Question

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.

Answer 1

A. -0.003

B. 0.02

Step-by-step 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)

`q_(∞) =(1)/(2)\rho*v^(2)`

`q_(∞) =(1)/(2)1.225*100^(2)`= 6125 N/m²

`C_(mcg,w) =(M_(cg,w) )/(q_(∞)*S*C )`

`C_(mcg,w) =(-12.4)/(6125*1.5*0.45 )` = -0.003

`C_(mcg,w)= C_(ac,w)= -0.003` 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):

`C_(mcg) =(20.67)/(6125*1.5*0.45)` = 0.005

`C_(mcg,w) = C_(ac) ,w + C_(l)(h-h_(ac))`

`h-h_(ac)= (C_(mcg,w) -C_(ac,w))/(C_(l) )`

`h-h_(ac)= (0.005-(-0.003))/(0.4)`=0.02

the location of the aerodynamic center = 0.02