Ballistic Coefficient & Bullet Math : Long-Range Shooting Science

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Tom says Ballistic Coefficient & Bullet Math is simple, keep reading to learn some shooting skills in our new long-range shooting science series.

When Long-Range Shooting distances increase, details like ballistic coefficient of your bullets become a significant factor.
Ballistic Coefficient & Bullet Math : When Long-Range Shooting distances increase, details like ballistic coefficient of your bullets become a significant factor.

USA –-(Ammoland.com)- Here’s why obscure [and some say boring] bullet ballistic concepts like ballistic coefficient and sectional density are essential if you want to hit targets regularly when shooting at long-ranges. Let’s assume you’re shooting a .308 rifle and you have two types of bullets of identical weight.

One is a 150-grain Sierra Pro-Hunter. It’s a lead-tipped, jacketed bullet with a flat-point tip and a flat base. It’s great for lever-action rifles and hunting.

 

This .308 150-grain Sierra Matchking has a high ballistic coefficient due to its sleek aerodynamic shape.
This .308 150-grain Sierra Matchking has a high ballistic coefficient due to its sleek aerodynamic shape.

The other is a 150-grain Sierra Matchking. It’s a jacketed bullet with a tiny hollow-point, non-expanding design. The base is a boat-tail shape. It’s great for accurate target shooting. Now, let’s launch them both at 2,750 feet per second from a Sierra Bullet Blaster 7000 rifle and see what happens.

After running the trajectory numbers based on atmospheric conditions here where I live in South Carolina, we get the following results.

Sierra .308 150-grain FPSierra .308 150-grain Matchking
Muzzle Velocity2,750 fps2,750 fps
Velocity, 100 yards2,379 fps2,510 fps
Velocity, 500 Yards1,334 fps1,649 fps
Velocity, 1,000 yards868 fps1,029 fps
Muzzle Energy2,543 ft-lbs2,534 ft-lbs
Energy, 100 yards1,885 ft-lbs2,098 ft-lbs
Energy, 500 yards592 ft-lbs906 ft-lbs
Energy, 1,000 yards251 ft-lbs352 ft-lbs
Bullet Drop, 100 yards0.00”0.00”
Bullet Drop, 500 yards-79.30”-63.24”
Bullet Drop, 1,000 yards-678.10”-475.78”
10mph Crosswind, 100 yards-1.50”-0.93”
10mph Crosswind, 500 yards-44.69”-28.36”
10mph Crosswind, 1,000 yards-206.53”-142.47”

These two bullets, while of the same weight, have different ballistic coefficients. The flat point Pro-Hunter has a ballistic coefficient of 0.185. The Matchking has a coefficient of 0.417. In the world of ballistic coefficients, a bigger number means that a bullet flies more efficiently.

This Sierra Pro-Hunter is also a .308, 150-grain bullet, but it has a much lower ballistic coefficient.
This Sierra Pro-Hunter is also a .308, 150-grain bullet, but it has a much lower ballistic coefficient. Note the bullet shape.

OK, so with the Sierra flat point Pro-Hunter, I picked an unusual bullet to illustrate a long-range shooting ballistic concept, but that’s OK. As a shorter-range hunting bullet, it’s going to show the impacts of differences in ballistic coefficient more dramatically.

Rest assured, there will be performance differences between every two bullet designs of the same weight and different shape, just not as dramatic.

So why the significant differences even though bullets were of the same diameter, weight, and velocity? That boils down to more complex factors like shape, length, and weight distribution. Two measurements that help define the downrange performance of a bullet are ballistic coefficient and sectional density. As Sectional Density is a key input to Ballistic Coefficient, we’ll look at that first.

What is Sectional Density?

Sectional Density is a measurement that reflects the ratio of something’s mass to its cross-sectional area. That’s way too complicated, so let’s use an illustration.

Imagine launching a quarter at a target, but we somehow get it to fly face first, so the “top” flat side with George’s head is leading the way. We’ve got a big wide object pummeling its way through the air towards the target. From front to back along the flight path, the quarter is only 0.069 inches “long” when it’s flying face first because that’s the thickness of a quarter. A quarter flying this way makes a lousy bullet, right? So, in this case, the quarter has a very low sectional density because its mass is divided by a large number that represents its surface area.

Now imagine a nail flying point first. It’s long and narrow, so the surface area pointing into the wind is very small. The nail flying point forward has a very high sectional density because it’s long and skinny.

Simply put, sectional density is the ratio of weight to the diameter of the bullet. Technically, it’s the ratio of the weight to the surface area, but it’s easier to think in terms of diameter as that's how bullets are measured. To grossly abuse math and physics, bullets with high sectional density are long and skinny. Bullets with low sectional density are short and fat.

Oh, and because our two example bullets above have the same weight and diameter, hence the same frontal surface area, the sectional density numbers are the same: .226.

What is Ballistic Coefficient?

Ballistic coefficient (BC) is a mathematical representation of how efficiently a bullet flies through the air. A bullet with a high ballistic coefficient is slippery and less subject to drag (slowing down) as it continues on its merry way. Here’s why.

The original ballistic models were based on a standard bullet like this. Ballistic Coefficient numbers are fudge factors that adjust for how each projectile performs relative to the standard model.
The original G1 ballistic bullet models were based on a standard bullet like this. Ballistic Coefficient numbers are fudge factors that adjust for how each projectile performs relative to the standard model.

Simply put, ballistic coefficient is a fudge factor. Back in the day, guys with lots of time on their hands fired boatloads of projectiles to figure out how they behaved in flight. The goal was to be able to predict how far projectiles would travel, the arc of flight, and at what velocity they would impact targets. Given that there is an infinite number of bullet types, weights, and shapes, doing all the math for each would be an impossible task. So, someone said, “Hey! Let’s design a ‘standard’ bullet and do all the math for that one. Then, for other bullet types, we can create a fudge factor that adjusts the standard bullet trajectory model.” That’s basically what the ballistic coefficient does. It adjusts the trajectory prediction for each bullet type.

As a fudge factor, the ballistic coefficient is usually a number between one and zero, but not always. Some big, heavy, and efficient bullets like the .50 BMG can have a ballistic coefficient greater than one, but that topic is for another day. The bottom line is this. The bigger the ballistic coefficient number, the more slippery the bullet, so it flies farther and faster than one with a lower coefficient. Remember that in our example, the Matchking had a coefficient of 0.417 while the Pro-Hunter had a BC of 0.185.

One more thing. You might see different BC numbers for bullets at different velocity ranges. That’s because the BC varies with speed. You don’t have to worry about that as your ballistic software will deal with it.

Drag Models

Originally, those smart people who did a lot of testing on the range worked out predictive models for bullet flight based on that “standard” projectile shape. If you look at the G1 bullet image, you’ll see that it resembles a common projectile shape from the 1800’s era, give or take. Since those early days, other smart folks have developed different predictive models on bullet flight based on a variety of bullet types.

Bullet Types:

  • G1 (flat base with two caliber (blunt) nose ogive)
  • G2 (Aberdeen J projectile)
  • G5 (short 7.5° boat-tail, 6.19 calibers long tangent ogive)
  • G6 (flat base, six calibers long secant ogive)
  • G7 (long 7.5° boat-tail, ten calibers tangent ogive)
  • G8 (flat base, ten calibers long secant ogive)
  • GL (blunt lead nose)
The G7 drag model is constructed around a bullet type that more closely matches the long range projectiles used today.
The G7 drag model is constructed around a bullet type that more closely matches the long range projectiles used today.
Kestrel Elite with Applied Ballistics unit
Kestrel Elite with Applied Ballistics unit

These days, most bullet data is published with BC numbers for the traditional G1 drag model, but given the explosion of long-range shooting interest, more are also publishing numbers for the G7 model which is more accurate for sleek and slender long range bullets.

Here’s what you need to know about drag models. Ballistic calculators like smartphone apps and Kestrel devices take as inputs ballistic coefficients for a given drag model. That means that the BC numbers for a G1 and G7 drag model are different.

When entering this stuff into your Kestrel or ballistic smartphone app, be sure to use the right BC number with its corresponding drag model. As an example, the Hornady 6.5mm ELD Match bullet has a BC of 0.646 for the G1 drag model but a BC of 0.326 for the G7 drag model.

If your app or device asks for a G1 number, be sure to use 0.646. If it asks for a G7 number, use the 0.326 figure. Make sense?

The Bottom Line

All of this algebra and calculus mumbo jumbo is intended to solve one thing: to predict the behavior of a bullet as it flies through the air. The ability to know, in advance, how much a bullet will drop or drift in the wind at a certain distance allows you, the shooter, to make scope holdover adjustments that will increase the odds of you hitting your target. It’s that simple.


Tom McHale
Tom McHale

About Tom McHale

Tom McHale is the author of the Practical Guides book series that guides new and experienced shooters alike in a fun, approachable, and practical way. His books are available in print and eBook format on Amazon. You can also find him on Facebook, Twitter, Instagram and Pinterest.

  • 14 thoughts on “Ballistic Coefficient & Bullet Math : Long-Range Shooting Science

    1. I don’t see how a BC can be constant for varible velocities over a given trajectory. It get that G1 is an average under 500 yds and G7 is an average over 500 yds up to sonic velocity when everything falls apart. Fluid properties (air) vary with velocity and environment. I wonder if anyone has validated a continuum mechanics equation with rifle testing a super high speed sensors.

    2. I assume the muzzle energy for the 2 bullets has a typo. If they have the same mass and velocity, the energy should be identical.

    3. Your choide for the two examples was excellent.. at first I wondered why you were trying to compare two radically diffferent bullet shapes.. THEN it hit me… the differences would be so radical they would be very distinct, then you could go into the details and explain WHY.

      Someday maybe I’ll have the time and money to play in the long range sweepstakes game… one friend is regulalry hitting his targets at 800 yards, and often at 1000 yds….. me, I’m happy at present if I can hit at a couple hundred yards……

      Need more range time. Another factor is that I know I need to get into handloading… capital precludes such “silly” activities just now.

      1. @Tio, The thought part is the most important and that costs nothing. There are lots of ways to get around the expense
        of all the other stuff like rifle, ammunition and even reloading.

    4. BC = Section Density divided by Form Factor.
      (w/7000)
      Section Density = ————– w = bullet weight in grains
      (caliber diameter squared) cal dia in inches

      BC – Section Density divided by Form Factor i

      Form Factor, usually represented as I, is the ratio of the aerodynamic drag of subject bullet to the standard bullet. In addition to the standard “G” series bullet profiles, a Custom Drag Curve (CDC) can be used for a specific bullet which is the actual drag characteristics for that bullet. In this case, the Form Factor becomes 1.0 and the BC equals the Section Density. CDC’s are very appropriate as a bullet nears the transonic region (about 1325fps down through the speed of sound about 1120fps….temperature variable) where G profiles diverge significantly from the specific bullet’s CDC. Applied Ballistics has determined accurate CDCs for over 750 popular bullets. G1, G7, and CDCs are available within AB ballistic solvers featured in Sig Kil02400ABS range finder and the Kestrel 5700 Ballistics weather meter, plus other computer and mobile device formats. Many individuals may fear the math. But, actually understanding the information makes it much more interesting and increases one’s ability to become proficient in long range shooting. There I go again…..geeking out. Once an engineer, always an engineer. But that one- mile-plus first shot “GONG” is addictive!!!!
      NOW, ABOUT THAT THINGY CALLED WIND.

    5. Next article—-Brass how to choose —which is better? Remember “High Cost” does not equal “High Performance”

      Article No. 2—-Reloading— the “real Pleasure” of the shooting with math.

      1. … I do not know how I could have possibly left out Lapua bullets. Even their ammo is great. CNC machined solids are probably the best for higher BC (handloaded only) and the most expensive to produce.

        Making those long range shots past a 1000+ nice! Not so long ago a Barrett or Cheytac was needed at a high price for shots out to a mile+. But in a shtf scenario the gun I want is a AC-130 Spectre… a lottery winner’s dream come true. No math just brute force raining down pain.

    6. Nice article, well explained except for the fact that you assumed people would know that they were both zeroed at 100 yards

    7. Good write-up Tom. I agree with the entire article and it’s explaining of coefficients and their applications. Understanding basics means more game on the table, and more steel pings.

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