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

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    Drag Induced
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Discussion Overview

The discussion centers around the optimal circulation for minimizing induced drag in a biplane configuration. Participants explore the complexities of induced drag, the influence of wing interaction, and the potential differences from single-wing configurations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that the circulation minimizing induced drag in a biplane may not be straightforward and could depend on various factors, including the aerodynamic interaction between the two wings.
  • One participant mentions that while an elliptical distribution is generally efficient for minimizing wing tip vortices, the upper wing operates in a "ground effect," which complicates drag predictions.
  • It is suggested that the stagger between the wings and their vertical separation significantly impact the induced drag on the lower wing, making predictions challenging.
  • Another participant believes that when the wings are very distant, they can be treated as independent wings, thus favoring an elliptical distribution, but acknowledges that finite distances introduce complex interactions.
  • A participant references an article that may provide further insights into the topic, indicating ongoing exploration of the question.

Areas of Agreement / Disagreement

Participants express differing views on the influence of wing interaction on induced drag, with no consensus on a single optimal circulation model for biplanes. The discussion remains unresolved regarding the specific effects of wing separation and configuration.

Contextual Notes

Limitations include the dependence on specific configurations of the biplane, the assumptions made about wing independence at large separations, and the unresolved nature of the empirical results related to interference drag.

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

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