School Me On Ballistic Coefficient (BC)

[D.B. Cooper]

So, as I understand it, and set me straight if I'm wrong, BC is an inverse scale. The higher the BS, the less the bullet it is effected by aerodynamic drag in flight.

My understanding of drag in flight is from my days working in aviation, in that it resists forward movement in flight. Does BC also apply to crosswind pushing the bullet off target, or is that simply a function of the bullet's mass and velocity? And if it's solely mass and velocity, which has the greater resistance to crosswinds?

What I know I don't know (that's my Dick Cheney impersonation) is if the scale of BC numbers are linear, logarithmic, or something else. What is the difference in drag resistance between a .331 and a .333 BC bullet? (Ironic how those two numbers match exactly the Barnes 80 grain TSX and 85 grn TTSX 243 cal bullets, and I just happen to have some of those bullets on my bench right now.)

I understand that the higher the BC, the higher the terminal velocity downrange, all other things being equal. However, is it better to sacrifice BC for a heavy bullet that would resist crosswinds at longer ranges (300 yrds)?

I'm really just trying to work out which of the two bullets to focus on as I start to work up a load for caribou.

 

[Hondo 60]

Excellent question!
Hopefully someone much smarter than I comes by to answer.
I wish I could be helpful.

 

[earplug]

mass resists side winds. I'm a uneducated bullet tosser that bought a inexpensive app for my phone that gives me that sort of information. Plug in bullet weight, BC and velocity, add what ever wind your dealing with and magic happens. You will have to determine what attribute is most important for you. You rifle might complain and shoot one bullet better then the other.
If you have my luck you will pick a heavy bullet with a lower BC to deal with cross wind and end up shooting into the wind. downhill.

 

[mustanger98]

My understanding is that BC has to do with how long/heavy for diameter a bullet is.

Take 150gr SP's... a .277 will be longer than a .308. The two, running at the same muzzle velocity, will get to 300yds, but to hear Jack O'Connor tell it, the .277 will have more energy, more inertia. Sounds like less drag to me.

Don't know about wind drift, but I'm sure I've heard it argued both ways.

 

[Random 8]

You've basically nailed BC as the higher BC, less resistance to forward movement. It's not logarithmic, but not exactly linear either as Velocity gets squared in the equation, so that variable will affect resistance and time of flight TOF.

That leads us to the wind drift question which is central to the consideration of BC in a hunting bullet (I'll leave target bullets off the table for now) and also determines remaining energy at distance. Assuming proper bullet construction for the game targeted, as well as sectional density (which has more to do with penetration but is often correlated to BC), if you're gunning for the least effect of wind, generally the most important variable will be TOF. The better a bullet maintains velocity, the shorter the time of flight will be to target assuming identical muzzle velocity. Mass and surface area do have an effect, but the changes are very minor compared to the time of flight of the bullet. Basically the less time wind has to act on the bullet in flight, the less drift you will have. There's that pesky Vsquared again, but this time imparting a lateral vector rather than resisting forward movement. Drift accelerates as range increases, imparting a lateral vector to your trajectory, so this effect is greatly amplified at greater distances and higher wind velocities. Not logarithmically, but also not linear.

I'd have to run the numbers, but I'm guessing that with your 2 bullets, the lighter slug will resist drift better due to higher MV, at least to practical ranges. The BCs are nearly identical so should be little difference there, they might even be within the margin of error of testing equipment, and definitely within the margin for field riflery. Hope this helps.

 

[MEHavey]

Atmospheric Bullet Drag Force ~ Gi(M)/Ci

G is the drag function (which changes with the Mach speed -- M mach number), and C is the ballistic coefficient related to bullet shape.

As you can see, the higher the ballistic Coefficient, the lower the drag

 

[sota]

tagged to read later, as all the high level thinking is making my head hurt this early.

 

[JimKirk]

https://www.amazon.com/Ballistic-Pe...d=1545225849&sr=1-2&keywords=bryan+litz+books

worth reading....

 

[Toprudder]

https://www.amazon.com/Ballistic-Pe...d=1545225849&sr=1-2&keywords=bryan+litz+books

worth reading....

Yes! Excellent book! I've only read portions of it so far, but it was all very informative.

 

[D.B. Cooper]

I used a website called shooterscalculator.com and look at some windage, trajectory, and velocity statistics for the two bullets I'm experimenting with.

Interestingly...the lighter (80 grn TTSX) bullet has about half the bullet drop at 300 yards than does the heavier (85 grn TSX) bullet. The effect of a 10 mph, 90˚ crosswind only 0.34" difference between the two-negligent. (It's still nearly a 9" total wind drift however.)

Even terminal velocity at distance is negligible between the two. The 80 grn bullet is traveling 2281 fps @ 300 yrds, and the 85 grn bullet is traveling 2203 fps @ 300 yrds. I consider 2200 fps as the absolute minimum to get proper expansion.

I can't really calculate time of flight because the projectile speed is constantly decelerating from the moment it leaves the barrel. So the only advantage is the flatter trajectory of the lighter projectile.

 

[someguy2800]

Ballistic coefficient has a huge effect on wind drift all else being equal.

For example if you plug in a 10 mph crosswind and a 150 grain bullet with a BC of .5 and a velocity of 2800 fps the wind drift at 500 yards is 18.5 inches.



If you leave all else the same but change the BC to .3 the wind drift will be 35.1 inches

 

[jmr40]

The best way to understand BC is to go to one of the online ballistic calculator programs and simply plug in different numbers and look at wind drift, drop and retained velocity down range. For long range target shooters it is huge. But it plays a bigger role for hunters at even moderate ranges than most guys understand. The chart in the post above is a good example.

If you're concerned about bullet drop more velocity will almost always trump higher BC. At least at ranges 90% of shooters shoot. While higher BC bullets retain speed much better at long range, they don't overcome the faster speeds when it comes to trajectory. This is the principle behind the old school magnums shooting light bullets as fast as possible. Hunters used to obsess over flat trajectory and point blank zeros because of old school optics.

Small differences such as .331 vs .333 are insignificant. But with my 308 I have bullets that range from .415 to .626. The bullets with a BC of .626 are 50 gr heavier, leave the muzzle 400 fps slower and will never match the lighter, faster bullet with a BC of .415 in trajectory. But at 500 yards the heavier bullet is now faster, hits MUCH harder on game, and will drift less in wind. Beyond 500 yards things aren't close, the heavier bullet does everything better except for bullet drop. And with modern optics, shooting at known ranges with range finders, it isn't hard to compensate for a little more bullet drop.

Here is another real world example of why it matters to hunters, even at moderate ranges. If we shoot a very poor BC 180 gr bullet from a 300 WM at 3000 fps vs one of the best BC 180 gr bullets from a 30-06 at 2800 fps the 30-06 load passes the 300 WM in velocity, and hit harder at only 75 yards. A 308 shooting the high BC bullet would pass 300 WM at only 175 yards. Beyond those ranges the 30-06 and 308 are hitting much harder. BUT... the 300 WM will still shoot flatter than 30-06 out to about 200-250 yards before that evens out.

By choosing better bullets and modern optics it allows hunters to drop down to a smaller cartridge with much less recoil and not give up anything to the old school heavy kicking cartridges. This is a huge part of the 6.5 CM's success. It kicks like a 243, yet kills game better than 270.

 

[rpenmanparker]

OP, the relative drop between the two bullets depends more on the muzzle velocities more than the terminal velocities. The relative weights of the bullets is much less important unless they are reflected in the muzzle velocities. If you load the cartridges for the same muzzle velocity, I bet most of the drop difference will disappear despite the weight difference.

 

[Random 8]

This one will calculate TOF, as well as several other interesting variables. Some interesting, some useful, some thoroughly arcane. https://www.hornady.com/team-hornady/ballistic-calculators/#!/4dof

As you've already learned from your foray into advanced ballistics, your two bullets are for practical purposes nearly an even shake. With your cartridge on a larger critter, 300 yards is probably the limit anyhow, and you need to be much less advanced at those distances. This is velocity over BC range, so shoot what groups well at the best speed with adequate sectional density for your game. BTW in high power competition, 200 and 300 yards are "short range" according to the target abbreviations. Best of luck on your 'bou hunt. I'm jealous.

 

[25-20 WCF]

Wind drift has more to do with time of flight than anything else. A high BC bullet will slow down less than a low BC bullet so it will take less time to reach the target. That means less drift. A low BC bullet can have less drift if it has a very high velocity, it’s all about time of flight.


.

 

[labnoti]

With practical hunting in mind, we can see a real difference with bullets in the 0.1 range of BC's -- handgun bullets that have enough drag that they either lose too much velocity to carry sufficient energy beyond ~100-150 yards, or they slow enough to go transonic, yaw and become unstable and inaccurate.

Going up to around 0.2 G1 BC we have bullets that can stay supersonic and accurate out to as much as 300 yards from cartridges like .30-30 or .450 Bushmaster, or even .45-70.
As you can see, with these low BC's, extreme brute force would be needed to extend the range over which the bullets could remain supersonic, stable and accurate. For big game hunting, it makes more sense to increase bullet weight while the BC's and range remain low. But for varminting, .22-250 can push low BC bullets over 4400 fps from the muzzle so they stay accurate out to 500 yards.

Stepping up to 0.3 BC which we might see from a short .30 caliber like 7.62x39 or larger calibers as seen on .35 Remington or even .416 Rigby, we continue to see a limited range of supersonic flight out to 400 or perhaps 500 yards with the lighter bullets due to higher muzzle velocities. Obviously, the bullet weight and design are much more significant here than how the AK is shooting a .295 vs the Rigby's .319 BC.

BC's over 0.4 can preserve supersonic speed on bullets out to 600 or 700 yards out of otherwise modest cartridges like the .308. But the 0.5 and up "extremely low drag" bullets allow the same modest cartridges to maintain supersonic bullet speed beyond 1000 yards whereas with a higher drag bullet, large magnum cases would be required to do the same. Cartridges that are optimized for long, low-drag bullets can make even more of BC's over 0.7

While I haven't answered the questions about drift, I think others have (a slower bullet will drift more as will a lighter one and comparison is probably best done by calculation), and my key point would be to consider how the BC can determine how far out supersonic flight can be maintained from a given muzzle velocity and therefore the effective range over which the bullet will be accurate before it goes transonic and could become unstable. The difference between G1 BC's of .331 and .333 is insignificant. What would be far more meaningful to consider between the two would be bullet weight, subsequently the velocity they can be propelled to, the velocity at which they're designed to expand, and the resulting penetration. Those factors should be given consideration in light of the intended range and target.

 

[someguy2800]

OP, the relative drop between the two bullets depends more on the muzzle velocities more than the terminal velocities. The relative weights of the bullets is much less important unless they are reflected in the muzzle velocities. If you load the cartridges for the same muzzle velocity, I bet most of the drop difference will disappear despite the weight difference.

You would be very wrong

 

[someguy2800]

Time of flight is not what determines wind drift. The BC is a much bigger factor than time of flight. Let’s do an experiment.

Let’s say we are shooting a 180 grain RN bullet from a 300wm with a BC of .300. Muzzle velocity is 3000 FPS, velocity at 200 yards will be 2400 FPS. With a 10 mph crosswind the wind drift will be 4.2”

Now let’s say we do the same with a 308 and a 180 grain bullet with a BC of .600. With a muzzle velocity of 2400 FPS the velocity at 200 yards will be 2127 FPS. However the wind drift will only be 2.8”

No obviously the first bullet had a shorter time of flight, it was traveling faster the entire way to the target, yet it has 50% more wind drift.

The reason for this is wind drift works by creating uneven pressure on one side of the bullets shock waves. A high BC bullet creates much smaller shock waves in the air so the wind simply doesn’t have as much to push against.

 

[rpenmanparker]

You would be very wrong

No, it is you who are wrong. Same muzzle velocity with same or similar drag factor and ballistic coefficient will give very nearly the same vertical trajectory over a wide range of bullet weights. Queen got it right: "Galileo, Galileo, Galileo, Galileo!"

If two bullets start at the same velocity and are slowed very similarly by air drag, they will take just about the same amount of time to get to the target. So they will be acted upon by gravity for nearly the same amount of time. With the almost same ballistic coefficient they will respond to gravity by falling at the same acceleration. Therefore they will both drop about the same distance on the way to the target. I did the calculations on www.shooterscalculator.com and was proved correct for 80-100 gr bullets with 2200 fps muzzle velocity, G1 drag factor and .31-.33 ballistic coefficient. In my calculation the drop over 300 yards relative to a 100 yard zero point was about 2.5 inches for both.

 

[rpenmanparker]

Time of flight is not what determines wind drift. The BC is a much bigger factor than time of flight. Let’s do an experiment.

Let’s say we are shooting a 180 grain RN bullet from a 300wm with a BC of .300. Muzzle velocity is 3000 FPS, velocity at 200 yards will be 2400 FPS. With a 10 mph crosswind the wind drift will be 4.2”

Now let’s say we do the same with a 308 and a 180 grain bullet with a BC of .600. With a muzzle velocity of 2400 FPS the velocity at 200 yards will be 2127 FPS. However the wind drift will only be 2.8”

No obviously the first bullet had a shorter time of flight, it was traveling faster the entire way to the target, yet it has 50% more wind drift.

The reason for this is wind drift works by creating uneven pressure on one side of the bullets shock waves. A high BC bullet creates much smaller shock waves in the air so the wind simply doesn’t have as much to push against.

You are right and you are wrong. BC is a very significant factor increasing in importance more than linearly as it decreases. Time of flight is not quite as significant because it is just proportional, i.e. linear. In other words the wind drift must be nearly proportional to the time of flight. Twice as long a flight time will give about twice as much drift all other factors being the same. So that may be negligible in your examples, but valid examples can be created in which it is very significant.

To better understand this it is important to realize that time of flight is not inversely proportional to muzzle velocity. So a 1,000 fps bullet at the muzzle will drift much less than twice as much as a 2,000 fps bullet at the muzzle. Why? Because the faster bullet at the muzzle slows down faster than a slower one. The two bullets become much more similar in velocity by the time they reach a far target.

 

[Toprudder]

With practical hunting in mind, we can see a real difference with bullets in the 0.1 range of BC's -- handgun bullets that have enough drag that they either lose too much velocity to carry sufficient energy beyond ~100-150 yards, or they slow enough to go transonic, yaw and become unstable and inaccurate.

I can attest to that! I have a 9mm AR that is accurate at 100 yards (even though the bullets drop through transonic @75 yards). The bullets still group fairly well at 200 yards, but they drift to the right significantly, like 8" or more, that could only be attributed to the bullet yawing and causing spin drift.

 

[coondogger]

The formula for determining ballistic coefficient of a small projectile, ie a bullet, is as follows:

You take cross sectional area (d), square it, then multiply it times coefficient of form (i) and divide the result into the bullet's mass (m). So you can see that cross section has a disproportionately large effect since it is squared. This makes sense intuitively. No matter what the mass or speed, surface area makes something easier to get pushed around by wind.

 

[rpenmanparker]

The formula for determining ballistic coefficient of a small projectile, ie a bullet, is as follows:

You take cross sectional area (d), square it, then multiply it times coefficient of form (i) and divide the result into the bullet's mass (m). So you can see that cross section has a disproportionately large effect since it is squared. This makes sense intuitively. No matter what the mass or speed, surface area makes something easier to get pushed around by wind.

No doubt but time of flight is not negligible.

 

[coondogger]

Yes, bec

No doubt but time of flight is not negligible.

Yes, because it will magnify MOA.

 

[GooseGestapo]

Toprudder; check your scope to be sure that your cross hairs are vertical to the axis of the bore. If the horizontal cross hairs aren’t level, you are tilting the gun to hold the cross hairs horizontal.
This causes the bullets path to take an angular track, relative to the vertical axis.

Most of the used guns at shops I look at don’t have the cross hairs aligned with the axis of the bore. It won’t affect a shot at the range it’s zero’d At, but as the distance increases, the angular error increases.
In other words, it’s not the bullet, it’s the gun causing the drift observed.
This is assuming that you aren’t seeing wind drift.

This is why the long range shooters use leveling devices for scope mounting, and have spirit levels attached to their scopes to preventing canting the rifle.