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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
```

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.