If you’re angling to fix your uphill downhill shooting dilemma, keep reading. We have a simple solution.
- Bullet trajectories change with the angle of the shot.
- Downhill shots strike higher.
- Uphill shots strike higher too!
Uphill Downhill Shooting Phenomena Explained
It makes sense that bullets fired downhill would land higher than normal because gravity is accelerating them, right? It makes no sense that they’d also strike higher going uphill where gravity is working against them. But the acceleration of gravity has minimal impact on this because it’s pulling just 32 feet per second and bullets are flying at thousands of feet per second.
The “shoot high” effect results from the angle at which gravity pulls against the bullet’s line of travel. The steeper the angle, the more it alters the trajectory curve. Remember, when shooting “on the level,” a bullet’s trajectory curve is maximized because gravity pulls it at a 90-degree, right angle. As the slant of the bullet’s line-of-departure changes, the angle of gravity’s pull is reduced, thus so is its effect on the trajectory curve. Gravity still pulls 32 feet per second per second, but it no longer pulls at a 90-degree angle. In essence, the trajectory curve flattens, which results in the bullet striking higher.
An Einsteinian Thought Experiment Clarifies Uphill Downhill Shooting
To more clearly comprehend this, let’s indulge a thought experiment. Albert Einstein did thought experiments to come up with his famous theories, so it ought to work for us, too. Imagine you are hovering directly above your target in a helicopter. Shoot straight down and gravity will pull straight down on your bullet. There will be no curve to its trajectory, no drop. It will never fall below its line-of-departure. Next stand on the ground and shoot straight up. Once again, there is no curve to the bullet’s path because gravity is pulling it straight down, the same angle at which it was launched. If everything is perfectly aligned and there is no force like wind working on the bullet, it should fall straight down again and land in the muzzle! That, my friends, is a FLAT trajectory. (We’re ignoring yaw, spin drift and similar anomalies here.)
Of course, we can’t get such a flat trajectory shooting on the level because of that darned gravitational pull at a 90-degree angle. This exerts maximum effect on the bullet’s flight path, so much that it forces us to angle our barrels slightly above our targets in order to hit them downrange. If you aimed the world’s fastest bullet perfectly on plane with a target just 100 yards away, you’d miss it. Not by much, but a 32-grain V-Max from a 204 Ruger at 4,200 fps would drop 1.09-inches. A 300-grain AccuBond from a 338 RUM at 2,640 fps would fall 2.58 inches. That’s why we sight-in our rifles to hit dead on at 100, 200, 250, or 300 yards. We’re compensating for the maximum drop when shooting on the level. And that complicates selecting the proper aiming point during uphill and downhill shooting.
So it only follows that the farther we depart from a 90-degree angle, the less the drop and the higher our bullet strikes from the horizontal drops we expect. It’s the degree of the angle that matters, not whether it is up or down.
An Intuitive Method for Understanding Uphill Downhill Shooting Effects
An easy way for many to understand this phenomenon is by thinking of the horizontal distance versus vertical distance to the target. If a goat is standing 300 yards away at a 600 angle uphill, only half that distance will be horizontal. Since gravity has almost no effect on the trajectory path for the vertical component, your bullet will strike as if fired at the horizontal distance only. If your rifle is sighted to strike 3 inches high at 150 yards and 8 inches low at 300 yards, don’t hold for the 300-yard shot at the 600 angle or you’ll shoot over. Hold for a 150-yard hit.
A Simple Uphill Downhill Shooting Fix
If you’re in a hurry or mentally flustered (big bucks and rams do that to you,) the safest, or at least fastest and easiest way to compensate for angled shooting is to aim lower but not off the animal. But how much lower? Well, this depends on many complicating factors including muzzle velocity, bullet BC, your zero range, how high your scope is mounted above your barrel, the degree of slant, and the distance to the target.
Yikes. We’d better modify our “easiest” definition: The easiest way to handle angled shooting is to sneak closer. (That’s the solution to virtually every shooting problem.) But it’s not always an option, so…
The Quick Fix Solution for Uphill Downhill Shooting
The next easiest solution is the Quick Fix which works well for big game at most sensible hunting ranges. Here’s how it works (trigonometry warning!):
On a 30-degree slope, subtract 10% of the distance to target. A 300-yard shot would then have the drop component of a 270-yard shot. On a 45-degree slope, subtract 30%. A 300-yard shot would be the drop equivalent of a 210-yard trajectory. A 60-degree angle (almost unheard of when hunting) requires a 50% reduction. Just cut the range in half. A 300-yard shot becomes a 150-yard slam dunk. Wouldn’t you know it, the easiest math solution is the rarest shot.
The technical way to factor these is with trigonometry. Each of these angles has a cosine that you multiply by the range to get your shoot-to distance. The solutions aren’t precise, but more than close enough for targeting big game.
Example: Ram is 300 yards downhill at a 45° angle. Multiple the .7 cosine times the distance to the ram and you get 210. You would hold as if he were only 210 yards away. Important note: this is only for drop considerations, not drift. The wind will be influencing the bullet for the total distance to the target. Remaining kinetic energy doesn’t change from the horizontal, either. And you must still aim precisely enough to hit a 300-yard target. The true distance to target is 300 yards, but because of the slant, your drop is the equivalent to a 210-yard shot.
Doing these cosine calculations requires knowing the angle. Most of us severely overestimate uphill downhill shooting angles because we spend most of our lives on flat to fairly flat ground. A bit of a slope in vast mountain country can really fool us. Stand on a 150 or 200 slope and it seems as if we’re looking at a 300 to 450 slant. We need to train to more accurately judge slope angles.
You can do this with a clinometer or angle indicator that clamps to your scope; with a cheap protractor and plumb line; by pointing your rifle at the target and eyeballing the slant compared to horizontal and vertical; or by using a laser rangefinder with a built-in clinometer and digital readout.
Getting a Laser Focus on Uphill Downhill Shooting
A laser rangefinder with angle or ARC (angled range calculation) built in is the absolute easiest method. It not only measures the slant, but does the math to spit out a precise solution. Some rangefinders provide the compensation distance, some the true-hold or shoot-to distance. You aim your laser at the target and discover it is not at 325 yards on a 520 slope like you thought, but 550 yards on a 300 angle and the shoot-to distance is 495 yards. You aim as necessary for a 495-yard drop. Too easy.
Using such an angle compensating range finder is ideal, but rain, fog, severe backlighting, intervening brush and more (like dead battery) can compromise those, so have a backup plan. A data card with drops for various ranges at these three main angles is quite useful. I recommend Holland’s Signature Series Data Cards. Holland’s website has been malfunctioning lately, so just call 541-439-5155 (Pacific time zone.) Specify the Ron Spomer Special discount. You’ll get the $75 software for just $20. It can print out custom data in MILS or MOA, G-1 or G-7 drag functions, force balance BCs with click values, calculate angled shooting solutions and more.
Here are some basics about uphill downhill shooting to keep in mind.
- The steeper the angle and the greater the range, the greater the change in your horizontal trajectory curve.
- You can minimize the differences between horizontal and slant trajectories by shooting a high BC bullet as fast as possible.
- If target distance is 250 yards or less, point-of-impact changes will be minimal, probably not enough to worry about on 10” to 8” targets even at a 450 slant.
- If angles are less than 30 degrees, impact changes will be minimal out to 250, perhaps 300 yards depending on your MV and BC.
- Most shooting angles are less than 30 degrees! Seriously. It’s rare to find open shots at game beyond 250 yards at angles steeper than 30 degrees, even in Rocky Mountain canyon country.
- Considering all the above, your safest compensation for a hurried, “steeply angled shot” inside of 300 yards is to merely aim lower on your target than you would for a level shot at the same range. “Don’t hold off hair!” veteran mountain hunters say. Just hold low on the chest. At most your bullet might land 2 to 6 inches higher than normal, and that’s easily inside the vital zone of most big game.
- At 300 yards and beyond with angles of 20-degrees or more, calculations become critical because bullet drops at those distances become severe.
Branded Rock Canyon Trains Uphill Downhill Shooting
We teach both the theory and practical application of uphill downhill shooting as part of the Branded Rock Canyon Precision Shooting Program near Grand Junction, CO. Shots there range from flat to 45-degrees and nearly 60-degrees in a couple of hairy, cliff-side locations — should you be brave enough to try them. Ranges extend to thousands of yards, and wind currents swirl every direction including up and down. It’s the perfect venue for really learning the ups and downs of shooting.
The author has often gotten the drop on mountain game, only to discover the slant range was enough to confuse the issue. He wishes he were a trig whiz. Have you ever tried multiplying .7 x 473 while lying on a tundra rock watching a 40-inch ram walk toward a ridge? Maybe he should practice multiplication as much as he does trigger control.