A small plane has a wing surface area of 240 m^2 and it has a mass of about 15,

Question

A small plane has a wing surface area of 240 m^2 and it has a mass of about 15, 400 kg. The density of air is rho_air = 1.29 kg/m^3. Ignore the height different between the top and bottom of the wing, i.e. y_1 almostequalto y_2 almostequalto 0. During takeoff, the wind speed v_top = 70 m/s and v_bot = 63 m/s. Calculate top a) The minimum force require to takeoff. b) The pressure on the top of the wing c) The pressure at the bottom of the wing d) The net forces exerted by the pressures e) Can the plane takeoff at these conditions? Why?

Explanation / Answer

Here ,

a) minimum force to lift off = m * g

minimum force to lift off = 15400 * 9.8

minimum force to lift off = 150920 N

b)

pressure at the top = -0.50 * p * v^2

pressure at the top = -0.50 * 1.29 * 70^2

pressure at the top = -3160 Pa

c)

pressure at the bottom = -0.50 * 1.29 * 63^2

pressure at the bottom = -2560 Pa

d)

net force by pressure = (-2560 - (-3160)) * 240

net force by pressure = 143998 N

e)

No, the plane will not lift off

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