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, an aircraft travels at 58 m/s, so that the air speed relative to the bottom of the wing is 58 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? v_2 = (b) How fast must air move over the upper surface at a cruising speed of 240 m/s and at an altitude where air density is one-fourth that at sea level?

Explanation / Answer

(a) According to Bernoulli's equation,

P + (v2)/2 + gh = 0

Here, P = 1000 N/m2, h = 0 (negligible height difference between the upper and lower portions of the wing)

So,

1000 + [1.29 * (582 - vtop2) / 2] = 0

=> vtop = [582 + (2 * 1000 / 1.29)]1/2 =  70.1 m/s

(b) Applying Bernoulli's equation again, we get,

1000 + [(1.29 / 4) * (2402 - vtop2) / 2] = 0

=> vtop = [2402 + (2 * 1000 * 4 / 1.29)]1/2 = 252.6 m/s

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