Question

Consider a thin symmetrical airfoil of chord length c. It is equipped with a simple flap

at the rear of the airfoil that is one quarter the length of the airfoil.

If the flap is deflected downward through an angle = 10° and the freestream is at an angle of attack = 5° (relative to the unflapped airfoil), estimate lift coefficient, c, and moment coefficient about the leading edge, cm,LE.

Answer 1

To estimate the lift coefficient (Cl) and moment coefficient about the leading edge (Cm,LE) of an airfoil with a simple flap, we can use equations that consider the contributions from the flap and angle of attack.

Step-by-step explanation:

Given an airfoil with a simple flap at the rear, we can estimate the lift coefficient and moment coefficient about the leading edge. The lift coefficient (Cl) is a dimensionless quantity that relates the lift generated by the airfoil to the dynamic pressure of the air. The moment coefficient about the leading edge (Cm,LE) accounts for the pitching moment exerted on the airfoil.

To estimate Cl, we can use the equation:

Cl = Cl0 + Cl_f + Cl_a

where Cl0 is the lift coefficient of the unflapped airfoil, Cl_f is the contribution from the flap, and Cl_a is the contribution from the angle of attack. Since the flap is one quarter the length of the airfoil, we can assume that Cl_f is one quarter of the increase in lift coefficient due to the flap deflection.

To estimate Cm,LE, we can use the equation:

Cm,LE = Cm,0,LE + Cm,f,LE + Cm,a,LE

where Cm,0,LE is the moment coefficient about the leading edge of the unflapped airfoil, Cm,f,LE is the contribution from the flap, and Cm,a,LE is the contribution from the angle of attack. Similar to Cl, we can assume that Cm,f,LE is one quarter of the increase in moment coefficient due to the flap deflection.