Trajectory & Long Range Shooting
Taking full advantage of your Barrett?s long-range accuracy with BORS!
What do you consider long range? For hand-gunners, 50 yards may be long range. For a typical deer hunter, anything past 300 yards may be long range, but an antelope hunter may think of 300 yards as moderate range. A varmint hunter may push shooting out past 500 yards.
In the military, the trend to downsize the service cartridge seen over the past 50-plus years has been the result of most engagements taking place at 300 yards or less. There has always remained, however, a need in the military to reach out a long distance to effectively deny the enemy territory or freedom of movement. This may demand capabilities reaching 1500 to 2000 yards, beyond the range of a battle rifle.
Then there are the competition shooters. Normal High Power competition goes out to 600 yards, and the Palma matches are fired at 1000 yards. With the popularity of .50 BMG rifles, matches are now held with targets up to a mile away.
Regardless to how easy it looks on TV, shooting in general, and particularly at long ranges, is difficult to say the least. For the purpose of this discussion, we’ll define long range as anything past 500 yards.
Anyone who has spent time trying to shoot anything at 500 yards knows that’s a difficult task in itself. When you triple the yardage, otherwise small factors are magnified that affect the bullet during its travel to the target.
Some of the primary considerations affecting projectiles over long ranges are:
• Trajectory
• Range determination
• Wind
• Angle up or down
• Sight cant
• Atmospheric conditions
This is not an all-inclusive list. It does cover those factors having the greatest effect on the bullet and those which must be understood before any other factors matter.
Any shooter has some basic familiarity with trajectory. It is the bullet path from the muzzle to the target, also termed exterior ballistics. If we don’t know the trajectory of the bullet we are shooting, long range shooting becomes an exercise in frustration.
The trajectory is based on the line of sight. The line of sight (LOS), as defined as looking through the open sights, or through a scope, is just that—a line. The trajectory, as you know, is not a straight line. The bullet normally starts from below the line of sight, arcs upwards through the LOS, then falls back through the LOS and continues to fall until it hits the ground, or the target, whichever comes first.
The first crossover point, where the bullet is rising, has been useful to sight in the rifle if you don’t have a full range to allow sighting-in at the actual zero range. Perhaps you want to zero your rifle at 300 yards, but your range only has 100 yards available. Knowing the first point the bullet crosses the LOS, with respect to the trajectory for the bullet over 300 yards, allows sighting in at the shorter range and having some confidence of being “on” at the zero range.
For long-range shooting, the bullet is climbing so fast that the short range crossover will be very quick, perhaps much closer than we really want to shoot. Knowing the trajectory allows sighting in at a shorter range by adjusting the point of impact to match the trajectory for that range.
Trajectory Science
First off, where do we get a trajectory? You could spend a great amount of time, effort and money conducting firing tests using the rifle and ammunition you are interested in, and such effort has been done in the past. Some of the first studies in rifle trajectory were done empirically by firing through a series of large sheets of paper at known distances to the target. Research into ballistics has seen many countries, including Russia, Germany, England and the United States, adding tremendously to our knowledge of ballistics. Such research continues today.
For most, the use of a computer and a ballistics program can furnish the trajectory data needed. The first digital computer, the ENIAC, was developed to construct ballistics tables for the Navy. The Navy tends to shoot really long ranges, measured in miles. This was before the use of missiles, and big naval guns were capable of firing more than 20 miles.
If you have read any history about World War I, you know that there were artillery pieces, notably the Paris Gun, that could propel shells more than 70 miles. This sort of long range brings in factors we will not examine, but remain important at such extreme ranges. They are real for our ranges, but small compared to the pivotal factors under discussion.
There are many ballistics programs available, both commercially and for free. Like many things in life, you will likely try several and stay with the one that you feel most comfortable with that gives good results. I’m currently using the Sierra Bullets Infinity ballistics program. Sierra has a solid history of bullet design and research, and the Infinity program gives good results and is easy to use.
I developed a trajectory table from the Infinity program for a .50 BMG. Actually, all that is needed is the ballistic coefficient, the muzzle velocity, zero range and height of the LOS over the bore, but we, as people, are more comfortable knowing that we are using a .50 BMG with a bullet weight of 750 grains and a muzzle velocity of 2,650 fps. Add the sights being 1.6 inches over the bore and that we want to zero the bullet at 1,000 yards.
One real utility of a program like Infinity is the ease of changing conditions. If we are stuck with a trajectory table developed for firing at sea level, what happens when we find we are up higher? The accompanying table shows the differences in trajectory for the same bullet at sea level and at an elevation of 1785 feet. It’s important, though, to shoot the rifle and ammunition enough to know that the trajectory chart and the actual shooting results reasonably match. They should, but real life always trumps theory.
First, Know the Range
Along with knowing the trajectory of the bullet we are shooting, we must have some good idea of the range we are shooting. The range can be known through use of a laser range finder, pre-measured, or with accurate maps, or the range can be estimated. Obviously, for long-range shooting, knowing the range is better than estimating, but we don’t always have the ability to know the range precisely.
Even at shorter ranges, such as those seen in hunting deer, knowing the range is important. If you know the hunting area, you can scout it before the season, pacing off distances, or otherwise making range determinations if you know where you will be. More often, we are faced with a shot at an unknown range. A laser rangefinder is your friend, yielding good range figures.
There will be times, though, that the laser may not give a reasonable number, or the batteries die, or you plain forgot to pack it, requiring you to make the range estimate. Some scope reticles, such as the Mil Dot, allow refining the estimate by adding references on which to base the estimate.
Each dot in the Mil Dot reticle is 1 mil from the next dot, center to center. The dot itself is a known diameter, normally about 0.2 mil. Since the mil has a fixed relationship with respect to the range, it gives a reasonable means of estimating the range. The rule is to find something of known size and determine how many mils it spans. Suppose you can see a fence post near the target that you know is four feet high. You find it covers 1.5 mil. Multiply the known height (4’) by 1000 and divide by the number of mils it spans (1.5). Here, this gives 4,000 feet divided by 1.5, or 2,667 feet, equaling 889 yards. That counts as long range.
Using the 50 BMG data with an altitude of 1,785 feet, we see that the bullet will be 33.6 inches high at 900 yards. You could extrapolate the trajectory at 889 yards. Depending on the size of the target, it may be close enough to use the 900-yard trajectory figure. For those really interested, the 889-yard trajectory would be almost 3 inches higher than the 900 yard figure.
You can see the importance of knowing the trajectory and the range to hit the target. This is important in any shooting, but at long range it is crucial.
Real life tends to throw a few more problems into the mix, like wind. Wind will affect the bullet as it travels to the target. The longer the range, the longer the wind has to affect the bullet.
As you might expect, shooting directly into the wind, or conversely with the wind, will have little or no affect on the bullet. But shooting with a crosswind is the worst case situation.
Try to spend some time on a range with wind flags, or set up your own, and watch the flags in the wind. Set up the flags so that you have one every 10 or 20 yards for the length of the range, or, at least a couple of hundred yards. Even for 100 yards you will have 5 or 10 flags to watch, and that is enough to tell you a lot. You will see that the wind does not have a constant speed over even 100 yards, and that it may change direction within that same space, maybe even more than once.
The ability to calculate the effect the wind will have on the bullet has been around for some time, with the restriction that the wind be constant, both in direction and velocity. It gives a useful guide, but no one, to my knowledge, has been able to plug in enough data to account for all the changes in the field. With the ability of the wind to change direction, perhaps multiple times over the range in question, combined with the varying velocity, there’s simply no way to get all the necessary data to allow calculating the final effect on the bullet.
With that understanding, we still need to understand wind effects. With a worst-case crosswind, we can multiply the difference in time from the actual time of flight and the time of flight in a vacuum by the wind velocity to determine the bullet drift. Once again, ballistic programs, like Sierra’s Infinity, will give you values for various wind speeds and angles.
A commonly seen value for the wind velocity is 10 mph. That’s a bit less than 15 fps. If our 889-yard shot was subjected to this wind, it would drift more than 28 inches (more than 2 feet) in the direction the wind is blowing. The formula is Wind Drift = VW x (TA x (R/VB), where VW = wind velocity, TA = actual time of flight, R = range and VB = muzzle velocity. Be careful to keep the units consistent.
Guestimating the Wind
Almost as bad as trying to estimate the range, is trying to estimate wind velocity. There are portable instruments that will give you the wind speed, and these can be very handy. They will only give you the wind speed where you are, however.
Some military manuals give a means of estimating the wind velocity by observing flags. They say to note the angle of the flag relative to the flag pole. Divide that angle by 4 to get an approximate wind speed in mph. If the angle between the flag and the pole is 60º, dividing by 4 indicates a 15 mph wind. If a flag cannot be used, dropping a light object (capable of being pushed by the wind) and noting the angle between you and where it hits the ground can do the same as the flag.
Another common problem encountered while shooting is that the earth is not flat everywhere. Everything so far has figured on a flat and level range. What happens if you are shooting up or down hill? It changes things. Notably, it changes the point of impact for the bullet.
What if our firing point is higher, making the shot at a downward angle of 15º? In uphill, or downhill shooting, you need to figure the horizontal range component of the line of sight range. It works the same whether uphill or downhill.
If our earlier situation had the line of sight range as 889 yards, but it is downwards at 15º, the range times the cosine of 15º gives a horizontal range of 858 yards, some 30 yards shorter than the line of sight range of 889 yards. While the 889-yard shot, on level ground would have seen a point of impact 36 inches high, the 858 yard shot will be some 44 inches high. This 8 inch difference is why so many shooters miss when shooting uphill or downhill. The bullet trajectory, and thereby the point of impact, will equate to the horizontal range, meaning you will need to hold low on the target. How much depends on the angle and corresponding level range equivalent.
The air itself, outside of wind, will affect the bullet. The air density, as affected by altitude, temperature and humidity, plays an important part in ballistics. The denser the air, the more drag it will cause on the bullet, meaning the bullet will lose velocity quicker. Temperature and humidity act to change the air density.
The amount of water vapor in the air (humidity) acts inversely to what we would think. Water vapor is less dense than dry air, so the greater the humidity, the lower the air density. This translates to less drag on the bullet as the humidity increases. Note that some references will say just the opposite of this, with respect to humidity.
As temperature rises, it makes the air less dense, as you would think. Elevated altitude also decreases air density. Elevated altitudes normally see decreases in temperature, but the elevation thins the atmosphere and lowers air density that mostly affects the trajectory. If you are up high, and it’s hot, it will definitely change the ballistics.
Effects of Elevation
As mentioned earlier, the accompanying table shows the differences in trajectory between sea level and 1785 feet of elevation, but leaves the atmospheric conditions alone. The Infinity program does allow changing the altitude and temperature (the aspects with the greatest effect) to generate trajectory tables under the conditions you specify.
There are other factors that will affect the bullet during its travel, but these are the principle factors. These factors (and the others) are always present, but at shorter ranges their effect is minimal. As the range increases, their affects become more noticeable.
Eliminate as many variables as you can. Know your rifle and ammunition. Shoot without canting the rifle, if possible. There are several different products available to help you, from simple bubble levels that attach to the rifle/scope, to scopes with built-in bubble levels, to electronic levels, as seen in the Barrett Optical Ranging System (BORS).
The BORS is a small computer that interfaces with your scope. It contains common ballistics tables for popular cartridges, or, through software available from Barrett, which works on your home computer, you can download the exact trajectories for your bullet into the BORS. Once set up and zeroed, the BORS allows easy adjustments for the range you specify.
A laser range finder can be a valuable tool. Scopes with Mil Dot reticles, or other systems of range estimation may be a good investment, to back-up the range finder.
There is never anything that beats practice and experience. Get out and shoot as much as you can, in all sorts of conditions. Every aspect of shooting can be improved with practice, whether improving your trigger control, to reading the wind.
Marksmen have never had better tools, but it is still the man behind the gun that makes it all work.
