# Why arrow stays tangent to its trajectory? [duplicate]

I'm making custom game engine, with custom physics simulation. I ran into a problem while trying to simulate arrows. Here is what I got for now:

The problem is, I don't understand clearly why arrows or spears (I guess, artillery shells do this too?) always turn towards the ground when thrown/shot.

So far, I thought up only some rough clues. On the image below, you can see my idea.

I assumed that 2 points farthest from the center of body's mass might cause the rotation. When long body is moving straight, there is no rotation induced. But when gravity shifts velocity down, it creates angular velocity, although if body is ideally symmetrical this 2 velocities will cancel out. But if center of mass will be shifted backwards or forwards, angular velocities will not be equal, and object will rotate. I used kind of inverse of angular velocity to linear velocity formula, maybe this is not correct...

As far as I see, there should be no torque induced by gravity, it should be canceled out by torque from opposite side of body.

Anyway, I tried to use this approach and (surprisingly) it shows some close results, although not quite as expected...

I fear that I don't see a full picture of how this rotation works.

Related questions:

1. If you throw ideally balanced stick (ignoring air drag) it will not turn in flight?

2. If you shoot arrow in Earth orbit, will it stay tangent to it's orbit? (As far as I know, spacecraft doesn't change its orientation while orbiting, maybe because it has perfect center of mass...)

• Possible duplicate of Why do archery arrows tilt downwards in their descent? Commented Feb 15, 2018 at 10:27
• It's an air resistance effect, not gravity. Commented Feb 15, 2018 at 10:27
• Also your sticks are not arrows as intended. Perhaps there is more than one situation. Real modern arrows with a head and tail and simple sticks. Commented Feb 15, 2018 at 12:38
• @knzhou oh, so It's air drag? I suspected that at first, but than though that it would be too unrealistic. Eh. So arrow in Space will not rotate - no air drag... And stick with center of gravity perfectly in middle of it, will not rotate even with air? Makes sense, I vaguely remember throwing such sticks as a kid (i.e. shovel handles) and there was no rotation. Well this means, that my physics simulation must get much more complicated and simulate correct air drag >_< Commented Feb 16, 2018 at 4:44
• @Alchimista My 1st GIF looks like firing arrows on the Moon actually :D But with artificial, simple and crude air-drag. I basically just subtract linear velocity based on speed... Commented Feb 16, 2018 at 4:50