Topic of the Month:
September 2001
What is Ballistic Coefficient and
How is it Calculated?
Simply stated, the ballistic coefficient is
a measure of how well a projectile behaves in air. The ballistic coefficient is an
important and useful concept that relates the drag deceleration of a given projectile to
the drag deceleration of a standard bullet. The concept of the standard bullet and related
ballistic coefficients was a major step forward, because otherwise the drag characteristic
of every type of bullet fired would have to be measured individually – an impossible
undertaking.
Near the turn of the century, many tests
were made by the Krupp Company of Germany to determine the retardation or drop
characteristics of so-called standard bullets. Soon after the Krupp data were published a
Russian army colonel named Mayevski constructed a mathematical model for the drag
deceleration of a standard bullet. The standard bullet was one inch in diameter, weighed
one pound and had an ogive head of 8 calibers radius. Colonel James M. Ingalls of the U.S.
army later used Mayevski's mathematical model to compute his now famous ballistics table.
The standard Krupp bullet proved to be such
a good model for use in calculating the ballistics of most bullets used in sporting
firearms, that today most of the major bullet companies use the Ingalls or similar tables
together with test firings of production bullets to compute ballistic coefficients for
their bullets. These coefficients are published in most of the major reloading manuals.
Most ammunition manufacturers do not publish the ballistic coefficients of their bullets,
but instead include ballistic charts in their sales literature and catalogs that show drop
and remaining down range velocity for bullets used in each cartridge that they
manufacture.
The larger the ballistic coefficient, the
more efficient the bullet’s performance in air. It can be described as the ratio
it’s sectional density to its coefficient of form, where sectional density is the
weight of the bullet divided by the square of its diameter. It can be written as:
(1) C = SD/i = w/id2
Where C = ballistic coefficient
SD = sectional density
i = form factor
w = weight of bullet,
lbs.
d = diameter of the
bullet, in.
Coefficient of form, or form factor, is a
mathematical number that relates a bullet’s shape, smoothness and shape at the base.
The form factor compares the shape of a bullet being tested to the shape of a standard
bullet used in a particular ballistic table. The ballistic table referred to in this
discussion will be Ingalls table unless other wise noted.
No method is
known to calculate and describe the bullet’s shape in numbers suitable for
development of a mathematical formula. However, a chart of bullet shapes was developed by
Edgar Bugless and Wallace H. Coxe, Ballistic Engineers of the DuPont Co. and included in a
series of ballistic charts called "Exterior Ballistic Charts" published by E.I.
DuPont De Nemours & Co. In order to use the chart the user slides a bullet along the
chart until the shape matches the ogive or head radius of the bullet. This value is
transferred to an accompanying table to determine the form factor, based on muzzle
velocity and point of the bullet (normal point, hollow point or flat nose configurations).
A few example typical form factors are given below:
Blunt projectile, cylindrical
2.30
Blunt projectile, Taper sides 0.6 Cal.
1.10
Head radius of 8.0 Cal M.V. under 2000 f.p.s. 0.65
Balls with M.V. under 1000 f.p.s.
2.00
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Many bullet manufacturers used the form
factor method to estimate ballistic coefficients for their bullets until development of
the modern chronograph and other sophisticated electronic measuring equipment. Today, most
commercial bullet manufacturers determine ballistic coefficients by measuring muzzle
velocity and time of flight over a known range or measuring the velocity at two points
over a measured range. Because the test bullets often deviate from the standard projectile
model, the ballistic coefficient changes slightly with velocity. Most bullet manufacturers
list one ballistic coefficient for each bullet. One bullet manufacturer lists three or
four ballistic coefficients for each of their bullets, depending on the velocity of the
bullet downrange.
The ballistic coefficients published by the
bullet manufacturers are reported at standard conditions of temperature, elevation and
humidity. In order to calculate an accurate trajectory for your bullet the standard
ballistic coefficient must be corrected for shooting conditions at your location. Several
of the loading manuals show how this is done or you can use one of the ballistic software
computer programs to do this for you.
The Load From A Disk ballistics software
program, as described at this web site, will allow you to calculate the ballistic
coefficient three different ways. These are:
- Calculation of ballistic coefficient from
trajectory.
- Calculation of ballistic coefficient from
velocity at two points.
- Calculation of ballistic coefficient from
shape as described above.
This is the only ballistics program that
will allow you to calculate the ballistic coefficient by three different methods. The
shape method even allows you to print out the bullet shape chart to determine the correct
ogive for your bullet. This program also lets you correct the ballistic coefficient to
site conditions.
The method of calculating the ballistic
coefficient from velocity at two points was actually used to calculate the ballistic
coefficients of 19 different cast bullets for the rifle and 32 different cast bullets for
the handgun. The results of these tests were published in Rifle magazines #66 and
#70. Sixteen brands of .22 long rifle ammo were also tested and their ballistic
coefficients were published in the 36th Anniversary Edition of Gun Digest.
Watch our web site for the next topic of
interest "Trajectory and how it is used." Until then, shoot safely and know
where your bullets are going.
Sincerely,
The Ballistician
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