Ski Jump Landing Geometry Simulator

An interactive 2D physics simulation of ski jump landing geometry, built with Python and Pygame. Simulates a skier's inrun, takeoff, and flight trajectory against two analytically derived landing curves, each designed to limit the Equivalent Fall Height (EFH) to 1 m at the point of maximum impact. The landing curve geometry was calculated as part of a university course; this simulation was written to validate the results interactively. Developed as part of M.Sc. Sport Technology coursework at the University of Bayreuth.

Physics Background

In ski jump design, the shape of the landing slope directly determines the impact forces a jumper experiences on landing. The Equivalent Fall Height (EFH) is the standard safety metric used by the FIS, which represents the height from which a jumper would have to fall freely to experience the same normal impact force as on the actual slope. The two landing curves in this simulation were derived by computing discrete data points that satisfy EFH ≤ 1 m across the landing zone, then fitting a cubic polynomial to those points.

Simulation Modes

Mode	Button	Speed v_0	Landing Curve	Purpose
0	v_0=0 | L0	0 m/s	Calculated for 0 m/s	✅ Correct pairing
1	v_0=2 | L2	2 m/s	Calculated for 2 m/s	✅ Correct pairing
2	v_0=0 | L2!	0 m/s	Calculated for 2 m/s	⚠️ Intentional mismatch
3	v_0=2 | L0!	2 m/s	Calculated for 0 m/s	⚠️ Intentional mismatch

The landing curves are calculated based on the full takeoff velocity, which is composed of a fixed slope-parallel component of 18 m/s, representing the skier's speed along the jump, and an additional vertical takeoff component v_0. The parameter v_0 therefore refers exclusively to the vertical jumping speed at liftoff: 0 m/s for a passive skier leaving the jump without any vertical impulse, and 2 m/s for an active jump. Modes 2 and 3 use deliberately mismatched landing curves to visualize the consequence of applying a landing geometry that was not calculated for the actual v_0 condition. In this case the EFH constraint of 1 m is no longer satisfied. A jumper would either experience significantly higher impact forces than designed for, or the slope would be unnecessarily conservative.

Screenshots

Mode 0 — v_0=0, correct pairing	Mode 1 — v_0=2, correct pairing
Mode 2 — v_0=0, mismatched curve	Mode 3 — v_0=2, mismatched curve

Project Structure

.
├─ assets/                    
│   ├── demo.gif                 # demo animation for README
│   ├── screenshot_mode0.jpg
│   ├── screenshot_mode1.jpg
│   ├── screenshot_mode2.jpg
│   └── screenshot_mode3.jpg
├─ skijump_sim.py            # simulation script
├─ requirements.txt          # Python runtime dependencies
├─ requirements-build.txt    # dependencies to build the app bundle
├─ LICENSE
└─ README.md

Requirements / Tech Stack

• Python 3.10+
• Pygame 2.0+
• PyInstaller 6.0+ (only required for building app bundles)

Getting started

1. Clone the repository

git clone https://github.com/dagebg/ski-jump-simulation.git
cd ski-jump-simulation

2. Create virtual environment (optional, but recommended)

python -m venv .venv
source .venv/bin/activate        # on Windows: .venv\Scripts\activate

3. Install dependencies

pip install -r requirements.txt       # install runtime dependencies (enough for running the simulation)

# optional:
pip install -r requirements-build.txt # install dependencies for building the app bundle 

4. Run the simulation

python skijump_sim.py    # assuming 'python' points to Python 3.10+

Usage

Use the Starting Height slider to set the drop height, select a simulation mode, and press Start to run the simulation. Press Restart to reset and Stop to pause mid-flight.

Building and running as an app

macOS

pyinstaller --onefile --windowed --name SkiJumpSim skijump_sim.py

The app bundle is output to dist/SkiJumpSim.app. Launch it via Finder or from the terminal:

open dist/SkiJumpSim.app

Windows

pyinstaller --onefile --windowed --name SkiJumpSim skijump_sim.py

The executable is output to dist/SkiJumpSim.exe. Launch it via the file explorer or from the terminal:

.\dist\SkiJumpSim.exe

Note

After the first build, a SkiJumpSim.spec file is generated in the project root. Subsequent builds can use this file to generate the app bundle.

pyinstaller SkiJumpSim.spec

The app bundle is not signed. On macOS, you may need to right-click the app bundle and select "Open" on first launch to allow it to run.

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Roadmap

• EFH curve overlay — draw the Equivalent Fall Height live on the landing slope
• Live impact vectors — render velocity v, slope normal n, and normal component v⊥ at landing
• Trajectory trace — fading dotted flight path drawn after each jump
• CSV export — save jump parameters (start height, v_0, landing distance, EFH) to a .csv file
• Web version via pygbag — run the simulation directly in a browser
• Load hill geometry from a JSON/CSV config file instead of hardcoded coefficients
• Resizable window
• Split into multiple files: simulation.py, renderer.py, gui.py, constants.py, main.py

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License

The code in this repository is licensed under the MIT License - see the LICENSE file for details.