Question

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In prewar days there was a controversy, perhaps apocryphal, about whether the bumblebee has a legitimate aerodynamic right to fly. The average bumblebee (Bombus terrestris) weighs 0.88 g, with a wing span of 1.73 cm and a wing area of 1.26 cm². It can indeed fly at 12.5 m/s. Assume sea-level air, ρ = 1.225 kg/m³.

Using fixed-wing theory, determine the lift coefficient of the bee at this speed. Round the answer to two decimal places.

The lift coefficient is

Answer 1

Given Data:

Average bumblebee weight, m = 0.88 g

Wing Area, A = 1.26 cm²

Span, a = 1.73 cm

For sea level air at 20 ^oC

density of air, $\rho = 1.225\ kg/m^3$

Aspect ratio of airfoil is given as,

$AR=\frac{a^2}{A}=\frac{1.73^2}{1.26}=2.38$

Lift coefficient is given as,

$C_L=\frac{2W}{\rho A V^2}=\frac{2\times 0.88\times 10^{-3}\times 9.81}{1.225\times 10^2\times 1.26\times 10^{-4}}=1.12$

As drag coefficient is approachging maximum value $C_L\rightarrow C_{L, max}$ and bee could not fly slower than 10 m/s so its unrealistic situation.