A frequently quoted rule of thumb in aircraft design is that wings should produc

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.) At takeoff, an aircraft travels at 56 m/s. so that the air speed relative to the bottom of the wing is 56 m/s. Given the sea level density of air to be 1.29 kg/m3, how fast must it move over the upper surface to create the ideal lift? How fast must air move over the upper surface at a cruising speed of 242 m/s and at an altitude where air density is one-fourth that at sea level?

Explanation / Answer

According to the given problem,

Lift = ½A(U² - V²)

(a) 1000 N = ½ * 1.29kg/m³ * 1m² * (U² - (56m/s)²)
U = 68.457 m/s

(b) 1000 N = ½ * ¼ * 1.29kg/m³ * 1m² * (U² - (56m/s)²)
U = 96.63 m/s

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