Introduction to Boomerang Studio
A comprehensive physical simulation tool for designing, analyzing, and optimizing boomerangs.
Overview
Boomerang Studio is a web application that combines advanced aerodynamics, flight physics, and parametric design to help you create the perfect boomerang.
Key Features
- Parametric Design: Full control over blade geometry, chord distribution, and hub configuration
- Bézier Airfoils: Design custom blade cross-sections with real-time aerodynamic feedback
- BET Simulation: Blade Element Theory physics engine for accurate trajectory prediction
- 3D Export: Generate manufacturing-ready STL files for 3D printing
- Genetic Optimization: AI-powered design optimization for maximum return distance
Physics Fundamentals
Understanding boomerang flight requires knowledge of several key physical principles:
1. Lift Generation
Each blade acts as a rotating wing, generating lift force perpendicular to its motion. The lift coefficient (CL) depends on the angle of attack and airfoil shape.
2. Gyroscopic Precession
A spinning boomerang behaves like a gyroscope. When a torque is applied (from uneven lift distribution), the boomerang precesses—it turns instead of flipping. This is what makes it curve back.
Why It Comes Back
The advancing blade (moving into the wind) generates more lift than the retreating blade. This creates a rolling moment that, through gyroscopic precession, causes the boomerang to continuously turn left (for right-handed designs).
3. Moment of Inertia (I₃)
The moment of inertia about the spin axis determines how quickly the boomerang can change its rotation speed. Higher I₃ means more stable spin but slower response.
Recommended Workflow
- Tab 1 - Design: Define your boomerang's planform (blade count, lengths, angles)
- Tab 2 - Airfoil: Customize or select blade cross-section profiles
- Tab 3 - Simulation: Set launch parameters and run trajectory simulations
- Tab 4 - 3D Export: Generate STL for manufacturing
- Tab 5 - Optimization: (Optional) Let the genetic algorithm find optimal parameters
Tab 1: Design & Geometry
Define the shape and physical properties of your boomerang.
Global Parameters
These parameters apply to the entire boomerang and affect all blades uniformly.
| Parameter | Unit | Range | Physics Impact |
|---|---|---|---|
| Number of Blades | - | 2-6 | More blades = smoother flight, higher drag. Traditional boomerangs are 2-3 blades. |
| Chord | m | 0.02-0.10 | Blade width. Larger chord = more lift area but also more weight and drag. |
| Thickness | m | 0.001-0.02 | Material thickness. Affects mass and structural integrity. |
| Density | kg/m³ | 100-2000 | Material density. Wood ≈ 500-700, ABS ≈ 1050, Carbon ≈ 1500. |
| Hub Radius | m | 0.00-0.10 | Central disk size. Adds mass at center, affecting I₃ and CG position. |
Blade Configuration
Each blade can be configured independently for length and relative angle.
Blade Length
The length from hub edge to blade tip. Longer blades generate more lift at higher radii, increasing range but also moment of inertia.
Relative Angle
The angular spacing between blades. For a symmetric 2-blade design, use 107° (not 180°!) to optimize return characteristics. For 3 blades, 120° is typical.
Important: Asymmetric Designs
Most traditional returning boomerangs are NOT symmetric. The classic "L1" design uses blades with different lengths and a non-180° angle.
Section Editor
The Section Editor allows you to define chord variation along the blade span. This is critical for advanced designs.
Parameters per Section
- Position (%): Location along the blade (0% = root, 100% = tip)
- Local Chord: Blade width at this section
- Camber/Twist: Angular offset of the section (blade twist for pitch variation)
- Profile: Which airfoil to use at this section
| Pos (%) | Chord (m) | Camber (°) | Profile |
| 0% | 0.040 | 0.0 | Standard |
| 50% | 0.045 | 2.0 | Standard |
| 100% | 0.035 | 0.0 | Standard |
Hub & Elbow Configuration
The hub is the central region where blades connect. Two modes are available:
Disk Mode (Default)
A simple circular disk at the center. Adjust the hub radius to control the solid center area.
Elbow Mode
Enables a curved transition zone (elbow) between blades. This is more realistic for traditional wooden boomerangs and affects aerodynamics at the junction.
- Elbow Radius: Size of the curved transition
- Mid Chord: Chord width at the elbow apex
- Elbow Profile: Which airfoil to use in the elbow region
Handedness
Boomerangs are designed for either left-handed or right-handed throwers. This affects:
- Which blade is the "leading" blade
- Direction of rotation (CW vs CCW)
- Default layover angle and wind direction
| Handedness | Rotation | Turn Direction | Default Layover |
|---|---|---|---|
| Left-Handed (Gaucher) | Clockwise | Right Turn | 285° |
| Right-Handed (Droitier) | Counter-Clockwise | Left Turn | 75° |
Tab 2: Blade Profile (Airfoil Designer)
Design the cross-sectional shape of your blades using Bézier curves.
Bézier Geometry
The airfoil is constructed from cubic Bézier curves for both the upper and lower surfaces. Control points allow intuitive shaping.
Upper & Lower Surfaces
Upper Surface (Extrados)
| Height P1 (LE) | Controls the leading edge thickness on top |
| Position X P2 | Chordwise position of maximum thickness (0.3-0.4 typical) |
| Height P2 | Maximum camber/thickness of upper surface |
| Max Zone Width | Creates a flat region around maximum thickness |
Lower Surface (Intrados)
Same controls but for the bottom. Boomerang profiles typically have a flat or slightly concave lower surface.
Modifiers
LE Bulge (Bombé)
Adds extra thickness at the leading edge. Useful for creating traditional "undercamber" profiles.
Flat Zone
Creates a perfectly flat section on the upper surface. Useful for flat-bottom designs common in boomerang airfoils.
Aerodynamic Polars
Click "Generate Polars" to compute the lift and drag coefficients for your airfoil across a range of angles of attack.
Key Metrics
- Max CL: Maximum lift coefficient before stall
- Min CD: Minimum drag coefficient (at optimal angle)
- Best L/D: Maximum lift-to-drag ratio (glide efficiency)
- Alpha @ CL=0: Zero-lift angle of attack
NeuralFoil Engine
Polars are computed using a neural network trained on XFOIL data. Results are approximate but fast. For critical designs, validate with CFD or wind tunnel testing.
Profile Library
Save and manage multiple airfoil profiles. Assign different profiles to different blade sections for advanced designs.
- Standard: Default flat-bottom boomerang profile
- St10ext: Extended S-curve for improved lift
- coude2: High-camber elbow profile
Tab 3: Flight Simulation
Simulate the trajectory of your boomerang using Blade Element Theory physics.
Launch Parameters
| Parameter | Unit | Typical Range | Effect |
|---|---|---|---|
| Initial Speed (V₀) | m/s | 20-35 | Faster = longer range but faster rotation decay |
| Rotation Speed (ω₀) | rad/s | 40-80 | Higher spin = more gyroscopic stability |
| Elevation (α₀) | ° | 5-20 | Launch angle above horizontal |
| Layover (γ₀) | ° | 70-85 | Initial tilt from vertical (0° = flat, 90° = vertical) |
Environment (Wind)
Wind significantly affects boomerang flight. The simulation supports:
- Wind Speed: In km/h. Even 9-18 km/h makes a difference.
- Wind Direction: 0° = headwind, 90° = left crosswind, 270° = right crosswind
Optimal Wind for Return
For left-handed throwers, 90° wind (from the left) helps the return. For right-handed, 270° wind is optimal.
BET Physics Model
The simulation uses Blade Element Theory (BET), which divides each blade into small elements and computes forces locally.
Force Computation
Integrated Coefficients
- CL: Total lift coefficient
- CD: Total drag coefficient
- CTx: Rolling moment coefficient (precession driver)
- CTy: Pitching moment coefficient
- CQ: Torque coefficient (spin deceleration)
Trajectory Calibration
Fine-tune the physics model with these advanced parameters:
| k Induced Drag | Additional induced drag factor |
| k Magnus | Magnus effect strength (spinning lift) |
| Reynolds Exponent | How drag scales with Reynolds number |
| TipLoss Factor | Prandtl tip loss correction intensity |
| Ground Effect | Lift enhancement near ground |
Understanding Results
Key Metrics
- Return Distance: Distance from origin when landing. Goal is ~0m for perfect return.
- Max Range: Maximum distance reached during flight.
- Flight Duration: Time until landing.
Optimization Target
For a "returning" boomerang, the goal is to minimize Return Distance while maintaining a reasonable Max Range (typically 15-30m).
Tab 4: 3D Visualization & Export
Generate manufacturing-ready STL files for 3D printing or CNC machining.
STL Export
The STL generator creates a watertight mesh that matches the simulation model exactly.
Export Parameters
- Resolution: Number of points per blade. Higher = smoother but larger file.
- Center Hole: Optional hole for mounting or weight reduction.
- Hub Extra Thickness: Reinforce the center by adding material on top.
Volume Validation
The tab shows both the calculated volume (from Tab 3 physics) and the STL volume (measured from the mesh). These should match within 5%.
Volume Calibration
If volumes don't match, adjust the hub radius (Disk Mode) or thickness (Elbow Mode) until they align.
3D Printing Tips
- Use PLA+ or PETG for durability
- Print flat (horizontally) with the top surface facing up
- Use 100% infill for proper weight distribution
- Sand the edges for smooth aerodynamic flow
Tab 5: Genetic Optimization
Automatically find optimal design parameters using evolutionary algorithms.
Genetic Algorithm
The optimizer uses a genetic algorithm (GA) to evolve a population of designs towards an optimal solution.
How It Works
- Initialization: Create random population within bounds
- Evaluation: Simulate each design and compute fitness
- Selection: Keep the best performers
- Crossover: Combine parameters from good designs
- Mutation: Randomly adjust some parameters
- Repeat for N generations
Optimizable Parameters
Select which parameters the algorithm can adjust:
- Global: Chord, Thickness, Hub Radius, Rounded Tips
- Per Blade: Length, Relative Angle
- Per Section: Local Chord, Twist, Profile Index
Optimization Time
More parameters = longer optimization. Start with 2-3 parameters and add more once you understand the design space.
Objective Functions
Max Return
Minimizes the landing distance from origin. Best for returning boomerangs.
Return + Range
Weighted combination: maximize range while still returning. Use the slider to balance priorities.
Design Presets
Pre-configured designs for different flight characteristics.
Classic V-Shape
Traditional 2-blade design for reliable returns. Good for beginners.
Long Distance Hook
Extended blade for maximum range. Requires more skill.
MTA (Max Time Aloft)
Designed for maximum flight duration. Broad blades for high lift.