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/m^3, 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

a)

We will use Bernoulli’s equation,

P=1/2**(v22 – v12)

Flift/A = 1/2**(v22 – v12)

Flift= 1/2*A**(v22 – v12)

Plugging given data,

1000= ½*1.29*(v22 – 56^2)

v2 = 68.46 m/s

b)

1000= ½*1.29*(v22 – 242^2)

v2 = 245.18 m/s

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