Elevation and Point of Impact

[Adventurer 2]

Lets say you have a 22LR zeroed dead center at 100 yards on level ground.
If you took that same zeroed rifle and placed a target exactly 100 yards downhill or 100 yards uphill what effect would this have on the point of impact?
I had heard that shooting downhill requires holding below normal zero at the same range.
Feel free to post theories but if you have actually shot this on paper please say so in your reply.

 

[mete]

If you sight in at level you will shoot high if you shoot either up or down hill !!

 

[matthew temkin]

Either way requires a low hold.

 

[Trip20]

mete and matt are right. Always aim low whether up or down hill, but don't aim out of the fur (talking deer, and talking from experience ).

How low to aim is going to depend on the trajectory of that particular round, the angle of the shot, and the distance to the target. So there's no general answer to give a shooter for all scenario.

When I hunt squirrel with my .22lr (zero'd at 50yds), and the squirrel is directly straight above me on a tree limb (aiming perpendicular to level), I know to hold low about the size of 1 squirrel head (guestimation).

As I take shots farther away (i.e., not directly above me) I lessen the distance I hold off of the squirrels head. It can get tricky once in awhile even when dealing with such small distances... but a squirrel's head is small and I do miss now and then.

 

[garryc]

Put it this way. What counts is the distance the bullet travels in relation to a parallel to the gravitational force of the earth. So, think of the situation as a right triangle with the "A" leg parallel to the earth, The "B" leg being the vertical distance, or elevation, and with the distance you are shooting along the angle as the "C" leg, or hypotenuse, Then you can see that the distance the bullet travels parallel to the earths surface is less than 100 yards. So the bullet has not actually reached it's zero range and will strike high. So, as the angle increases, maintaining 100 yards along the hypotenuse, the "B" leg, or elevation, of the right triangle increases and the "A" leg must shorten to maintain 100 yards along the hypotenuse according to the Pythagorean theorem .
Now there are other factors when getting into extreme angles shooting but they very rarely become a factor.

 

[Adventurer 2]

I understand your explanation garryc - great job!
I was squirrel hunting yesterday and popped a squirrel at 84 yards in a very tall tree. At the time of the shot I thought the squirrel was much closer and held my crosshairs right on him (scope zeroed at 50 yards). Recent laser rangefinder purchase was put to use to get the 84 yards and I thought I should not have hit that squirrel where I was aiming (had I known the distance I would have aimed a little high and missed high).
This info solves a mystery for me from 1995 - hunting elk in Colorado. Took a long, down mountain, shot at an elk. Impact high but he was still standing in the same spot. Loaded another round - shot high again. Elk ran off. I though something had happened to my scope - Now I know.

 

[Jimro]

Multiply the distance (in your case 100 yards) by the cosign of the angle of elevation, then holdover based on the new calculated distance. Unless you are shooting REALLY small targets or have a really extreme angle it shouldn't be much at 100 yards.

Jimro

 

[Unclenick]

If you fire the muzzle of gun straight up on a windless day, gravity helps air resistance subtract from bullet velocity, but does nothing to pull the bullet out of line with the bore axis. When you shoot horizontally, gravity works only to pull the bullet out of line with the bore axis, but has no significant effect on how fast it gets where it is going. When you angle a shot, however, part of the gravitational effect is on the bullet’s velocity and part pulls it below the bore axis. Because gravity’s acceleration is a force normal to the earth’s surface, the effect may be quantified by vector trigonometry as described above. The result of that trig will be the bullet drop equals the horizontal drop for the same target range multiplied by the cosine of the angle above horizontal. You want to aim lower by the difference between that adjusted drop the drop you got on the horizontal plane. In other words, multiply horizontal drop by 1-cosine of the angle, then aim low by that amount.

When shooting straight down, gravity helps overcome air resistance rather than adding to it, but bullet drop off the bore axis fired at downward angles still turns out to be very close to the cosine of the angle times the drop for the same range when the gun is fired horizontally. You still adjust the sights low as for angle up.

Multiplying by the cosine is not exact because it does not consider aerodynamic effects on a spinning bullet. For example, a .308 168 grain match bullet travels about 600 yards in 0.9 seconds, but falls only 11 feet and not 13 feet, as it would if dropped from a stationary platform. This is due to lifting drag created by the slight upward pitch in its flight trajectory. This lift force has to be accounted for in solving the force vectors to be really precise and won’t be exactly same for angle-up and angle-down shooting because it varies with speed. Much more significant is that the sights will be angled down relative to the bore axis to get a horizontally fired bullet to strike the point of aim, and this must be taken into account for precision, since it is the angle of departure (where the bore axis points) and not the angle of the sight line that affects the bullet. Fortunately, neither of these precision considerations become significant until beyond around 400 yards. If you sight your gun by the late Col. Cooper’s method of zeroing at 200 yards and don’t try taking game beyond 400 yards, the precision concerns may be completely ignored with confidence.

Summary:
Multiply Horizontal drop at same range x (1-cosine of the angle). Aim low by this distance.

Nick

 

[Art Eatman]

If you look at trig tables, you'll see that it won't make much difference until you get beyond around twenty degrees. It's a function of the cosine of the angle. At twenty degrees, the horizontal distance is still 94% of the line-of-sight distance.

Art

 

[OneInTheChamber]

If you are firing uphill; aim lower than you normally would for that distance. That means if you are firing up a 20 degree, 500 yard foot long hill; you shouldn't be holding below the target with a .22LR. You'll still have to be holding above; but not as high as if it were a level surface.

Same thing goes for downhill.

The reasoning behind this is that when firing uphill, you are giving the bullet a trajectory that more defies gravity. Thus the bullet will drop less than if the barrel were on a level plane.