HuntingNet.com Forums - Weaponized Math: How much does Charge Weight Precision Matter?

Weaponized Math Preamble: by its nature, long range, precision marksmanship is rooted deeply with mathematics and physics. Intimate understanding of these principles is NOT required to be successful as a long-range marksman, but understanding and applying these concepts can help marksmen connect on target. For those interested, I’ll offer a series of these “Weaponized Math” topics to hopefully demystify some of the concepts, spur discussion, and help other shooters understand and apply these principles to improve their marksmanship.

Quite frequently, among new PRS competitors, comes up the conversation about what handloading equipment we should use, especially for powder dispensing and weighing. PRS competition incorporates the unique challenge of combining a relatively high expectation for precision and consistency with also a relatively high volume of fire. While most targets are 1-3moa, typically proportionately larger as distance increases, we may engage ½ moa targets out to 1200+ yards, and will typically fire 80-120 rounds per competition day, with most active competitors shooting multiple matches per month. So, we’re challenged to make a lot of ammo with a high grade of precision, in short time, and for most of us, that combination means very expensive powder dispensers which are extremely precise, as well as blisteringly fast. But do we really need that standard of precision?

Naturally, charge weight is one of the most carefully scrutinized control parameters of long-range reloading – but let’s explore the question – “why do we believe charge weight precision matters?” Understanding this question, and its answers, we can subsequently ask, and answer, “How precise do we need to be?” or rather answer, “how much does charge weight variability hurt our groups down range?”(Spoiler alert – it also answers why we choose to “load in the node,” even if the difference isn’t as bad as one might expect).

At the most basic level, when we fire a shot, we start a combustion reaction in which the Potential Energy stored in the powder is converted into Kinetic Energy of the bullet (and ejecta particulates & gases, and heat, noise, and deformation loss). When powder burns, it releases Chemical Potential Energy, which increases Heat and volume of the powder mass, resulting in increased Pressure inside the cartridge and bore; reminding here that Pressure is a Force distributed over an Area, P=F/A, and Force in a dynamic system results in Acceleration of affected Mass, F=MA, which in our case, and that Force acts on the bullet until it uncorks at the muzzle with its resultant Muzzle Velocity, and corresponding Kinetic Energy. It is well understood that increasing powder charge increases bullet velocity and kinetic energy, and vice versa – which comes with the consequence: if we load ammunition with variable powder charges, we also expect variable muzzle velocities. But the relationship between potential energy in and kinetic energy out isn’t a predictable curve, and certainly not linear, as we’ll explore below.

Study of external ballistics proves the relationship between muzzle velocity and trajectory. Simply stated, the faster a bullet travels, the less drop it will have at long range than it would at a slower speed. As an example, we know a 300win mag shoots flatter than a 308win with the same bullet, because of the increased velocity. A 308win shooting a 178ELD at 2550fps will have over 12ft more drop at 1000yrds than a 300win mag shooting the same bullet at 3050fps.

This principle applies in the same way between faster and slower powder charges within a given cartridge. If we have variable powder charges which result in variable muzzle velocities, some rounds flying faster than others, we’ll also have variable trajectories down range, some bullets within a group impacting lower than others. In this example, I have two targets, both shot at 875 yards; on our left, a 15 shot group with 6.5 Grendel, using ammunition which had 78fps extreme spread (fastest vs. slowest shot of the group), while on our right, two groups from a 6 creed, 3 shots to find the target downrange, after which I dialed 0.2mils to raise the impacts to my point of aim, then 12 shots, all 15 of which only had 24fps extreme spread. Accepting, the 6.5 Grendel is much slower and with a less aerodynamic bullet, so it has more sensitivity to velocity spread than the 6 creed, but we can see there is MUCH greater vertical dispersion in the group with the greater velocity spread.

So, knowing our trajectory is sensitive to muzzle velocity variability, and knowing our muzzle velocity variability can be at least partly influenced by our charge weight variability, we can explore: How precise does our charge weight need to be to avoid influencing our group size?

First, let’s take a look at how much control we can get from different reloading equipment.

Common electronic powder dispensers, such as the RCBS Chargemaster, Hornady AutoCharge, Lyman Gen5/6, Frankford Intellidrop, etc have stated precision of +/-0.1grn. This means from one charge to the next, we can only trust that two charges which both read 41.7grns are somewhere between 41.6grn and 41.8grn. Alternatively, there exist some high precision options for powder dispensing and weighing (massing, really) which utilize the A&D FX-120i analytical balance with repeatable precision down to +/-0.015grn, such as the SuperTrickler and the AutoTrickler (or the Prometheus). For reference, I’ve found H4350 and Varget, such as what I use for my PRS match rifles, and the data sets used for this analysis below, I tend to see approximately 62.5 kernels per grain of powder, or 0.016grn per kernel, meaning the FX-120i can resolve charge weights down to the nearest kernel. And as to be expected, this heightened precision does not come cheap – while conventional reloading powder dispensers are priced $250-400, these ultra precise units are priced around $1500. So how much group size does that extra precision, that extra $1000, really buy? I spent some time analyzing my own load development data to make some comparisons.

I started using the Satterlee Method for long range load development, or Velocity Curve Method, for the last ~8yrs, as an evolution of the Audette Ladder Method I had used for over a decade before. In this test, we load one or a few rounds of each of several small increments in increasing charge weight and measure the velocity of each step along the way. I had on hand many iterations of this test for my match rifles, as I reshoot my load development test before most matches – plotting the relationship between potential energy in and kinetic energy out as described above, over and over throughout a year. Slightly complicating the mathematics, but making our lives easier as shooters and handloaders, barrel harmonics break down the linear relationship between energy in vs. energy out and promote what we call “nodes,” which we see as flat spots in the curve. In these nodes, these flat spots, changing charge weight has less effect on muzzle velocity – to the point of having little to no effect at all.

These nodes are where we want to load, because they offer the greatest forgiveness in our powder charging method and indicate the greatest consistency of combustion from one round to the next. Below is an example of my own load development test in 6 Creedmoor, we can see a clearly defined node between 41.6grn and 41.8grn, circled in green. Loading in this region, targeting 41.7grn in the middle, I could accidentally load 41.6grn in one round and 41.8grn in another, or anything in between, and still expect the rounds to hit the same waterline downrange (same vertical point of impact).

But what is the worst-case scenario? What if we don’t know how to find a node, and what if we find ourselves loading in a less forgiving section of the curve? Circled above in red is considered an “anti-node,” meaning it’s the most unstable region of this curve, where an error up or down of 0.1grn in charge weight from 42.0 means almost 20fps velocity change. As described above, comparing my RCBS Chargemaster and my AutoTrickler V3, I have the choice to load either to the nearest 1/10th of a grain, OR to the nearest kernel – how much difference will I see on target between these options if loading 42.0grn?

Examining the data from this ladder, I can see that loading in the green circle, targeting 41.7grn, there’s no effective difference between loading to +/-0.1grn or +/-0.015grn with either of my dispenser options. Alternatively, loading in the red circle is showing up to 191.7fps per grain, so let’s use that as our worst-case scenario. 191.7fps per grain would mean +/-19.2fps per 0.1grn if loading with a Chargemaster at +/-0.1grn precision, or an expected 38.4fps extreme spread. Parsing that down to individual kernels, loading to +/-0.015grn on my AutoTrickler, I’d only expect +/-3fps, an expected ES of 6fps.

We can run these velocity spreads through our ballistic engine to see just how much each could change our point of impact on target. Comparing 1,000yrd drop for the velocity spread around our average of 3138fps for 42.0grn, running the ballistic engine at +/-19fps and +/-3fps:

However, those estimates are a projection of the maximum potential error, but in real-world application, we know we have multiple additional error contributors, and we know that multiple random errors do not stack like bricks. We know it’s incredibly unlikely that the highest-flying bullet of a raw group would also coincidentally be the highest crest of the shooters wobble zone when breaking the shot, AND coincidentally be the highest velocity round out of the group. Rather, we estimate compounding errors by taking the square root of the sum of the squares for each error. So, while the maximum potential trajectory difference of 7” of loading on a Chargemaster seems like much more than only 1” when loading with an AutoTrickler to the nearest kernel, when we compound the errors, we don’t actually see an additional 6” of vertical spread. If we compare a .25moa raw potential rifle, fired by a shooter with a 1/2moa wobble zone at 1000, shooting ~5.8” groups at 1,000yrds with perfect ammo, adding 7” of potential trajectory error only adds 3.3” of actual vertical when compounding the errors, whereas adding only 1” of trajectory error adds about 1/12” of compounded error – call it a difference of 3” at 1,000yrds.

What does that all mean for the shooter considering which powder dispenser to purchase? Well, considering this data, consistent with ~30 repetitions in 6 different 6creed barrels, dispensing powder with a Chargemaster with +/-0.1grn precision – at its very worst – won’t even induce as much error as 1 turret click difference compared to loading on SuperTrickler or AutoTrickler at +/-0.015grn precision. And for either equipment, loading within a velocity node would mean exactly no difference at all, since our nodes are as wide or wider than the precision of either method.