BallisticCalculator

LGPL library for small arms ballistic calculations based on point-mass (3 DoF) plus spin drift.

Table of contents

• Installation

  • Latest stable

• Usage

  • Simple example
  • Plot trajectory
  • Range card
  • Complex example

• Units of measure

  • Examples
  • Preferences

• Integration Engines

  • Modifying Presets
  • Custom integration engines

• Concepts

  • Coordinates
  • Slant / Look Angle
  • Danger Space

• Contributors

• About project

Installation

pip

pip install py-ballisticcalc

# Using precompiled backend (improves performance)
pip install py-ballisticcalc[exts]

# Using matplotlib and pandas uses additional dependencies
pip install py-ballisticcalc[charts]

uv

uv sync

uv sync --dev --extra exts

Usage

See Example.ipynb and ExtremeExamples.ipynb for detailed illustrations of all features and usage.

Simple Zero

# Establish 100-yard zero for a standard .308, G7 bc=0.22, muzzle velocity 2600fps
from py_ballisticcalc import *
zero = Shot(weapon=Weapon(sight_height=2), ammo=Ammo(DragModel(0.22, TableG7), mv=Velocity.FPS(2600)))
calc = Calculator()
zero_distance = Distance.Yard(100)
zero_elevation = calc.set_weapon_zero(zero, zero_distance)
print(f'Barrel elevation for {zero_distance} zero: {zero_elevation << PreferredUnits.adjustment}')

Barrel elevation for 100.0yd zero: 1.33mil

Plot Trajectory with Danger Space

# Plot trajectory out to 500 yards
shot_result = calc.fire(zero, trajectory_range=500, trajectory_step=Distance.Yard(1), extra_data=True)
ax = shot_result.plot()
# Find danger space for a half-meter tall target at 300 yards
danger_space = shot_result.danger_space(Distance.Yard(300), Distance.Meter(.5))
print(danger_space)
danger_space.overlay(ax)  # Highlight danger space on the plot
plt.show()

Danger space at 300.0yd for 19.7inch tall target ranges from 217.1yd to 355.7yd

Print Range Card

# Range card for this zero with 5mph cross-wind from left to right
zero.winds = [Wind(Velocity.MPH(5), Angular.OClock(3))]
range_card = calc.fire(zero, trajectory_range=1000, trajectory_step=100)
range_card.dataframe().to_clipboard()
range_card.dataframe(True)[
    ['distance', 'velocity', 'mach', 'time', 'slant_height', 'drop_adj', 'windage', 'windage_adj']].set_index('distance')

distance	velocity	mach	time	slant_height	drop_adj	windage	windage_adj
0.0 yd	2600.0 ft/s	2.33 mach	0.000 s	-2.0 inch	0.00 mil	-0.0 inch	0.00 mil
100.0 yd	2398.1 ft/s	2.15 mach	0.120 s	-0.0 inch	-0.00 mil	0.4 inch	0.12 mil
200.0 yd	2205.5 ft/s	1.98 mach	0.251 s	-4.1 inch	-0.57 mil	1.7 inch	0.25 mil
300.0 yd	2022.3 ft/s	1.81 mach	0.393 s	-15.3 inch	-1.44 mil	4.1 inch	0.39 mil
400.0 yd	1847.5 ft/s	1.65 mach	0.548 s	-35.0 inch	-2.48 mil	7.6 inch	0.54 mil
500.0 yd	1680.1 ft/s	1.50 mach	0.718 s	-65.0 inch	-3.68 mil	12.4 inch	0.70 mil
600.0 yd	1519.5 ft/s	1.36 mach	0.906 s	-107.3 inch	-5.06 mil	18.8 inch	0.89 mil
700.0 yd	1366.0 ft/s	1.22 mach	1.114 s	-164.8 inch	-6.66 mil	27.0 inch	1.09 mil
800.0 yd	1221.3 ft/s	1.09 mach	1.347 s	-240.9 inch	-8.52 mil	37.3 inch	1.32 mil
900.0 yd	1093.2 ft/s	0.98 mach	1.607 s	-340.5 inch	-10.71 mil	50.0 inch	1.57 mil
1000.0 yd	1029.8 ft/s	0.92 mach	1.891 s	-469.0 inch	-13.27 mil	64.8 inch	1.83 mil

Complex Example

Here we define a standard .50BMG, enable powder temperature sensitivity, and zero for a distance of 500 meters, in a 5°C atmosphere at altitude 1000ft ASL.

dm = DragModel(0.62, TableG1, 661, 0.51, 2.3)
ammo = Ammo(dm, Velocity.MPS(850), Temperature.Celsius(15), use_powder_sens=True)
ammo.calc_powder_sens(Velocity.MPS(820), Temperature.Celsius(0))
weapon = Weapon(sight_height=Distance.Centimeter(9), twist=15)
atmo = Atmo(altitude=Distance.Foot(1000), temperature=Unit.Celsius(5), humidity=.5)
zero = Shot(weapon=weapon, ammo=ammo, atmo=atmo)
zero_distance = Distance.Meter(500)
calc = Calculator()
zero_elevation = calc.set_weapon_zero(zero, zero_distance)
print(f'Barrel elevation for {zero_distance} zero: {zero_elevation << PreferredUnits.adjustment}')
print(
    f'Muzzle velocity at zero temperature {atmo.temperature} is {ammo.get_velocity_for_temp(atmo.temperature) << Velocity.MPS}')

Barrel elevation for 500.0m zero: 4.69mil
Muzzle velocity at zero temperature 5.0°C is 830.0m/s

Units

Examples

from py_ballisticcalc.unit import *

# Ways to define value in units
# 1. old syntax
unit_in_meter = Distance(100, Distance.Meter)
# 2. short syntax by Unit type class
unit_in_meter = Distance.Meter(100)
# 3. by Unit enum class
unit_in_meter = Unit.Meter(100)
print(f'100 meters: {unit_in_meter}')
# >>> 100 meters: 100.0m

# Convert unit
# 1. by .convert()
unit_in_yards = unit_in_meter.convert(Distance.Yard)
# 2. using shift syntax
unit_in_yards = unit_in_meter << Distance.Yard  # '<<=' operator also supports
print(f'100 meters in {unit_in_yards.units.key}: {unit_in_yards}')
# >>> 100 meters in yard: 109.4yd

# Get value in specified units (as float)
# 1. by .get_in()
value_in_km = unit_in_yards.get_in(Distance.Kilometer)
# 2. by shift syntax
value_in_km = unit_in_yards >> Distance.Kilometer  # '>>=' operator also supports
print(f'100 meters, value in km: {value_in_km}  (value type is {type(value_in_km)})')
# >>> 100 meters, value in km: 0.1  (value type is <class 'float'>)

# Getting unit raw value (a float)
rvalue = Distance.Meter(100).raw_value
rvalue = float(Distance.Meter(100))
print(f'100 meters in raw value: {rvalue}  (raw type is {type(rvalue)})')
# >>> 100 meters in raw value: 3937.0078740157483  (raw type is <class 'float'>)

# Comparison operators supported: < > <= >= == !=
print(f'Comparison: {unit_in_meter} == {Distance.Centimeter(100)}: {unit_in_meter == Distance.Centimeter(100)}')
# >>> False, compare two units by raw value
print(f'Comparison: {unit_in_meter} > .1*{unit_in_meter}: {unit_in_meter > .1 * unit_in_meter.raw_value}')
# >>> True, compare unit with float by raw value

Preferences

To change default units directly from code: use PreferredUnits object

from py_ballisticcalc import PreferredUnits, Velocity, Angular, Temperature, Distance

# Change default library units
PreferredUnits.velocity = Velocity.MPS
PreferredUnits.adjustment = Angular.Mil
PreferredUnits.temperature = Temperature.Celsius
PreferredUnits.distance = Distance.Meter
PreferredUnits.sight_height = Distance.Centimeter
PreferredUnits.drop = Distance.Centimeter

print(f'PreferredUnits: {str(PreferredUnits)}')
print(f'Default distance unit: {PreferredUnits.distance.name}')

# Can create value in default unit with either float or another unit of same type
print(f'\tInstantiated from float (5): {PreferredUnits.distance(5)}')
print(f'\tInstantiated from Distance.Line(200): {PreferredUnits.distance(Distance.Line(200))}')

Use new method to set preferred units/settings globally for the venv or the user:

Create .pybc.toml or pybc.toml file in your project root directory (where venv was placed). Or place this file in user's home directory. (The file in project root has priority.) Use loadMetricUnits(), loadImperialUnits() or loadMixedUnits() to manualy load one of presets. You can use basicConfig() function to load your custom .toml file

The references of .pybc.toml settings file you can get there and there. They include settings for metric, imperial and mixed mode. Mixed mode is using metric settings for angular, distance, velocity, pressure, and temperature units, and imperial for diameter, length, weight and adjustment units.

# Config template for py_ballisticcalc

title = "standard py_ballisticcalc config template"
version = "2.0.0b4"

[pybc.preferred_units]
angular = 'Degree'
distance = 'Yard'
velocity = 'FPS'
# ... other there

[pybc.calculator]
max_calc_step_size = { value = 0.5, units = "Foot" }
# ...

Load .pybc.toml presets

from py_ballisticcalc import loadImperialUnits, loadMetricUnits, loadMixedUnits

loadImperialUnits()
loadMetricUnits()
loadMixedUnits()

(Use just one of these three methods – only the last one called counts).

Custom .pybc.toml

from py_ballisticcalc import basicConfig

basicConfig("path/to/your_config.toml")

Integration Engines

Default engine is RK4. Recommended for speed: cythonized_rk4_engine or scipy_engine.

Comparison

See Engine Benchmarks for more detailed analysis and comparison of the engines.

Engine Name	Is Default?	Relative Performance	Dependencies	Description
rk4_engine	🟢	Baseline (1x)	None	Runge-Kutta 4th-order integration.
verlet_engine	🔴	0.7x (slower)	None	Velocity Verlet 2nd-order integration.
euler_engine	🔴	0.5x (slower)	None	Basic Euler integration: 1st-order but easiest to understand.
cythonized_rk4_engine	🔴	50x faster	py-ballisticcalc[exts]	Cython-optimized Runge-Kutta 4th-order integration.
cythonized_euler_engine	🔴	40x faster	py-ballisticcalc[exts]	Cython-optimized Euler integration.
scipy_engine	🔴	10x faster	scipy	Uses SciPy's advanced and optimized numerical methods.

Modifying presets

Using BaseEngineConfigDict:

from py_ballisticcalc import Calculator, BaseEngineConfigDict

config = BaseEngineConfigDict(
    # cZeroFindingAccuracy= ...,  # Max allowed slant-error (in feet) to end zero search
    # cMaxIterations= ...,        # Maximum number of iterations for zero search
    cMinimumVelocity=0,           # Min velocity (fps) to continue computing trajectory
    # cMaximumDrop= ...,          # Max drop (feet) from muzzle to continue computing trajectory
    # cMinimumAltitude= ...,      # Min altitude (feet, above sea level) to continue computing trajectory
    # cGravityConstant= ...,      # Gravitational acceleration in fps^2
    # cStepMultiplier= ...,       # Multiplier of integration step, to change calculation speed & precision
)
calc = Calculator(config=config)

Custom integration engines

Create custom engine module

To define custom integrator engine you can create separate module that should have class that implements py_ballisticcalc.generics.EngineProtocol. Also you have to add entry point py_ballisticcalc.my_awesome_engine in your module pyproject.toml/setup.py. Entry point name should end with _engine.

[project.entry-points.py_ballisticcalc]
my_awesome_engine = "my_awesome_engine_library.my_awesome_module:MyAwesomeEngine"

Custom engine usage

For Calculator instance definition with custom engine, install your library to virtual env and use your library name as _engine argument. It should load your engine class in background.

from py_ballisticcalc import Calculator

calc = Calculator(engine="my_awesome_engine")
# or
calc = Calculator(engine="my_awesome_engine_library.my_awesome_module:MyAwesomeEngine")

Test your custom engine

To test your custom engine compatibility you can use predefined tests from py_ballisticcalc

• Clone py_ballisticcalc to your environment
• Install py_ballisticcalc in editable mode with dev dependencies

  pip install -e .[dev]

• Run pytest with --engine argument

  pytest ./tests --engine="my_awesome_engine" 
  # or
  pytest ./tests --engine="my_awesome_engine_library.my_awesome_module:MyAwesomeEngine" 

Concepts

Coordinates

Gravity gives $y$: In ballistics, everything is referenced to the direction of gravity. The gravity vector points "down," and this defines the vertical direction. In 3D Cartesian coordinates $(x, y, z)$, the gravity vector is $(0, -g, 0)$, where $g$ is acceleration due to gravity (typically 32 feet/second² or 9.8 meters/second²). The $y$ coordinate describes vertical (up/down) position.

Horizontal: Having defined the vertical axis using the gravity vector, we can then define horizontal as any vector perpendicular (or orthogonal) to the direction of gravity.

Sight gives $x$: The second key reference in ballistics is the sight line. We set the origin of our coordinate system $(0, 0, 0)$ at the sight, which is usually either the shooter’s eye or the center of a sighting device like a scope. The sight line is the ray starting at the origin and pointing in the exact direction of the sight. The $x$ coordinate measures distance from the sight along a horizontal sight line.

The $z$ coordinate describes position orthogonal to both the direction of gravity and the sight line. From the perspective of the sight, this is lateral position, also known as windage.

Look angle

Look angle, a.k.a. slant angle, is the elevation of the sight line (a.k.a., Line of Sight, or LoS) relative to the horizon. For angles close to horizontal (flat fire) this does not make a significant difference. When the look angle is significantly above or below the horizon the trajectory will be different because:

1. Gravity is not orthogonal to the velocity
2. Air density changes with altitude, so the drag effects will vary across an arcing trajectory.

The shooter typically cares about the line of sight (LoS): Sight adjustments are made relative to LoS. Ranging errors – and hence danger space – follow the slant-height, not the horizontal height.

The following diagram shows how slant distance and slant height relate by look angle to the underlying (distance x, height y) trajectory data. Understanding Slant Angle covers these concepts in more detail.

Danger Space

Danger space is a practical measure of sensitivity to ranging error. It is defined for a target of height h and distance d, and it indicates how far forward and backward along the line of sight the target can move such that the trajectory will still hit somewhere (vertically) on the target.

About project

The library provides trajectory calculation for ballistic projectiles including air rifles, bows, firearms, artillery, and so on.

The 3DoF model that is used in this calculator is rooted in public C code of JBM's calculator, ported to C#, optimized, fixed and extended with elements described in Litz's Applied Ballistics book and from the friendly project of Alexandre Trofimov and then ported to Go.

This Python3 implementation has been expanded to support multiple ballistic coefficients and custom drag functions, such as those derived from Doppler radar data.

The online version of Go documentation is located here.

C# version of the package is located here, and the online version of C# API documentation is located here.

Contributors

This project exists thanks to all the people who contribute.

Special thanks to:

• David Bookstaber - Ballistics Expert
  For help understanding and improving the functionality
• Nikolay Gekht
  For the sources code on C# and GO-lang from which this project firstly was forked

RISK NOTICE

The library performs very limited simulation of a complex physical process and so it performs a lot of approximations. Therefore, the calculation results MUST NOT be considered as completely and reliably reflecting actual behavior or characteristics of projectiles. While these results may be used for educational purpose, they must NOT be considered as reliable for the areas where incorrect calculation may cause making a wrong decision, financial harm, or can put a human life at risk.

THE CODE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE MATERIALS OR THE USE OR OTHER DEALINGS IN THE MATERIALS.