Lift distribution on biplanes

Question

This Wikipedia page about biplanes says

in a wing of aspect ratio 6, and a wing separation distance of one chord length, the biplane configuration will only produce about 20 percent more lift than a single wing of the same planform.

My question is, does the wing of biplane share the lift load 50/50 ?
Secondly, what is the formula for calculating the interference drag of a biplane?

Answer 1

If both wings have the same incidence and the wings are not staggered (= they sit at the same lengthwise location along the fuselage), then yes, their lift is split equally between both.

Most biplanes were (and sometimes still are) single- or two-seaters and in order to give the pilot good forward and upward visibility, the upper wing is shifted forward a bit (positive stagger). This will place it closer to the upwash (flow field ahead of the wing with increased angle of attack) of the bottom wing and in turn place the bottom wing closer to the downwash (flow field past the wing with reduced angle of attack) of the top wing. This effect becomes stronger with increasing angle of attack of the whole biplane, in line with the lift coefficient. With positive stagger, the upper, forward wing carries the majority of the load. How much that is depends obviously on the amount of stagger.

The formula for the interference drag is the Biot-Savart law which describes the effect of one lift-creating object on its surroundings. Since both wings interfere mutually, the solution is not straightforward but needs several steps:

1. First, the location of a lift-creating vortex and its two trailing vortices is defined. A wing should be split into several sections which all have their own vortex strength. The more sections, the more precise the result will be. For a biplane this needs to be done twice, of course.
2. Then a number of points where the local flow direction is prescribed must be defined. Whereas the vortex usually is located at the quarter of the wing chord, those points are best placed at three quarters of the wing chord; again spread over the span of the wings. They are called control points.
3. Now the influence of a particular vortex on a particular control point is described using the Biot-Savart law. After this has been done for all vortices and all control points, those influences define a matrix.
4. By solving the matrix equation for tangential flow at the control points, the strength of the single vortices in the influence of all other vortices can be calculated.

A more elaborate description of the process can be found in NASA Technical Note D-5335.