Sources of Ballistic Program Inaccuraciesby Linden B. (Lindy) Sisk
Last Revision July 3, 2010*
Shooters using ballistic programs often find that their field shooting data does not precisely agree with the output from their program.
In addition, shooters comparing the outputs of different programs often find significant discrepancies between the programs. Why?
Below are listed the cause of some inaccuracies in the elevation predictions of ballistic programs. Windage calculations are beyond the scope of this article.
Uncalibrated scope clicks. For example, Leupold M1 dials I have tested are closer to 1 inch per hundred yards than 1 MOA. With a typical .308 load at 1000 yards, the difference in point of impact is about 20 inches. If you don't know how to check that calibration, you may find this article useful: Optically Checking Rifle Scopes
Normal variations in muzzle velocity. A good load may have a muzzle velocity standard deviation of 15 feet per second. That means that about two-thirds of the shots will fall in the range from 15 fps per second above the average velocity to 15 feet per second below the average. At 1000 yards with a typical .308 load, that range of variations will cause shots distributed over a 10 inch range. Nota bene: About one third of the shots will have variations from the average which are even greater. There are many causes of this velocity variation, and they are beyond the scope of this article.
Temperature variations in muzzle velocity. A pretty good powder will exhibit a variation in muzzle velocity of 1 foot per second per Fahrenheit degree. If you chronographed your load at 85 degrees and are shooting at 55 degrees, your muzzle velocity may be 30 feet per second slower than you think it is. I have measured variations as large as 5 feet per second per Fahrenheit degree. The only way to know how big that variation is, is to test it. In addition, my experience has been that the standard deviation of the muzzle velocity increases at low temperatures.
Muzzle velocity measurement errors. Do you believe your chronograph is accurate? The screen spacing of most chronographs is too short for accurate measurement. Some chronographs like the Oehler 35 series allow extending the spacing. The clock frequency of many chronographs is too slow to get accurate and consistent measurements, i.e., more than one shot with the identical muzzle velocity will be displayed with different measurements. Other common problems with chronograph data is failing to compensate for the distance between the muzzle and the chronograph screens, and failing to fire enough rounds to have a good average velocity. People with little understanding of statistics may have a very vague idea of what the chronograph output means. See Statistics for Rifle Shooters
Ballistic coefficient variations. Most manufacturers publish only G1 BCs for their bullets. The G1 coefficient doesn't match very well the shape of modern boattail bullets. To accomodate that, Sierra publishes BCs for their bullets in velocity ranges. However, many ballistic programs are not set up to handle multiple BC values. A better match to boattail bullets is the G7 BC, which will produce a better calculation of bullet velocity at range, which is useful to shooters who are operating near the transonic range of their bullets. Some bullets exhibit unpredicable behaviour in the transonic range. The Sierra 168 grain Matchking is one such bullet.
One source of G7 BCs produced by extensive testing is the book Applied Ballistics for Long Range Shooting by Bryan Litz. I highly recommend this book for anyone serious about shooting at extended distances.
In addition, the online program JBM Ballistics has some G7 BCs in its bullet library. It does not tell you what the G7 BC is - just select the a bullet with the label "(Litz)" after the listing in the bullet library. If there is no such label after the bullet you are using, a G7 coefficient is not available. Also select G7 in the main screen.
Range uncertainty. This is a prime cause of differences between the ballistic program output and field shooting data at long range. At 1000 yards with our typical .308 load, a range error of 20 yards will cause an elevation error of about 18 inches, which is 0.5 mil or almost 2 MOA. You may believe your laser rangefinder is accurate - but a one percent error at 1000 yards is 10 yards, and that's assuming that you actually managed to laser the target. The manufacturer of the common Leica 1200 claims an accuracy of +/- 0.5 percent beyond 800 yards.
Elevation variations caused by the headwinds or tailwinds. Headwinds slightly increase the drag on the bullet, and tailwinds reduce it. Not all ballistics programs correctly model this effect.
Aerodynamic jump. This is Bryan Litz's description of this factor: "Aerodynamic jump is what causes groups to slant when shot in varying wind conditions. Basically, when the bullet exits the muzzle into a cross wind, the bullet tries to yaw slightly to align itself with the airflow. When the bullet yaws to the side, gyroscopic action causes it to nose up or down by a small amount depending on the wind direction. This initial yaw has an effect on the trajectory, and is known as aerodynamic jump. The more severe the cross wind, the more pitch the bullet ends up with. Flying to the target at a pitch angle will result in an elevation error that's proportional to crosswind." From: Extending the Maximum Effective Range of Small Arms. That's a good article which describes some of the limitations of existing ballistic programs.
The Eötvös effect. This is an elevation variation caused by the earth's rotation. It is of most significance on long shots taken directly due east or west. Some ballistics program do not correctly model this effect. Bryan's Litz's book previously referenced has a section on how to calculate that effect if your ballistic program does not. The magnitude of this variation might be in the range of 10 inches maximum difference on a 1000 yard shot between a due east shot and a due west shot, depending on your lattitude.
Incorrect specification of atmospheric parameters. Many shooters do not understand the difference between station pressure and barometric pressure referenced to sea level. See Barometric Pressure and Ballistic Software.
Error in Inclined Shot Calculations. Many ballistic program do not correctly compensate for the difference between an uphill shot, where gravity slightly hinders the bullet, and a downhill shot, where gravity is slightly aiding the bullet. For example, on a 900 yard shot at a 30 degree angle, the difference between an uphill shot and a downhill shot is about one MOA. The magnitude of this difference increases with the angle. Most programs I have seen are doing a calculation appropriate to an uphill shot, so what one might do to compensate for that is to hold a little low on a downhill shot.
An additional possible error on an inclined shot is failure to compensate for the difference in air density between the firing position and the target. For example, on a 900 yard shot at a 30 degree angle, the altitude difference between the firing position and the target is 1350 feet. No ballistic program I am aware of attempts to compensate for that difference.
Parallax error caused by improper adjustment. When looking through the scope at the target, the reticle should not appear to move relative of the target when you make a slight movement of your head. If it does, parallax error is present and should be corrected.
Zero errors. If your hundred yard zero is off by a quarter of an inch, at 1000 yards your point of aim will be off by 2.5 inches.
Shooter variations. We have seen two shooters have different points of impact on the same target at long distance using the same rifle and load. That's because of differences in the way the rifle is held by the shooter.
Differences in atmospheric modeling between the programs.
Now that we know some of the causes, and have eliminated or compensated for as many of the variables as we can, what can we do?
We can systematically modify the program output by shooting long-range with our load, and then adjusting the muzzle velocity or BC input to the program until the program output matches the shooting data. I typically do this at a range of 1000 yards with a .308. Nota bene: it should be done at a range and under conditions where you know the bullet has not entered the transonic region. We might say the bullet has entered the transonic region if its velocity has decreased to within 110 percent of the speed of sound. (The speed of sound is about 1125 feet per second at 68 degrees F. It varies only with temperature.) So, if the speed of sound is 1125 feet per second, we might say the bullet is in the transonic region when the speed has dropped to 1238 fps.
If other sources of error discussed above have not been ruled out, it should be obvious that the correction obtained by this process will apply only to this load fired from one specific rifle with one specific scope - maybe.
Understand from this discussion that no ballistic program can produce an output sufficiently accurate to guarantee a first-round hit at ranges beyond a few hundred yards. A ballistic program is correctly used to get you close to that first-round hit under conditions you don't normally shoot in. An example is training with your rifle and load at sea level, and then trying to make a high-altitude shot.
When someone says that their un-tuned ballistic program was "right on at 1000 yards", I generally conclude that if they are telling the truth, they were lucky enough to have offsetting errors.
July 3rd, 2010. All that was changed was a link to the Engleman article on chronograph statistics.
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