 100" span
NOTE: overall wing efficiency at this condition (e = Oswalds efficiency >factor) is 0.8
Using the same method and calculating optimum AR for a full-size glider Starting assumptions:
Results: Optimum AR = 25, wing efficiency =0.74
These results clearly indicate that as RE# decreases, optimum AR also decreases, which is why Full-size AR are not efficient at model RE#'s.
Also wing efficiency decreases as AR increases, due to viscous effects.
These last two facts are what I previously posted without the explanation.