Question

A frequently quoted rule of thumb in aircraft design is that wings should produce about (1000 N) of lift per square meter of wing. (The fact that a wing has a top and bottom surface does not double its area.)

(a) At takeoff, an aircraft travels at (60.0 m/s), so that the airspeed relative to the bottom of the wing is (60.0 m/s). Given the sea-level density of air to be (1.29 kg/m^3), how fast must it move over the upper surface to create the ideal lift?
a) (45.0 m/s)
b) (75.0 m/s)
c) (90.0 m/s)
d) (120 m/s)

Answer 1

To create the ideal lift, air must move over the upper surface of the wing at a speed of 45.0 m/s.

Step-by-step explanation:

To calculate the speed at which air must move over the upper surface of the wing to create the ideal lift, we can use Bernoulli's principle. According to Bernoulli's principle, as the airspeed increases, the pressure decreases. In this case, the airspeed relative to the bottom of the wing is given as 60.0 m/s. Since the pressure on the lower surface is higher than that on the upper surface, the air on the upper surface must move faster to create the ideal lift.

To calculate the required speed, we can use the equation:

P_upper = P_lower + ½ ρv^2

Where P_upper is the pressure on the upper surface, P_lower is the pressure on the lower surface, ρ is the density of air, and v is the speed of air. Rearranging the equation, we can solve for v:

v = sqrt(2*(P_upper - P_lower)/ρ)

Given that the density of air is 1.29 kg/m³ and the lift per square meter of wing is 1000N, we can substitute these values and calculate:

v = sqrt(2*(1000N)/(1.29 kg/m³)) = 45.0 m/s

Therefore, the air must move over the upper surface at a speed of 45.0 m/s to create the ideal lift.