This article gives another perspective on understanding ballistics charts.
Introduction
I am not much of a hunter. Over the past five years going up to my in-law’s place, I’ve taken about a dozen shots at the feral pigs that root up sections of their land. I have zero hits on running pigs. If you line up a handful of soda cans filled with water at 25 yards, I can go town on those. But with the pigs out at 200 yards, I am about useless, even when the neighbor has lent me his really nice hunting rifle.
A few weeks ago I was up there and had the rare opportunity to miss twice in a single session. After my first shot they started running and I had about 100 yards of open field before they hit the tree line so, ever the optimist, I lined up and tried another shot. Nope.
Later that evening I was asking myself the question “How far should I lead them at that distance?”
Those of you who are actually proficient hunters will be chuckling and saying to yourself “About that much.” Because you’re already good at this and those things are just part of who you are. Me? I have to think about and do the math first.
How fast do pigs run? I need a number that is meaningful to me, so using miles just won’t work. How about feet? Starting with MPH and working to FPS, 1 mph is ~ 1.47 fps. Adult pigs will do 20-25 mph. While some can reach 30mph, 20-25 seems reasonable for an average adult and that translates 28-32 fps.
To take that number and then estimate how far I should have led them means I have to know how many seconds it takes for the bullet to get to them.
Wait! That’s not on the ammo box! There’s a drop chart on the ammo box and I know the rifle has been zeroed at 200 yards, but there’s nothing on the box that talks about time.
My mind was racing. Formulae from my high school physics class are echoing through my head. Ballistics charts comparing 5.56mm, 7.62mm and 6.5mm are being overlaid in my brain along with BC numbers and muzzle velocity and projectile weights and kinetic energy numbers. And, as I sat down and looked at the calculations, I realized that there was a gap in my understanding of ballistics: It’s about time.
The Drops
When we talk about battle rifles there are some things that we just “know”. For example, when comparing running a 5.56 vs. a .308 as our battle rifle, we “know” that:
- A 5.56 has lower recoil and is therefore quicker to get back on target
- That’s important because it takes multiple shots to guarantee the threat is neutralized
Inside the range of “normal” engagements, a 5.56 lets you hit more often, more quickly, and with enough kinetic energy to neutralize a threat effectively. - Beyond a “normal engagement range” where we switch to long-range shooting, the .308 is more accurate and has better kinetic energy on the target
What we’re saying, in short, is that 5.56 performs better at short range and .308 better at longer range. Let’s illustrate that with an example where we take a 5.56 and a .308 and zero them at 200 yards. While there are some variances, we’ll do what your high school and college physics teachers did and ignore them to keep things simple to start with. From a quick search for each caliber, we get the following drop chart that is likely to be familiar to most readers.
| Range (Yards) | 5.56mm Drop, in Inches |
7.62mm NATO / .308 Drop, in Inches |
| 200 | 0.0 | 0.0 |
| 300 | 7.4 | 8.1 |
| 400 | 22.2 | 24.2 |
| 500 | 46.5 | 49.7 |
| 600 | 95.1 | 86.5 |
| 700 | 156.4 | 136.6 |
If you’re looking at the amount of drop, you see that what we “know” is confirmed by the data. Somewhere after 500 yards, the .308 drops less for longer distances than the 5.56 does.
Why?
Because the .308 has a higher ballistic coefficient (BC).
Okay… But… if it has a higher BC, why doesn’t it perform better at shorter distances? What is it that changes around 500 yards? And what does that have to do with the amount of drop?
Time… It’s about time…
Back to high school physics.
Do The Math
From my high school physics days, the one formula that has stuck with me is the one used for calculating how far an object will drop due to gravity in a given amount of time. That’s the problem that we’re solving for, right?
d = ½ at2 + v0 ∆t
In English, the distance an object will travel, falling in this case, is one-half the acceleration rate (32 feet per-second, per-second) times the time in seconds squared. To take into account any velocity in place before we start the calculation, we add the initial velocity multiplied by the time we care about.
The vertical drop is completely independent of how far forward the bullet has moved. Let’s start with a simplifying assumption and ignore the fact that there is an upward arc required to get to a 200-yard zero. With that assumption, the bullet does not start to drop until it hits 200 yards. If I drop a bullet at the exact same moment that it hits 200 yards, the amount of drop will be the same for both. If we remove the simplifying assumption and toss the bullet up at the same vertical velocity as the bullet right at the same time it leaves the barrel, that bullet will come back to its launching point at 200 yards and will be moving downward at the same speed as the bullet is.
The bullet that I toss directly up will have the same amount of drop with zero forward motion as the bullet that left the barrel at greater than the speed of sound.
In essence: Vertical drop is about time, not distance.
The simplistic answer of “The .308 has a higher BC so it’s better at longer distances” can be restated as “Because the .308 is more energy efficient than the 5.56, it retains a higher percentage of its velocity during flight and that helps it overcome the initial difference in muzzle velocity.”
Or, “A .308 will have less drop than a 5.56 at longer distances because its time to target is lower at those distances. The 5.56 has less drop at shorter distances because it has a lower time to target than the .308.”
To answer the question that started this entire article, the 6.5 Creedmoor that I was using would take about three-tenths of a second to cover 250 yards. Given the 28-32 fps that an adult pig would be running at, that means leading them by 9-11 feet.
MPH or MPG?
Rephrasing What BC Means:
Previously, my thinking about what BC means was relatively simple – “A higher BC means better long range performance” or “A higher BC means better aerodynamics.”
And that’s not wrong.
However, changing my perspective on ballistic charts has also slightly changed my perspective on the meaning of ballistic coefficient numbers. And now I think there’s a different way to phrase it that remains fairly simple while also adding important, to me at least, nuance.
“A higher BC means lower time to target with a higher percentage of initial kinetic energy at longer ranges. In short, BC represents energy efficiency.”
Breaking Down What BC Is
But what exactly is BC?
It’s just a number. Sort of.
Breaking it down a bit, BC is a number that:
1. Combines multiple characteristics of a projectile into a single value that
2. Provides a quick and dirty comparison between similar projectiles
3. Of their respective energy efficiency at longer ranges
All About That Bass
BC takes into account sectional density, mass (aka weight), length, diameter, and drag coefficient. And there are, initially at least, some counterintuitive relationships in there. For example, a heavier projectile leads to a higher BC.
What does that look like in practice?
If you have two bullets that have everything else equal – muzzle velocity, length, diameter, and drag coefficient – a heavier bullet will drop less and have more kinetic energy at any given distance than a lighter bullet.
That… isn’t… obvious… is it? How does that work?
First, go read the book Applied Ballistics For Long Range Shooting, by Brian Litz. His explanation of ballistics is exceptional. I went through his book and wrote my own ballistics calculator and learned a lot from the process. If you don’t really want to do that, and I don’t blame you at all, I’ll give you a quick summary.
The first calculation you make is how much force is being applied to the projectile at any moment in time. That force is based on air density, drag coefficient of the projectile, and the speed of the projectile. The amount of force being applied is independent of the projectile weight. The projectile weight is included in the response to that force.
The response to the force is represented by the formula f = ma. The force is equal to the mass multiplied by the acceleration. What we care about is how quickly a projectile will slow down so we care about acceleration. We get that with a = f/m.
That tells us that if two objects experience the same force, a higher mass (aka heavier object) the acceleration the heavier object experiences will be of lower magnitude than experienced by a lighter object.
To translate that… All else being equal, a heavier projectile will slow down less than a lighter projectile.
Because… Physics!
Does Horsepower Matter?
My second bullet point above that BC “Provides a quick and dirty comparison between similar projectiles.” is important.
“Quick and dirty” means not exact. If you want exact, do the math and you have to run the tables. BC is not a guarantee of performance under specific conditions. There might be conditions where you sacrifice longer range energy efficiency in favor of shorter range performance. You might prefer a carbine chambered in 5.56 over a rifle chambered in .308 if your primary needs are short-to-mid-range engagements.
“Between similar projectiles” is also important. Does a .338 Lapua Magnum have a higher BC than a .17 WSM? Yes, it does. If I’m going out hunting for rabbits, do I care? No. Because I want to actually eat the rabbit after all is said and done. These are completely different projectiles designed for completely different scenarios.
Does a Corvette have more horsepower than a Prius? Absolutely. Am I going to drive a ‘Vette to work, doing Door Dash? Not so much.
EPA MPG
If you have two bullets that start out with the same amount of muzzle energy, the one with the higher BC is more fuel efficient and will be able to travel further, faster, and with more energy on target than the one with the lower BC.
Why is that important?
We fill our gas tank before we start our trip, and when we get to our destination we will want to make a grocery run. Will we have enough gas?
If we’re hunting rabbits for dinner, we don’t want our bullet to have so little energy remaining when it hits that it bounces off and the rabbit runs away.
When a bullet leaves the muzzle, it has an initial kinetic energy. That’s our energy budget. And just like with our car fuel, we need some energy left over when we get to our target so that we can accomplish our goals.
If we know how much energy we need to take our target humanely, (thank you Chuck Hawks), we have a selection of cartridges. We can use BC to help us make sure that we have the energy we need at range to remain humane.
Conclusion
Ballistics charts are amazingly useful tools. But they don’t tell us the whole story. They tell us about drop distance, which is amazingly useful. And when we remain supersonic for the entire trip and the target is stationary, time to target isn’t high on our mind. But there are circumstances where time is important, and understanding how time factors in is useful. (I avoided the pun of “there are times where time is important” because it was just awkward.)
The same applies for the BC of any particular cartridge. Incredibly useful, but it doesn’t tell us the whole story. Context is important.
Always remember the context that you’re working in and don’t try to prove something that the tool doesn’t actually prove. Your .760 BC being bigger than my .170 BC does mean that at 1,000 yards you are more likely to take out the engine of an APC than I am. But at 50 yards, I get to eat a rabbit that you would turn into pink mist for no good reason.
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