4.1
Basic Definitions
It has already been mentioned that a ballistic coefficient always refers to a particular standard drag model for a certain standard bullet. In this Manual, and in most other published material, the drag model is equivalent to the one used in the Ingalls Tables, and it is also known as the
G
1
model. There is no way, short of computing trajectories, to compare the ballistic properties of two bullets if their ballistic coefficients are referenced to different drag models.
The ballistic coefficient
C
is defined by the following ratio:
It must be noted that this definition involves not the drag force on the bullets, but the deceleration caused by the force. Since drag depends on velocity, it is implied in the definition that the same velocity is used for both bullets when the ratio is taken. The ballistic coefficient of the standard bullet is defined to be 1.000. It is also clear that when
C
is smaller than 1.000, which is the general case, it means that the actual bullet slows down faster than the standard bullet. It is also easy to see that the smaller
C
is, the faster the actual bullet slows down.
It is possible to give a mathematical definition for
C
, which is
Where
w
is the weight of the bullet in pounds,
d
is the diameter of the bullet in inches, and
i
is known as the form factor. This definition is instructive because it gives a general idea of the dependence of
C
on bullet weight and caliber. A problem arises because the form factor depends on many other things, bullet length, point design, and base design to name just a few. If bullets of pretty much the same shape and the same caliber are compared, the formula shows why the heavier bullets have larger ballistic coefficients. For example, take the six .30 caliber HPBT MatchKing bullets weighing 168, 180, 190, 200, 220, and 250 gr. and all having boat tails and similar point designs. The formula shows why the ballistic coefficients increase in that order. The diameter
d
is the same for all, the shapes are similar, and the weight increases in order.
On the other hand, compare the .30 caliber 165 gr. HPBT with the 168 gr. HPBT MatchKing. The weights are nearly equal, but the 165 gr. has a much lower ballistic coefficient. The reason is the shape factor. The 165 gr. bullet, designed for hunting use, has a much larger hollow point diameter, so its shape factor is larger than that of the MatchKing bullet.
The formula does not make the situation for smaller calibers very clear. Specifically, it is hard to see why smaller caliber bullets generally have lower ballistic coefficients than larger caliber bullets of similar shape, since as weight diminishes so does diameter. Some insight into the situation can be obtained by considering a needle. A needle has a very small drag, but it also has very little weight, so that the small drag causes a large influence on the motion.
The formula above also shows that ballistic coefficient is related to sectional density. The sectional density (
SD
) of a bullet is defined as
where again
w
is bullet weight in pounds and
d
is bullet diameter in inches. Bullet weights are always given in grains rather than pounds. Since there are 7000 grains in a pound, sectional density can be calculated from
Ballistic coefficient is simply sectional density divided by form factor:
