Aspect ratio of multi-element wing?

[fpm]

Hi, I've had great help on here before, so I hope you guys can maybe help me out this time too!

Its a simple question:
I know how to calculate the aspect ratio of a simple rectangular wing, but how do I do it if the 'wing' consists of more than one element?

Is it (AR1+AR2+AR3)/something??, or do you consider the chord of the entire system (i.e leading edge of wing 1 to trailing edge of wing 3), and treat it all like a bigger rectangular wing?

Thanks a lot.
FP

 

[rb1957]

when you say "multi-element wing" do you mean (as i first thought) a wing with retractable slats and flaps or three fixed wings flying in close formation.

if the latter, i suspect that horner "Fliud Dynamic Lift" should hace something about the effective chord of closely spaced wings. intuitively, it'll depend on the spacing and the relative pitch orientation of the wings (to account for the leading planes downwash).

 

[fpm]

Thanks rb1957,
I'm looking at a racecar wing with a main plane, and 2 trailing edge flaps.
Thanks,
FP

 

[rb1957]

i think you're aking a very complicated question, and providing very little information.

possibly the best approach is to model the configuration in a CFD program, as i think the answer is highly dependent on foil profile, lay-out, etc ...

i assume you're mostly interested in maximising downforce and 2ndly minimising drag. why focus on aspect ratio ?

 

[rb1957]

a quote from horner "fluid dynamic lift", pg 20-12 ...

"a pair of tandem wings [of the same design] is expected to have together a lift curve slope equal to that of one wing [of the same profile] having twice the chord and 1/2 the aspect ratio"

that'd imply that if the folis are all the same (and not inclined relative to each other) that you just "merge" them together. but i suspect in your case the different foils are chambered differently, inclined to one-another, etc.

i suspect too that most of the effect you're looking for is accounted for by the foil acting as a deflector and less like a classical wing.

i'd look into car aerodynamics texts for your answer.

 

[fpm]

Thanks again rb...
In one way it was more out of curiosity to be honest, as I realised I'd never seen anything about calculating the aspect ratio of a multi-element wing.
As you guessed, the flaps are not only different profiles to the main plane, but also inclined!
I will be running some CFD, but I wanted to be able to do some calculations as well, to have something to check the CFD against.
As my time on CFD will be limited, I've been playing with Foilsim to narrow in on the best configs to spend time on using CFX. Although its 2D, it does take in an aspect ratio value, and it does have quite an effect on Lift coeffs (as you'd expect). So its difficult for me to do meaningful comparisons using Foilsim without haveing a correct AR for multi-element wings.
I'm not going to have time to run dozens of configs in CFX...
FP