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.

FLift = ½ × ρ × V² × S × CL // ρ = air density, V = velocity, S = area

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.

I₃ = ∑ mᵢ × rᵢ² // Sum of mass × distance² for each element

Recommended Workflow

  1. Tab 1 - Design: Define your boomerang's planform (blade count, lengths, angles)
  2. Tab 2 - Airfoil: Customize or select blade cross-section profiles
  3. Tab 3 - Simulation: Set launch parameters and run trajectory simulations
  4. Tab 4 - 3D Export: Generate STL for manufacturing
  5. 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.
Simulated UI: Global Parameters Panel

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
Simulated UI: Section Editor Modal
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.

LE TE Upper Surface Lower Surface

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.

Simulated UI: Flat Zone Controls
Enable Flat Zone

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)
Simulated UI: Launch Controls

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

dL = ½ × ρ × Vrel² × c × dr × CL(α) // Local lift per element
dD = ½ × ρ × Vrel² × c × dr × CD(α) // Local drag per element

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

  1. Initialization: Create random population within bounds
  2. Evaluation: Simulate each design and compute fitness
  3. Selection: Keep the best performers
  4. Crossover: Combine parameters from good designs
  5. Mutation: Randomly adjust some parameters
  6. 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.

Blades2
Chord40mm
Length300mm
Angle107°

Long Distance Hook

Extended blade for maximum range. Requires more skill.

Blades2
Chord35mm
Length400mm
Angle95°

MTA (Max Time Aloft)

Designed for maximum flight duration. Broad blades for high lift.

Blades3
Chord50mm
Length280mm
Angle120°