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 as 1.29 kg/m^3, how fast must it move over the upper surface to create the ideal lift? (b) How fast must air move over the upper surface at a cruising speed of 245 m/s and at an altitude where air density is one-fourth that at sea level?

a) 90 m/s, 300 m/s
b) 120 m/s, 600 m/s
c) 150 m/s, 800 m/s
d) 75 m/s, 400 m/s

Answer 1

The question relates to calculating the necessary airspeed over an airplane wing at different speeds and altitudes to produce the required lift, using the known sea level air density and assuming Bernoulli's principle applies.

Step-by-step explanation:

The problem involves applying Bernoulli's principle to find the speed of air over an airplane wing necessary to produce a certain amount of lift. Given a standard sea level air density of 1.29 kg/m³ and a liftoff speed of 60.0 m/s for the underside of the wing, to generate 1000 N of lift per square meter using Bernoulli's principle, the speed of air over the upper surface must be greater than 60.0 m/s.

However, to provide an exact answer, we need to calculate the required speed difference using the lift equation and Bernoulli's equation, considering variables like the area of the wing as well as the pressures and speeds below and above the wing. For part (b), with a cruising speed of 245 m/s and a quarter of sea-level air density, a similar approach is used to determine the speed over the wing that would produce the desired lift at cruising altitudes.