Posts Tagged ‘ballistic coefficient’
by Tom Gaylord, a.k.a. B.B. Pelletier
This report addresses:
• Definition of ballistic coefficient (BC).
• How are BCs determined?
• Bullets and pellets have an additional factor.
• BCs are not constants.
• BC is an expression of how much velocity is lost in flight.
• How to cheat the BC numbers.
If ever there was an elephant in a room full of airgunners — this is it! Ballistic coefficient. It seems like everybody talks about it, but what does it mean?
Ballistic coefficient (BC) is the measure of a ballistic projectile’s ability to overcome air resistance in flight. It’s stated as a decimal fraction smaller than one. When diabolo pellets are discussed, the BCs are very low numbers in the 0.010 to 0.045 range because diabolos are purposely designed to slow down in the air. Their wasp waists, flared skirts and hollow tails all contribute to very high drag that rapidly slows them down — much like a badminton birdie. Lead bullets, in contrast, have BCs between 0.150 and 0.450.
The long lead bullet on the right has a higher BC than the short fat bullet on the left. When they’re both fired at the same speed, the bullet on the right will not slow down as fast as the bullet on the left.
How is it determined?
To physicists, BC is a function of mass, diameter and drag coefficient. This set of parameters seems simple until you examine it closer. A round ball made of pure lead should always weigh the same, as long as the diameter is the same. But a diabolo pellet is conical in shape and can be much longer than the diameter of a round ball of the same caliber. Depending on how the pellet is designed (i.e., how hollow or solid it is), it can also be much heavier because it contains more lead than the ball.
Bullets and pellets have an additional factor
For pellets and bullets, there’s an additional factor to consider — shape. For that reason, there’s a separate definition for the ballistic coefficient of bullets that takes into account the sectional density dictated by the form or shape of the projectile.
I’m purposely avoiding any discussion of BC that includes formulas. Stated simply, a pellet or bullet with a high BC (a large number) will continue to fly much longer than a pellet or bullet with a low BC: A high BC means the pellet will fly farther!
BCs are not constants
Okay, you say, that’s exactly what I want! Give me only those pellets that have high BC numbers.
Not so fast! However, as the velocity of a projectile changes, so does the projectile’s BC. BCs are not constants. There’s no such thing as a pellet with a BC of 0.035. But there are plenty of pellets that will achieve a BC of 0.035 at a certain velocity. When a BC is given, it means something only if the velocity at which that BC was obtained is given with it.
This could get confusing, couldn’t it? Yes, it can be confusing if you try to force numbers onto pellets when they don’t apply. But when you understand that the BC of a pellet is actually a sliding scale, you begin to understand the ballistics of airguns.
The ballistic coefficient of a single pellet can change this much with velocity changes.
So what? Who cares about all this sliding scale stuff? You do, and I’ll tell you why. Let’s say there’s a pellet with a BC of 0.042. Wow! That’s a very high number for a diabolo pellet! I’m gonna get me some of them!
Hold on, pardner. What if I told you that pellet was the JSB Exact King in .25 caliber, and that it has that BC only when it’s moving at 1,250 f.p.s.?
BUMMER! You don’t own an air rifle that will propel a .25-caliber JSB exact King up to 1,250 f.p.s. In fact, almost no one does. Therefore, the fact that the pellet has that high a BC at that particular velocity does nobody any good.
If you think about this for a moment, it’ll dawn on you that a particular BC relates to the airgun being used, almost as much as it does to the pellet. Your rifle may only be able to launch the .25-caliber JSB Exact King out the muzzle at 760 f.p.s. At that speed, the BC of the pellet might be 0.033 (these are not the actual numbers, but they’re very close). By the time the pellet has gone 25 yards from the rifle, its velocity has dropped to 635 f.p.s. and the BC is down to 0.030.
BC is an expression of how much velocity a pellet loses in flight
We know that pellets slow down rapidly after leaving the muzzle. Pellets with higher BCs retain their velocities longer than pellets with lower BCs. A pellet with a BC of 0.040 at 900 f.p.s is going to go farther than a pellet with a BC of 0.020 at 900 f.p.s. Both pellets will change their BCs in flight, but the pellet that has the higher BC will never drop below the pellet with the lower BC at the same distance.
Range equals velocity — how to cheat!
I think most shooters know that the velocity of a pellet starts to decrease the moment it leaves the muzzle of the gun. And the BC is a measure of how much velocity a pellet loses in flight. If I want to get higher BCs, I can get them by measuring velocity closer to the muzzle, where the velocity loss will be less than when the pellet has traveled farther. For example, if I were to measure the BC of a pellet by comparing its muzzle velocity to the velocity at 10 meters, the BC would be higher than if I were to compare the muzzle velocity of the same pellet to its velocity at 25 meters.
I can cheat the numbers by measuring velocity loss at a very close range. The pellet that gives me a BC of 0.033 at 25 meters might give me a BC of 0.040 if I measure the velocity loss at just 10 meters. Standards are needed to make sense of these numbers.
Sometimes, people don’t WANT to make sense! Sometimes, people just want to report a high number because the folks reading the numbers think they mean something good.
In that respect, the discussion of BC among those who don’t really understand what it means is not unlike the discussion of muzzle velocity among new airgunners. Some airgun manufacturers proudly advertise their air rifles can achieve 1,300-1,600 f.p.s. People who are new to airgunning think that’s a good thing. We know it isn’t. We know that to achieve such high velocities requires the use of trick pellets no one would ever use in the field because they’re hopelessly inaccurate.
There’s a whole lot more to this topic. For example, as the velocity of diabolo pellets rises up into the transsonic region, the BC often starts dropping, again. At supersonic speeds, the pellets are very negatively affected.
We’ll also look at the pellet’s shape, for shape is what makes the BC of bullets and pellets different from other BC numbers. Technically, it’s called “form,” but the term shape is clear enough for everyone to understand.