Consider a model of a wing-body shape mounted in a wind tunnel. The flow conditions in the test section are standard sea-level properties with a velocity of 100 m/s. The wing area and chord are 1.5 m2 and 0.45 m, respectively. Using the wind tunnel force and moment-measuring balance, the moment about the center of gravity when the lift is zero is found to be -12.4 N-m. When the model is pitched to another angle of attack, the lift and moment about the center of gravity are measured to be 3675 N and 20.67 N-m, respectively. Calculate the value of the moment coefficient about the aerodynamic center and the location of the aerodynamic center.

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onyebuchinnaji onyebuchinnaji · Answer 1 · 2020-01-06T21:32:38+01:00

Answer:

A. -0.003

B. 0.02

Explanation:

Step 1: identify the given parameters

Giving the following parameters

Wing area (S)= 1.5 m²

Wing chord (C) = 0.45 m

Velocity (V) = 100 m/s

moment about center of gravity(Mcg) = -12.4 N-m

at another angle of attack, L = 3675 N and Mcg = 20.67 N-m

Step 2: calculate the value of the moment coefficient about the aerodynamic center (Cmcg)

[tex]q_{∞} =\frac{1}{2}\rho*v^{2}[/tex]

[tex]q_{∞} =\frac{1}{2}1.225*100^{2}[/tex]= 6125 N/m²

[tex]C_{mcg,w} =\frac{M_{cg,w} }{q_{∞}*S*C }[/tex]

[tex]C_{mcg,w} =\frac{-12.4}{6125*1.5*0.45 }[/tex] = -0.003

[tex]C_{mcg,w}= C_{ac,w}= -0.003[/tex] at zero lift

Step 3: calculate coefficient of lift

Cl = L/q*s

Cl = 3675/6125*1.5 = 0.4

Step 4: calculate the location of the aerodynamic center

New moment coefficient about the aerodynamic center (Cmcg):

[tex]C_{mcg} =\frac{20.67}{6125*1.5*0.45}[/tex] = 0.005

[tex]C_{mcg,w} = C_{ac} ,w + C_{l}(h-h_{ac})[/tex]

[tex]h-h_{ac}= \frac{C_{mcg,w} -C_{ac,w}}{C_{l} }[/tex]

[tex]h-h_{ac}= \frac{0.005-(-0.003)}{0.4}[/tex]=0.02

the location of the aerodynamic center = 0.02