Bullet physics worth understanding
By Don Lewis
Published: Friday, June 22, 2007,
Sectional density is mixed through gun articles the same way promises are worked into political speeches. Once uttered, they are forgotten. But the fact remains that sectional density can be accurately determined and verified.
Sectional density is the bullet's weight in pounds divided by the square of its diameter in inches. The higher the SD reading, the better the penetration. A good exampfe is the 105-grain 6mm bullet. To convert its weight to pounds, divide by 7,000 (the number of grains in a pound). This gives 0.015. Then divide this by .243 (its diameter in inches) squared, or 0.059. Its sectional density is determined by the bullet's weight and diameter; it does not change with shape. In other words, all 105-grain 6mm bullets have the same sectional density no matter what the shape or style. The same would hold true for 150-grain .308 bullets or 55-grain .224 bullets.
It's worth noting that sectional density can be misleading, and it should not be the primary reason for choosing a bullet. It's not uncommon to get two bullets of nearly identical SD, yet that does not mean they will have identical power or efficiency. The SD of a 100-grain .243 bullet is .242, while that of a 165-grain .308 is .248. With a muzzle velocity of 2,960 feet per second, the .243 has a kinetic energy of 1,945 foot pounds, while the .308 at a somewhat slower velocity of 2,700 fps has a far greater energy -- 2,670 foot pounds. It stands to reason the .308 would be a better big-game choice, although the sectional density of these two bullets is almost the same.
As the science of bullet making grew, designers became acutely aware that shape is important. A more streamlined bullet slips through the air easier than a blunt-shaped one, thus does not lose velocity as fast, and therefore retains more kinetic energy at long range. It will have a flatter trajectory, too. That's where the term ballistic coefficient t comes in.
The BC figure is actually a mathematical expression of a bullet's ability to overcome atmospheric resistance. It is closely related to sectional density, and in fact begins with the same basic formula. Perhaps sharing the thoughts of William C. Davis, ballistic editor for the "American Rifleman" and noted ballistic authority will help understand the mysterious BC.
He says, "Briefly defined, the ballistic coefficient is a quantitative indicator of the bullet's ability to maintain its velocity as it flies through the air. It is defined mathematically by the expression C=W/(I x D squared), where W is the bullet's weight in pounds, 'D' is its diameter in inches, and I is a so-called form factor which depends on the bullet's shape."
To show that the BC ties in with the SD, he explains, "The same equation can be rearranged to read C=W/D squared/I, and in that form we might recognize the expression (W/D squared) as the sectional density of the bullet, so we see that the ballistic coefficient can also be defined as the sectional density divided by the form factor. The form factor (I) is a dimensionless number which expresses the aerodynamic efficiency of a bullet's shape, relative to the shape of some particular standard projectile. More specifically, the form factor of a particular bullet is the ratio of the drag coefficient of that bullet, to the drag coefficient of the standard projectile. If all bullets were of the exactly the same shape as the standard projectiles to which they are compared, then the form factor would always be exactly one, and the ballistic coefficient would always be exactly equal to the sectional density."
Kenneth Oehler of Oehler Research, maker of the sophisticated Model 43 Personal Ballistic Laboratory and whose name is synonymous with precision chronographs, explains, "A BC of .41 just means that the bullet is 41 percent as efficient at retaining its velocity as was the 'standard' bullet for which the drag table was determined. You use the BC of .41 as the 'conversion key' with the standard drag table to determine remaining velocity, drop, etc.
"The BC of .41 was determined by a test at a particular velocity and it represents the adjustment of key required to fit the bullet to the standard drag table at (or near) the test velocity. If you measure the BC at a different velocity level: you may get a different BC. Nothing about the bullet changes as velocity changes, but a different key or BC may be required to make the bullet's behavior fit the standard table at the new velocity.
"You use the BC measured at the higher velocity to compute the ballistics until the velocity drops to a mid level, then you use the other BC for computations in the lower velocity range. The alternative to using multiple BCs is to provide each bullet its own downrange table. The military does just that with their 'firing tables' for particular bullets."
Oehler mentions this is financially prohibitive for the majority of handloaders, so they have to use one "standard" downrange table, and then use the BC to make the table fit the bullet. If we can't find a single BC that makes the bullet test data fit the entire table, we break the table into sections and use a different BC to force a fit one section at a time.
How did the standard model bullet come into existence• According to Oehler Research, a few decades ago the commercial firearms and ammo people decided on a standard model to describe the exterior ballistic performance of sporting ammo (there are other drag functions for different types of bullets). They chose a drag function named G1 to represent typical performance of a sporting bullet. While "G1 drag function" sounds impressive, it's only a table showing how fast the standard projectile is losing velocity versus the momentary velocity of the projectile. If a tested bullet loses velocity twice as fast as does the standard bullet, has a BC of 0.500. If a tested bullet loses velocity three times as fast as does the standard bullet, it has a BC of 0.333. If the tested bullet loses velocity at the same rate as the standard bullet, it has a BC of 1.000. If the tested bullet retains its velocity better than the standard bullet, it has a BC greater than 1.000.
To measure BC you must know both how fast your bullet is going and how fast the bullet is losing velocity. Suppose that your bullet starts at 2,500 fps and loses 312 fps in 100 yards. The standard bullet loses only 84 fps starting at the same velocity under the same atmospheric conditions. The BC of your bullet is approximately 84/312 or 0.269.
Measuring chamber pressure, ballistic coefficient and standard deviation, which indicates the uniformity of velocity, may not seem important to many handloaders, likely because there was no way of obtaining this data on the home level. Since the Oehler Model 43 Personal Ballistic Laboratory gives all this ballistic information and also serves as a conventional chronograph, handloaders are no longer forced to accept book figures, and, basically, book figures are relative only to the particular riffe fired in thetest. The M-43 PBL gives ballistic data from the handloader's own firearms.
The ballistic coefficient is not just a loose mathematical ballistic term. It plays a major role in the flight of the bullet. We don't have to worship the BC anymore than we have to believe implicitly in the standard deviation, but we shouldn't ignore them, especially when there are devices to measure them.
Not knowing the BC or SD of your particular bullet will not keep you from getting a deer at 150 yards or a prairie dog at long range. Still, it's only common sense that the more we know about internal and external ballistics from our own rifles, the higher quality our reloads will be and the more accuracy we'll develop with them. You can write that in stone.
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