Based on pure aerodynamics of the type mentioned in problem 12.9, bumblebees are not supposed to be able to fly. Assume that the average bumblebee has a mass of about \(0.9 \mathrm{~g}\), a wingspan of \(1.75 \mathrm{~cm}\), and a wing area of about \(1.3 \mathrm{~cm}^{2}\). Such a bee can fly at about \(10 \mathrm{~m} / \mathrm{s}\).

a. What sort of lift coefficient would be needed to support such a bee?

b. Given the flat plate expression for the lift coefficient, what kind of angle of attack is required?

The actual wing motion and what gives bumblebees their flying prowess is discussed in [26].

Problem 12.9

We introduced the concept of lift in conjunction with potential flow about a sphere. Plate-like objects such as your hand outside a moving car window also experience lifting force depending upon your hands “angle of attack” with respect to the direction of air motion. A positive angle of attack provides an upward force while a negative angle provides a downward force. We define a lift coefficient in the same manner we derive the drag coefficient as:

For a flat plate, it turns out the lift coefficient is related to the angle of attack by:

A falcon has a wingspan of about 80 cm with a wing area of about 0.11 m2. If the falcon has a mass of 0.6 kg and likes to glide at an angle of attack of about 6°, at what speed must the bird fly so that the lift force just balances out its weight? Assume standard temperature and pressure.

Transcribed Image Text:

CL T FL pvAp