Ballistic 6-DOF Flight Simulator

A rigid-body six-degree-of-freedom ballistic flight simulator written in C++17 with Eigen, featuring interactive Python/Matplotlib visualization and 3D animation.

The simulator models a spinning projectile subject to gravity, aerodynamic drag (Mach-dependent), Magnus effect, gyroscopic moments, Coriolis acceleration, and 3-axis wind integrated with a 4th-order Runge-Kutta solver at a 50 μs timestep.

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Features

• Full 6-DOF dynamics quaternion orientation, spin, precession, and nutation
• Mach-dependent drag interpolated Cd table across subsonic, transonic, and supersonic regimes
• Coriolis effect latitude-dependent Earth rotation coupling
• 3-axis wind headwind, crosswind, and vertical wind components
• Gyroscopic stability spin-dependent Magnus force and pitch damping
• Interactive 2D plots side view (trajectory + velocity) and top view (drift)
• Interactive 3D animation real-time bullet model with orientation, Mach-colored trail, telemetry HUD, playback controls, and zoom

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Requirements

Component	Version
C++ compiler	C++17 (tested with MinGW/GCC)
CMake	3.10+
Eigen	5.0
Python	3.10+
matplotlib	3.10+
numpy	latest

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Building

cd ballistic6dof/build
cmake .. -G "MinGW Makefiles" -DEIGEN_DIR=/path/to/eigen
cmake --build .

Note: The -DEIGEN_DIR flag can be omitted if Eigen3 is installed system-wide and discoverable by CMake's find_package.

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Usage

The simulator reads all parameters from a config file:

./ballistic6dof.exe ../configs/default.cfg

This will:

1. Load the config and print the parameters
2. Run the 6-DOF simulation
3. Write a text report and CSV to the config file's directory
4. Launch the interactive 2D plot windows
5. Launch the interactive 3D animation

Pre-made configs

Config	Round	Range
default.cfg	.308 Win 150gr	1,000 m
308_long_range.cfg	.308 Win 175gr SMK	1,500 yd
308_windy.cfg	.308 Win 175gr (20 mph crosswind)	1,000 yd
556_nato.cfg	5.56 NATO 62gr M855	600 m
762_soviet.cfg	7.62x39 123gr FMJ	500 m
6.5_creedmoor.cfg	6.5 CM 140gr ELD Match	1,500 m
300_winmag.cfg	.300 Win Mag 190gr SMK	1,500 m
338_lapua.cfg	.338 Lapua 250gr SMK	2,000 m
50bmg.cfg	.50 BMG 647gr M33 Ball	2,500 m
9mm_pistol.cfg	9mm Luger 124gr FMJ	200 m
45acp.cfg	.45 ACP 230gr FMJ	150 m
howitzer_105mm.cfg	105mm M1 HE shell	12,000 m

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Configuration Reference

Config files use a simple key = value format. Lines starting with # are comments. Any missing key uses the built-in default.

# --- Projectile ---
mass_gr           = 150.0       # bullet mass in grains
caliber_in        = 0.308       # bullet diameter in inches
length_in         = 1.12        # bullet length in inches

# --- Launch ---
muzzle_velocity_fps = 2750.0    # muzzle velocity in feet per second
twist_rate          = 12.0      # barrel twist rate in inches per turn
elevation_deg       = 0.5       # launch elevation in degrees
azimuth_deg         = 0.0       # launch azimuth in degrees (0 = north)

# --- Environment ---
latitude_deg      = 45.0        # shooter latitude (for coriolis)
headwind          = 0.0         # headwind in m/s (positive = into shooter)
crosswind         = 0.0         # crosswind in m/s (positive = left to right)
vertical_wind     = 0.0         # vertical wind in m/s (positive = upward)

# --- Simulation ---
max_range_m       = 1000.0      # stop simulation at this range in meters
timestep_us       = 50.0        # integration timestep in microseconds

Demos

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105mm Howitzer — Artillery (15 kg HE shell, 40° elevation)

Extremely large artillery rounds such as the 105mm howitzer round are particulalry fun to simulate as the projectiles travel great distances at extreme speeds.

Side View — Trajectory & Velocity

Top View — Drift

3D Trajectory Animation

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Unstable .308 Caliber

This particular bullet was configured incorrectly, but I feel that it is a good example of how poorly designed projectiles are simulted in this environment. When entering the trans-sonic region, trans-sonic instabillity is induced and the bullet starts to oscillate towards the end of the simulation.

Side View — Trajectory & Velocity

Top View — Wind Drift

3D Trajectory Animation

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3D Animation Controls

Input	Action
Mouse drag	Orbit camera around projectile
Scroll wheel	Zoom in / out
Space	Pause / Resume
Up / Right / +	Speed up (2x)
Down / Left / -	Slow down (0.5x)
T	Toggle Mach-colored trail
G	Toggle ghost trajectory
R	Reset & rewind to start
Q / Escape	Quit

The animation also includes a Play/Pause button, time scrub slider, and speed multiplier slider in the right panel.

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Output Files

Each simulation run produces two files in the same directory as the config:

• ballistic_report.txt — human-readable summary (muzzle conditions, time of flight, apogee, impact velocity)
• ballistic_trajectory.csv — full trajectory data at ~10 yard intervals with columns: time, range, crossrange, altitude, velocity, mach, spin_rpm, pitch, yaw, roll, alpha, beta

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Project Structure

ballistic6dof/
  CMakeLists.txt
  README.md
  configs/            # simulation config files
  docs/               # demo images
  src/
    main.cpp          # config parser + entry point
    solver.cpp        # 6-DOF RK4 integrator
    atmosphere.cpp    # ISA standard atmosphere model
    aero.cpp          # drag lookup + default aero coefficients
    projectile.cpp    # mass properties + moments of inertia
    report.cpp        # text report + CSV output
  include/
    solver.hpp
    state.hpp         # state vector + quaternion utilities
    flight_record.hpp
    projectile.hpp
    atmosphere.hpp
    aero.hpp
    constants.hpp
  plot/
    plot_trajectory.py   # interactive 2D plots
    animate_3d.py        # interactive 3D animation
    generate_demo.py     # static image + GIF generator
  build/