School Me On Ballistic Coefficient (BC)

[GooseGestapo]

re: b.c.
The original work undertaken as to long range ballistics of small arms was by a ballistician with one of the government Arsenal’s.
The reference projectile was the 750gr spitzer boattail bullet used in the .50BMG. The observed trajectory performance was assigned a value of 1.00.
All other observed trajectories such as that observed for the .30/06 M1 projectile we’re assigned a value representing a ratio, or equivalent value to the original, therefore b.c. Is not an absolute number. And, it is only determined by actually firing and measuring. However, charts were developed with form profiles that provided good approximations of expected performance.

Additionally, b.c. Is not static. It changes at different velocities. The Sierra manuals contain a good explanation of this observed phenomenon. Specifically, most boatail bullets tend to fare better trans-sonic and subsonic.
It really IS rocket science.

 

[D.B. Cooper]

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.

Time for a comedic "brain break" for a moment. WHen I was coaching the high school rifle team, I saw a lot of kids cant their rifles inward, (clockwise for a right-handed shooter.) I would walk up and down the firing line saying "Turn that rifle straight up and down; that's not a Glock and this ain't Chicago!"

Carry on.

 

[Toprudder]

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.

Good point, but does not apply in this case. The cross hairs would have to be tilted somewhere around 20 degrees or more to cause this much drift. I've had other shooters more knowledgeable than me look at it, too. No wind on the days I checked it. I have actually thought about tilting the reticle 20 degrees to the left, though.

The only reason I put a scope on this rifle was to work up accurate loads for the gun. I intended to put a red dot on it once I was done, but plinking steel targets at 200 yards is just so much fun.

 

[ATLDave]

Additionally, b.c. Is not static. It changes at different velocities. The Sierra manuals contain a good explanation of this observed phenomenon. Specifically, most boatail bullets tend to fare better trans-sonic and subsonic.
It really IS rocket science.

And trajectory calculators are using an approximation based on some idealized shapes. G1 and G7 are the most common. There is a G1 drag curve (that shows drag changing over velocity) and a G7 drag curve. Coefficients are commonly used to roughly "fit" a given projectile to that curve, but it's an approximation. To have a truly, truly reliable traj calculator, you need a custom drag curve based on that particular projectile's actual shape.

Bryan Litz's numerous books on ballistics are fascinating reading if this is of interest.

 

[someguy2800]

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.

Your original statement reads to me that two bullets of the same weight and velocity will always have the same drop which is wrong. You didn't say anything about ballistic coefficient. You can have very different BC's with the same bullet diameter and weight, and the drop will be significantly different.

 

[ATLDave]

Your original statement reads to me that two bullets of the same weight and velocity will always have the same drop which is wrong. You didn't say anything about ballistic coefficient. You can have very different BC's with the same bullet diameter and weight, and the drop will be significantly different.

But that's a function of the BC influencing the velocity decay and, therefore, the time of flight.

Bullets don't generate lift. Their "drop" is just a function of the earth's gravity pulling on them. The less time of flight, the less time gravity has to accelerate them downward.

A bullet shot from a gun perfectly parallel to the ground and a bullet dropped from precisely the same height as the muzzle at precisely the same time the bullet leaves the muzzle will strike the ground at the same time*. The BC of either bullet won't change that. But the faster the fired bullet is traveling, the further it will go before it strikes the ground... even though the time on the clock will be the same regardless of its speed.

Higher BC can help keep velocity higher over longer flight times. This reduces flight times for a given range. That's how BC relates to drop.

*Disregarding any infinitesimal consequence of the curvature of the earth.

 

[rpenmanparker]

But that's a function of the BC influencing the velocity decay and, therefore, the time of flight.

Bullets don't generate lift. Their "drop" is just a function of the earth's gravity pulling on them. The less time of flight, the less time gravity has to accelerate them downward.

A bullet shot from a gun perfectly parallel to the ground and a bullet dropped from precisely the same height as the muzzle at precisely the same time the bullet leaves the muzzle will strike the ground at the same time*. The BC of either bullet won't change that. But the faster the fired bullet is traveling, the further it will go before it strikes the ground... even though the time on the clock will be the same regardless of its speed.

Higher BC can help keep velocity higher over longer flight times. This reduces flight times for a given range. That's how BC relates to drop.

*Disregarding any infinitesimal consequence of the curvature of the earth.

Yep. Thanks for the help explaining to him.

 

[Random 8]

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.

I've done some more reading, including some interesting literature from Berger, and some proprietary information from the Swiss National Marksmanship program, and I must stand partially corrected. I was going off of years of coaching I received on the high power line, including High Masters, State Champions, Olympic shooters and guys who went CMP distinguished before I was born. Almost universally I was told BC only influences drift insofar as it influences TOF. Some of these guys even shoot special short range loads at 200 and 300 with a lighter, faster, lower BC bullet based on this belief. Apparently this is a very common misconception, as is the misconception that heavy bullets drift less because they are heavy, not because they have a higher BC. TOF still plays a significant role when I ran some test numbers focused on loads I'm familiar with. The .308 155 and 168 BTHPs and the 168 ELD at 7.62 speeds as well as .223 68, 75 BTHP and 75 ELDM at 5.56 speeds. The higher BC bullets universally modeled less drift at shorter ranges regardless of TOF, not just the longer ranges where I would expect them to, however shorter TOFs did make the race closer or even between the lower BC slugs and the heavier, higher BCs when I tweaked the velocity up to the ceiling of safe loads in those rounds, showing a significant but not dominant effect so long as the BCs were not radically different as in 68BTHP vs 75ELDM. This is only modeling. Wind drift is extraordinarily difficult to test in the field at distance, so not sure how the models would match up with field results.

 

[someguy2800]

Yep. Thanks for the help explaining to him.

Let me reiterate. You said two bullets of the same weight and muzzle velocity will always have similar drop. That is a false statement. Unless I misread what your saying. I understand time of flight and drop, but drop and drift work differently. Drop is a constant over time, drift is not.

 

[rpenmanparker]

Let me reiterate. You said two bullets of the same weight and muzzle velocity will always have similar drop. That is a false statement. Unless I misread what your saying. I understand time of flight and drop, but drop and drift work differently. Drop is a constant over time, drift is not.

Similar bullets. I followed up with that stipulation. The whole point was to instruct OP not to be concerned with final velocity. Focus on muzzle velocity.

 

[rpenmanparker]

I've done some more reading, including some interesting literature from Berger, and some proprietary information from the Swiss National Marksmanship program, and I must stand partially corrected. I was going off of years of coaching I received on the high power line, including High Masters, State Champions, Olympic shooters and guys who went CMP distinguished before I was born. Almost universally I was told BC only influences drift insofar as it influences TOF. Some of these guys even shoot special short range loads at 200 and 300 with a lighter, faster, lower BC bullet based on this belief. Apparently this is a very common misconception, as is the misconception that heavy bullets drift less because they are heavy, not because they have a higher BC. TOF still plays a significant role when I ran some test numbers focused on loads I'm familiar with. The .308 155 and 168 BTHPs and the 168 ELD at 7.62 speeds as well as .223 68, 75 BTHP and 75 ELDM at 5.56 speeds. The higher BC bullets universally modeled less drift at shorter ranges regardless of TOF, not just the longer ranges where I would expect them to, however shorter TOFs did make the race closer or even between the lower BC slugs and the heavier, higher BCs when I tweaked the velocity up to the ceiling of safe loads in those rounds, showing a significant but not dominant effect so long as the BCs were not radically different as in 68BTHP vs 75ELDM. This is only modeling. Wind drift is extraordinarily difficult to test in the field at distance, so not sure how the models would match up with field results.

Heavier bullets resist wind drift more than lighter bullets. Very simple. F=ma. a = F/m. As mass increases, acceleration due to wind force decreases. So the amount of drift decreases over the same time of flight. Hard to dispute.

 

[D.B. Cooper]

Similar bullets. I followed up with that stipulation. The whole point was to instruct OP not to be concerned with final velocity. Focus on muzzle velocity.

However, in this narrowly defined application of hollow point hunting bullets that require significant velocity on impact to open and perform as designed, terminal velocity is important. If I hit aa caribou with a hollow-point hunting bullet traveling 800 fps, I might as well as shoot cast lead projectiles.

If, however, we were discussing putting holes in paper, I think you might be right; the idea of heavier bullets buck the wind better than light bullets has been around since before I was born; there is probably some truth to that.

 

[ATLDave]

Heavier bullets resist wind drift more than lighter bullets. Very simple. F=ma. a = F/m. As mass increases, acceleration due to wind force decreases. So the amount of drift decreases over the same time of flight. Hard to dispute.

A sailboat weighs more than 50 pounds, but will be moved by wind much more than a 50 lb rock. Shape matters.

Of course, most bullets are made out of pretty much the same material (lead with a thin jacket of slightly lighter metal), and have to be rotationally symmetrical, so there's only so much variation in what area gets presented to the wind for a given weight. But if you had, for instance, two bullets of the same diameter and weight, but one had very large hollow cavity, then the one with the larger cavity will have more area "exposed" to side wind.

I think the external ballistics on crossing winds are a little more complicated than windless trajectory calculations, and I'm not confident any of the typically-available numbers - whether weight or length or forward-facing BC - fully captures/predicts exactly how much a given crosswind will move the projectile. But, I'm not an aeronautical engineer; I feel much less confident in my grasp of this than some other aspects of elementary ballistics.

 

[someguy2800]

Like most myths there is a large grain of truth to old adage that heavier bullets drift less. The grain of truth is that heavier bullets of the same nose profile almost always have higher BC’s. The wording of the statement though is false. If you play with a billistics calculator you’ll see that increasing the weight of the bullet while leaving the BC and velocity the same will result in the exact same drift and drop figures. So no, a heavier bullet does not actually drift less. Whichever one has the better BC will drift less. So a heavier bullet only drifts less IF it also come with a higher BC to the other bullet your comparing it too.

 

[someguy2800]

A sailboat weighs more than 50 pounds, but will be moved by wind much more than a 50 lb rock. Shape matters.

Of course, most bullets are made out of pretty much the same material (lead with a thin jacket of slightly lighter metal), and have to be rotationally symmetrical, so there's only so much variation in what area gets presented to the wind for a given weight. But if you had, for instance, two bullets of the same diameter and weight, but one had very large hollow cavity, then the one with the larger cavity will have more area "exposed" to side wind.

I think the external ballistics on crossing winds are a little more complicated than windless trajectory calculations, and I'm not confident any of the typically-available numbers - whether weight or length or forward-facing BC - fully captures/predicts exactly how much a given crosswind will move the projectile. But, I'm not an aeronautical engineer; I feel much less confident in my grasp of this than some other aspects of elementary ballistics.

The wind doesn’t actually push directly against a supersonic bullet. It pushes against the pressure waves generated by the bullet, which create uneven pressure on one side thus deflecting it. It’s kind of like if you drive two boats close together their wakes tend to push each other apart.

 

[ATLDave]

Interesting. Puzzling, too. The shock waves coming off the bullet move away from the bullet (at the speed of sound, IIRC), and trailing out at some angle from the bullet. What exactly is the mechanism by which the shock waves are transmitting force back to the bullet? Feel free to link to an explanation if there is a good one out there. As I wrote above, I feel like my grasp on crosswinds in the physics of ballistics is pretty flimsy.

 

[rpenmanparker]

However, in this narrowly defined application of hollow point hunting bullets that require significant velocity on impact to open and perform as designed, terminal velocity is important. If I hit aa caribou with a hollow-point hunting bullet traveling 800 fps, I might as well as shoot cast lead projectiles.

If, however, we were discussing putting holes in paper, I think you might be right; the idea of heavier bullets buck the wind better than light bullets has been around since before I was born; there is probably some truth to that.

Please understand I was not suggesting what you should be shooting, just than you can't compare terminal velocity of two bullets to try to match them re: drop to target. It is more (not all, just more) a function of muzzle velocity.

 

[Random 8]

Heavier bullets resist wind drift more than lighter bullets. Very simple. F=ma. a = F/m. As mass increases, acceleration due to wind force decreases. So the amount of drift decreases over the same time of flight. Hard to dispute.

I did not mean to imply that mass plays no role in drift, simply that velocity, time of flight, and as I've recently learned BC as a variable independent of mass or velocity(bullet) play larger ones. Velocity (wind) is squared in the acceleration equation, playing a larger role than mass.