Ground effect on planes (and cars?)

Ground effect has two components, iirc: First the wingtip vortices, which reduce lift, are disrupted. Second, air traveling below the plane gets more pressurized because it can't 'get out of the way' when pushed down by the wing.

You can do this easily enough by having the front of the car lower than the back

Can you explain that second reason?. I mean, give a mathematical reason for what are you saying. I've tried to explain it above, but I've reach a paradox using bernoulli equation. I'm wrong, but I don't know where.

Many pilots mistakenly believe that ground effect is the result of air being compressed between the wing and the ground.

To understand ground effect it is necessary to look again at the upwash. Notice in Figure 15 that the air bends up from its horizontal flow to form the upwash. Newton's first law says that there must be a force acting on the air to bend it. Since the air is bent up the force must be up as shown by the arrow. Newton's third laws says that there is an equal and opposite force on the wing which is down. The result is that the upwash increases the load on the wing. To compensate for this increased load, the wing must fly at a greater angle of attack, and thus a greater induced power. As the wing approaches the ground the circulation below the wing is inhibited. As shown in Figure 16, there is a reduction in the upwash and in the additional loading on the wing caused by the upwash. To compensate, the angle of attack is reduced and so is the induced power. The wing becomes more efficient.

I don't agree. Perhaps this enhances the top air stream being deflected upwards and creating a downwards force. But it is not what is called ground effect. F1 cars have half of a convergent-diverging nozzle at their bottom. The proper F1 bottom structure is curved like the narrower part of the half part of a convergent-divergent nozzle. I mean, like this:

-------\____________/------- F1 bottom
--->
-----------------------------ground

The basic idea is to create a volume of low pressure underneath the car, which sucks the car to the road. Naturally, to maximize the force one wants the maximal volume at the minimal pressure. Racing car designers have achieved low pressure in two ways: first, by using a fan to suck air out of the cavity; second, to design the underside of the car as an inverted aerofoil so that large amounts of incoming air are accelerated through a narrow slot between the car and the ground, lowering pressure by Bernoulli's principle.

In either case, I know of no reason a plane would be "smoother" just before it lands, other than that its engines are throttled back.

The Russian Ekranoplan looks like an aircraft but it only flies a few metres above water. Translated the Russian name Ekranoplan means sea skimmer and this is exactly what the Ekranoplan does. The Ekranoplan is what is known as a Ground Effect Vehicle, it operates on the principle of wing in ground effect, where the air gap between a wing and the ground is small enough for the air to be compressed.

Born out of the Soviet Unions Central Hydrofoil Design Bureau it was developed by their chief designer Rostislav Alekseev. Several different Ekranoplan's were developed from 1961 to 1990. Since the fall of the Soviet Union many of the design team from the CHDB have formed a new company with plans to develop new craft for passenger and cargo usage. Also 11 small 5 passenger craft were constructed between 1995 and 1997, they were used in trial commercial operation in USA and the Bahamas....

...The largest Ekranoplan called the KM was built in 1967, it was dubbed the Caspian Sea Monster after the sea it was on when first seen by the west. It was almost twice the length of a Boeing 777-200 but as with all Ground Effect Craft it need only half the wingspan. At over 100 m long, weighing 540 tons fully loaded, the KM could travel over 400 km/h mere meters above the surface of the water. Once moving at speed, the Ekranoplan was no longer in contact with the water, and could move over ice, snow, or level land with equal ease.

The important design principle is that the wing lift reduces the further above the surface of land or sea that the ekranoplan "flies". Thus its dynamically stable in the vertical dimension.

These craft were originally developed by the Soviet Union as very high-speed (several hundred km/hour) military transports, and were mostly based on the shores of the Caspian Sea and Black Sea. The largest
could transport over 100 tonnes of cargo. [continued]