# Ground effect and Lift coefficient

Is there a correlation between the lift coefficient and the proximity between the wing and the ground? I know that the lift coefficient is dependent on angle of attack; However, based on experiments that I have conducted, the results disproved the claim somehow, at the same angle of attack (0 degrees), the lift generated is higher when in ground effect than out of ground effect. Based on the experiment, given that wind velocity, wing span and density (according to the ISA) is the same, does this meant that ground effect (proximity when in ground effect) can bring a change in lift coefficient? Moreover, is there a specific correlation,is it linear or exponential?

It is really weird how I can find literally anything but the correlation between proximity and lift (or lift coefficient), there are essay on how ground effect affects forward swept wing aircraft, and yet there's not a single essay about proximity and lift coefficient :(

Graph from https://www.faatest.com/books/FLT/Chapter17/GroundEffect.htm

My collected data

• According to Youtube, the lift is exponential to proximity when in ground effect Jul 17, 2021 at 12:29
• What is the source of your graphs? ANA? Should include citation in question. Jul 17, 2021 at 13:42
• I've learned, that a wing in ground effect behaves like having a higher aspect ratio. So i would guess this increase in cl-slope comes from higher virtual aspect ratio. But it is just a guess. Jul 17, 2021 at 14:17
• @JVAV_master what type of airfoil did you use? What do your results "disprove"? Jul 17, 2021 at 22:48
• "the lift generated is higher when in ground effect than out of ground effect" is pretty much the definition of ground effect. Jul 18, 2021 at 12:34

Setting the "experiment" aside for now, we can see that ground effect does indeed increase Lift. The first picture of the excellent reference Chapter 17 Ground Effect tells much. As one our most prominent writers often tells us, the vortex rolls off the entire trailing edge, not just at the wing tips.

Further reading compares ground effect (on induced drag) at 1 span length, 1/4 span length and 1/10th span length. 1/10th span length lowered induced drag by over 40%!

Reasons for this may lie beyond "coefficient of lift", which deals with airfoil type and Angle of Attack.

From the first picture, we can see downwash is reduced. From the graphs, stall (of the upper wing) occurs at lower AoA. This implies weakened circulation over the top of the wing, resulting in earlier flow separation. This would seem to make ground effect bad but ...

Greater lift is generated by increased air density underneath the wing. This is not unlike the phenomena of "water skiing" where the (much) greater density of water can hold up the entire weight of a person at less than 20 knots. Water skis are not know for their top lift.

There is also the thought that ground effect extends wingtip vortices away from the wingtip.

In summary, increased air density under the wing allows the plane to maintain lift at a lower AOA. Combined with reduced wing tip vortex drag, induced drag decreases as ground proximity increases.

• So is the increased air density under the wing a factor of the change in lift coefficient? Since I was thinking of using the ISA density at sea level to calculate the lift coefficient of the experiment. Jul 18, 2021 at 3:11
• JVAV_master well, technically, density Rho is considered separately in the Lift Equation, but you're on the right track. Jul 18, 2021 at 3:23
• Robert, at clearly subsonic speeds density changes very little, it is pressure that is increased on the lower side. Jul 18, 2021 at 3:41
• From PV=nRT one can express higher pressure from higher density. Certainly not comparable in strength to a shockwave, but over the entire bottom of the wing. Jul 18, 2021 at 4:11
• well with the experiment the wind speed is roughly around 3.4m/s, which is pretty slow but still works for a smaller model. Jul 18, 2021 at 13:39

As mentioned in this excellent answer, ground effect of aeroplanes can be modelled as extra lift from the mirror image of the plane. The image above depicts the effect on the tail plane, main wing is identical.

This Prandtl Lifting Line Theory can be explained as extra lift from the mirror image of the wing. Torenbeek Appendix G.7 contains some expansion of the ground effect with flaps extended, with three diagrams on its effect on airfoil lift, below.

Graph b. shows the two lift slopes of a wing in and out of ground effect. For a given angle-of-attack $$\alpha$$, there is indeed a higher $$C_L$$ in ground effect.

• I submit there is higher Lift for a given AoA. Coefficient of lift is AoA (and airfoil type). Could your "mirror image" also be the lower wing of a biplane? It is said most of the lift is from the upper wing but ... Jul 18, 2021 at 11:19

Ground effect is complicated. That is because it actually consists of at least two effects, subsumed under a single term:

1. The wake cannot continue downwards past the wing, so it is deformed when the ground blocks it, and
2. Air flow on the lower side of the wing is partially blocked.

The first effect depends on the height of the wing relative to wingspan and the second one on the height of the trailing edge relative to wing chord. Therefore, plotting all effects over one single parameter will only be valid for a narrow range of conditions, and omitting those makes the graph worthless.

Take angle of attack (AoA): At low AoA, the lift curve slope is higher than in free flow while at high angle of attack it becomes lower. Hing AoA means also high induced angles, so here the blocking effect of the wake by the ground becomes more pronounced and reduces induced effects. To say that "ground effect increases lift curve slope" is only valid for low AoA.

Next, AoA is based on the definition of the wing reference chord. It does not include the lift provided by camber, neither does it make clear how twist, changes in airfoils, flap deflections and washout change the local lift over span. Only when that information is included can ground effect be described properly.

Or look at how height is measured. Is that the height of the leading edge, or the quarter chord line or the trailing edge? Some authors even omit that distinction and seem to think it doesn't matter how height relative to the ground is defined. This also makes their graphs effectively worthless.

And then there are authors who present their results without labels or legends. Your question is testament to you being part of this distinct group. I am sorry to say that this makes your graph worthless as well.