Long Range Shooting: Understanding Extreme Spread And Standard Deviation
September 05, 2018
With the increase in interest in long-range shooting, the terms extreme spread (ES) and standard deviation (SD) are being thrown around a lot. What exactly is ES and SD? More importantly, should you really care about them? And what do they mean to the expected performance of your ammunition? I will offer some definitions and examples for the first question and the answer to the second question depends on whether you are a handgunner or rifleman, a plinker or a precision shooter.
First off, let's discuss the definition of ES and SD. ES and SD are mathematical terms that define the extremes, uniformity and expected variation in a sample of data or numbers.
ES is pretty simple, it is the extremes of values of a set of data or numbers. As it applies to ammunition, it almost always refers to either the velocities or pressures produced by a sample of ammunition. Let's say we test 20 rounds of ammunition and measured the pressure and velocity of each round. The ES of pressure would be the difference between the highest and lowest pressure. Likewise, the ES of velocity would be the difference between the highest and lowest velocity. As it turns out, with ammunition, the pressure and velocity ES go hand in hand. What one does the other will mirror. You're going to get small pressure ES with a small velocity ES and vice versa. The more consistent the components of the ammunition are and the more consistently they are loaded the lower the ES you would expect.
SD is not as straight forward a concept. To be technically correct and to satisfy all the math majors out there, let's start off with the mathematical definition of SD. The SD of a random variable, statistical population, data set, or probability distribution is the square root of its variance. Wow, what does that mean? Put in terms those of us that are math challenged can understand, SD is a measure of how spread out numbers, data or whatever we are sampling is from the average. The smaller the SD, the less variation there is of the data from the average. The bigger the SD, is the bigger the variation there is of the data points from the average.
For example, suppose we shoot three, 10-shot groups and record the velocities with a chronograph. Table 1 shows the data for these three groups of velocities along with the mean or average, and the ES and SD for each 10-shot group. You can see that as the ES changes so does the SD.
You can see that as the difference between the highest and lowest velocity, or ES, gets greater, so does the SD. The expected variation of numbers from the mean, the SD, is getting larger as the ES gets larger. Hopefully this gives some insight into what ES and SD are.
OK, enough of this math stuff, it's making my head hurt! What insights can you gain from the ES and SD measurements on your chronograph about the quality of the ammunition you are using? In the end, what really matters with your ammunition is how it performs. The reloader or ammunition manufacturer can use very high-quality components, but if they are not loaded properly, the ammunition will not perform well. To reduce the variables that can impact the shooting results, we generally want the most consistent performing ammunition we can get or figure out how to load.
Many things go into determining how consistently ammunition will perform, such as case capacity and hardness consistency, neck thickness and diameter consistency, projectile weight and diameter consistency, primer performance consistency and perhaps most importantly, propellant charge weight consistency and quality. In handloaders' quest for the best results, this is why it is always stressed to use the same lots of components. No matter how hard manufacturers try to produce consistent products, there is always some variation in materials and tooling wear from lot to lot. It is a tribute to modern manufacturing practices that we have achieved the level of consistency in ammunition products that we currently enjoy.
The ES and SD values you measure on a chronograph when testing ammunition is a direct measurement of the quality of components and how well those components work together. It is also a measure of the care and precision taken when assembling these components. As general rules of thumb, ammunition that performs at or less than 50 feet per second (fps) ES is pretty good ammunition. Ammunition that shoots under 35 fps ES is really good ammunition. Ammunition, factory or otherwise, that performs consistently below 25 fps ES will be extremely difficult to realize. You can use these values as indicators of the quality of ammunition you are shooting and the level of accuracy you would expect from your ammunition.
Let's apply ES and SD to practical shooting examples and see how they can give insight into ammunition performance expectations. We will look at rifle shooting first. Let's start this discussion by stating up front, if your primary interest in shooting is plinking, shooting at cans, rocks, etc. at short ranges, you really don't need to pay much attention to ES or SD. However, if your shooting interests are in any discipline where high levels of accuracy are desired, you should definitely pay attention to ES and SD. Several rules of thumb have application here. Anytime you are shooting at long ranges, beyond 300 yards, or are shooting relatively low ballistic coefficient (BC) projectiles, say below .300 G1, the lower the ES and SD, the tighter the groups you will shoot, particularly in elevation. Let's look at a couple of shooting examples and vary the muzzle velocity ES and see what it does to the elevation point of impact (POI) strictly because of muzzle velocity variation. For the first example, we'll use a .223 Remington with a 55-grain projectile that has a .240 G1 BC at a nominal muzzle velocity of 3,250 fps. We'll see what the elevation variation is because of ES for ranges of 200, 300 and 400 yards. We will use ES values of 25, 50 and 75 fps. Table 2 shows results for this study. The JBM Ballistics solver was used for the trajectory calculations.
As you can see from the table, it would take a large ES to make a noticeable effect in elevation POI at 200 yards. By 400 yards, the muzzle velocity ES is beginning to show.
Now, let's look at a more extreme example. Take a .300 Winchester Magnum (WM) firing a 225-grain projectile with a .375 G7 BC at a nominal muzzle velocity of 2,775 fps. We'll use the same 25, 50 and 75 fps ES values. This time we'll look at the effects of ES at 300, 1,000 and 1,500 yards. Table 3 shows the results for this study.
You see that as ranges get longer and longer, ammunition ES is critically important to the results. This also gives insight into what the limiting accuracy expectations are for extreme long-range shooting. Recall that to get ammunition that will consistently shoot 25 fps ES or better is a tall order.
Let's take a look at what the effects are on pistol ammunition. Several things are different for pistol ballistics. The first is that velocities are much lower, and in many cases subsonic or below Mach 1. This means that for any subsonic pistol projectile the drag on a projectile or the BC is nearly constant, the rate of velocity loss is nearly constant. For a high-velocity rifle projectile, the drag or BC is very much dependent on velocity. Muzzle velocity variations for a high-speed rifle projectile show more effect on POI because of the changing drag as a function of velocity. The biggest difference for a pistol shooter is, of course, the range is generally much shorter. On the short ranges pistols are generally used at, the time of flight is much shorter than a rifle and differences in muzzle velocity don't have enough time to have as much effect in the POI. Let's look at an example and examine the elevation POI differences. We will shoot a .45 ACP with a 230-grain projectile with a .185 G1 BC at a nominal muzzle velocity of 900 fps. We will shoot at ranges of 25, 50 and 75 yards and use ES values of 25, 50 and 75 fps. Table 4 shows the results for this study.
The table shows that a pistol sees the same type of effects in the elevation POI as a rifle, just not the same order of magnitude over their useful range. I don't know any pistol bullseye shooter who would be willing to ignore a variable that can add upwards of an inch to the size of the groups they shoot.
There is one more effect of the ES that we need to discuss. As I mentioned earlier, the velocity ES is directly tied to a variation in the pressure the ammunition produces. These variations can be caused by component variations as well as propellant charge variations. What effect would these variations have on the felt recoil on a .300 WM shooter versus a 1911 shooter? We'll compare the recoil energy of a 12-pound .300 WM versus a 2.75-pound 1911. We'll use an ES of 75 fps for each, with the nominal muzzle velocity we used above. Table 5 shows the study results.
As can be seen from Table 5, there are differences in recoil because of the velocity ES of the ammunition. I would argue that the typical rifle shooter would have a hard time noticing a 41/2 percent difference in recoil in a .300 WM and it would be unlikely to affect their shooting. On the other hand, a 15 percent difference in recoil in a handgun is going to be noticeable and would likely have some effect on the shooter.
Hopefully, after reading this you have an understanding of what ES and SD mean the next time you read about it or it comes up in conversation. Depending on your shooting discipline, ES and SD may not matter much to you. However, if you are a long-range rifle shooter or involved in any shooting sport that demands precision and accuracy, ES and SD are extremely important to your end goal. The availability of reliable, low-cost chronographs give shooters an invaluable tool to measure and quantify the uniformity performance of their ammunition and make informed choices about their ammunition of choice or their pet loads.