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.)

(a)At takeoff the aircraft travels at 61.0 m/s, so that the air speed relative to the bottom of the wing is 61.0 m/s. Given the sea level density of air to be 1.29 kg/m3, how fast (in m/s) must it move over the upper surface to create the ideal lift?

(b) How fast (in m/s) must air move over the upper surface at a cruising speed of 250 m/s and at an altitude where air density is one-fourth that at sea level? (Note that this is not all of the aircraft's lift--some comes from the body of the plane, some from engine thrust, and so on. Furthermore, Bernoulli's principle gives an approximate answer because flow over the wing creates turbulence.)

Explanation / Answer

Lift = ½A(U² - V²)

(a) 1000 N = ½ * 1.29kg/m³ * 1m² * (U² - (61m/s)²)

= 1000N = 0.645U^2 - 2400
U = 72.60 m/s

(b) 1000 N = ½ * ¼ * 1.29kg/m³ * 1m² * (U² - (61m/s)²)

= 1000N = 0.16125U^2 - 600
U = 99.61 m/s

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