An airplane cruises at 10,000 ft, with a velocity equal to 341 mph (500 ft/s). T

Question

An airplane cruises at 10,000 ft, with a velocity equal to 341 mph (500 ft/s). The aircraft has a gross weight equal to 10,000 lbf. The wings have a combined plan area equal to 145 ft^2, and an aspect ratio equal to 5.0. The wing design has similar cross sections based on a standard NACA cambered airfoil, with the ratio of maximum camber to chord equal to 0.0175. Using basic airfoil theory, estimate the required angle of attack at this condition. Assume that the fluid is at 23.5 degree F, 10.1 psia (p = 0.00176 slugs/ft^3, mu =3.52 times 10^-7 lbf s ft^2, v = 2.01 times 10-4 ft^2/s).

Explanation / Answer

Given

U = 500 ft/s

W = 10000 lbf = 321700 lb-ft/s2

A = 145 ft2

= .00176 slugs/ft3 = 0.057 lb/ft3

Aspect ratio = 5

But, Aspect Ratio = Wing span/Mean Chord = b/C = b2/A

From here, b2 = 5 * 145

b = 26.92 ft

Also as, Aspect Ratio = b/C

Therefore C = 5.39 ft

Now for steady state condition:

Weight of airplane = 0.5 CL . . A . U2

From here,

CL = 0.16

Also we know,   CL= 6.28 * sin

So,    = 1.45 degree

Where is the required algle of attack

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