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Ballistic Coefficient Basics

44K views 26 replies 9 participants last post by  Tazman1602 
#1 · (Edited)
A ballistic coefficient is a number that rates how well a bullet slices through air. The number itself scales the effect of drag on a bullet to the effect of drag on a thoroughly studied standard projectile. This saves having to separately study drag on individual bullets or having to program the drag function of every bullet into a ballistics calculator. So, it is really a ballistic shortcut. Instead of measuring exact bullet behavior at all ranges and velocities, you simply fire a few to find the BC, then use that number to multiply or divide the standard projectile's behavior as needed to get your bullet's flight characteristics.

Drag determines how fast air resistance slows a projectile down. By using the BC to scale drag effect to your bullet, your bullet's time of flight may be determined and, in turn, the amount of drop in bullet trajectory and the effect of wind may be calculated for it. The effect of drag on a projectile varies with velocity, but the idea is that because that has all been measured in detail for the standard projectile, the ballistic coefficient scaling of that recorded data will produce the effect of drag on your projectile at the same velocities, or close enough to it.

Ballistic coefficients are based on comparison to standard projectile's that, by convention, are 1" in diameter and weigh one pound. Since sectional density is a projectile's weight in pounds divided by the square of its diameter in inches, the standard projectile's all have a sectional density of 1. Mathematically, a ballistic coefficient is the sectional density of a projectile divided by its form factor. Form factor is the ratio of the reference projectile's drag coefficient to the drag coefficient of the projectile for which the BC is being calculated. Since the reference projectile's drag coefficient divided by its own drag coefficient also equals 1, its form factor is 1, and when you divide 1 into a sectional density of 1, you get the reference projectile's ballistic coefficient, which also equals 1.

Projectiles that are slowed faster by drag than the standard projectile will have BC's lower than one. Those that are not slowed as quickly will have BC's greater than 1 (artillery shells, for example). All bullets that are the same exact shape will have ballistic coefficients with respect to that standard projectile that are simply equal to their sectional densities. Other, more or less aerodynamic shapes, will have a form factor (that drag coefficient ratio) to correct them for the fact they fly farther or shorter than sectional density alone would indicate in comparison to a standard projectile.

The effects of drag on those different shapes may be scaled to match the standard projectile pretty closely over any narrow range of velocities, but drag doesn't tend to change at the same rate with change in velocity for different shapes. As a result, if your projectile's shape does not match that of the standard projectile, the form factor will shift with velocity, changing the ballistic coefficient needed to scale the behavior of the standard projectile to fit. This is why Sierra and others publish multiple BC's for match bullets which change at different velocity limits.

For example, to find how far your particular bullet travels as it drops from velocity A to velocity B, just multiply your bullet's ballistic coefficient by the distance the tables show the standard projectile travels as it drops from velocity A to velocity B. That is what is meant by scaling your projectile's performance to the standard projectile's performance. (Hatcher's Notebook has the tables for the G1 standard projectile SAAMI adopted and for which most ballistic coefficients are commonly given.)

The calculation: Suppose you have a bullet with a ballistic coefficient of .462 (just to pull a number out of the air). You fire it with a muzzle velocity of 3100 feet per second. You want to know how far it will travel before its velocity drops to 3000 fps in standard sea level atmospheric conditions?* So, you look up those velocities in the standard projectile's tables, and find that it drops from 3100 fps to 3000 fps over a range of 100 yards in those conditions. You take that 100 yard figure and multiply it by your ballistic coefficient. The result is 46.2 yards. That's how far your bullet will travel in dropping from 3100 fps to 3000 fps. Obviously, the higher your bullet's ballistic coefficient, the farther it travels in losing that velocity.

Conversely, suppose you want to know how much velocity your bullet will lose in traveling a certain distance? You divide the ballistic coefficient into one, then multiply the distance you want to know about by the result. Use the tables to look up how much velocity the standard projectile loses over that resulting new distance, and you will know what your bullet loses? For the bullet in the first example, suppose you still have a muzzle velocity of 3100 feet per second. This time you want to know how much velocity it will lose going 100 yards? You divide the BC into one. 1/.462=2.16. Multiply 100 yards by 2.16 and you have 216 yards. Go to the G1 projectile tables. Start at 3100 fps and see how much velocity the standard projectile lost 216 yards later? The standard projectile, starting at 3100 fps drops to 2658 fps over the succeeding 216 yards. So, at 100 yards your bullet will be going 2658 fps.

You can use the ballistic coefficient not only to figure out how far a bullet will travel in dropping from one particular velocity to another, but also to figure out how much velocity your bullet will lose over a given range, or to figure out how long it will take to get to the target? That travel time is how much time gravity has to pull the bullet down off a straight line from the barrel, so it lets you calculate bullet drop. It also tells you how much more time it takes for the bullet to get to the target than it would do if the muzzle velocity stayed constant (as it would in a vacuum). That extra travel time due to atmospheric drag turns out to be proportional to the effect of a side wind on a bullet. It lets you calculate wind drift.

All external ballistics programs have the performance of the standard projectile under standard metro conditions built into them in tables and use your bullet's given ballistic coefficient(s) to calculate its trajectory in comparison to the standard projectile's. It adjusts the drag function for non-standard conditions of temperature, pressure, and R.H., all of which change the density of air.

The system of standard projectiles and ballistic coefficients is a shortcut that dates back to the second half of the 19th century. Artillery required a means of calculating where a shell would fall, but the mathematics for calculating projectile aerodynamics didn't exist then, and would have been too complicated to solve in the field without computers anyway. They were faced with having to spend years making thousands of measurements of each projectile, which would often be obsolete by the time they were completed. So they came up with this idea of using their crude (by modern standards) electromechanical ballistic chronographs to make thousands of measurements of a standard projectile, and determine its velocity loss ranges, fps by fps, over a very wide range of velocities, then using the ballistic coefficient to scale their other projectiles to its results. Tables in Hatcher's Notebook have them from 3600 fps to 100 fps. This Since it is easy to calculate a trajectory in a vacuum, this velocity loss information may be applied to adjust the vacuum trajectory, incrementally.

Today there are analytical methods that come from more comprehensive understanding of bullet aerodynamics, and computers can handle the volume of calculations needed to solve them in a reasonable time (once you've determined an individual projectile's drag function). But the work needed to make that determination for each bullet is more than the manufacturers of small arms bullets want to undertake, and it is more complexity than most users can make use of, so the old method persists for its relative simplicity.

The main problem with the old method is, as I mentioned earlier, that the real drag function of a bullet changes with its shape. For that reason the ballistic coefficient as a means of adjusting a bullet's trajectory really only works perfectly when your bullet has the exact same shape as the standard projectile the ballistic coefficient is referenced to. When the standard projectile is a big, heavy, flat base, small ogive radius, 19th century artillery shell, the match is seldom right for modern bullets. Nonetheless, it is the standard SAAMI adopted, called the G1 ballistic coefficient for French naval artillery's Gavre Commission which conducted a lot of the 19th century test firings and that published an updated table of the results in 1917 that are the basis for this G1 ballistic coefficient. As a result, though, you can find a matching ballistic coefficients over a narrow range of velocities for that old shape (this is just a curve fitting activity). The BC number will change over wider velocity ranges as the G1 drag function and your bullet's actual drag function diverge. As a result, you see manufacturers give tables of ballistic coefficients for different velocity ranges or, as Berger now does, they give a second ballistic coefficient referenced to a more similarly shaped standard projectiles, like the G7 standard projectile. An example is the Sierra 168 grain MatchKing's ballistic coefficients for the G1 reference projectile, taken from the BRL's measured drag function for this bullet.

Code:
G1 BC  Velocity Boundary
.462
        3000 fps
.453
        2600 fps
.437
        2100 fps
.419
        1600 fps
.394
        1500 fps
.379
           0 fps
That information will let most trajectory programs get reasonably close to the performance of that bullet, but it isn't perfect. The Army Ballistic Research Laboratory, came up with a compromise alternative to determining the drag function of each individual small arms projectile. They fired a series of different shaped standard projectiles so one may select the standard a particular bullet's shape is closest to. Using the ballistic coefficient determined for that closer shape lets you make more accurate trajectory calculations than the G1 ballistic coefficients does, even with velocity range adjustments. Those and others have been worked out over the years. Some are listed below.

G1 or G1.1 in last version, (Flat base, 2 caliber ogive, SAAMI adopted and the default published type)
G2 (Aberdeen J projectile)
G5 or G5.1 (short 7.5° boattail, 6.19 caliber tangent ogive)
G6 or G6.1 (flat base spire point, 6.09 caliber secant ogive)
G7 or G7.1 ((VLD type long 7.5° boat-tail, 10 calibers tangent ogive)
G8 (flat base, 10 caliber secant ogive)
GI (Ingalls tables projectile)
GL (blunt lead nose, like a soft point tubular magazine bullet)
GS (Spherical, measured with 9/16" projectiles)
RA or RA4 (.22 Rimfire standard projectile)

Berger publishes both G1 and G7 ballistic coefficients. The numbers are not comparable because the shapes of their standard projectiles are not comparable, though, in general, G7's will be smaller numbers for a bullet than its G1 numbers because the G7 standard projectile looses speed more slowly than the G1 standard projectile. You can use the G7 BC in the trajectory tables of the free online JBM calculators. Also, RSI's Ballistic Lab software and QuickTARGET Unlimited software will work with those alternative BC types.


Tech Corner

If you want to figure out the G7 or any other number for a bullet like the Sierra bullet in the table above, you can get pretty close using the free JBM online calculators. Look at the middle two BC numbers in the table. They have both upper and lower velocity limits. Pick one of those two ranges. Use its limits with JBM's trajectory calculator for the G1 BC. Note the distance traveled starting at the first velocity and ending at the next. Now plug those same two velocity limit numbers and the distance you noted into JBM's BC calculator and pick the standard you want the new BC for (G5. G7, etc)? The returned number should be close and in trajectory programs that have the other BC types available to use, should give you better trajectory predictions outside that velocity range than the G1 BC does.

For example: Using the first BC limits of 2600 fps and 2100 fps and the G1 BC given as .447, I run the JBM trajectory table for G1 in one yard increments to 300 yards (enough to drop to 2100 fps). I start with a muzzle velocity of 2600 fps, setting the chronograph distance to zero. The resulting table starts at 2600 fps and scrolling down I find 2101 fps at 262 yards, and 2099.2 fps at 263 yards. I extrapolate to get 262.6 yards as the point at which velocity was 2100 fps.

Next I go to the velocity-based ballistic coefficient calculator. I plug in a start velocity of 2600 fps and an end velocity of 2100 fps. I put 262.6 yards (don't forget to select yards; default is inches) into the distance. I run it once with the G1 number selected to be sure it returns the same 0.447 BC I started with. If not, I've entered something wrong somewhere. But in this case it does return 0.447. Next I select the form I want. In this case G5 looks closest. G7 is for VLD shapes. I get back 0.228. So the G5 BC for this bullet is 0.228. Now I can go back to the first trajectory calculator and set it to work with G5 BC's and enter .228 and get a more accurate trajectory table than I would with .447 and the G1 BC.


*U.S. Army standard meteorological conditions (abbreviated, Std. Metro.), are often used as the standard sea level conditions in BRL data. Modern commercial BC's more often are figured for ICAO standard conditions. The Army Std. Metro Conditions are: 29.53 inches mercury (14.504 psi), 59°F, and 78% relative humidity. The ICAO standard conditions are: 29.92 inches mercury (14.504 psi), 59°F, and 0% relative humidity.
 
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#2 ·
Ballistic coefficients reported by different bullet manufacturers may not be comparable due to the method of calculation and the accuracy of reporting. So BCs should only be used as a reference point and actual shooting should be done to determine your bullet trajectory under your conditions and velocities.
 
#5 ·
Glad that helps. I should point out his program that comes on the CD that comes with the book is the same one you can download free at Berger's site except Litz adds a stability factor calculator. Nonetheless, the Berger version gives you a way to try it out. Also note that all Berger's BC's are now measured by Litz as he has become Berger's in-house ballistician.
 
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#6 · (Edited)
This is an area which I really am "under" informed in, as you will probably determine very quickly...:eek:

But, is is safe to (logically) assume, that...
If a Bullet is very streamed lined, like a slender pointed (Spear) tip and has a Boat Tail,
that it will shoot flatter and longer distance than one which is blunt (FN/Wadcutter) ?
(assuming all else (diameter/muzzle vel/weight/environmental) are the same.

This works for just about everything else, but I thought I'd just ask.
 
#8 ·
But, is is safe to (logically) assume, that...
If a Bullet is very streamed lined, like a slender pointed (Spear) tip and has a Boat Tail, that it will shoot flatter and longer distance than one which is blunt (FN/Wadcutter) ?
(assuming all else (diameter/muzzle vel/weight/environmental) are the same.
Yep. That's basically how it works. The longest, pointiest, most streamlined bullets are called VLD (Very Low Drag) designs. The more pointy and streamlined the shape, as Bryan Litz puts it, the better it slices through air. If you want to know how well it slices through air, relative to a standard projectile, the ballistic coefficient tells you that. Higher is better.
 
#7 ·
Wikipedia has a nice tome, a basic formula that may or may not freak you out depending on your math background, but which is your basic add/ subtract, multiply/divide thingy...lots of definitions and other links that will give you a nice ride and should fulfill your needs.

Basically BC is just a number that indicates how "slick and pointy" a bullet is ...how easy it overcomes air resistance. Hi BC-are long, slender and pointy, slips smoothly through the air...low BC are short, fat with a flat nose...a flying beer cans.
 
#9 ·
NFG, Nick, thank both of you for your prompt and informative replies.

I thought as much, but always like to discuss issues when I can.

I have bought a very basic "Rock Chucker" reload press and some other supplies, which I have squeezed a few rounds together already. Part of that "other" are a couple Books on recommended weight/powder combinations.

One thing that actually prompted my original question, is realizing that one can overdo the load quite easily, and there's no telling where that Round will go, regardless of how pointy it is.

My original thought was...
If it moves faster, it will not drop as much, and be more accurate.

HA, that's not the case, I found out ! :eek:

My next question is...
Why isn't that true. Just what causes that instability with the increase of speed ?
 
#10 · (Edited)
Stability actually increases with speed slightly, but only up to the point other issues start to sabotage the effort. If you spin a bullet fast enough, one problem you get is wobble in flight. This is where mass symmetry imperfections are spun so fast that centrifugal effects cause the spin to become eccentric around the trajectory.

Another problem is core stripping. This happens inside the gun barrel, and occurs when the rotational acceleration of a bullet is so great that the jacket slips against the lead core as it accelerates. The bullet then exits with the jacket and core rotating at different speeds. As soon as they exit, friction causes their rotational speeds to equilibrate to a match. The core spins down up and the jacket spins up, but because the jacket has less mass, it loses more rotation than the core gains. At this point you have a bullet that's got speed bumps inside where the rifling pushed through the jacket and the cross section isn't very round, so again wobble gets into the picture and precision on the target deteriorates.

Finally, every once in awhile a long sleek bullet will actually disintegrate in flight. You can actually see a kind of gray streak when that happens in bright light. The eccentricity just grows by distorting the bullet until the stresses make it fly apart. This happens with long bullets in particular because long-for-weight bullets need the highest rate of spin to remain stable, subjecting them to higher centrifugal effects. You may have noticed before that long match bullets often come with a minimum rifling twist on the box, and this is why. The longer the bullet, the longer the lever arm drag has for overturning it, so the faster it has to spin to have the gyroscopic stability needed to prevent that occurring.

So, your first instinct is correct that fast shoots flatter. That's the reason for overbore cartridges like the .220 Swift. The Swift shoots the same bullet a lot faster than a .223, and therefore shoots farther more quickly and flatter. But the Swift also typically has only a 14" twist barrel instead of 7's, 8's, 9's and 12's that a .223 has. This prevents it over-spinning the bullet by the great acceleration it applies and causing the above problems, but it also means the bullet you use in it can't be too long or it won't stabilize adequately. You get a fast, flat shooter, but your bullet selection becomes limited to lighter bullets that are shorter and have lower BC's than the long ones the fast twist .223's can shoot. So it's a trade-off in capability that has advantage for the Swift only to limited distances. Beyond that, because the low drag bullets lose velocity in air more slowly than higher drag shapes do, they finally catch up to and pass the shorter, lighter bullets the .220 Swift is limited to. You just have to do more trajectory calculating to put those slower bullets where you want them. The longer it takes a bullet to make its journey, the farther gravity pulls it down.
 
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#11 · (Edited)
Nick, wow, what a very comprehensive reply ! :cool:

If I may comment on this succintly...

"If you spin a bullet fast enough, one problem you get is wobble in flight."
I understand that. Much like a Speed Rating/Balance for an Automobile Tire. If you exceed that, you cause vibrations and instability's.

"the jacket and core rotating at different speeds".
Wouldn't this imply that a "Cast" Bullet would be better? One which does not have multiple metals in it. Or is that not done? Do all Bullets have more than one type metal in their construction?

"long match bullets often come with a minimum rifling twist on the box".
Just Match Bullets? I think it would be very advantageous to a Loader, for the manufacturer of those products to list that information on ALL Bullets! Additionally, why not list the FPS it can handle as well?

"the Swift also typically has only a 14" twist barrel instead of 7's, 8's, 9's and 12's that a .223"
I think this is the most interesting statement of all. Would this imply, that a Firearms Manufacturer actually sets up a condition via the size, length and twist of a Barrel, for only one type, weight, speed and rotation of round, for a given Firearm? Then subsequently, varies the specifications on the Barrels of it's products, to accommodate the application of a given Firearm.
 
#12 · (Edited)
"the jacket and core rotating at different speeds".
Wouldn't this imply that a "Cast" Bullet would be better? One which does not have multiple metals in it. Or is that not done? Do all Bullets have more than one type metal in their construction?
It's just peculiar to cup an core construction. You can, of course, shoot cast bullets, though they are not normally as hard as copper and it takes some skill and know how to load them to jacketed bullet velocities without leading or other problems. You can shoot solid copper (e.g., Barnes and Hornady GMX) without that issue arising, and I'm sure bonded core bullets withstand higher torque than the standard press fit designs do.

"long match bullets often come with a minimum rifling twist on the box".
Just Match Bullets? I think it would be very advantageous to a Loader, for the manufacturer of those products to list that information on ALL Bullets! Additionally, why not list the FPS it can handle as well?
Some do list suggested twists, but you can use the free JBM Ballistics site stability estimator for yourself, as well. You need the bullet length for that, but they have a growing database of lengths, here. The calculator is good because you can adjust the muzzle velocity and weight and length and twist and air temperature and barometric pressure and see how all these factors interact to affect stability. That's an education in itself.

The FPS the bullet can be driven to without core stripping or disintegration depends on the rate of twist of the bore and the length of the barrel and the pressure curve of the powder you use. Too many possible combinations for a definitive single answer. The greatest acceleration of the bullet takes place during peak pressure which occurs when the bullet is still in the first couple of inches of travel, so that's where stripping initiates, well before final velocity is reached.

"the Swift also typically has only a 14" twist barrel instead of 7's, 8's, 9's and 12's that a .223"
I think this is the most interesting statement of all. Would this imply, that a Firearms Manufacturer actually sets up a condition via the size, length and twist of a Barrel, for only one type, weight, speed and rotation of round, for a given Firearm? Then subsequently, varies the specifications on the Barrels of it's products, to accommodate the application of a given Firearm.
They usually try to find a compromise for a range of bullets and accuracy requirements. For .223 Remington/5.56×45 NATO cartridges, the 7" twist now in military barrels is chosen to stabilize long, light tracer rounds. All other military bullets are spun unnecessarily fast by it, but the AR platforms aren't loaded to super high velocities like a .220 Swift, so it apparently hasn't caused a problem for military accuracy requirements (which allow something like 7" groups at 100 yards before a barrel is rejected and replaced).

The 7", 7½",and 8" twist commercial barrels are mainly geared toward match shooters who will mostly shoot long boattail bullets in the 69-80 grain range, with an occasional 90 grain bullet shooter squeezing in. They can shoot a 53 grain flat base MatchKing just fine for standing offhand and sitting rapid, where accuracy requirements aren't as high.

The 9" twist is a compromise for folks shooting a range of bullet sizes ranging from light bullets to some stubbier match bullet shapes, but many match bullets don't stabilize well enough in them. The old 12" twist was always for lighter bullet weights that preceded the availability of long match .224" diameter bullets. It started with the original AR development which used a 14" twist for 50 grain bullets, like the .222 Remington, but it was changed after testing found those bullets weren't adequately stable in extremely cold air, so it was changed to 12" for early AR production.
 
#13 ·
Nick,

THANK YOU !, for those links. Specially the "calculator" type. With my math skills, I need all the help I can get ! :D

It's becoming very apparent, that one needs to be aware of just what he's shooting. Knowing specifications like Twist and Length of Barrel, are a great deal more important, than I once thought.

I was looking at some 357 Mag specs at Buffalo Bore at...
Heavy 357 Magnum Pistol & Handgun Ammunition
and FINALLY noticed that there was a VAST difference in MVel, given which length Barrel one would use. But, I'm still bewildered at their implied difference between a Pistol and a Hand Gun. There's SO much more I need to know about this. ;)

Just to make sure...
I've seen several "opinions" offered, as to just how to measure a Barrel Length.
Should that measurement include the Chamber, or, from the front of a loaded Cartridge to the front end of the Barrel (excluding the chamber) ?

On the Twist of a Barrel...
I have rarely seen information regarding this. It seems like most Manufacturers don't regard it as being very important for the Customer to know. I'm finding that's definitely not the case. I will attempt to research the Firearms I have, and try to come up with that.

However, in the mean time...
IF I can't determine from any resource, what that given Twist is, what is the best way for me to check that on a given Firearm.

Nick, I can't tell you how appreciative I am, for your help with all this, and am very glad this Forum has an edit feature. :eek:
 
#14 · (Edited)
You are welcome.

These days Handgun is the generic umbrella term to distinguish handguns from long guns. Pistol refers to pretty much all handguns that are not revolvers, and revolvers get their own category. In old times the revolver gunslingers were called pistolero's so I think this use of the terminology is modern only and perhaps is English only, but don't know that for sure.

Barrel lengths of all kinds except revolver barrels are measured from the breech face of the gun to the muzzle, not including flash hiders, suppressors or other non-rifled extensions. For revolvers the barrel starts at the forcing cone which begins right in front of the cylinder where there is normally a few thousandths of an inch gap, and is measured from there to the muzzle. So, for a rifle or pistol you close the action and drop a cleaning rod in and measure how far it sticks in. For a revolver you open the cylinder, put something flat against the back of the barrel, then drop the rod in.

Many makers do actually publish barrel twist on their web site. You weren't looking before, but you'll start finding them now.

You can measure twist by pushing a tight dry patch through a barrel and watching how far it rotates over a given distance and figure out how far one turn takes or would take if the barrel were long enough. Inches per turn is the standard unit for rifling pitch in this country.
 
#15 ·
Note: Moved Scot's other questions to new thread in handloading, here.
 
#16 ·
Truth in Published B.C. by major bullet manufacturers ?

I shoot 7mm and I have noticed
some hi B.C. claims by some mfgrs on some bullets that seem all out of proportion
with the claims of competitors bullets and I wonder if any of the mfgrs are
developing a reputation of stretching their B.C. performance optimistically ?
I look at Barnes, Speer, Sierra and Berger mainly. 140 to 168gr bullets.
 
#17 ·
Get a copy of Bryan Litz's book, Applied Ballistics for Long Range Shooting. He has tested something like 250 bullets all by the same method to get a valid comparison. It is certainly the case that many published single number ballistic coefficients are valid only at some muzzle velocity. Some pick a velocity higher than others, making their bullets look better than they actually are. It is a result of believing that many shooters, given an array of similar choices, will just pick the bullet with the highest BC number. That's probably so for some.
 
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#18 ·
Get a copy of Bryan Litz's book, Applied Ballistics for Long Range Shooting. He has tested something like 250 bullets .

I am sure it is a good book but I aint paying Fifty bucks to get the truthful data that
the manufacturers should be supplying as description of their products. I realize he needs
to be paid for his work in uncovering the virtual fraud that is taking place in the
bullet industry but I think the mfgrs should be paying him.

Take a look at some samples of his work re 7mm bullets from Hornady and Sierra
The yellow highlighted numbers are his real world tested data and the G1 column
are what the manufacturers for the most part are using. HORRIBLY EXAGGERATED !
 

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#19 ·
Well, yes and no. What many shooters don't realize is that BCs can change dramatically just with the load data and individual barrel. I think that Rick Jamison did an article in Shooting Times many years ago, shooting a number of loads of one bullet in the same barrel and measuring the downrange velocities.

It varied much more than you'd think.

So.... with a long heavy barrel on a rigid test gun in a wind tunnel with perfectly tuned loads, they might well get much better numbers than a random sporter barrel out in the wind with who knows what load.

I'm not saying they are not exaggerating - I'm saying there is a lot more tolerance in these numbers than you'd think.
 
#21 ·
If you want to learn a lot more about how much the mfgrs quoted B.C.s are off,
google "Bryan Litz ballistics" etc and you will see why the quoted B.C.s are meaningless
except for Bergers for which Bryan Litz is the ballistician.

Somewhere I thought I read where most of the contents of his book are available
on the internet somewhere but I cant seem to find it now.

There is also some great educational stuff explaining the difference between G1 and G7 and
the evolution of the science etc
 
#22 ·
preventec said:
Somewhere I thought I read where most of the contents of his book are available on the internet somewhere but I cant seem to find it now.
If so, unless Litz did it himself, it's probably a violation of Litz's copyright. Stealing from him would not be acceptable, and I would expect him to get a site who hosted it without his permission to pull down or else be sued. It's what I would do in his shoes.

I am sure it is a good book but I aint paying Fifty bucks to get the truthful data that the manufacturers should be supplying as description of their products.
I wouldn't do that either, as I can measure my own BC's. But the book is worth it for all the other information in it on long range shooting. He also gives you a disc with it that includes his point mass solver, which is the same one on the Berger site except his version also figures bullet stability factor from the length, weight, muzzle velocity and barrel twist. It's on a disc that comes with the book.

Also, Litz has all his bullet information in his smart phone app based on his program. It claims to have a 1300 bullet BC library. It's $30.

I realize he needs to be paid for his work in uncovering the virtual fraud that is taking place in the bullet industry but I think the mfgrs should be paying him.
Understandable. Most of us would prefer to have someone else to pay for what we want to use. But the bullet makers other than Berger and Sierra aren't rushing to fix this. They compete based on their BC numbers.

Sierra determines their own G1 BC's in a 300 yard indoor range they own, so theirs are pretty good numbers. This is because Sierra is in the match bullet business and it matters more to them that their customers can get accurate trajectory calculations than that they necessarily have the tip top highest BC numbers.

Litz works for Berger (I don't think it's full time, since he has his own company for the book and product line and I believe I also saw there that he consults on ballistics. So Berger has paid Litz for his work on their particular bullets, but the book and that stuff is his own separate company. Nobody has paid him to cover the cost of printing the book and running all the other bullets and doing all the other writing about how to shoot accurately at long range. I expect he has a lot of effort and time in it.

Take a look at some samples of his work re 7mm bullets from Hornady and Sierra The yellow highlighted numbers are his real world tested data and the G1 column are what the manufacturers for the most part are using. HORRIBLY EXAGGERATED !
No. As Chev said, you are looking at G1 BC's and comparing them to G7 BC's. That's like comparing inches to centimeters and declaring one of them is fraudulent because they aren't the same size. They are simply two different length standards, just as G1 and G7 are two different aerodynamic standards. They are not comparable.

Instead, what you find in Litz's stuff is more like the following. This example is one of the biggest disagreements with manufacturer numbers that I've noticed in his book:

Nosler's published G1 BC for their .308" 168 grain Custom Competition Match bullet:

0.462 @ all velocities

Bryan Litz's measured G1 BC's for the same Nosler bullet:

0.442 @ 3000 fps
0.433 @ 2500 fps
0.430 @ 2000 fps
0.400 @ 1500 fps

0.426 = Average

So the Nosler BC is probably true if the bullet is fired at 4000 fps, but I don't know anything that will do that, offhand.

Incidentally, there are other sources of error in published bullet BC's from some manufacturers. One is that many times a manufacturer doesn't own a nice indoor range like Sierra does. So, instead of measuring actual velocity loss over distance, they use tables of nose and tail shapes and estimate the BC's from those. Litz describes how to do this in his book. Or they plug the dimensions into a computer program that estimates the BC's for them. Worse, they may take the bullets to the range and try to estimate the BC from measured bullet drop over a range long enough that wind can cause vertical as well as horizontal POI error. It's not an easy to get an accurate result that way. Bottom line, most of the numbers are guestimates rather than measured.
 
#23 ·
No. As Chev said, you are looking at G1 BC's and comparing them to G7 BC's. That's like comparing inches to centimeters and declaring one of them is fraudulent because they aren't the same size. They are simply two different length standards, just as G1 and G7 are two different aerodynamic standards. They are not comparable. .
That is not the way I read it. G1 #s I recall was comparing bullets flight with a hundred year
old artillery shell shape and G7#s was comparing flight path with modern shaped bullet design.
(obviously comparison with a horribly performing standard is going to make you look better)

If your bullet is a modern shaped bullet design and using a G1 B.C. number you are comparing
its performance with a standard shape projectile that is shaped like a hundred year old artillery
shell. AND if you plug those BC no.s into a calculator you will get exaggerated optimistic
performance numbers. If you want realistic trajectory forcast for your bullet you need to
use the "relevant" G7 BC numbers

There is a website with highly developed calculators and seemingly have loaded into
the calculator the bullet database along with Litz's measured BC performance numbers into
the bullet database.

Check it out. VERY impressive.
here JBM - Calculations - Trajectory
 
#24 · (Edited)
Preventec47,

If you looked at my first post that began this thread four years ago, you’ll find another link to the JBM site there, as well.

Sorry to take so long getting back to this, but I had to find a little time to assemble it in one place.

Preventec47 said:
That is not the way I read it.
I'll walk through a sample calculation of two standard projectile referenced BC’s, then you can see how accuracy compares:

I’ll take a bullet for which an individual drag coefficient table is available. The 168 grain Sierra MatchKing bullet was measured by the U. S. Army Ballistics Research Laboratory (BRL) for M852 ammunition using Doppler RADAR. It is less comprehensive than the standard projectile table, but over short monotonic intervals, it yields to regression within one digit in the fourth decimal place, so I’ll fill in with that as needed here. This will make for a good apples-to-apples comparison.

First note the ballistic sectional densities of all the projectiles involved:

G1 Standard Projectile ballistic sectional density = SDG1 = 1 lb/in²
G7 Standard Projectile ballistic sectional density = SDG7 = 1 lb/in²
168 grain SMK ballistic sectional density = SD168SMK = 0.253 lb/in²

Next I get their drag coefficients from tables. I’ll compare these projectiles at Mach 2.5, under U. S. Army Standard Meteorological Conditions (Army Std. Metro.), which works out to 2801 fps. From BRL tables of measured values:

G1 Standard Projectile Mach 2.5 drag coefficient = CdG1_M2.5 = 0.5397
G7 Standard Projectile Mach 2.5 drag coefficient = CdG1_M2.5 = 0.2697
168 grain SMJ Mach 2.5 drag coefficient = Cd168SMK = 0.3200

Where i = form factor = Cdany projectile / Cdreference projectile

BC = SDany projectile / SDreference projectile / i

Most BC’s formulas omit division by the reference projectile SD, leaving that implicit. This is because BRL reference projectiles are 1 inch wide and weigh 1 lb to give them a ballistic SD of 1, and dividing by 1 doesn’t change your result magnitude. Any other weight and diameter ratio would require doing the division. The reason this division has to be done, albeit implicitly, even for a value of 1, is to cancel out the SD units of lb/in². When you do it implicitly you have to remember to drop the SD units to arrive at the dimensionless BC.

I will drop the extra division notation from this point forward and leave it implicit, as is conventional. This leaves:

BC = SDany projectile / i

So let’s get the G1 and G7 BC’s for the 168 grain SMK at Mach 2.5:

168 SMK G1M2.5 BC = SD168SMK / (Cd168SMK_M2.5 / CdG1_M2.5) = 0.253 / (0.3200/0.5397) = 0.4267

168 SMK G7M2.5 BC = SD168SMK / (Cd168SMK_M2.5 / CdG7_M2.5) = 0.253 / (0.3200/0.2697) = 0.2132

Now I'll run a check to see how accurate they are?

Where:
lbm = pounds mass = 0.031085 slugs¹
lbf = pounds force
ρ = Air Density at Army Std. Metro. = 0.0023353 slugs/ft³
A = Cross-sectional area of projectile in ft²
v = 2801 fps (Mach 2.5 in U. S. Army Std. Metro conditions)
Cd = Drag Coefficient for shape of projectile
-F = Drag Force in lbf = ma = ½ρAv²Cd
m = mass in slugs = lbm/g = 0.031085 slugs per lbm
-a = deceleration = -F/m

G1 and G7 reference projectile 1” diameter cross-sectional area = 0.785398 in² = 0.00545415 ft²
Mach 2.5 = 2801 fps at Army Std. Metro. = v
v² = 7,843,781 ft²/s² at Army Std. Metro.
CdG1_M2.5 = 0.5397

So I have:

G1 reference projectile deceleration = -F/m = -½ρAv²Cd/0.031085 slug =
-0.5×0.0023353 × 0.00545415 × 7843781 × 0.5397 / 0.031085 = -867.3 ft/s²

CdG7 = 0.2697

G7 reference projectile deceleration = F/m = -½ρAv²Cd/0.031085 slug =
0.5 × 0.0023353 × 0.00545415 × 7843781 × 0.2697 / 0.031085 = -433.4 ft/s²

Next I calculate what deceleration is estimated for the 168 grain SMK using these BC's:

-867.3 ft/s² / 168 SMK G1<sub>Mach2.5</sub> BC = 867.3 ft/s² / 0.4267 = -2033 ft/s² from G1 BC
-433.4 ft/s² / 168 SMK G7<sub>Mach2.5</sub> BC = 433.4 ft/s² / 0.2132 = -2033 ft/s² from G7 BC

What is the actual rate of velocity loss in the 168 grain SMK?

168 SMK cross-sectional area = 0.074506 in² = 0.0005174 ft²
Cd168SMK_M2.5 = 0.3200
168 SMK mass in slugs = 0.00074594

168 SMK projectile deceleration = -F/m = -½ρAv²Cd/0.00074594 slugs =
-0.5 × 0.0023353 × 0.0005174 × 7843781 × 0.3200 / 0.00074594 = -2033 ft/s²

Well, there you have it. Both the G1 and G7 BC’s, though different in value, were equally accurate in predicting the 168’s deceleration when divided into the decelerations of their respective reference projectiles.

If you’ve been following, you’ll realize this was a rigged game. The result is circularly dependent on how the definitions of BC’s are solved with the ratio of SD’s and drag coefficients for a particular velocity in the first place. But that is not sleight of hand. It’s the way the system works.

So, why prefer a G7 BC to a G1 BC? The answer is not in how accurately you can choose the BC with respect to any reference projectile at one velocity. You can make the BC for any reference projectile perfectly accurate when you only concern yourself with one velocity. Rather, it is about how well each value holds up over a range of different velocities. Let’s try using those same Mach 2.5 BC’s I calculated to predict how fast the 168 grain SMK will lose velocity at Mach 1.5.

From BRL tables of measured values:

G1 Standard Projectile Mach 1.5 drag coefficient = CdG1_M1.5 = 0.6573
G7 Standard Projetile Mach 1.5 drag coefficient = CdG7_M1.5 = 0.3440
168 grain SMK Mach 1.5 drag coefficient = Cd168SMK_M1.5 = 0.396

v at Mach 1.5 in Army Std. Metro. = 1680.4 fps
v² = 2823761 ft²/s²

G1 reference projectile deceleration at Mach 1.5 = F/m = -½ρAv²Cd/0.031085 slug =
-0.5 × 0.0023353 × 0.00545415 × 2823761 × 0.6573 / 0.031085 = -380.4 ft/s²

G7 reference projectile deceleration at Mach 1.5 = F/m = -½ρAv²Cd/0.031085 slug = -0.5 × 0.0023353 × 0.00545415 × 2823761 × 0.3440 / 0.031085 = -195.3 ft/s²

Using the G1 Mach 2.5 BC: -380.4 ft/s / 0.4267 = -891.6 ft/s² G1 Prediction

Using the G7 Mach 2.5 BC: -195.3 ft/s / 0.2132 = -916.0 ft/s² G7 Prediction

And how do these compare to the actual projectile:

168 SMK projectile actual deceleration = -F/m = -½ρAv²Cd/0.00074594 slugs =
-0.5 × 0.0023353 × 0.0005174 × 2823761 × 0.396 / 0.00074594 = -905.5 ft/s²

So:

-905.5 / -891.6 = +1.56% error for using the G1 Mach 2.5 BC

-905.5 / -916.0 = -1.15% error for using the G7 Mach 2.5 BC

So the G7 tracks more closely when velocities differ, and that’s the reason it is preferred. But as you can see, that antique G1 doesn't do as badly as you might have supposed.

Hope this helps clarify things.


¹ In the in-lb-sec system, slugs have to be used for mass for the numbers to come out with the correct magnitude without adding a correction constant.
 
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#26 · (Edited)
If you are referring to John Schafer's (Fr. Frog) article here, those smooth surfaced drawings are schematic drawings showing the main projectile feature dimensions, but ignoring smaller features like the driving bands for these solid iron projectiles. McCoy's book, Modern Exterior Ballistics, has more detailed drawings. Here's one of the G1 projectile I did based on his data. The others have similar feature additions. You don't need them to see which shape your bullet is closest to, though. For that the schematics are all you require.

 

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