The Rifleman’s Rule (Angle Firing)

When I teach ballistics, I love to ask people how you should compensate your aim when firing uphill and downhill. People usually get the downhill portion right. It’s intuitive. The bullet is “going down a hill.” The idea that it picks up speed, goes further, and thus would hit higher is quite easy for most to grasp. You compensate by aiming low. Likewise, they assume that for an uphill shot, you must aim high. The reasoning is similar; “the bullet has to climb up a hill, so it must slow down more and fall more, thus you aim higher.” This is incorrect. In both the uphill and downhill cases, you must aim lower.

For both uphill and downhill firing, the reasoning that the bullet gains or loses much steam due to the altitude change is incorrect. The difference in bullet speed by firing uphill or downhill is generally negligible compared to the deceleration due to air resistance. Rather, the major factor in the changing trajectory is that the effect of gravity is no longer full. As with most things, a picture is best:

Flat firing:


Uphill firing:



The trajectory “bends” because of gravity. When gravity is at an angle to flight, the trajectory bends less. The more the trajectory bends, the more drop you have. The less it bends, the less drop you have. That’s why shooting uphill produces less drop. If you are still struggling with this, I give you two more pictures.

In this first picture, you are firing flat. The bullet leaves at a slightly upward trajectory to compensate for drop. This is a typical trajectory.


In this second image, you are shooting the gun straight up. Again, the direction of fire is canted slightly due to the normal angular difference between your line of sight and the actual direction the barrel is pointed. The blue trajectory was right before, but is now quite wrong. The green trajectory is correct. In this extreme case, you must aim below your target to hit it.


The Rifleman’s Rule

The Rifleman’s Rule is a simple formula to help shooters make accurate angle shots in the field. It’s quite simple:

Whether shooting uphill or downhill, correct only for the horizontal distance, not the straight line distance. In layman’s terms, do the following:

  1. Establish a range for your target.
  2. Measure the angle away from horizontal.
  3. Correct for range * cosine(angle)

As an example, imagine I am shooting at a target 500 meters away. I am shooting down a steep hill, at a 45° angle. Instead of correcting for 500, I correct for 500*cos(45) = 353 meters. My normal 500 meter correction for my Mk12 clone would be 3.67 mils. The correction for 353 meters is 1.87 mils. It’s an easy calculation. This method is even more field-worthy if you memorize a few big cosine values. In fact, knowing that cosine(25°) = .9, cosine(45°) = .7, and cosine(60°) = .5 will get you most of the way home in angle firing.

How accurate is this method? Well, the real calculated trajectory of this 500 meter shot at 45° is 2.23 mils. The Rifleman’s Rule is about a half mil off, or 25 centimeters at 500 meters. It’s close enough for government work, but the error is significant. The Rifleman’s rule is a great tool for field use. Even better is the angle fire function of Sendit Ballistics. This feature will be available for In-App Purchase in late April. The angle fire function adds another layer of accuracy to the trajectory, even accounting for the slight change in air density as the bullet gains or loses altitude. While you wait for this feature to become available on the App Store, give Sendit Ballistics a try. It’s free out to 500 meters.

Sendit Ballistics Released

Sendit Ballistics finally released on March 6, 2017. As expected, downloads and sales are rather slow. The ballistics calculator market is somewhat saturated. However, Sendit Ballistics has a cleaner user interface, and an al-a-carte pricing scheme which will appeal to users. As the app gains features, we expect to slowly carve out a major segment of the ballistics app market.

It’s a free download, give it a try today!

How Temperature Affects Your Bullet

Most long range shooters are aware that weather conditions affect bullet trajectories, though maybe not by how much or to what degree. In this post, I’m going to take you through all of the effects of temperature, in order of importance. First I’ll talk about the comfort level, and then we’ll discuss the science of how external flight changes. Finally, we’ll look at some sample results from the Sendit Ballistics engine at varying temperatures.

The most important effect temperature has, in my opinion, is shooter comfort. Anyone who has laid in the prone for hours on a cold day knows the difficulty of keeping concentration, and minimizing shivering while making a long shot. On hot days, the shooter’s eyes burn with sweat, and mirage can make the target difficult to see. I have seen square targets at 700+ meters whipping back and forth like a flag through my scope due to the massive mirage. But what do you care about comfort? You’re tough and can deal. You came to read this for the science.

Temperature Effect on Internal Ballistics

Colder bullet powder has less internal energy, resulting in a lower muzzle velocity. The powder combusts more slowly, and simply doesn’t generate as high of pressures as it would on a hot day. The end result is that from freezing cold to burning hot, your bullets may have a variation of 200 feet per second or more on muzzle velocity. This leads to drastically different trajectories. For a more in-depth look at this phenomenon and the history, see a great post on the topic at Firearms History, Technology, and Development. The advanced trajectory package on Sendit Ballistics will account for the internal ballistics variation brought on by temperature changes.

And now, a graph showing the difference in trajectory between two 5.56mm rounds given a muzzle velocity change of 200fps. As you can see, at 1000m, it’s near a 2 meter difference in drop:

Temperature Effects on Bullet Flight (External Ballistics)

By the Ideal Gas Law, we can predict that the air will be less dense as temperature rises. Some quick math:

pressure = density*R*T  (T is temp, R is a constant)


density = pressure / (R*T)

Higher temperature leads to lower density. What effect does this have? Let’s check it out from 0 degrees C to 40 degrees C (roughly 32 to 100 F):

It’s a meter or so difference. But not so fast. A change in temperature also leads to a change in the speed of sound. In this case, it’s about a 25m/s difference. That’s important because it means your bullet has a different Mach number at given trajectories. Mach number is important because projectiles experience very different drags at different Mach numbers. Here is the trajectory, only varying speed of sound:

It’s a slight advantage to the cold temperature. Now, for all temperature effects combined:

Happy hunting.

Introducing Sendit Ballistics

It is my pleasure to introduce Sendit Ballistics to the world. I can’t say that it’s going to revolutionize shooting, but it certainly will improve the process of getting rounds on target.

As a sniper, I have been frustrated with the user interface of every ballistics calculator I have tried. They take too long to issue valid corrections. They are clunky, requiring far too much information from a user before issuing a correction. They are not field friendly.

Sendit Ballistics is none of those things. It’s designed around “the shot.” The first thing a user sees upon opening the app is a big bold elevation correction. A single finger flick of the slider changes the range, and a new correction appears. And then, in the words of a good spotter, “SEND IT!”

Head on over to the app’s page for more information.