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:

\[C_{L}=\frac{F_{L}}{\frac{1}{2} ho v_{\infty}^{2} A_{p}}\]

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

\[C_{L}=2 \pi \sin (\alpha) \quad \alpha-\text { angle of attack(radians) }\]

A falcon has a wingspan of about \(80 \mathrm{~cm}\) with a wing area of about \(0.11 \mathrm{~m}^{2}\). If the falcon has a mass of \(0.6 \mathrm{~kg}\) and likes to glide at an angle of attack of about \(6^{\circ}\), at what speed must the bird fly so that the lift force just balances out its weight? Assume standard temperature and pressure.