# How to calculate forces and moments on an aircraft in ground effect

I am looking to calculate the six degree of freedom forces and moments (lift, drag, side force, roll, pitch, yaw moments) on an aircraft (fixed wing) in ground effect, but I do not know how to do this. Any suggestions will be very much appreciated.

Thank you

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
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Commented Jan 29, 2023 at 23:41
• Hello Lilliane. What you are asking is kind of clear to me, as I have done something similar in the past. Knowing what is your starting point would help in giving you an answer. Commented Jan 30, 2023 at 6:03
• @Federico thank you for your reply. I am basically trying to determine the change in lift, drag, side force, roll moment etc when the aircraft is in ground effect compared to out of ground effect. I cannot really find any equations to do this so I came on here Commented Jan 30, 2023 at 10:21
• For the pitch effect of ground effect please see this answer Commented May 4, 2023 at 19:33

I am basically trying to determine the change in lift, drag, side force, roll moment etc when the aircraft is in ground effect compared to out of ground effect.

There is no way to do this in a reliable manner without conducting a flight test measurement campaign.

You can find rule of thumb formulas in books, such as Roskam's "Airplane Aerodynamics and Performance", but they will never be very accurate.

In Roskam there is a reference to "Fundamentals of Aircraft Design" from Nicolai as the source of a diagram linking $$A/A_{eff}$$ to $$2h/b$$, but no explicit equation is given.
Roskam provides the following equation for the change in effective angle of attack:

$$\Delta \alpha_0 = \frac{t}{c} \left( -0.1177\frac{1}{(h/c)^2} +3.5655 \frac{1}{(h/c)} \right)$$

Then, applying this equation they derive the change in lift coefficient:

$$C_{L_g} = C_L \frac{C_{L_{\alpha_g}}}{C_{L_\alpha}} - C_{L_{\alpha_g}}\Delta \alpha_{0_g}$$

For induced drag the following equation is offered

$$\Delta C_{D_{i_g}} = -\sigma' \frac{C_L^2}{\pi_A}$$

with

$$\sigma' = \frac{1 - 1.32(h/b)}{1.05 + 7.4(h/b)}$$

"Wing resistance near the ground" from Wieselberger, aka NACA TM 77 is cited as reference.

No other formula is provided.

Having tried to use this in the past, I would like to stress that these might be useful to get a feeling for the quality of the changes, but they are absolutely not a sufficient substitute for proper modelling or in-flight measurements to get a representative quantitative behaviour.

• Thanks a bunch! which edition of the book are these in? do you know if there are any formulas for the pitching moment or yawing moment in ground effect? Commented Jan 30, 2023 at 14:26
• @LillianneF there's no other formula. I think I have the first edition, but I can double check later. Commented Jan 30, 2023 at 15:03