Ballistics of high mountain shooting, long-range hunting

Mountain hunting, an extremely technical practice; demanding physical condition, very light equipment, important ballistic knowledge, in short, a practice a little apart that makes many of us fantasize. Today we propose to lay the foundations of the ballistics necessary for the good preparation of a shot on a slope (often synonymous with mountain shooting but not only!).

A little story first,

Pierre, a novice hunter, decides to go hunting in the mountains, he observes a magnificent chamois overlooking his position, 230 meters telemetered. He says to himself as it is towards the top, so he decides to put a little more towards the top than his usual correction. He shoots, and lobs his target by a hair... Fortunately no injuries but it was close!

But what happened to Pierre?

This is what we will try to explain to you in a “scientific” way in order to prevent this bad experience from ruining your day…

I) The relief and its impact on our shots

The mountain regularly implies that our target is not necessarily at the same level as us, it can be lower or higher. Thus leading to a shot on a slope whether it is positive (upwards) or negative (downwards). This angle relative to the horizontal is an extremely important element to take into account, in fact it will strongly influence the fall of our projectile. But also our ability to be stable and to manage the recoil in sometimes difficult positions.

But first how do you measure the angle of the shot?

There are several techniques that are more or less easy to implement to measure the angle towards our target. The simplest is often included in our rangefinder; in fact, many of them measure both the distance and the angle relative to the horizontal.

Some so-called "ballistic" rangefinders also allow the measurement of atmospheric pressure as well as temperature, thus making it possible to do without a weather station.

It is possible to use a ballistics application that uses your phone's camera as well as the phone's sensors to determine the angle (Example: Strelok).

There are also “inclinometers” which are now obsolete and overpriced…

Go your own way..

But why is this angle important?

Shooting at an angle, whether upwards or downwards, implies that the horizontal distance between us and the target decreases compared to a “flat” shot. This decrease in the so-called “projected” distance results in a decrease in the work of the weight of the projectile and therefore a decrease in the distance of the projectile from the line of sight. (it feels like the bullet is falling less). Quite counterintuitive for many of us!

In summary: The greater the angle for a given distance, the less we will need to correct the fall of our projectile.

And so Pierre did the opposite by deciding to correct more (aim higher, when he should have aimed lower than a flat 230m shot..)

-> The greater the angle, the less the bullet will fall in our reticle.

A view of the mind to understand: (not to be reproduced)

If we aim at a target 600 meters perfectly vertically from our position, then there will be no drop of the projectile visible in our reticle, in fact, the horizontal distance of our target is now 0m (600m x cos (90) = 0m. Gravity, instead of deflecting the projectile from its trajectory, will only have the effect of slowing the projectile if I shoot vertically upwards or of limiting the loss of speed of the projectile if the shot is vertically downwards.

But how do we calculate the correct correction to make to our shot?

To do this you need to determine what is called the projected distance (sometimes called the corrected distance)

Some rangefinders give it directly, others don't, so we'll explain how to obtain it by a relatively simple calculation:

Corrected distance = Distance measured by the rangefinder x cosine (angle of the shot).

For most of us, we have a smartphone in our pocket that allows us to do this calculation, if however you do not have one, it is possible to print a small table such as this one to help you in your calculations

And so you can use the “flat” correction at the corrected distance to make your shot on a slope.

Let's take an example:

The rangefinder measures 600 meters of distance and an angle of 25°, the rangefinder then offers you the following corrected distance: 543 meters.

What the rangefinder did internally was the following calculation:

Measured distance x cosine of the angle.

So here: 600 x cosine (25°) = 600 x 0.906 = 543 meters.

So what the rangefinder is telling us is to use our flat ballistic table correction for the 543 yard distance…

So even if your bullet is going to travel 600 meters you will put the necessary clicks to shoot 543 meters flat.

When should the angle be taken into account?

We note that at an angle of 8° the value of the cosine of the angle is greater than 0.99, i.e. a difference of less than 1%...

So, when the measured angle is less than 8°, it is not necessary to take it into account.

pull up or down a matter?

Cos(-25°) = Cos(25°), no it doesn't matter whether you pull up or down, the compensation to be put will always be governed by the same calculation.

An example to understand:

My target is 600 yards away, 25° angle up.

The weather conditions are as follows:

Atmospheric pressure 880 Hpa

Temperature 0 degrees

I shoot 6.5mm, 143gr ELD-X ammunition at 861 m/s with a ballistic coefficient of 0.315 G7.

The drop of my projectile announced by a ballistic calculator will then be 3.4 milliradians (or 11.6 MOA for MOA scopes), i.e. a drop of 202 cm compared to my setting at 100 meters.

In comparison, a shot at 600 meters flat (0° angle) in the same weather conditions (880 Hpa, 0°C) would have resulted in a projectile drop of 3.8 milliradians (or 13.2 MOA) or 230 cm.

-> A gap of 28 centimeters could easily result in a miss or worse a bad shot.

This same shot at 600 meters but this time with a 25° downward angle:

Correction: 3.4 milliradians (or 11.6 MOA for MOA scopes) or a drop of 202 cm compared to my setting at 100 meters.

-> NO DIFFERENCE WHETHER I PULL UP OR DOWN!

How do you determine how many clicks it takes to shoot beyond 200 yards?

Given the number of variables (distance, angle, temperature, atmospheric pressure, bullet exit velocity, etc.), we can only recommend the use of a high-performance ballistic calculator for this type of shooting in order to guarantee an ethical and properly prepared shot.

There are now a number of easy-to-use and free applications on Android and iOS (Strelok / Lapua Ballistics / Norma Balistics / Applied Balistics / Hornady / …)

Some ballistics basics to better understand the results of the ballistic calculator:
The bullet, as soon as it leaves the barrel, falls because it is attracted by the Earth's gravity.

We are lucky, the Earth's attraction varies only slightly with altitude and therefore this force has a direction and intensity considered as a constant whatever your point on Earth (directed towards the center of the Earth with an intensity such that P = mxg)

Go further: 

Where P = Weight = mass (m) X Gravitational constant (g)

However, the mass of a projectile remains identical over its trajectory and the gravitational constant varies very little with altitude.

g at ​​sea level = 9.779m/s-2

g at ​​2857 m = 9.772 m/s-2

We will consider that the weight (the force which makes our projectile fall) is constant whatever the altitude.

Visualize the phenomenon:

Whether you are at sea level or on top of Everest, you will always be pulled towards the center of the earth with the same intensity.

Our projectile will also brake as soon as it leaves the barrel , and this is mainly due to friction between the air and the projectile. This friction dissipates kinetic energy (and therefore speed) and heats the atmosphere and the projectile (do not try to pick up a freshly fired projectile on the ground, it is hot).

These frictions are very dependent on the density of the air. However, the density of the air depends on the atmospheric pressure but also on its temperature.

In the mountains, the higher you go, the lower the atmospheric pressure, the less dense the air, the less your projectile will brake.

Visualize the phenomenon:

Atmospheric pressure decreases with altitude, and therefore the higher you go, the fewer air molecules each cubic meter will contain (mainly O2 and N2), which is why many mountaineers climb the highest peaks with oxygen reserves to avoid this lack of oxygen.

source: météo france

The mountain sometimes rhymes with quite extreme temperatures in one sense as in the other. The temperature will also have an impact on the atmospheric pressure, therefore on the density of the air and therefore on the resistance to the advancement of your projectile.

low temperature = denser air = greater resistance to forward movement = more fall.

High temperature = less dense air = less resistance to forward movement = less fall.

In order to take into account these physical data accurately, we can only encourage the use of a Kestrel type weather station in order to know precisely the atmospheric pressure of the air at the time of your shot. This data can then feed a high-performance ballistic calculator. (Strelok / Applied Balistic / Hornady 4 DOF / …)

Did you know?

We often forget it but the speed of our bullet is not constant; ammunition having a speed of 860 m/s at 20 degrees, this same ammunition would give for example a speed of 840 m/s at 0 degrees… Thus, it is important to know its projectile speeds whatever the outside temperature in order to guarantee the accuracy of the exit speeds.

-> Be careful, not all powders are equally stable at temperature! A chronograph and ammunition baked at different temperatures highlight this phenomenon.

The great unknown: The wind

Calculating and compensating for the fall of a projectile is truly within everyone's reach today in 2024. On the other hand, there remains a big unknown in our equation: the wind.

Indeed, the relief causes winds that are very difficult to read, the intensity and direction of which can vary with distance, making long-distance shots in windy conditions an exercise to be reserved for a trained elite.

Unfortunately, we do not have a miracle recipe here, nor any clever calculations to explain this phenomenon, which can only be mastered by experience of the terrain and a good reading of the relief in order to understand the flow of air along it.

A solution is still within our reach: use a projectile adapted to long-range shots (offering a good ballistic coefficient and working at low speed).

Let's take an example:

For two projectiles of similar mass, which will exit at the same exit velocity (860m/s), at a distance of 600 meters flat in the same wind conditions: 5 m/s at 3h

140 gr Hornady Interlock SP G1 ballistic coefficient of .465
143 gr ELD X G1 ballistic coefficient of .625 (0.315 in G7)

The Interlock SP projectile will experience a trajectory deviation of 1.6 mil / (5.25 MOA) / 93 cm.

The ELD X projectile will experience a trajectory deviation of 1.1 mil / (3.7 MOA) / 65 cm.

Same weight, same speed, and yet the ELD X projectile will be 30% less influenced by the wind! Thus minimizing the big unknown that remains: the wind.

In addition, the impact speed of this ELD X projectile will be 612 m/s for an energy of 1739 Joules when the residual speed of the interlock projectile will only be 537 m/s, i.e. a kinetic energy of 1309 Joules!

Added to this is the fact that the ELD X projectile was designed to deform properly at low speeds, something that the interlock is not capable of doing.

Conclusion :
Mountain shooting is complex when the distances and inclinations increase, we can only encourage training in these conditions of slopes and altitudes before taking a shot at an animal.

The distances mentioned in the article allow to accentuate the phenomena, we do not encourage people who are beginners in the practice to indulge in this kind of hunting shots. A consistent training will be required