The American-made Cessna 172 is the most popular aircraft in the world with a to

Question

The American-made Cessna 172 is the most popular aircraft in the world with a total of over 43,000 of its many variations being constructed since 1956. A typical Cessna 172 has a maximum takeoff mass of 1,157 kg and a total wing area of 16.2 m2. Assuming an air density of 1.225 kg/m3 and that the air over the top surface of the Cessna's wings on average flows 43.0 % faster during takeoff than over the bottom, compute the minimum take-off speed in both m/s and miles per hour. For simplicity, assume that the speed of the plane through the air and the speed of the air over the bottom of the wing are equal.

Explanation / Answer

Applying Bernolli equation between a point ovr the wing and another under it,

P1 - P2 = 1/2*(V22 - V12) = 1/2*V12((V2/V1)2-1) = 1/2*1.225*V2(1.432-1) = 0.64*V2

For takeoff, (P1-P2)*A = mg

So, 0.64*V2 * 16.2 = 1157*9.81

So, V = 33.1 m/s = 74 mph

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