What is Ballistic Coefficient?

[bigshow]

I am new to reloading and was woundering about ballistic coefficient of bullets. What do the numbers mean? thanks

[Brian Pfleuger]

Essentially, it is a measure of how efficiently a bullet moves through the air.

Higher is better, so .276 beats .195.

[snuffy]

A round ball has a BC of 0. Any bullet that has a longer shape than a round ball has a higher BC than that. The long sleek bullets like the Berger VLD,,(stands for Very Low Drag), have a very high BC. A long slopping nose shape and an extreme boat tail make for a bullet that will penetrate the air easily and hold it's velocity better.

[Mike Irwin]

Also, generally, the higher the ballistic coefficient, the more slowly velocity is lost, and the better the trajectory over the bullet's flight path.

Ballistic coefficient isn't an absolute, either. It can be affected by air density and actually changes somewhat as the bullet loses velocity.

Here's a decent wikipedia discussion of it.

http://en.wikipedia.org/wiki/Ballistic_coefficient

[Unclenick]

A ballistic coefficient scales the effect of drag on a bullet to the effect of drag on a particular standard projectile. Drag determines how fast air resistance slows a projectile down. From that BC adjusted drag effect, the time of flight can be determined, and in turn, the amount of drop in trajectory and the effect of wind may be calculated. The effects of drag on a projectile vary with velocity, but because that has all been recorded in detail for the standard projectile, the ballistic coefficient scales that recorded data to give the effect of drag on your projectile at the same velocities.

You can read my whole diatribe on the subject, here. It is a work in progress that I edit every time I think of a better way to say something, so it likely includes some editing errors. But I do give some simple examples of calculations that can be made using the ballistic coefficient.

A round ball does not have a ballistic coefficient of zero. For that to be true it would have to stop at the muzzle and fall straight to the ground. Instead, the standard projectile to which the ballistic coefficient is referenced has a defined ballistic coefficient of 1.000. Another common misconception is that the BC of 1.000 represents an ideal bullet and that no real bullet can have an actual BC of 1.000. The standard projectile has that BC and it is not ideal. Indeed, there is a whole selection of different standard projectile shapes available with different aerodynamic shapes of varying effectiveness. Their drag functions are different, so the BC that scales your bullet to any one of them are different for each one. SAAMI has simply standardized on the G1 projectile so that all published BC's are comparable. It is perfectly possible for a big, heavy, sleek artillery shell to have a BC several times bigger than 1 (and many do) just because they are harder for air resistance to slow down than the standard projectile is.

[mehavey]

Boy did you open a can of worms....



http://www.frfrogspad.com/extbal.htm

Bottom Line#1: Higher BC's are better than lower BC's . . . maybe.

Bottom Line#2: Fr. Frog's Rules of External Ballistics:

1) There ain't no magic bullets! (Although some are better than others for a particular purpose.)
2) Divide the range at which someone claims to have shot their deer by 4 to get the real range.
3) Always get as close as possible.
4) Don't believe manufacturer's claims.
5) Velocity erodes, mass doesn't
6) In the battle between velocity and accuracy, accuracy always wins.
7) Inconsequential increments are meaningless.
8) Most gun writers are pathological liars.

[wncchester]

"8) Most gun writers are pathological liars."

I disagree; I believe it's an acquired skill.

[Scorch]

Ballistic coefficient is a projectile's relative ability to overcome drag as compared to an "ideal projectile". Ballistic coefficient is a calculated comparison of a particular bullet to an "ideal projectile", i.e. a 1" diameter lead projectile weighing 1 lb and with a 2 caliber (2X the diameter of the projectile) ogive curve. For years, every projectile BC in every manufacturer's catalog was calculated this way (G1). There are a few manufacturers now who determine the projectile's BC by plugging empirical results into the formula and backing into what the bullet's BC is, but most are still calculated by comparing to "ideal projectiles".

[Zak Smith]

Scorch's answer is the technically correct answer. Most published BC values are G1 BC values. By definition, these BC values are the ratio of the bullet's drag coefficient curve to the drag coefficient curve of the standard G1 projectile.

[Old Grump]

The fun part is when you realize that the most efficient bullet, ie. the one with the higher BC isn't necessarily the best bullet for a specific job. Target small game, short range, long range, medium thin skin game, large thick skin game, long range (600+ paper targets), (600+ game or boogerman), all require a specific bullet to do what they do best. That little uber velocity bullet that will blow up on Mr. Prairie Dog might not be what you want for shooting a squirrel you want for lunch and definitely not what you want for poking a pig or collecting some venison for the freezer.

You just entered the wild and wacky world of ballistics and now you know why so many manufacturers make so many different kinds of bullets. Because their 'AINT' no single best caliber and their 'AINT' no single best bullet.

[brickeyee]

Scorch's answer is the technically correct answer. Most published BC values are G1 BC values. By definition, these BC values are the ratio of the bullet's drag coefficient curve to the drag coefficient curve of the standard G1 projectile.

And notice how it all varies as a function of speed (Mach number).

A single B.C. is valid over only a small section of the velocity envelope.

[Zak Smith]

And notice how it all varies as a function of speed (Mach number).

A single B.C. is valid over only a small section of the velocity envelope.

Not exactly, although it is kind of true.

You are confusing the coefficient of drag (Cd), which is what the graph is of, and BC. Cd absolutely changes as a function of mach. BC only changes as a function of mach when the profile of the bullet diverges significantly from the profile of the base Cd curve, e.g. the G1 projectile.

If we use the G1 BC as example: BC is the ratio of "this" bullet's Cd curve to the G1 bullet's Cd curve. Yes, the ratio of "this" Cd to the G1 Cd at any place on the mach axis may not be the same. If you graphed the ratio of the two Cd curves (ie the BC), it might fluctuate a small amount around the "BC" value. However, for projectiles that follow more or less the G1 profile, it will be more or less the same throughout the mach range.

If anyone wants to dive into this, I recommend the McCoy book. It is "the bible" on external ballistics of symmetric projectiles.

[Jim Watson]

Berger has added the G7 BC to their catalog because it is a better fit for the shape of their VLD bullets and does not require the kluge of adjusting G1 BC versus velocity like Sierra does. Somebody figured it out and the difference is not huge, G1 will get you on paper.

[Jim243]

Boy did you open a can of worms....

Geezzz, my head is spinning. Now who's the smart egg that asked this question. I have to go off and cool off my brain with something simple like the tax laws.

Jim

[brickeyee]

You are confusing the coefficient of drag (Cd), which is what the graph is of, and BC

.

Nothing matches the test projectile except the test projectile.

Variation shows up even with simple size scaling of the test projectile.

The use of all the differnt test projectiles has been to try and find a better curve with less variation with other shapes.

* G1 or Ingalls (by far the most popular)
* G2 (Aberdeen J projectile)
* G5 (short 7.5° boat-tail, 6.19 calibers long tangent ogive)
* G6 (flatbase, 6 calibers long secant ogive)
* G7 (long 7.5° boat-tail, 10 calibers tangent ogive, preferred by some manufacturers for very-low-drag bullets[10])
* G8 (flatbase, 10 calibers long secant ogive)
* GL (blunt lead nose)

And even more, but that is the quick to find wiki list.

It is an absolute bear to even model the test projectile (with lots of data to compare the model) with six and seven degree of freedom aeroballistic software.

You can tweak the model to match one projectile, but it no longer matches the others adequately.

[Zak Smith]

And notice how it all varies as a function of speed (Mach number).

The "it" in this sentence refers to the graph, which shows the Cd values for the G1 and the Ingalls projectiles/model. Those two curves show how Cd varies model to model, not how other bullets vary from the test projectile:

Nothing matches the test projectile except the test projectile.

That is why I emphasized the difference between BC and Cd. It is true that when a particular bullet diverges from this Cd curve, the corresponding BC curve will obviously be a function of mach; however, the use of multiple BCs is not required for most practical purposes. If you plug in the multiple BC values that Sierra publishes and then plug in the average BC value for the cartridge in question (its velocity), the results will be virtually identical.

[B.L.E.]

A round ball has a BC of 0.

Not true.

From Lyman's Black Powder Handbook

.350 round ball BC .049
.440 round ball BC .062
.495 round ball BC .070
.535 round ball BC .075
.562 round ball BC .079
.735 round ball BC .104

Ballistic coefficient is a projectile's relative ability to overcome drag as compared to an "ideal projectile".

Actually it's a "standard" projectile which is a small 1 inch diameter cannon bullet. Notice how the round balls BCs are higher with larger diameter? It's very likely that the bullets shot from 16 inch naval guns have BCs considerably higher than 1.00.

[Unclenick]

It should probably also be clarified that Cd is a coefficient that provides error correction to a simple V² proportional drag model that doesn't work at supersonic velocities. Cd is what amounts to error correction with respect to that model. It is not a curve showing drag itself, which is proportional to the integral of the Cd curve times the simple V² function.

Cd, by the way, is actually the Aerodynamic Drag Coefficient. It is related to the Ballistic Drag Coefficient, Kd, by,

Cd=8Kd/pi

Cd has superseded Kd because it is used in other industries where drag is of importance, such as automotive and aircraft design and analysis.






Brickyee,

Here are a couple more for your collection, though these don't follow the 1" diameter 1 lb convention:

*RA4 rimfire .22 ammunition reference projectile
*GS spherical projectile (there are two of these, the SAAMI 9/16" ball drag function and Don Miller's flesh out of McCoy's spherical drag function.)

Note that the QuickTARGET Unlimited program that comes with QuickLOAD and the original QuickTARGET also includes the unmodified Ingalls drag function from McCoy's Modern Exterior Ballistics, the Soviet 1943 drag function, the British 1909 drag function from Hatcher's Notebook, and additionally has individual drag functions measured for some specific projectiles and loads to skip the BC shortcut altogether. The file names are below and include the source (brl for the U.S. Army Ballistics Research Laboratory, Rad for Doppler Radar continuous velocity measurements, in some instances.

no9_shotlead.drg
no7_5-shotlead.drg
tenex_r50.drg
224-blackhills mk262-1in7twist_radar.drg
224-gp90-sm.drg
224-l110-brl.drg
224-m193_fmj_55g.drg
224-m193_g.drg
224-m855-brl.drg
224-m856-brl.drg
224-s109-brl.drg
224-sierra 77g mk-1in7twist_radar.drg
224-sierra 80gr mk9390-radar.drg
243-berger 105gr-vld hp_radar.drg
264-hornady 140gr amax_radar.drg
264-lapua 139gr scenar_radar.drg
264-sierra 142gr mk_radar.drg
284-hornady 162gr hp_radar.drg
284-sierra mk 130gr #1903_radar.drg
308-hornady 168gr a-max_radar.drg
308-m80-brl.drg
308-m188-brl.drg
308-sierra168mk-brl.drg
308-sierra190mk-brl.drg
7.62mm_ak47_8gramm.drg
338-sierra 300gr mk_radar.drg
9mm_fmj_8gramm.drg
50_ball_m33.drg
510_ball_m33.drg
510-barnes a 800gr_radar.drg
510-hornady amax 750gr_radar.drg

[bigshow]

Boy did I open a can of worms! Lots of good info! I now know what the numbers mean. lots of good answers. THANKS GUYS FOR ANSWERING!

[rrp]

WOW!!!!

[brickeyee]

Cd for ballistics is not eh same as Cd for other engineering drag functions.

In other fields it has dimensions of force /area.

In ballistics it rolls in a standard projectile's drag curve.

It can be used with units thus hiding the standard curve ratio that it depends on, but does not have to be.

Pejsa has a better method of determining and modeling the actual drag curve.

The problem that occurs is that the basic equations of state change as you approach the speed of sound.

The compressible nature of air leads to Mach waves (standing pressure waves) and the assumption of incompressible flow goes out the window.

If you look at a drag curve it rises about v^2 to around mach 0.9, then flattens out as the shock waves form and attach, then starts dropping with increased Mach as the angle of the Mach waves becomes smaller.

Yeager was the only pilot at the time to push the throttle to get past the buffeting as Mach 1 is apporched and the shock waves form and attach.

To this day we do not operate aircraft AT Mach 1.

You stay just below forming shock waves in the flow (top side of wing, things sticking out into the airstream) or get above so the shock waves are attached and stable.

All while keeping shock waves out of the jet engine inlet, or air flow is reduced or stopped and the jet engine choked off.

Propeller planes cannot operate above Mach 1 because the shock waves kill the thrust from the propeller before the plane gets there.
They can dive and exceed Mach 1, but are not actually in powered flight at that point.

Mach buffeting was an issue for dive bombers in WWII.
Control could be marginal, altered, or lost completely.

The attachment of Mach waves (and collapse of the waves when slowing to below the speed of sound) are what disturbs trajectory at longer ranges as the bullet slows.

[Don P]

Boy am I glad I don't got to worry about this for my handgun loads. I'm so confused

[noyes]

http://www.hornady.com/ballistics-resource/external

[B.L.E.]

The difference between BC and Cd is that if you make a bullet out of aluminum or lightweight plastic instead of lead, you will not change its Cd at all but you will dramatically alter its BC.

The reason a roundball's BC goes up with increasing diameter is that doubling the diameter of a roundball increases its mass eightfold but only quadruples its frontal area and surface area.
This is also why even the best .224 or .308 bullet cannot match the BC of a .50 BMG bullet and why the best .50 BMG bullet cannot match the BC of an artillery round.

[Mike-Mat]

Never looked at it much. Good Info Guys. I would have thought the opposite. But I guess I'm thinking about Drag Coefficient. How much resistance the bullet experiences as it moves thru the air. I would have thought 0 = no drag and anything higher is how much additional drag is placed on the bullet.