Originally Posted by ShoeDLG

I think ground effect offers a very clear example of where the air's rate of momentum change may not be equal to lift.

Perhaps, although I also think it easy to explain ground effect in a way that keeps the momentum equality in place.

As you correctly stated the streamlines of airflow change when a wing enters ground effect. So the dynamics of the wing's effect on the air changes. It seems reasonable that these changes in airflow would alter the momentum change imparted. This change does not require the ground's force on the air to be included. The ground is involved, but the effect upon the wing is explained by the changed response of the air to the wing.

It is also my understanding that the air pressure under the wing increases in ground effect, and that could be used as the explanation for the increased lift. I don't think that explanation is wrong, but I think that the second law still needs to satisfied, and I think it is. If the air pressure is higher, then the air is more dense. If the wing deflects the same volume of air as when out of ground effect (that is an assumption on my part, I have no proof but it seems reasonable) then the mass of deflected air increases. Momentum is proportional to mass not volume, so the second law is still satisfied.

You can certainly propose an explanation of ground effect where lift and momentum transfer are balanced. The question then becomes: does your description accurately represent what is taking place? Given that global application of Newton's Second Law is not sufficient to determine whether or not lift and momentum transfer are balanced in ground effect, you have to look somewhere else to validate your description.

You could measure the rate of change of momentum transfer taking place directly, but that is extremely tedious. You could instead apply conservation of mass, momentum and energy, not in a global sense, but to each element of the air surrounding the wing. When you do this, you arrive at a coupled set of 5 non-linear partial differential field equations. By solving these equations (or an appropriately simplified version of them) subject to the appropriate boundary conditions, you can predict the flow conditions at any point in the air flowing around the wing.

With these predictions in hand, you can define a volume of air surrounding the wing, and sum up all of the momentum change taking place inside it. When you do this, do you find that the rate of momentum change is equal to the lift?

Sometimes you do, sometimes you don't. It depends on the extent to which the wing is in ground effect. And even when the wing is "completely" out of ground effect, it depends on the volume of air you consider. So what is the correct choice of volume to consider? The answer is a volume that includes all of the air being accelerated by the wing. By making the volume very big, you might think you would be able to account for all of the air accelerated by the wing. It turns out that you can't ever quite get there. Even with a very large volume, making it just a bit wider (along the wingtip-to-wingtip axis) will always reduce the rate of momentum transfer, and making it taller will always increase the rate of momentum transfer. The end result is that you can get any answer you want between no momentum transfer and transfer equal to the lift. This is entirely consistent with Newton's Laws because the net force acting on the boundary of the volume is always equal to the rate of momentum change inside the volume (as the volume changes, so do the forces acting on its boundaries). An outline of how you might approach this analysis is provided here.

So when a wing is out of ground effect, you can always identify a large volume of air surrounding the wing inside of which the downward momentum is changing at a rate equal to the lift. But at the same time you can also always identify a large volume of air surrounding the wing inside of which the downward momentum isn't changing at all.

What this means is that you cannot (correctly) say that the lift on a steadily translating wing is purely a result of the wing pushing down on the air and imparting downward momentum to it (as you can for a rocket or a rotor hovering far above ground effect). Saying that a wing creates lift by pushing down on the air with the same force that the ground pushes up on the air (with no net momentum transfer) is an equally valid description.

I think if you read my posts carefully, you'll find that I'm not suggesting that a momentum-based description of lift is wrong. What I am suggesting is that a "pure momentum" description of lift breaks down in ground effect, and presents a misleadingly incomplete description of how a wing interacts with the air when out of ground effect.

Wow! I think we are all [or at least more than a few] finally on the same planet or page .... having arrived by different paths in many cases.

Can we quit now? [just joking: the exercise has involved quite a bit of healthy brain-stretching!]

Originally Posted by xlcrlee

Can we quit now?

We can perhaps quit for now, but someone will eventually come back exclaiming that NASA says lift comes from Newton (without acknowledging the limited extent to which that is true).

The attached image shows a comparison of the streamlines around a NACA 0012 airfoil at 9 degrees AOA with a chord-based Reynolds Number of 3,000,000. The blue lines correspond to no ground present, and the red lines correspond to the wing section operating in ground effect with a height-to-chord ratio of 0.35. (streamlines generated by JavaFoil).

When out of ground effect, the airfoil is operating at a lift coefficient of just under 1.0. When in ground effect, the airfoil is operating at a lift coefficient of just under 1.1 (in ground effect, the airfoil is generating about 10% more lift). Do the streamlines indicate that the airfoil is adding more downward momentum to the air in ground effect?

The red streamlines (in-ground-effect) undergo noticeably less angular deflection as they cross the image from left to right compared to the blue streamlines (out-of-ground-effect). This means that the air is experiencing less change in vertical velocity (less downward acceleration) as it passes by the airfoil. In other words, the airfoil is imparting less downward momentum to the air when in ground effect than when out of ground effect.

So in ground effect, the airfoil is generating more lift, but adding less downward momentum to the air. This indicates pretty clearly that pure momentum change cannot account for the lift in all cases. It also shows that the lift and rate of momentum change cannot always balance.

Originally Posted by ShoeDLG

The attached image shows a comparison of the streamlines around a NACA 0012 airfoil at 9 degrees AOA with a chord-based Reynolds Number of 3,000,000. The blue lines correspond to no ground present, and the red lines correspond to the wing section operating in ground effect with a height-to-chord ratio of 0.35. (streamlines generated by JavaFoil).

When out of ground effect, the airfoil is operating at a lift coefficient of just under 1.0. When in ground effect, the airfoil is operating at a lift coefficient of just under 1.1 (in ground effect, the airfoil is generating about 10% more lift). Do the streamlines indicate that the airfoil is adding more downward momentum to the air in ground effect?

The red streamlines (in-ground-effect) undergo noticeably less angular deflection as they cross the image from left to right compared to the blue streamlines (out-of-ground-effect). This means that the air is experiencing less change in vertical velocity (less downward acceleration) as it passes by the airfoil. In other words, the airfoil is imparting less downward momentum to the air when in ground effect than when out of ground effect.

So in ground effect, the airfoil is generating more lift, but adding less downward momentum to the air. This indicates pretty clearly that pure momentum change cannot account for the lift in all cases. It also shows that the lift and rate of momentum change cannot always balance.

Is there any accounting for possible pressure and air density differences between the two cases?

Originally Posted by Yoda466

Is there any accounting for possible pressure and air density differences between the two cases?

Not explicitly, but the accounting is straightforward. If the airfoil is moving at 100 knots, the free-stream Mach number will be about 0.15. The first attachment below shows the pressure coefficient around the airfoil in ground effect under these conditions. A maximum pressure coefficient of about 1.02 occurs at the stagnation point. At 100 kts, a pressure coefficient of 1.02 corresponds to a local pressure increase of less than 0.25 psi, and a density increase of less than 2%.

The density of the air does increase below the wing in ground effect, but by less 2% (in most places it increases by less than 1%). Keep in mind that the density also increases below the wing when it is out of ground effect (pressure coefficient plot shown in second attachment... both are at 9 degrees AOA), so the density increase associated with ground effect is a small fraction of a percent.

Density variation does not come anywhere near accounting for the increase in lift or reduction in streamline deflection associated with ground effect (and even less so as the speed goes down). Fortunately Newton’s Second Law is satisfied exactly in ground effect through the upward force exerted by the ground on the air.

Originally Posted by ShoeDLG

Not explicitly, but the accounting is straightforward. If the airfoil is moving at 100 knots, the free-stream Mach number will be about 0.15. The first attachment below shows the pressure coefficient around the airfoil in ground effect under these conditions. A maximum pressure coefficient of about 1.02 occurs at the stagnation point. At 100 kts, a pressure coefficient of 1.02 corresponds to a local pressure increase of less than 0.25 psi, and a density increase of less than 2%.

The density of the air does increase below the wing in ground effect, but by less 2% (in most places it increases by less than 1%). Keep in mind that the density also increases below the wing when it is out of ground effect (pressure coefficient plot shown in second attachment... both are at 9 degrees AOA), so the density increase associated with ground effect is a small fraction of a percent.

Density variation does not come anywhere near accounting for the increase in lift or reduction in streamline deflection associated with ground effect (and even less so as the speed goes down). Fortunately Newton’s Second Law is satisfied exactly in ground effect through the upward force exerted by the ground on the air.

Ok. I'll buy that. What about accounting for any variations in wingtip vortices' behavior as a result of the proximity of the ground?

You can treat the 3D case (to include the effects of wake vorticity) and the effect is the same. Because the air cannot flow into or out of the ground, the vertical velocities induced by the wing are reduced by the presence of the ground. Again, the force exerted by the ground on the air accounts for the reduced momentum transfer.

The attachment shows the crossflow streamlines looking upstream at the wake of a wing that is well above what would normally be considered ground effect (8 spans above the ground). The solid lines show the streamlines when the ground is present, and for comparison, the dashed lines show the streamlines when the ground is removed. Similar to the airfoil case, you can see how the ground reduces vertical velocities in the wake by bending the streamlines.