Calling all snipers and hunters.

[C-dub]

I have a trajectory problem and since I am neither a sniper or hunter I thought I'd ask you all.

Does a bullet's trajectory change depending on whether your target is below, above, or level with you? Let's say I'm using iron sights and I have to aim two inches higher than where I want the bullet to strike at 150 yards to hit the bulls-eye. Now, I'm 15 feet off the ground in a tree stand. Do I still aim two inches higher than where I want the bullet to strike? What about if I'm on the ground and notice the deer up on a ledge above me. Where do I aim now?

A friend at work asked me about this today and I wasn't sure how to answer. I know what the answer is if I'm playing golf, but I'm not sure for shooting.

[ajwakeboarder]

The way I do it and what works for me is, If your higher than your target at 100 yards, aim a little low. If your lower, aim a little high. Like i said, i'm not an expert, but it works for me.

[Thomas]

Does a bullet's trajectory change depending on whether your target is below, above, or level with you?

Yes, by definition of "trajectory". However there is always one constant force in one constant direction - Gravity. Whether you are aiming up or down, gravity will still make your bullet drop from where you aim.

Let's say I'm using iron sights and I have to aim two inches higher than where I want the bullet to strike at 150 yards to hit the bulls-eye. Now, I'm 15 feet off the ground in a tree stand. Do I still aim two inches higher than where I want the bullet to strike?

I'm no physicist, sniper, or hunter, but yes.

What about if I'm on the ground and notice the deer up on a ledge above me. Where do I aim now?

"two inches higher" still.

[ajwakeboarder]

In theory, gravity is always acting on the bullet, so it will drop. However, you sight in you rifle on a horizontal trajectory. If your aiming at something above you, gravity is acting on the bullet more than when you sighted it in, so it will drop more. But if you aim at something below you, It's acting on the pullet the same, but the bullet is also traveling closer to the direction gravity is pulling so it won't be affecting it as much. Does that make sense or do I sound crazy? I might be alone in my thought process here.

[snatchel]

Let me go to sniper mode on Modern Warfare 3 and see...





...... Ok. I can definately confirm it doesn't matter.

No, seriously. It doesn't matter. Gravity is the same. The only time that this really changes is if you were shooting from hundreds of feet up- which you wouldn't be. When you are shooting from an extreme vertical angle at hundreds of feet, the gravity will cause the bullet to move faster (think of how some jets will nose-dive in order to gain speed) thus affecting the trajectory. So unless your shooting from say.... a 100+foot higher elevation and say... 300+yards distance, you wouldn't see any noticable difference.

Aim normally.

[couzin]

When shooting steep uphill or downhill you need slightly less holdover. Goto the Chuck Hawks discussion at http://www.chuckhawks.com/shooting_uphill.htm

[MoJo]

AndyC, nailed it again.

[C-dub]

You calculate drop over the horizontal distance - calculate the true horizontal distance (because gravity affects bullets only straight down) using cosine tables.

For example - a 600 yard shot at a 40 degree up-angle (or down-angle, makes no difference).

To calculate this, you'd need a Cos table and two things:

1. Distance to your target (laser rangefinder or similar)
2. Angle of the shot (how you get this is up to you - there are various gadgets to do this)

Assume your measured 600 yard shot and 40 degree upward angle.

Look up 40 degrees in your Cos table and you'll see the value is .766

Simply multiply your measured 600 yards by .766 (the Cos value of 40 degrees) and you'll get the horizontal distance: 459.6 yards. This is the distance you use.



In short, if you're shooting at an upward or downward angle, the target is actually closer (in terms of horizontal distance) than your rangefinder indicates - which is why people typically shoot over the target; their sights are set too high.

Cosine table just for grins:

This is along the lines I was thinking and it is sort of similar to golf. If the hole (target) is below where you lay the actual (level) distance to the target is shorter than the ground distance so I use a shorter club depending on how much lower the target is than me. I think this translates to the following. If on level ground I would aim two inches above the bulls eye, then if the target is below me at the same ground distance I might aim only one inch high to hit the bulls eye? And if the target were above me I might aim three inches high or only one inch high because the level distance is also shorter here just like if the target is below me?

[C-dub]

I didn't see the table below in your post Andy. Sorry.

I get it. I was thinking that was a possibility with shooting versus golf. So, the downhill shot is similar to golf and the uphill shot is the same in shooting either way, but the opposite in golf. Cool.

Thanks Andy.

[texasmusic]

Should be the the same effect shooting uphill or down. So take off an inch holdover either way. The gravity is the same in both cases here but the difference is you have a smaller force acting normal to the line of sight. In the uphill case the sin(angle) of gravity is pulling the bullet back towards you (something to remember when firing guns directly upwards ) and in the downhill case, the sin(angle) is pulling it directly away from you. In both cases the Cos(angle) is the only force affecting flight along your line of sight. And as we all remember from high school, cosine of positive and negative small angles are the same.

[steve817]

Man! I love it when I learn something new! Thanks for asking C-Dub and thanks to Andy for answering.

[RoyGBiv]

The effect of gravity will change with altitude, but not measurably if the change in altitude is only 15 feet (or even 100 feet). Actually, there is a change, but you'd need some high-falootin instrumentation to measure it and it's not enough to affect your aim point over a distance of 150 yards.

Edited to add:
As Andy points out, if your vertical height difference between you and your target is great, the horizontal distance will be shorter than it appears... and it's the horizontal distance that needs to be accounted for in setting your sights.

In his example above, to achieve a 40-degree angle over a 459.6 yard shot, the difference in elevation between the target and the shooter would be 385.7 yards (1,157 feet)

[Jumping Frog]

You calculate drop over the horizontal distance - calculate the true horizontal distance (because gravity affects bullets only straight down) using cosine tables

This is a good approximation, but it is not the complete answer.

Using your example, the actual bullet drop will be greater than the bullet drop for a "pure" 459.6 yard horizontal shot.

Why? Because the trigonometry does not take wind resistance into account. A bullet fired horizontally for 459.6 yards will travel approximately the same distance. However, firing up or down at 40 degrees means the bullet will still travel 600 yards total distance (the hypotenuse), thus increasing the amount of time in the air and resulting in a slower velocity at impact with a greater bullet drop (due to longer time in flight).

How much lower? That is entirely empirical, depending upon the bullet's ballistic coefficient, air pressure/temperature, wind speed etc. But for long distance shooting, the difference is definitely measurable.