## Angular Trajectory

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GMWeezel
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### Angular Trajectory

According to my father if you shoot a bullet parallel to the earth or perpendicular to the radius of the earth, it will curve upward and back down to the earth. someone care to explain or disprove this phenomenon?

bitwiseshiftleft
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I'm pretty sure that your father is wrong unless he's talking about rail guns.

Not accounting for air resistance (I'll get to that), the trajectory of a bullet is elliptical until it crashes into earth.

Any curving up would happen at nearly horizontal angles, that is, at the beginning of the bullet's flight. Of course, the faster you fire the bullet, the more it will curve up at the beginning. If you fire it fast enough to orbit at constant height (excluding air resistance), it will obviously stay at constant height and not curve up at all. Therefore it can't "curve up" at the beginning of the flight at any lower velocity than that.

How fast would you have to fire it to reach orbital speed? g=a=v^2/r, so v = sqrt(rg) > mach 23. Not going to happen.

Ah, but what about air resistance? Well, air resistance slows the bullet, exerting a force in the opposite direction to the velocity, so locally it just makes any "curve" more pronounced. And it certainly doesn't help the bullet attain orbital velocity. So it won't help an ordinary bullet to curve up.

SpitValve
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Most likely it'll hit a wall or a hill

You mean tangential to the surface of the Earth? If it goes in a "straight line" it'll look like it's going upwards, but the effect of gravity will depend on the speed of the bullet I guess.

Hawknc
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From the curved reference frame of the Earth's surface, it may look like it's going up before gravity pulls it back down. From an external frame of reference, it's just being pulled towards the Earth's centre.

Gordon
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I know that bullets are made to spin as they leave the barrel of a gun and the spinning helps counter act gravity allowing it to fly horizontal longer.

Of course us true gangsters always hit our targets so the whole point is moot.
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GMWeezel
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### Color me skeptic

Hawknc wrote:From the curved reference frame of the Earth's surface, it may look like it's going up before gravity pulls it back down. From an external frame of reference, it's just being pulled towards the Earth's centre.

That's what I thought he was referring to but he insists it eixists; Im skeptic.

GMWeezel
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### Rifleing

Gordon wrote:I know that bullets are made to spin as they leave the barrel of a gun and the spinning helps counter act gravity allowing it to fly horizontal longer.

Of course us true gangsters always hit our targets so the whole point is moot.

Yea; the rifling helps give it more lateral inertia to help stabalize it and keep it from flipping and becoming less accurate.

Edit: Sorry about the double post. /when i was writing the first post, Gordons had not yet appeared.

evilbeanfiend
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we still would need to show that the bullet doesn't generate lift (like a wing) to prove it doesn't go up then down. given that its a fast moving curved spinning surface i suspect this is non trivial to calculate.
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Hawknc
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Unless the bullet is non-symmetrical, I can pretty well guarantee that it won't generate lift if it's rotating axially. Lift can be generated by rotating on an axis perpendicular to the direction of motion, but that's precisely what rifling is designed to avoid.

Does your father offer an explanation as to what is causing this apparent lift?

evilbeanfiend
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apparently most hunting rifles have the sights at a slight vertical angle to the bore so a level shot through the sights will result in a trajectory that rises a small amount (this is done for increased range i think) this is probably the cause of the disagreement?

hawknc, yeah obviously for smooth bore (and i think there are some sort of semi-rifled bores which still let a bit of tumbling for increase damage at the expense of accuracy) that doesn't apply but then the the spin should be in a random direction not just up.
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Hawknc
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Yeah, it's not necessarily lift, depends on which way the bullet is rotating. (The Magnus Effect, for anyone who isn't aware of it)

Andrew
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Hawknc wrote:Yeah, it's not necessarily lift, depends on which way the bullet is rotating. (The Magnus Effect, for anyone who isn't aware of it)

That would only happen in a pretty string sidewind, though, wouldn't it? (Or, presumably, a thermal would lift the bullet slightly.)

Hawknc
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For axially rotating bullets, yes...and "strong sidewind" would have to be pretty damn strong. It's more if the bullet gets a perpendicular tumble that it might become relevant. I think this might all be somewhat tangential to the actual topic, though.

QuantumTroll
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### orbital mechanics to the rescue!

Ignoring air resistance, if you shoot a bullet tangentially to the Earth's surface, it will follow an elliptical path, with the starting point as the perigee or apogee of the orbit.

-If the bullet moves slower than orbital speed, then your position is at apogee, and the bullet will fall towards the center of the Earth.
-If the bullet moves faster than orbital speed, your position is at perigee, and the bullet won't reach its farthest point from the surface until it's on the other side of the planet.

Draw a few pictures, and it should be obvious that the bullet can't move away from the surface before coming closer.

Air resistance is a dissipative force, so it won't make the bullet rise or speed up. Ergo, your dad is incorrect.