What is the optimal circulation for minimizing induced drag in a biplane?

[traianus]

Hello,
Does anyone know what is the circulation that gives the minimum induced drag in a biplane? Is it elliptical like a single wing?
Thanks

 

[RainmanAero]

Hello,
Does anyone know what is the circulation that gives the minimum induced drag in a biplane? Is it elliptical like a single wing?
Thanks

Interesting question. And as always, the answer begins with "it depends...". The main thing to understand is that, while induced drag is important, it may not be the most important consideration in a bi-plane design. The aerodynamic interaction of the two wings can become significantly more important depending on the specific configuration. Some analysts have even given a name to a different type of drag in such cases and called it "interference drag". Basically, empirical results have shown that Total Drag <> Drag of Body A + Drag of Body B when the two bodies are flying in vicinity of one another.

In general, the elliptical distribution is still the most efficient for the upper wing in a biplane configuration because it will still minimize wing tip vortices. But when you think about it, the upper wing is also operating in what is similar to "ground effect". Ground effect aerodynamic theory tells us we do get more lift (from the "air cushion" effect) but we also create more drag which (empirically) is a function of the height of the wing above the fixed surface (in this case the lower wing) divided by wingspan.

Predicting induced drag on the lower wing is where things get difficult. Even if you assume the same wing shape, wing span, and dihedral (if any) as the upper wing, one of the biggest parameters that will impact its induced drag is how much stagger (fore/aft) exists between it and the upper wing. And of course the distance between the two wings will also affect the shape of the "lift bonnet" created by the lower wing and its interference with the flowfield from the upper wing.

Like I said, it is an interesting question, but not as straightforward as one would hope.

Rainman

 

[traianus]

Thank you for you very good answer.
I think that when the two wings are very very distant from a practical point of view they can be viewed as two independent wings (no interaction) and so the "best" distribution is the elliptical one. What about when the distance is finite? the wings A and B influence each other in a not clear way.

 

[traianus]

It seems that I found the answer to my questions. See the article

http://pdf.aiaa.org/jaPreview/JA/2006/PVJA15982.pdf