Ballistics Engine

A high-performance ballistics trajectory calculation engine with comprehensive physics modeling, automatic zeroing, and statistical analysis capabilities.

Project Website: https://ballistics.rs/

Features

Full 3D Trajectory Integration - Six-state ballistic modeling with adaptive RK45 and fixed-step RK4 integration methods
Advanced Drag Models - Support for G1 and G7 reference curves (with automatic transonic corrections) plus user-supplied custom Cd(Mach) drag tables (--drag-table, used as-is with endpoint hold outside their measured domain, no transonic correction applied — see CLI_USAGE.md; bc_value is ignored while a custom table is active)
Automatic Zeroing - Calculate sight adjustments and apply zero angles automatically
Canted-Rifle Modeling - Model a rifle zeroed level but fired canted (--cant <DEGREES>, alias --cant-angle, on trajectory/monte-carlo); clockwise cant shifts point of impact right and low downrange for a rifle with an upward zero correction — see CLI_USAGE.md
Moving-Target Lead - Wind-aware hold tables for targets moving at a constant speed/angle, with iterative intercept-range correction for non-perpendicular motion (lead subcommand; public ballistics_engine::calculate_lead API) — see CLI_USAGE.md
Mover Ring - Field-tested alternative for engaging movers: a per-point ring radius (target_speed × time-of-flight) falls out of an already-solved trajectory with no second command or re-entered ballistic data (trajectory --target-speed, additive across table/JSON/CSV output); lead also gained trajectory's powder-temperature flags for muzzle-velocity parity between the two — see CLI_USAGE.md
Side-by-Side Load Comparison - Compare 2-8 loads at identical conditions with per-load independent zeroing (compare --load "NAME:DRAG:BC:MASS:VELOCITY[:DIAMETER]", mixable with saved profiles); JSON/CSV output carries per-row deltas against the first load — see CLI_USAGE.md
Powder Temperature Command - Resolve the temperature-adjusted muzzle velocity standalone, without a trajectory solve (powder subcommand): linear fps-per-degree model or a measured temperature→velocity curve, optional --sweep velocity ladder and muzzle energy; shares the solvers' exact resolution code (public resolve_powder_adjusted_velocity API) — see CLI_USAGE.md
Unit Conversion - Seamless switching between Imperial (default) and Metric units
BC Segmentation - Velocity-dependent ballistic coefficient modeling with automatic estimation
Atmospheric Modeling - Temperature, pressure, humidity, and altitude effects with ICAO standard atmosphere
Wind Effects - 3D wind calculations with altitude-dependent wind shear modeling, downrange-segmented wind (--wind-segment SPEED:ANGLE:DIST[:VERTICAL], repeatable — model wind that varies along the path, e.g. muzzle plus downrange sensor readings), and vertical wind (--wind-vertical <SPEED> on trajectory/monte-carlo, or the segment's optional 4th field; positive = updraft, raises point of impact) — see CLI_USAGE.md
Oblique Wind-Drift Cards - Wind dope cards at any wind-FROM angle, not just full-value 90° crosswind (wind-card --wind-angle <DEG> or --wind-angles <CSV> for one card per angle); each cell is a real trajectory solve, default (no flags) unchanged from the classic full-value 90° card — see CLI_USAGE.md
Monte Carlo Simulations - Statistical analysis with parameter uncertainties
BC Estimation - Estimate ballistic coefficients from trajectory data
Advanced Physics:
- Spin Effects: Magnus effect and empirical Litz spin drift
- Earth Effects: Coriolis effect with latitude-dependent calculations
- Angular Motion: Gyroscopic precession and nutation physics
- Transonic Analysis: Pitch damping coefficients and stability warnings
- Trajectory Sampling: Regular interval data collection for analysis
- Form Factor Corrections: Bullet-specific drag adjustments
Multiple Output Formats - JSON, CSV, formatted tables, and printable PDF dope cards
Terminal Chart - Inline drop-vs-range and drift-vs-range charts right in the terminal (trajectory --plot, Unicode braille-dot canvas by default, --plot ascii fallback); pure Rust, zero new dependencies, no ANSI colors — see CLI_USAGE.md
Profile import: ballistics profile import file.a7p — imports ArcherBC2 .a7p profiles (rifle, bullet, atmosphere, zero) with a full mapping report; --dry-run previews without saving

Installation

From crates.io

cargo install ballistics-engine

From Source

git clone https://github.com/ajokela/ballistics-engine.git
cd ballistics-engine
cargo build --release

The binary will be at: target/release/ballistics

Feature Flags

Feature	Default	Description
`online`	✅ Yes	HTTP client for API integration (`--online` flag)

To build without network capabilities:

cargo build --release --no-default-features

Quick Start

Basic Trajectory (Imperial Units - Default)

# .308 Winchester, 168gr bullet at 2700 fps
./ballistics trajectory -v 2700 -b 0.475 -m 168 -d 0.308 --max-range 1000

# With automatic zeroing at 200 yards
./ballistics trajectory -v 2700 -b 0.475 -m 168 -d 0.308 --auto-zero 200 --max-range 500

Metric Units

# Same bullet in metric units
./ballistics trajectory --units metric -v 823 -b 0.475 -m 10.9 -d 7.82 --max-range 1000

Unit Systems

The engine supports two unit systems, selectable with the --units flag:

Imperial (Default)

Velocity: feet per second (fps)
Mass: grains
Distance: yards
Diameter: inches
Temperature: Fahrenheit
Pressure: inHg
Wind: mph

Metric

Velocity: meters per second (m/s)
Mass: grams
Distance: meters
Diameter: millimeters
Temperature: Celsius
Pressure: hPa (millibars)
Wind: m/s

Commands

Trajectory Calculation

Calculate ballistic trajectory with environmental conditions:

# Imperial units (default)
./ballistics trajectory \
  -v 2700          # Velocity (fps)
  -b 0.475         # Ballistic coefficient
  -m 168           # Mass (grains)
  -d 0.308         # Diameter (inches)
  --drag-model g7  # G7 drag model
  --angle 0        # Launch angle (degrees)
  --max-range 1000 # Maximum range (yards)
  --wind-speed 10  # Wind speed (mph)
  --wind-direction 90  # Wind from right (degrees)
  --temperature 59     # Temperature (Fahrenheit)
  --pressure 29.92    # Pressure (inHg)
  --humidity 50       # Relative humidity (%)
  --altitude 0        # Altitude (feet)
  --full             # Show all trajectory points

Auto-Zero Feature

Automatically calculate and apply the zero angle for a specific distance:

# Zero at 200 yards and show trajectory to 500 yards
./ballistics trajectory \
  -v 2700 -b 0.475 -m 168 -d 0.308 \
  --auto-zero 200 \  # Automatically zero at 200 yards
  --max-range 500 \
  --full

# Custom sight height for auto-zero
./ballistics trajectory \
  -v 2700 -b 0.475 -m 168 -d 0.308 \
  --auto-zero 100 \
  --sight-height 0.055  # 2.2 inches in yards

Zero-Day Conditions (zero shift)

A rifle's zero is a fixed barrel angle set on the day you sighted in. If you later shoot in different weather — or with a different muzzle velocity (e.g. a cold vs. warm powder temperature) — the point of impact shifts. By default --auto-zero solves the zero angle using the same conditions you pass for the shot, which assumes you zeroed in today's conditions. The --zero-* flags let you decouple the two: the zero angle is solved under the conditions the rifle was actually zeroed in, while the trajectory itself runs under the current shot-day conditions.

# Zeroed on a cold morning (28 F) at 2600 fps; shooting this afternoon at 85 F / 2700 fps.
# The zero angle is solved for the cold/slow load, then the warm/fast trajectory is
# computed against it — so the dope correctly shows the point of impact drifting high.
./ballistics trajectory \
  -v 2700 -b 0.19 -m 77 -d 0.224 --drag-model g7 \
  --temperature 85 --pressure 29.92 \
  --auto-zero 100 --max-range 1000 --full \
  --zero-velocity 2600 \
  --zero-temperature 28

Available overrides (each independently optional; any omitted flag falls back to the shot-day value, so leaving them all off reproduces the previous behavior exactly):

Flag	Meaning	Units (imperial / metric)
`--zero-velocity`	Muzzle velocity on the zeroing day	fps / m·s⁻¹
`--zero-temperature`	Air temperature on the zeroing day	°F / °C
`--zero-pressure`	Barometric pressure on the zeroing day	inHg / hPa
`--zero-humidity`	Relative humidity on the zeroing day	percent
`--zero-altitude`	Altitude on the zeroing day	feet / meters

Powder Temperature

Propellant temperature changes muzzle velocity. Two models are available:

Linear — a constant sensitivity (fps or m/s per degree) applied relative to the temperature the load was chronographed at:

./ballistics trajectory -v 2700 -b 0.19 -m 77 -d 0.224 --drag-model g7 \
  --temperature 85 --use-powder-sensitivity \
  --powder-temp-sensitivity 1.2 --powder-temp 70   # +1.2 fps per F above 70 F

Measured curve (non-linear) — real powders aren't perfectly linear (temperature- stable powders flatten; others steepen when hot). If you've chronographed the load at several temperatures, pass the points directly and the muzzle velocity is interpolated at the powder temperature (clamped at the endpoints — no extrapolation). This overrides --powder-temp-sensitivity when supplied:

./ballistics trajectory -v 2700 -b 0.19 -m 77 -d 0.224 --drag-model g7 \
  --temperature 85 \
  --powder-temp-curve "40:2620,70:2700,100:2760"   # TEMP:VELOCITY points

Powder temperature vs air temperature. The curve maps powder temperature to velocity, while --temperature drives air density. These are decoupled: the curve is looked up at --powder-temp when given, otherwise at --temperature (powder assumed at air temperature). So a load left in a hot chamber or a cold pocket:

# 85 F air (density), but the powder is at 60 F (velocity from the curve at 60 F)
./ballistics trajectory ... --temperature 85 --powder-temp 60 \
  --powder-temp-curve "40:2620,70:2700,100:2760"

Both powder models compose with --auto-zero, symmetrically. For the linear model, --zero-temperature resolves zero-day velocity relative to the reference --powder-temp. For a curve, --zero-powder-temp overrides the powder lookup; otherwise an explicit --zero-temperature is used, or the shot-day --powder-temp is inherited when no zero-day temperature was supplied. Zero-day atmosphere flags still drive air density independently. An explicit --zero-velocity takes precedence over either powder model.

Bore Height and Ground Impact

Control bore height above ground and ground impact detection:

# Set bore height for prone shooting position (2 feet)
./ballistics trajectory \
  -v 2700 -b 0.475 -m 168 -d 0.308 \
  --auto-zero 100 \
  --bore-height 2  # 2 feet (imperial) or meters (metric)

# Disable ground impact detection for full trajectory to max range
./ballistics trajectory \
  -v 2700 -b 0.475 -m 168 -d 0.308 \
  --auto-zero 100 \
  --max-range 1000 \
  --ignore-ground-impact

Bore height defaults: 5 feet (imperial) / 1.5 meters (metric) - standing position.

Advanced BC Modeling

Enable velocity-dependent BC modeling for more accurate long-range predictions:

# Enable BC segmentation (velocity-based BC changes)
./ballistics trajectory \
  -v 2700 -b 0.475 -m 168 -d 0.308 \
  --use-bc-segments \
  --auto-zero 600 \
  --max-range 1000

Advanced Physics - Magnus and Spin Drift

Enable advanced gyroscopic and aerodynamic effects:

# Magnus effect and spin drift calculation
./ballistics trajectory \
  -v 2700 -b 0.475 -m 168 -d 0.308 \
  --twist-rate 10      # 1:10" barrel twist
  --twist-right        # Right-hand twist
  --enable-magnus      # Enable Magnus effect
  --enable-spin-drift  # Enable empirical Litz spin drift
  --wind-speed 10 \
  --wind-direction 90 \
  --max-range 1000

# Coriolis effect for extreme long range
./ballistics trajectory \
  -v 3000 -b 0.750 -m 250 -d 0.338 \
  --enable-coriolis \
  --latitude 45        # Shooting latitude
  --shooting-angle 90  # Azimuth (0=N, 90=E)
  --max-range 2000

Zero Calculation

Calculate the sight adjustment needed to zero at a specific distance:

# Calculate zero for 200 yards
./ballistics zero \
  -v 2700 -b 0.475 -m 168 -d 0.308 \
  --target-distance 200

# With custom sight height (default is 0.05 yards / 1.8 inches)
./ballistics zero \
  -v 2700 -b 0.475 -m 168 -d 0.308 \
  --target-distance 300 \
  --sight-height 0.055  # 2.2 inches

# Metric example
./ballistics zero --units metric \
  -v 823 -b 0.475 -m 10.9 -d 7.82 \
  --target-distance 200  # 200 meters

Output includes:

Zero angle in degrees
Adjustment in MOA (Minutes of Angle)
Adjustment in mrad (milliradians)
Maximum ordinate (highest point of trajectory)

Monte Carlo Simulation

Run statistical analysis with parameter variations:

./ballistics monte-carlo \
  -v 2700         # Base velocity (fps)
  -b 0.475        # Base BC
  -m 168          # Mass (grains)
  -d 0.308        # Diameter (inches)
  -n 1000         # Number of simulations
  --velocity-std 10    # Velocity std dev (fps)
  --angle-std 0.5     # Angle std dev (degrees)
  --bc-std 0.01       # BC std dev
  --wind-std 2        # Wind speed std dev (mph)
  --wind-direction-std 5  # Wind direction std dev (degrees)
  --target-distance 300  # Target distance for hit probability

BC Estimation

Estimate ballistic coefficient from observed trajectory data:

./ballistics estimate-bc \
  -v 2700 -m 168 -d 0.308 \
  --distance1 100 --drop1 0.0   # First data point
  --distance2 200 --drop2 0.023  # Second data point

True Velocity (Velocity Truing)

Calculate the effective muzzle velocity that produces a measured drop at a known range. This helps "true" your ballistic system by identifying discrepancies between chronograph readings and real-world performance.

# Basic offline calculation
./ballistics true-velocity \
  --measured-drop 5.1 --range 600 \
  --bc 0.27 --drag-model g7 \
  --mass 140 --diameter 0.264 \
  --offline

# With chronograph comparison
./ballistics true-velocity \
  --measured-drop 5.1 --range 600 \
  --bc 0.27 --drag-model g7 \
  --mass 140 --diameter 0.264 \
  --chrono-velocity 2822 \
  --offline

# With BC5D tables for improved accuracy
./ballistics true-velocity \
  --measured-drop 5.1 --range 600 \
  --bc 0.27 --drag-model g7 \
  --mass 140 --diameter 0.264 \
  --bc-table-auto --offline

# Joint MV + BC calibration from multiple observed impacts
./ballistics true-velocity \
  --range 300 --measured-drop 1.30 \
  --observed 600:4.40 --observed 900:9.00 \
  --bc 0.45 --drag-model g1 \
  --mass 168 --diameter 0.308

Use case: A shooter measures 5.1 MIL of drop at 600 yards. Their chronograph showed 2822 fps. The command calculates the effective velocity is actually ~2740 fps, suggesting a -82 fps adjustment for accurate ballistic predictions.

Joint velocity + BC truing. With two or more --observed RANGE:DROP impacts spanning supersonic to transonic ranges, true-velocity fits both muzzle velocity and ballistic coefficient against the real trajectory solver. When the observation set is too short/closely-spaced to separate the two, it refuses the joint fit, trues velocity only, and says so — no false-precision BC. See CLI_USAGE.md for details.

Plan the observations before shooting (MBA-1346). plan-truing evaluates a discrete set of ranges with the same forward model and finite-difference Jacobian used by the fitter, then chooses an exact-size, minimum-separation-compliant design. It reports information gain, singular values, conditioning, rejected/unreachable candidates, and an explicit MV-only recommendation when the available facility cannot identify BC:

./ballistics plan-truing \
  -v 2700 -b 0.475 --drag-model g1 -m 168 -d 0.308 \
  --candidate-ranges 200,300,400,500,600,700,800,900 \
  --observation-count 3 --minimum-separation 100 \
  --measurement-resolution 0.03 --drop-unit mil

--measurement-resolution is the assumed independent one-standard-deviation impact-reading error, not a tolerance or extreme bound. A saved scalar G1/G7 profile may replace the explicit load flags (--profile NAME); velocity-banded BC profiles and custom drag curves are rejected because they do not have one scalar BC parameter to identify.

Quantify what the observations actually learned (MBA-1353). Add --observation-sigma to opt into a weighted joint MV/BC MAP fit and local Gaussian uncertainty report. A third --observed RANGE:DROP:SIGMA field overrides the default for one reading. Optional priors are always visible and explicit; predictive output separates uncertainty in the modeled drop from the wider interval for a future reading:

./ballistics true-velocity \
  --range 500 --measured-drop 3.18 \
  --observed 600:4.35:0.03 --observed 900:8.89:0.02 \
  --observation-sigma 0.03 \
  --bc 0.45 --drag-model g1 --mass 168 --diameter 0.308 \
  --predict-range 1000 --prediction-sigma 0.03 --output json

The report includes MV/BC 95% intervals, covariance and correlation, chi-square, effective degrees of freedom, prior-domination/weak-identification warnings, and propagated drop bands. Declared sigmas are treated as absolute known errors, so the covariance is not rescaled by residual RMS. With no uncertainty flags, the existing point estimate and output schema are unchanged.

Advanced Features

Online Mode (API Integration)

The CLI can query a remote ballistics API server instead of calculating locally. This enables access to enhanced BC data, ML-augmented predictions, and doppler-derived drag curves.

Important: The --online feature connects to a proprietary cloud service that is not covered by the MIT license. When using --online, trajectory parameters and your IP address are transmitted to our servers. See ONLINE_SERVICE.md for full terms, privacy policy, and data handling practices.

# Use online mode to query the API
./ballistics trajectory \
  -v 2700 -b 0.475 -m 168 -d 0.308 \
  --online \
  --max-range 1000

# Custom API endpoint
./ballistics trajectory \
  -v 2700 -b 0.475 -m 168 -d 0.308 \
  --online \
  --api-url https://your-api.example.com/v1/calculate \
  --max-range 1000

Default API: https://api.ballistics.7.62x51mm.sh/v1/calculate

Online mode benefits:

Enhanced BC data - Access to doppler-derived ballistic coefficients
ML predictions - Machine learning augmented trajectory calculations
BC segments - Velocity-dependent BC modeling from measured data
Form factor corrections - Bullet-specific drag adjustments

Data transmitted when using --online:

All trajectory parameters (BC, mass, velocity, wind, atmospheric conditions, etc.)
Your IP address and client version
Request logs retained for 30 days, then deleted

To use only local calculations (no network, no data transmission):

cargo install ballistics-engine --no-default-features

Integration Methods

The engine supports two numerical integration methods:

RK45 (Dormand-Prince Adaptive) - Default method, provides best accuracy with adaptive step sizing
RK4 (Runge-Kutta 4th Order Fixed-Step) - Available with --use-rk4-fixed flag for faster computation

Wind Shear Modeling

Model altitude-dependent wind variations:

./ballistics trajectory -v 2700 -b 0.475 -m 168 -d 0.308 \
  --wind-speed 10 --wind-direction 90 \
  --enable-wind-shear \
  --max-range 1000

Transonic Stability Analysis

Analyze projectile stability through the transonic regime:

./ballistics trajectory -v 3000 -b 0.475 -m 168 -d 0.308 \
  --enable-pitch-damping \
  --max-range 2000

Provides warnings about transonic instability and minimum pitch damping coefficients.

Trajectory Sampling

Collect trajectory data at regular intervals for detailed analysis:

./ballistics trajectory -v 2700 -b 0.475 -m 168 -d 0.308 \
  --sample-trajectory \
  --sample-interval 25  # Sample every 25 meters
  --max-range 1000 -o json

Angular Motion Physics

Model precession and nutation of spinning projectiles:

./ballistics trajectory -v 2700 -b 0.475 -m 168 -d 0.308 \
  --twist-rate 10 \
  --enable-precession \
  --max-range 1000

Complete Advanced Physics Example

./ballistics trajectory \
  -v 2850 -b 0.690 -m 230 -d 0.338 \
  --drag-model g7 \
  --twist-rate 8.5 --twist-right \
  --enable-magnus \
  --enable-coriolis \
  --enable-spin-drift \
  --enable-wind-shear \
  --enable-pitch-damping \
  --enable-precession \
  --sample-trajectory \
  --latitude 38.5 \
  --shooting-angle 45 \
  --wind-speed 15 --wind-direction 270 \
  --altitude 6000 \
  --max-range 2000

Physics Modeling

The ballistics engine implements comprehensive physics modeling for accurate trajectory prediction:

Aerodynamic Effects

Drag Modeling - Multiple drag functions (G1-G8, JBM, custom curves) with transonic flow corrections
Form Factor - Projectile efficiency corrections based on shape and design
Reynolds Number Effects - Reynolds diagnostics and an opt-in helper for genuinely low-Re flow; standard drag tables are not multiplied by an extra correction

Gyroscopic Effects

Spin Drift - Lateral deviation due to gyroscopic and Magnus effects
Precession - Gyroscopic precession of spinning projectile
Nutation - Oscillatory motion superimposed on precession
Spin Decay - Reduction in spin rate over time due to aerodynamic damping
Pitch Damping - Aerodynamic moments opposing angular motion

Environmental Effects

Coriolis Effect - Earth's rotation influence on long-range trajectories
Magnus Effect - Force from spinning projectile in crossflow
Wind Shear - Altitude-dependent wind variations
Atmospheric Stratification - Density and sound speed variations with altitude

Stability Modeling

Dynamic Stability - Gyroscopic and aerodynamic stability calculations
Yaw of Repose - Gravity/gyroscopic equilibrium yaw; crosswind yaw is a transient handled by aerodynamic jump
Limit Cycle Yaw - Bounded oscillatory motion analysis

Language Bindings

Official language bindings are maintained as separate projects:

Python: ballistics-engine-py - PyO3 bindings via maturin
Ruby: ballistics-engine-rb - Magnus bindings via rb_sys

These bindings depend on the ballistics-engine crate published on crates.io.

WASM / npm Package

The engine also compiles to WebAssembly (src/wasm.rs, wasm-bindgen) and already powers ballistics.sh and ballistics.rs in the browser. It is not yet published to npm for third-party use — scripts/build-npm.sh builds and prepares a publish-ready package; publishing itself is a manual step (see below).

scripts/build-npm.sh

This builds two wasm-bindgen targets, both with --no-default-features (the default pdf/online features pull in printpdf/ureq+ring, which do not compile for wasm32-unknown-unknown — see "Updating the WASM Module" in CLAUDE.md):

pkg/ — --target bundler, the package meant for npm publish. Consumed via a native .wasm ES import by bundlers that understand it (webpack with experiments.asyncWebAssembly, Vite, Rollup + @rollup/plugin-wasm, Parcel).
pkg-web/ — --target web, a no-bundler build for direct <script type="module"> browser use or manual Node usage without a bundler — the same --target already used to build ballistics.sh/ballistics.rs's WASM. Documented and built for completeness; not published under the primary package name in this initial pass.

wasm-pack has no built-in dual-target/"publish both" mode, and stitching bundler- and web-target output into one package.json via manual exports conditions isn't something wasm-pack generates or tests for you — see the comment header of scripts/build-npm.sh for the full reasoning. A single bundler-target package as the published npm artifact, with the web build documented separately, is the ecosystem-standard shape for wasm-bindgen crates on npm.

The script also post-processes each package.json (name, description, license, repository, keywords, and the files list — including an LICENSE-APACHE entry wasm-pack itself omits even though it copies the file) and installs README-npm.md as the package's README.md.

Before publishing, edit pkg/package.json's "name" — it ships as the placeholder "@SCOPE/ballistics-engine". Replace SCOPE with the maintainer's real npm org/user scope (a scope decision, plus an npm account with publish rights to it, are both needed and don't exist yet as of this writing). Then:

scripts/build-npm.sh
cd pkg
npm pack --dry-run   # sanity-check the tarball contents first
npm publish --access public

(--access public is required the first time a scoped package is published, since scoped packages default to private on free npm accounts; pkg/package.json also sets publishConfig.access to public so a plain npm publish works too.)

FFI Layer

The library includes a Foreign Function Interface (FFI) layer for integration with iOS, Android, and other platforms. The FFI provides C-compatible bindings for all major functionality.

FFI Features

C-Compatible Structures - All data structures use C-compatible layouts
Safe Memory Management - Proper handling of memory across language boundaries
iOS/Swift Integration - Ready for use with Swift through bridging headers
Android/JNI Support - Compatible with Java Native Interface
Monte Carlo Simulation - Statistical analysis with parameter variations
Error Handling - Graceful error propagation across FFI boundary

Example FFI Usage (C/Swift)

// Create input parameters
FFIBallisticInputs inputs = {
    .muzzle_velocity = 823.0,        // m/s
    .ballistic_coefficient = 0.475,
    .mass = 0.0109,                  // kg
    .diameter = 0.00782,             // meters
    .drag_model = 0,                 // G1
    .sight_height = 0.05,            // meters
    .temperature = 15.0,             // Celsius
    .altitude = 0.0
};

// Calculate trajectory. The final argument is the integration step in milliseconds
// (minimum 0.1 ms; smaller or non-finite values return NULL).
FFITrajectoryResult* result = ballistics_calculate_trajectory(&inputs, NULL, NULL, 1000.0, 0.1);

// NULL also reports invalid inputs or the 250,000-point resource ceiling.
// Increase the step, reduce the range, or use adaptive RK45 for an over-budget solve.
if (result != NULL) {
    printf("Max range: %.2f meters\n", result->max_range);
    ballistics_free_trajectory_result(result);
}

Monte Carlo Simulation via FFI

// Set up Monte Carlo parameters
FFIMonteCarloParams params = {
    .num_simulations = 1000,
    .velocity_std_dev = 10.0,       // m/s variation
    .angle_std_dev = 0.001,         // radian variation (elevation)
    .bc_std_dev = 0.01,             // BC variation
    .wind_speed_std_dev = 2.0,      // m/s wind variation
    .target_distance = 600.0,       // Target at 600m
    .azimuth_std_dev = 0.001        // radian variation (horizontal)
};

// Run simulation with an independent 0.1-radian wind-direction sigma.
// Use ballistics_monte_carlo(...) when no direction variation is desired.
FFIMonteCarloResults* results =
    ballistics_monte_carlo_with_direction_std_dev(&inputs, NULL, &params, 0.1);

// Use statistical results
printf("Mean range: %.2f m (σ=%.2f)\n", results->mean_range, results->std_dev_range);
printf("Hit probability at 600m: %.1f%%\n", results->hit_probability * 100);

// Access individual shots
for (int i = 0; i < results->num_results; i++) {
    printf("Shot %d: Range %.2f m, Impact velocity %.2f m/s\n", 
           i, results->ranges[i], results->impact_velocities[i]);
}

// Clean up
ballistics_free_monte_carlo_results(results);

Output Formats

All commands support three output formats via the -o flag:

table (default) - Formatted ASCII table for terminal display
json - Complete data in JSON format for programmatic use
csv - Comma-separated values for spreadsheet analysis

Practical Examples

Hunting Zero

Zero a hunting rifle at 200 yards with environmental conditions:

# Calculate zero angle
./ballistics zero \
  -v 2650 -b 0.460 -m 180 -d 0.308 \
  --target-distance 200

# Verify trajectory with auto-zero
./ballistics trajectory \
  -v 2650 -b 0.460 -m 180 -d 0.308 \
  --auto-zero 200 \
  --max-range 400 \
  --wind-speed 15 \
  --wind-direction 270 \
  --temperature 32 \
  --humidity 30 \
  --altitude 5000 \
  --full

Long Range Shooting

Analyze trajectory for 1000-yard shot:

./ballistics trajectory \
  -v 2850 -b 0.690 -m 230 -d 0.338 \
  --drag-model g7 \
  --auto-zero 100 \
  --max-range 1100 \
  --wind-speed 10 \
  --wind-direction 45 \
  --full \
  -o json > trajectory.json

Load Development

Compare different loads using Monte Carlo:

# Load 1: Higher velocity, more variation
./ballistics monte-carlo \
  -v 2750 -b 0.475 -m 168 -d 0.308 \
  -n 1000 \
  --velocity-std 15 \
  --target-distance 600

# Load 2: Lower velocity, more consistent
./ballistics monte-carlo \
  -v 2680 -b 0.475 -m 168 -d 0.308 \
  -n 1000 \
  --velocity-std 8 \
  --target-distance 600

Advanced Features

BC Segmentation

Velocity-dependent BC modeling accounts for how ballistic coefficient changes as the bullet slows down. Enable with --use-bc-segments:

Automatically estimates BC segments based on bullet characteristics
No external data required - uses caliber, weight, and BC
Identifies bullet type (Match, Hunting, VLD, etc.) from parameters
Applies physics-based BC degradation curves

Example:

./ballistics trajectory -v 2700 -b 0.475 -m 168 -d 0.308 --use-bc-segments --max-range 1000

Manual velocity-keyed BC segments — supply your own VMIN:VMAX:BC pairs (repeatable, velocities in --units) instead of the auto-estimated/table ones. Keyed to velocity, so it composes with distance-keyed --wind-segment; implies --use-bc-segments and overrides --bc-table and --bc-table-dir:

./ballistics trajectory -v 2600 -b 0.243 -m 175 -d 0.308 --drag-model g7 --max-range 1000 \
  --bc-segment 1800:4000:0.243 --bc-segment 1500:1800:0.228 --bc-segment 1200:1500:0.205

BC5D Correction Tables

BC5D tables provide ML-derived, 5-dimensional BC corrections indexed by weight, BC, muzzle velocity, current velocity, and drag model. Tables are caliber-specific and capture the complete velocity-dependent behavior.

Auto-Download Mode (requires online feature):

# Downloads tables automatically on first use
./ballistics trajectory -v 2700 -b 0.475 -m 168 -d 0.308 --bc-table-auto

# Force refresh cached tables
./ballistics trajectory -v 2700 -b 0.475 -m 168 -d 0.308 --bc-table-auto --bc-table-refresh

Offline Mode with pre-downloaded tables:

./ballistics trajectory -v 2700 -b 0.475 -m 168 -d 0.308 --bc-table-dir ./bc_tables/

Available calibers: .224, .243, .264, .277, .284, .308, .338

Cache locations:

macOS: ~/Library/Caches/ballistics-engine/bc5d/
Linux: ~/.cache/ballistics-engine/bc5d/
Windows: %LOCALAPPDATA%\ballistics-engine\cache\bc5d\

Tables are approximately 1-1.5 MB each and include CRC32 validation to ensure data integrity.

Advanced Physics Modeling

When enabled, the engine calculates:

Magnus Effect - Side force from spinning projectiles
Spin Drift - Lateral drift due to gyroscopic effects
Coriolis Effect - Earth rotation effects (with latitude input)
Transonic Drag - Enhanced drag modeling in transonic regime
Low-Reynolds Helper - Opt-in viscous correction below the standard projectile-table regime

Building from Source

Requirements

Rust 1.70 or later
Cargo build system

Build Commands

# Debug build
cargo build

# Release build (optimized)
cargo build --release

# Run tests
cargo test

# Build documentation
cargo doc --open

Library Usage

Use as a Rust library in your own projects:

use ballistics_engine::{
    BallisticInputs, TrajectorySolver, 
    WindConditions, AtmosphericConditions
};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let inputs = BallisticInputs {
        muzzle_velocity: 823.0,  // m/s
        launch_angle: 0.0,       // radians
        ballistic_coefficient: 0.475,
        mass: 0.0109,            // kg
        diameter: 0.00782,       // meters
        sight_height: 0.05,      // meters
        ..Default::default()
    };
    
    let wind = WindConditions {
        speed: 5.0,              // m/s
        direction: 1.5708,       // 90 degrees in radians
        ..Default::default()
    };
    
    let atmosphere = AtmosphericConditions {
        temperature: 15.0,       // Celsius
        pressure: 1013.25,       // hPa
        humidity: 50.0,          // %
        altitude: 0.0,           // meters
        ..Default::default()
    };
    
    let solver = TrajectorySolver::new(inputs, wind, atmosphere);
    let result = solver.solve()?;
    
    println!("Max range: {:.2} m", result.max_range);
    println!("Max height: {:.2} m", result.max_height);
    println!("Time of flight: {:.3} s", result.time_of_flight);
    
    Ok(())
}

Performance

Optimized Rust implementation provides:

Single trajectory (1000m): ~5ms
Monte Carlo (1000 runs): ~500ms
BC estimation: ~50ms
Zero calculation: ~10ms

Common Ballistic Coefficients

Caliber	Weight	BC (G1)	BC (G7)	Description
.223	55gr	0.250	-	FMJ
.223	77gr	0.362	0.182	Match
.308	168gr	0.475	0.224	Match
.308	175gr	0.505	0.253	Match
.308	180gr	0.480	-	Hunting
.338	300gr	0.768	0.383	Match
6.5mm	140gr	0.620	0.310	Match
.50	750gr	1.050	0.520	Match

Troubleshooting

Trajectory hits ground early

Check if you're using --auto-zero or setting --angle manually
Default angle is 0° (horizontal), which will hit ground quickly
Use --auto-zero <distance> to automatically calculate proper angle

Units confusion

Default is Imperial (fps, grains, yards)
Use --units metric for metric system
All inputs must match the selected unit system

Unexpected BC behavior

G1 and G7 models have different BC values for same bullet
G7 typically better for boat-tail bullets
BC segmentation automatically applied based on bullet type

Contributing

Contributions are welcome! Please:

Fork the repository
Create a feature branch
Add tests for new features
Run cargo test and cargo fmt
Submit a pull request

License

This project is licensed under the MIT License - see LICENSE file for details.

Note: The MIT license applies to the open source ballistics-engine library, CLI, and FFI bindings. The --online feature connects to a proprietary cloud service with separate terms. See ONLINE_SERVICE.md for details.

Acknowledgments

Ballistics physics based on Robert McCoy's "Modern Exterior Ballistics"
Drag tables from military ballistics research
BC segmentation algorithms from Bryan Litz's research
Community contributions and testing

Support

For issues, questions, or contributions:

GitHub Issues: github.com/ajokela/ballistics-engine/issues

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.github		.github
benches		benches
data		data
doc		doc
docs		docs
examples		examples
fonts		fonts
fuzz		fuzz
scripts		scripts
src		src
tests		tests
.gitattributes		.gitattributes
.gitignore		.gitignore
CHANGELOG.md		CHANGELOG.md
CLI_USAGE.md		CLI_USAGE.md
Cargo.lock		Cargo.lock
Cargo.toml		Cargo.toml
LICENSE		LICENSE
LICENSE-APACHE		LICENSE-APACHE
MCCOY_MIGRATION.md		MCCOY_MIGRATION.md
ONLINE_SERVICE.md		ONLINE_SERVICE.md
README-npm.md		README-npm.md
README.md		README.md
analyze_drift.md		analyze_drift.md
ballistics_standalone.rs		ballistics_standalone.rs
ios.png		ios.png
test_drift.rs		test_drift.rs
test_user_drift.html		test_user_drift.html

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Ballistics Engine

Features

Installation

From crates.io

From Source

Feature Flags

Quick Start

Basic Trajectory (Imperial Units - Default)

Metric Units

Unit Systems

Imperial (Default)

Metric

Commands

Trajectory Calculation

Auto-Zero Feature

Zero-Day Conditions (zero shift)

Powder Temperature

Bore Height and Ground Impact

Advanced BC Modeling

Advanced Physics - Magnus and Spin Drift

Zero Calculation

Monte Carlo Simulation

BC Estimation

True Velocity (Velocity Truing)

Advanced Features

Online Mode (API Integration)

Integration Methods

Wind Shear Modeling

Transonic Stability Analysis

Trajectory Sampling

Angular Motion Physics

Complete Advanced Physics Example

Physics Modeling

Aerodynamic Effects

Gyroscopic Effects

Environmental Effects

Stability Modeling

Language Bindings

WASM / npm Package

FFI Layer

FFI Features

Example FFI Usage (C/Swift)

Monte Carlo Simulation via FFI

Output Formats

Practical Examples

Hunting Zero

Long Range Shooting

Load Development

Advanced Features

BC Segmentation

BC5D Correction Tables

Advanced Physics Modeling

Building from Source

Requirements

Build Commands

Library Usage

Performance

Common Ballistic Coefficients

Troubleshooting

Trajectory hits ground early

Units confusion

Unexpected BC behavior

Contributing

License

Acknowledgments

Support

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