shooter_sim

FRC 2026 Turret Ball Shooter Simulation — a physics-based tool for computing optimal launch angles and velocities for a ball shooter mechanism targeting an elevated hub.

Overview

This project simulates a ball shooter with quadratic air drag (smooth-sphere model) to help FRC teams tune their shooter subsystem. It provides:

• Graphical analysis — sweep a range of distances and visualize optimal angles, velocities, and trajectories
• Command-line lookup — quickly query the recommended angle/velocity for a specific distance, or find angles for a known velocity
• 2D lookup table generation — pre-compute a grid of (distance, turret height) → (angle, velocity) for use on a robot

Physics Model

Trajectory integration uses symplectic Euler with quadratic drag, JIT-compiled via Numba for ~50–100× speedup over pure Python:

$$a_x = -\frac{k}{m} \lvert v \rvert , v_x, \qquad a_y = -g - \frac{k}{m} \lvert v \rvert , v_y$$

where $k = \tfrac{1}{2} C_d \rho A$ is the drag constant for a smooth sphere ($C_d = 0.47$) at sea-level air density.

Default Parameters

Parameter	Value
Ball diameter	5.91 in
Ball mass	0.448–0.500 lb (avg ≈ 0.215 kg)
Hub height	72.0 in
Turret height	27.0 in (configurable)
Drag coefficient	0.47

Files

File	Description
shooter_physics.py	Shared physics engine — constants, Numba-JIT trajectory simulation, solvers
shooter_sim.py	Graphical analysis — sweeps distances and generates matplotlib plots
shooter_lookup.py	CLI lookup tool — recommend, angle, and table commands
generate_table.py	Generates a 2D interpolation table saved to shooter_table.npz

Installation

Requires Python 3.8+.

pip install numpy scipy numba matplotlib

Usage

Graphical Simulation (shooter_sim.py)

Sweeps a range of distances and produces plots of optimal launch angle, required velocity, sample trajectories, drag comparison, and velocity penalty from air resistance.

# Default parameters
python shooter_sim.py

# Custom turret height and distance range
python shooter_sim.py --turret-height 30 --dist-min 5 --dist-max 20

# Save figure to file instead of displaying
python shooter_sim.py --save output.png

Options:

Flag	Default	Description
--turret-height	27.0	Turret height in inches
--hub-height	72.0	Hub target height in inches
--dist-min	5.0	Minimum distance in feet
--dist-max	25.0	Maximum distance in feet
--num-points	50	Number of sample distances
--save	(none)	Save figure to file path

Shooter Lookup (shooter_lookup.py)

Quick command-line queries for shot parameters.

# Recommend optimal angle & velocity for a 15 ft shot
python shooter_lookup.py recommend --distance 15

# Find launch angle(s) for a known velocity
python shooter_lookup.py angle --distance 15 --velocity 28

# Print a full lookup table
python shooter_lookup.py table --dist-min 5 --dist-max 25 --step 2

Commands:

• recommend — Given a distance, returns the optimal (minimum-velocity) launch angle and required velocity, plus wheel RPM estimates for 4″ and 6″ shooter wheels.
• angle — Given a distance and velocity, finds all valid launch angles (low arc / high arc) using root-finding.
• table — Prints a formatted lookup table of angle and velocity across a range of distances.

All commands accept --turret-height and --hub-height overrides.

Table Generation (generate_table.py)

Pre-computes a 2D grid of solutions across distance (3–30 ft) and turret height (18–42 in), saving the result to shooter_table.npz for fast interpolation on a robot.

python generate_table.py

Output file contains NumPy arrays: distances_ft, turret_heights_in, hub_height_in, angle_deg, and velocity_fps.