# Estimating Moment Coefficient about Aerodynamic Center for wing-body combination

Are there any references or analytical methods to estimate the moment coefficient about the aerodynamic center, C_M,ac for a given wing-body combination? Even something rough would be useful such as "adding fuselage to the wing increases magnitude of CMac by ~x%". If anything, I'm looking for a conservative estimate that overpredicts C_M,ac for some 1st principals structural calcs.

I understand that C_M,ac for the wing alone can be obtained from XFOIL/airfoil databases. Adding a fuselage will contribute a negative increment to C_M,ac. The resulting C_M,ac for wing-body is usually measured in a wind tunnel.

Wind tunnel measurements are used to characterize interference effects between the wing and fuselage, which are difficult to predict theoretically. Because of this, the moment due to the wing-body combination isn't simply just the sum of the separate wing and fuselage moments. This being understood, I wonder if the sum of individual moments would give a conservative estimate for C_M,ac that I can use.

In this case the NACA report 711 is your friend.

It gives a very easy empirical equation to evaluate the fuselage's moment coefficient based on flight tests. The report is quite old but if your fuselage has a conventional shape then the value given by this equation should be reasonable.

$$\frac{dC_m}{d\alpha}=\frac{k_fw²_fL_f}{cS}$$

where:

• $$\frac{dC_m}{d\alpha}$$ is the moment coefficient's derivative, i.e. the variation of the moment coefficient in respect to $$\alpha$$;
• $$k_f$$ is an empirical value given by the following plot;
• $$w_f$$ is the fuselage's width;
• $$L_f$$ is the fuselage's length;
• $$S$$ is obviously the wing surface;
• and $$c$$ the mean aerodynamic chord.

Units of measurement are feet and degrees.

• Thank you sophit - this is very helpful. I also found NACA Report No. 540 to be super useful as well (one of the references in Report 711)
– Seth
Oct 18, 2022 at 20:58
• @Seth: I'm glad I could help :) Oct 19, 2022 at 0:45