In Soaring FAQ on Web page: 

http://www.geocities.com/Athens/3171/soar-faq.htm#589884

I read about aspect ratio (AR). Can author (I do not know who is) of this text (or 
someone else) help me with equations to calculate the optimum AR according to text. 

Any help will appreciated.

Thanks Brane V.

Here I quote the text:

A few days ago I sent out a critical reply to a discussion on aspect ratios. I did not 
however provide any insight or answers. I apologize and will make amends now. 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: Velocity=35ft/s, Average chord = 8", e inv = 0.98, Weight =6 lbs.
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: Velocity = 90ft/s, Average Chord =4 ft., weight =1000# (I made these 
numbers up, I don't know how accurate they are) 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. 

NOTE: These are approximate values, I used numerical CD methods to approximate the 
drag components. Accuracy could be improved by using wind tunnel drag data for your 
specific airfoil. (If you have the data available at your desired RE#) Well I hope 
this helps. If anyone would like a better explanation and the governing and optimizing 
equations, then e-mail me your mailing address, and I will be glad to send it to you. 
So why believe me? I am an Aerospace Engineer for NASA Ames Research Center, where I 
am a Test Manager at the National Full-Scale Aerodynamics Complex. I am also 
completing a masters degree this march, specializing in applied aerodynamics.

End of quote.


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