Ballistic coefficient

A selection of bullets with different shapes, and hence, different ballistic coefficients.

In ballistics, the ballistic coefficient (BC) of a body is a measure of its ability to overcome air resistance in flight.^[1] It is inversely proportional to the negative acceleration: a high number indicates a low negative acceleration—the drag on the body is small in proportion to its mass. BC can be expressed with the units kilogram per square meter (kg/m²) or mass pound per square inch (lbs/in²)^[2] (where 1 lbs/in² corresponds to 703.069581 kg/m²).

Formulas[]

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General[]

${\displaystyle BC_{Physics}={\frac {m}{C_{d}\cdot A}}={\frac {\rho \cdot \ell }{C_{d}}}}$

Where:

• BC_Physics = ballistic coefficient as used in physics and engineering
• m = mass
• A = cross-sectional area
• C_d = drag coefficient
• ${\displaystyle \rho }$ = density
• ${\displaystyle \ell }$ = characteristic body length

Ballistics[]

The formula for calculating the ballistic coefficient for small and large arms projectiles only is as follows:

${\displaystyle BC_{Projectile}={\frac {m}{d^{2}\cdot i}}}$ ^[3]

Where:

• BC_Projectile = ballistic coefficient as used in point mass trajectory from the Siacci method (less than 20 degrees).^[4]
• m = mass of bullet
• d = measured cross section (diameter) of projectile
• i = Coefficient of form

The Coefficient of form (i) can be derived by 6 methods and applied differently depending on the trajectory models used: G Model, Beugless/Coxe; 3 Sky Screen; 4 Sky Screen; Target Zeroing; Doppler radar.^[5][6]

Here are several methods to compute i or C_d:

${\displaystyle i={\frac {2}{n}}\cdot {\sqrt {\frac {4n-1}{n}}}}$ ^[7][6][8]

Where:

• i = Coefficient of form.
• n = number of calibers of the projectile's ogive.

Where n is unknown:

${\displaystyle n={\frac {(4\cdot \ell ^{2}+1)}{4}}}$ ^[7]

Where:

• n = number of calibers of the projectile's ogive.