From 3a4361e5e6b98f2725c5a2b4786473f74ca953a0 Mon Sep 17 00:00:00 2001
From: Tobias Bengfort <tobias.bengfort@posteo.de>
Date: Mon, 24 Sep 2018 22:06:25 +0200
Subject: [PATCH] fix air friction calculation

The code is slghtliy confusing because `velocityPrevX` and
`velocityPrevY` actually define a distance. The real velocity can be
calculated as `velocityPrevX / deltaTimePrev` and `velocityPrev /
deltaTimePrev` where `deltaTimePrev = deltaTimeScaled / correction`.

This is the formular without air friction:

```
velocity.x = velocityPrevX * correction + body.force.x / body.mass * deltaTimeSquared
```

Air friction is a force that acts in the opposite direction of the
velocity. It is proportional to velocity (for small velocity):

```
velocity.x = velocityPrevX * correction + (body.force.x - (body.frictionAir * velocityPrevX / deltaTimeScaled * correction)) / body.mass * deltaTimeSquared
```

which can be converted to:

```
velocity.x = velocityPrevX * (1 - body.frictionAir * deltaTimeScaled / body.mass) * correction + body.force.x / body.mass * deltaTimeSquared
```
---
 src/body/Body.js | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/body/Body.js b/src/body/Body.js
index a02647e..65cbae1 100644
--- a/src/body/Body.js
+++ b/src/body/Body.js
@@ -602,10 +602,11 @@ var Axes = require('../geometry/Axes');
      * @param {number} correction
      */
     Body.update = function(body, deltaTime, timeScale, correction) {
-        var deltaTimeSquared = Math.pow(deltaTime * timeScale * body.timeScale, 2);
+        var deltaTimeScaled = deltaTime * timeScale * body.timeScale;
+        var deltaTimeSquared = Math.pow(deltaTimeScaled, 2);
 
         // from the previous step
-        var frictionAir = 1 - body.frictionAir * timeScale * body.timeScale,
+        var frictionAir = 1 - body.frictionAir * deltaTimeScaled / body.mass,
             velocityPrevX = body.position.x - body.positionPrev.x,
             velocityPrevY = body.position.y - body.positionPrev.y;