Ballistic coefficient: What is it? Part 2
by Tom Gaylord
Writing as B.B. Pelletier
Last week I republished Part 1 of this discussion about ballistic coefficients because I was out of town helping my sister. I’m back in the office, but Part 2 of this report is necessary to close the loop. So here we go.
This report covers:
• Today’s discussion
• Round balls
• Conical bullets
• Smokeless powder
• A big point
• Round balls — again
• The bottom line
I’ve taken 11 months to return to this subject of ballistic coefficients (BC). That was in spite of some tremendous interest in Part 1 of this report last May.
I’m purposely avoiding all discussion of mathematics, which is difficult, since ballistics is a discipline that heavily employs mathematics. But I’m not qualified to write about the math; and, more importantly, I know that 99 percent of my readers would be turned off if I were to write the report that way.
Last time we learned that the BC of a pellet:
• Is an extremely small decimal fraction compared to the BC of a conical bullet.
• Varies with the velocity of the pellet.
• Varies with the shape (form) of the pellet.
We also learned that the stated BC of a pellet can be forced to vary by the distance from the muzzle at which the measurements are taken.
We understand that diabolo pellets are designed to slow down rapidly in flight, and that the BC is a measure of the velocity retained in flight. So, a pellet’s BC rapidly changes over a short distance.
We learned that a pellet’s BC varies between 0.010 and 0.045. We also learned that pellets that have a relatively high BC (the larger numbers) will take longer to slow down than pellets that have a relatively low BC. Even though all diabolo (wasp-waisted with a hollow tail) pellets slow down rapidly, the higher BC numbers are given to the pellets that slow down the least in relation to all diabolo pellets.
Today, we’ll look at the impact that shape (form) has on the BC. We’ll also look at the impact velocity has on the BC. Let’s begin with that.
When firearms were first invented (we now believe that was in the 1300s), the earliest formal shape for missiles was either a shaft (arrow or dart) or a ball. The earliest ball-like projectiles were probably just stones, but that soon gave way to uniform lead projectiles that were easy to cast. Cannon balls were still chiseled from tough rock for many years before they, too, were cast from iron into spheres.
The round ball became more than just a projectile of choice. It became synonymous with the title — bullet. From some time in the 1400s to around 1840, the word bullet meant a round ball. Round balls are easy to enter into formulas and ballistics tables because the form is always the same. The weight varies with the caliber, but not the form (shape). Because of this, the early science of ballistics was built around a spherical bullet, and everything was fine.
Conical bullets (oddly referred to as conical balls in their early days) changed everything. Ballistics had to expand to adapt to these new projectiles. Several ballisticians worked out new formulas to account for the different new forms, but by now the forms were changing faster than the science could keep up.
Then, smokeless gunpowder came on the scene and things changed again. Velocities with black powder (which, up to that time was just called gunpowder) topped out somewhere around 1,600 f.p.s. Within 20 years, smokeless power doubled that speed; and in another decade, it added another thousand f.p.s. Suddenly, bullet makers had to be concerned with shapes that flew at ultrasonic velocity. This was decades before anything else approached that speed, so things like wind tunnels weren’t even available for modeling.
It may seem like I’m getting far from the topic, but here’s why I am telling you this. In 1870, the Rev. Francis A. Bashforth — the inventor of the first (?) electronic chronograph — discovered that drag increases with the square of the velocity at speeds between 430 f.p.s and 830 f.p.s. — but with the cube of velocity at speeds between 830 f.p.s. and 1,000 f.p.s.! That higher range is the trans-sonic region that we tell airgunners to be wary of. We used to think it caused inaccuracy, but I disproved that in 2011 in an 11-part blog series titled Velocity versus accuracy. But what it definitely does do is increase the rate at which projectiles slow down.
I could easily get into a discussion of the ideal shape for supersonic projectiles, and there are many airgunners who would like that. “Just design a solid pellet that has a boattail, and all your problems are solved,” they say. Yes, all problems are solved, save one — accuracy. No airgun I know of is capable of accurately shooting those solid pellets (that I’ll now call bullets) at supersonic speeds. In fact, very few airguns can get them up to supersonic speeds at all! So, the discussion is over before it begins.
A big point
If something can’t be done, it makes very little sense complaining about what “they” should do. The blog readers know that I’m not a negative person. I’m willing to try anything that has a chance of success. But physics is physics! I’ve learned in all my experiments and reading that airguns have practical velocity limits. We may not be at the limit today, but we’re very close. Because, to push a pellet any faster than about 1,500 f.p.s. (1,486 f.p.s. is the fastest pellet I’ve ever observed), requires us to do things with compressed air that it just doesn’t want to do. The speed of sound governs how fast air can flow. Pellets can be pushed faster than the speed of sound; but to go much beyond 1,500 f.p.s., we’re going to have to use a different compressed gas.
So, pellets that top 1,000 f.p.s. are slowing down at least at the cube of their velocity. That’s what Bashforth tells us. Take another look at the chart I showed you in Part 1:
The ballistic coefficient of a single pellet can change this much with velocity changes.
The chart isn’t real, which means it wasn’t generated by actual test data, but the relationship of the BC decline at the trans-sonic region is representative. Lighter pellets fall off their BC at lower velocities, so take the entire curve and move it to the left. The same thing happens — just at lower velocities. Heavier pellets fall off at higher velocities, too. But all of them fall off in the same way.
Enough talk about velocity; now let’s look at what the shape (form) of a pellet does to the BC. Just as certain shapes work well at supersonic speeds, there are also good shapes for subsonic speeds, where most pellets live. A domed nose with a solid cylindrical body is very good at subsonic speeds. And the more it weighs, the higher the BC will be.
The shape or form of the pellet has a lot to do with the ballistic coefficient.
The wadcutter, by contrast, is the worst shape — or at least it’s down there with the worst of them. Some people feel that hollowpoint pellets are even worse because their hollow points act like air brakes. Others believe the hollows fill with air under pressure, and the pellets then act like wadcutters.
The pointed pellet is not as aerodynamic as its shape seems. While it looks sleeker than a dome, it doesn’t turn out to work that way at subsonic pellet velocities. A point is great for supersonic speed, but it does very little below the speed of sound. Pointed pellets do penetrate deeper in solid media; but in the air, they aren’t that different from domes.
Round balls — again
Round balls — remember them? As it turns out, a round ball is sleeker at subsonic velocities than any diabolo pellet. Only when the pellet weighs considerably more than a ball of the same caliber (and may be too heavy to shoot effectively) will it have a superior BC. Round ball BCs hover around the 0.07 mark. That’s about double what the best diabolo pellet offers and several times what the average diabolo has.
So, why not just shoot round balls? Simple answer — accuracy. Round balls don’t have any accuracy at longer distances. The high drag of the diabolo pellet — the very thing that destroys their BC — is also what helps them be so accurate.
The bottom line
Yes, the BC of a pellet is important, but only after you know that it’s accurate. If you can’t hit what you’re shooting at, the retained velocity of your pellet means nothing.
So, search for accuracy first and a high BC second. Or, in some cases, such as long-distance hunting, look among the pellets with high BC numbers for the one that’s the most accurate. Don’t just shop for the highest BC unless you also understand the relationship of your gun to that number (re-read Part 1 to understand).
Is that all there is? Of course not. We could go on and talk in more detail about form, but I think the basics have been covered.
I know that many of you use the Chairgun program and find it very useful. One of the things Chairgun requires is the input of the BC of the pellet in question. Sometimes, you only discover how close that BC is after shooting your gun and matching the results to the Chairgun predictions.
I don’t know if I’ve helped you understand ballistic coefficients or if I’ve just confused you more. If you remember the basic things I’ve outlined in this report, it’ll stand you in good stead in your future shooting.