Load Distribution on a Tapered Wing

[rxmelaun]

I cannot find a formula for calculating load distribution on a tapered wing. I am calculating deflection of a spar and the formula I'm using (D = WL^4/8EI where D is deflection) assumes that w is a uniform load along the span. I'm not sure if that assumption is correct for the wing design (I do not think it is as the wing has a taper ratio of .48) or if the assumption makes the results pessimistic (actual deflection will be less than calculated) or optimistic (deflection greater than predicted). Obviously, I'd prefer the former or, better still, something resembling reality.

Rich

 

[astroclone]

Reality in engineering? Pshaw! We're inventing letters now, we already got the imaginary numbers.
Anyway, pay no attention to the engineer who thinks he's funny.

So, go to John Anderson's book Fundamentals of Aerodynamics and I believe it is chapter 5 that has a decent numerical procedure for calculating the spanwise lift distribution of a wing.
That is all,
Tony

 

[rxmelaun]

Thank you so much -
Rich

 

[laro]

get connected to Desktop Aeronautics, Inc. for procurement of one of the appropriate programs. one of the best sources for classic wing designs.

 

[pja]

Loading will decrease toward the tip for a tapered wing..however the larger taper the larger the local loading(while still being less than root loading)

 

[rxmelaun]

Thanks guys - hadn't seen Desktop Aero; I've sent them an e-mail regarding LinAir 1.4 as it appears to fit my needs.
I think my planform comes close to the "ideal" elliptical lift distribution - if I get the washout correct.

I did a quick & dirty calculation using the so-called Schrenk method cited in Alex Strojnik's "Laminar Aircraft Design." When I plot the local Cl I get a hump in the distribution about 2/3 out on the semispan. Since I plan to use a slotted single-element flap, and haven't accounted for that in the calculation, my biggest fear is a nasty tip stall. Guess that's what I get for using a tapered planform.

Thanks again for the suggestions.
rich

 

[Mattoo]

you might also want to check for gust loading on your wing

 

[Sparweb]

When you put out a flap, you change the incidence of the wing in the flapped area. Now you don't need to pitch the nose of the aircraft so high to get the necessary total lift. While this is happening, the flapped area is at a high angle of attack, but the unflapped area is at a LOWER angle of attack than it once was.
Your lift distribution will completely change if you have a partial span flap installed. I expect you would find that the tip of the wing has a lower Cl with the flaps out. Tip stall becomes less of a problem if this is the case.


STF

 

[cawiddison]

Rich
You can remove the hump in the spanwise loading by using washout - twist the wing so that the incidence of the airfoils decreases from root to tip.

 

[DORD2002]

Another good source for determining the lift dist across a tapered wing is "Theory of Wing Sections" by Ira H. Abbott and Albert E. Doenhoff. The discussion and calculations in this book take into account different airfoils at the root and tip of the wing. Very informative book!