# The Ballistic Model

Sellier & Bellot

**Sellier & Bellot**, in collaboration with a leading Czech ballistics expert, has developed an advanced ballistics model to calculate the performance and trajectory of ammunition.

The basic element of ballistic calculations is the ballistic coefficient (BC), which is used to evaluate the missile in terms of external ballistics and flight characteristics in the real atmosphere (ATM). BC can also be described as the ability of the missile to penetrate the ATM.

It is true that a missile with a higher BC penetrates ATM better and vice versa that a missile with a lower BC is more inhibited by ATM.

Sellier & Bellot calculates the BC of a labored bullet by accurately measuring the velocities of a sample of 10 bullets on a 100 m range. The measured bullet velocity values, together with the actual temperature, humidity and absolute air pressure, are used to calculate the published BC of the bullet converted to standard ICAO air conditions (temperature 15°C, relative humidity 0% and absolute pressure 1.013.25 hPa). This provides the ability to compare individual missiles with each other.

For the need of an accurate long range firing model, a model based on the equations of motion of the mass point under the influence of gravitational acceleration and environmental drag force is used.

The algorithm for calculating the ballistic elements of the projectile is performed by numerical integration of the general equations of motion of the mass point using a modified Euler method.

### Overview of the use of Gx resistive functions:

Type of projectile |
Resistance function |
---|---|

SP, HP, FMJ | G1 |

FMJ, FMJBT, HPBT, SP | G7 |

An advanced and physically accurate ballistic model is the basis for development of ammunition, helps you select the right cartridge and shoot perfectly.

### Definition of the ballistic coefficient of a missile in imperial units:

$$\mathrm{BC}=\frac{m/\mathrm{7000}}{i*{d}^{2}}$$

Where **BC** is the ballistic coefficient of the projectile *(lb/in ^{2})*,

**m**the mass of the projectile

*(grs)*,

**d**the diameter of the projectile

*(in*),

**i**the dimensionless coefficient of the shape of the projectile.

Where **BC** is the ballistic coefficient of the projectile *(lb/in ^{2})*,

**SD**is the cross-sectional load of the projectile

*(lb/in*,

^{2})**i**is the dimensionless shape factor of the projectile.

Where **SD** is the cross-sectional load in *(lb/in ^{2})*,

**m**is the mass of the projectile in

*(grs)*,

**d**is the diameter of the projectile in

*(in)*.

### Example:

A 0.308 in HPBT bullet weighing 175 grains has a cross-sectional load of **SD** and **BC**:

$${\mathrm{BC}}_{\mathrm{G7-ICA0}}=\frac{\mathrm{175}/\mathrm{7000}}{\mathrm{1.1046}*{\mathrm{0.308}}^{2}}=\mathrm{0.239}{lb/in}^{2}$$

To simplify calculations and evaluation of projectiles, standard resistance functions for precisely defined projectile shapes, the so-called G resistance functions, have been introduced. Ballistic coefficient values according to the standard G1 and G7 drag functions are available for most projectiles.