Final answer:
Using thin airfoil theory and the known relationship between the leading edge moment coefficient and the aerodynamic center moment coefficient, the most likely estimate for the NACA 2412 airfoil is option (c) Lift coefficient = 0.200, Moment coefficient about the aerodynamic center = 0.050.
Step-by-step explanation:
The NACA 2412 airfoil with a moment coefficient about the leading edge of -0.1 requires estimation of the 2D coefficients of lift and moment about the aerodynamic center using thin airfoil theory.
According to thin airfoil theory, the moment coefficient about the aerodynamic center (Cm_ac) for a symmetric airfoil is -0.25, and for cambered airfoils it typically ranges between -0.1 and -0.05 depending on the specific airfoil design. Given this information, we are looking for a combination of lift coefficient (Cl) and Cm_ac where the Cm_ac is consistent with the theory.
If the moment coefficient about the leading edge (Cm_le) is known to be -0.1, then we can use the relationship between the aerodynamic center and leading edge, which is Cm_ac = Cm_le + (Cl/4). Solving for Cl with the given Cm_le of -0.1, we obtain Cm_ac = -0.1 + (Cl/4).
Since the coefficient of moment about the aerodynamic center for a NACA 2412 airfoil is typically around -0.05 to -0.1, option (c) Lift coefficient = 0.200, Moment coefficient about the aerodynamic center = 0.050 seems most plausible, as it aligns with the general range expected from thin airfoil theory and the relationship between Cm_le and Cl.