Ballistics: Trajectory at an angle?

[gotime]

I'm just getting into rifle shooting and was wondering about the trajectory of a bullet when fired at an angle. So for a rough example, a typical 22lr when zeroed at 25 yards will rise and then fall back to "zero" at 75 yards... What if this is fired at a 45 degree angle? Would the bullet follow the same basic trajectory or is there a noticeable difference? Thanks for answering the noob question.

[Hoologan]

The bullet's trajectory will always be the same because of gravity. Are you asking what the recoil would do?

[armygunsmith]

The trajectory will change, but the trajectory will still be a parabola. It can be calculated, but I don't remember how.

[orangeusa]

Bullets don't rise if fired at a flat trajectory. I.e. straight forward.

The rise in ballistics charts are due to parallax (distance between center of bore vs center of scope/sight). Suppose you have 1 1/2" between scope and barrel center. If you shoot a target at point blank (using eye at sight or scope), scope and POI will be 1 1/2" different. As range increases, this distance reduces to roughly p/r (i.e. p=parallax= 1 1/2") r=range to target.
(assuming small angle sin(x) ~= x)

Okay, with that out of the way, the rest is a ballistics calculation - find in a physics book. I have a semi-decent link below. Basically shooting flat, gravity will drop the bullet at a given rate, long before the bullet loses much velocity. As you increase angle, you are compensating for gravity drop (which is same rate as before..)

I know this sounds hard, but it really isn't...

This is pretty good (ignore the crap at the top) see "Range of Trajectory"
The graph below that - just enter time and initial velocity of round (meters/sec, not feet/sec)
And calculation of peak height is kind of interesting. Max range is at 45 degrees BTW!!!

http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

The wiki stuff was horrible. Had errors, was incomplete and way too complicated.

Hope I didn't complicate things more than they needed to.

[Plisk]

Here's a more basic way to think about it. If you remember the pythagoras theorem from school, it's all you need to know. A2 + B2 = C2

Look at the picture, then imagine you're shooting at a level angle. 0 degrees. And B is the distance to your target. Let's call that 100 yards. And lets say your bullet drop is 1' at 100 yards.

Now imagine that A is a 25' yard high tower. Now obviously the distance of C is greater than B. But the bullet drop is only affected by gravity. Angle doesn't matter to gravity, it will only pull it down over the lateral distance is travels.

So basically it means that if you're shooting along B, or along C you're drop will be the same.

[gotime]

excellent. thanks guys.

[mjsweims]

Here's a more basic way to think about it. If you remember the pythagoras theorem from school, it's all you need to know. A2 + B2 = C2

Look at the picture, then imagine you're shooting at a level angle. 0 degrees. And B is the distance to your target. Let's call that 100 yards. And lets say your bullet drop is 1' at 100 yards.

Now imagine that A is a 25' yard high tower. Now obviously the distance of C is greater than B. But the bullet drop is only affected by gravity. Angle doesn't matter to gravity, it will only pull it down over the lateral distance is travels.

So basically it means that if you're shooting along B, or along C you're drop will be the same.

Not quite right. The distance C is greater so the bullet has to travel longer and further. The acceleration due to gravity is causing the bullet to drop for longer causing the drop to be greater. Add to that the fact that the bullet is slowing due to friction and surface tension in the air.

[Plisk]

I know its not 1:1 the same for drop I don't know the exact mathematics off hand, but it's close.

[SJgunguy24]

You ever throw a football? Exactly the same thing. 5 yard toss, pretty much straight throw. 75 yard pass, your release point will put an arc on the ball to reach the target. Same goes with the barrel of a gun. Your eyes stay on the same plane but the barrel is slightly upward (release point) to impart an arc on the bullet (ball) to hit the target. Same goes for lead angle on moving targets.