Consider a 2000 N airplane with 50 m^2 wing-area in a level cruise flight: sea-l

Question

Consider a 2000 N airplane with 50 m^2 wing-area in a level cruise flight: sea-level altitude, 150 m/sec velocity. If it is to execute a coordinated turn (constant altitude, constant velocity) at the same altitude with the same velocity with a bank angle of 10 degree, determine a) the magnitude of lift needed, b) the load factor n (=L/W), and c) the required change in angle of attack. The airplane's C_L - alpha characteristics is linear with a slope of 2 pi/rad. You may make additional assumptions, but only in case of missing data in this problem statement.

Explanation / Answer

a) The lift is given by the relation,

L = 1/2 x rho x V^2 x A x CLalpha

Since the aircraft is banked at an angle of 10 deg the component of W reduces to W cos 10.

During ideal flight conditions the L = W,

1/2 x rho x V^2 x A x Cl alpha = m x cos 10

1/2 x 1.25 x 150^2 x 50 x CL alpha = 2000 cos 10 / 9.81

CL alpha = 2.85 x 10^-4

b) Since the flight maintains a level flight at the same altitude and under ideal conditions the load factor L / W is 1.

c) The required angle of attack for the ideal airfoil is given by,

CLalpha = 2 pi alpha,

So alpha = CL alpha / 2 pi

alpha = 2.85 x 10^-4 / 2 x 3.14 = 0.00004 rad or 0.002 deg

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