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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:

First_Prot

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.

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...

Idea

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...)

Qmechanic
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ScienceDiscoverer
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    Possible duplicate of Why do archery arrows tilt downwards in their descent? – knzhou Feb 15 '18 at 10:27
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    It's an air resistance effect, not gravity. – knzhou Feb 15 '18 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. – Alchimista Feb 15 '18 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 >_< – ScienceDiscoverer Feb 16 '18 at 04:44
  • @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... – ScienceDiscoverer Feb 16 '18 at 04:50
  • With any vehicle/projectile in air, there are two centers, the center of mass/gravity or CG, and the center of aerodynamic pressure CA. You get the CG by balancing it against gravity. You get the CA by balancing it against a wind coming from the side. Stability requires that the CG is forward of the CA. Arrows have fins to move the CA aft. Aircraft have tail empennage to do the same thing. A good way to make either one tumble is to add weight in the rear, or remove the fins. – Mike Dunlavey Feb 18 '18 at 20:08
  • @MikeDunlavey Yea, all clear now! Check this out! – ScienceDiscoverer Feb 20 '18 at 04:10

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