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 63 m/s, so that the air speed relative to the bottom of the wing as 63 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? (b) How fast must air move over the upper surface of m/s and at an attitude where air density is one-fourth that at sea level?

Explanation / Answer

(A)

From bernoulli's equation,

P1 + (1/2)rho*v1^2 = P2 + (1/2)rho*v2^2

rho*v2^2 = 2(P1 - P2) + rho*v1^2

v2 = sqrt (2(P1 - P2) / rho + *v1^2)

v2 = sqrt (2*1000 / 1.29 + 63^2)

v2 = 74.3 m/s

(B)

Speed of air on upper surface of air is,

v2 = sqrt (2(P1 - P2) / rho + *v1^2)

v2 = sqrt (2*1000 / (1.29/4) + 243^2)

v2 = 255.44 m/s

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