Simulated Gravity: Slow down on ground approach

Question

I'm looking for some math, nothing language dependant.

"Standard" gravity for an object in a game would go something like this:

if player.y > ground.y {
   player.velocity.y = player.velocity.y - gravity
}

In the little simulation I'm implementing I would actually like the gravity to weaken, and the velocity to slow, as the player approaches the ground.

IE: When the object is 100m above ground it should fall faster than when it's 1m above ground. It should land like a feather in a way.

I imagine the gravity needs to be some kind of function of the distance between the object and the ground.

I've been searching around Google but as I've not done math in a while and I don't know the name of what I'm looking for, I've not had much luck.

(Note: I considered posting on the SE: Game Dev but as it's more about math/programming than game design itself I though it would be more appropriate here)

Answer 1

You're correct in your assumption that gravity needs to be a function. The following snippet (source: http://gafferongames.com/game-physics/integration-basics/) applies more gravity for higher values of x, where State is a struct for position and velocity in a single dimension.

float acceleration( const State &state )
{
    const float k = 10;
    const float b = 1;
    return -k * state.x - b*state.v;
}

You want the reverse of this, which you can achieve by changing the value of b based on distance to the ground, or applying negative acceleration after some threshold.