Wing configuration - Biplane

Keywords

aircraft design, wing, biplane, aerodynamics, drag, lift, induced drag

Let us assume that a wing configuration is required to generate \(L = W\) lift. We can generate this lift with a single wing, or with two wings. The question is, which configuration is better from the perspective of aerodynamics? The answer is not straightforward, and depends on the design requirements. In this section, we will discuss the advantages and disadvantages of the biplane configuration.

Firstly, we note that both the configurations will have to generate the same lift. Criteria for merit is obviously the drag generated by the configuration. Aerodynamics group will prefer a configuration that generates the least amount of drag to generate the requisite lift.

We also note that drag as two major components: skin friction drag (\(C_{D_0}\)) and induced drag (\(C_{D_i}\)). Skin friction drag only depends on the wetted surface area of the wing, while the induced drag is influenced by the aspect ratio of the wing (\(C_{D_i} = \frac{C_L^2}{\pi e AR}\)).

Important

Throughout this discussion, we assume that the we are dealing with a rectrangular with with constant airfoil section along the span. Same airfoil section is used for monoplane as well as biplane configuration.

Also, in the biplane configuration, both the wings are assumed to be identical.

Since the monoplane and biplane configurations are made of similar wings, the Oswald efficiency factor \(e = e_1 = e_2\) is assumed to be the same for both the configurations.

Scenario 1: Same area, same span

We have

\[ S = S_1 + S_2\ \text{and}\ b = b_1 = b_2. \]

This means that effectively the chord of the biplane wing is half the chord of the monoplane wing and the aspect ratio is double.

\[ c_1 = c_2 = c/2 \ \Rightarrow \ AR_1 = AR_2 = 2\,AR\ \Rightarrow\ \ K_1 = K_2 = K/2. \]

Since,

\[ L = L_1 + L_2,\ \Rightarrow\ \ C_L = C_{L_1} + C_{L_2} \]

The induced drag can be compared as

\[ \frac{D_i}{D_{i_1} + D_{i_2}} = \frac{C_{D_i}}{C_{D_{i_1}} + C_{D_{i_2}}} = \frac{K C_L^2}{K_1 C_{L_1}^2 + K_2 C_{L_2}^2} = \frac{2 C_L^2}{C_L^2 - 2 C_{L_1} C_{L_2}} = \frac{1}{0.5 - C_{L_1} C_{L_2}/C_L^2} \]

\[ C_{D_i} = \frac{C_L^2}{\pi e AR} = \frac{C_{L_1}^2}{\pi e AR_1} + \frac{C_{L_2}^2}{\pi e AR_2} \]

Clearly, the skin friction drag will be doubled from monoplane to biplane. However, the induced drag will be halved from monoplane to biplane. The net effect is that the biplane configuration will have a lower drag coefficient than the monoplane configuration.

Advantages

The biplane configuration has the following advantages:

• The biplane configuration has a higher lift coefficient than a single wing of the same span. This is because the biplane configuration has a higher aspect ratio than the single wing. The higher aspect ratio reduces the induced drag, and therefore the lift coefficient can be higher.

Disadvantages

The biplane configuration has the following disadvantages:

• The biplane configuration has a higher drag coefficient than a single wing of the same span. This is because the biplane configuration has a higher wetted area than the single wing. The higher wetted area increases the skin friction drag, and therefore the drag coefficient can be higher.