Gravr, simulating physics with SFML

Gravr is a real-time 2D physics simulation that models falling objects under the influence of gravity and air resistance. Built with C++ and SFML, the simulation supports accurate drag computation, collision physics, and user interaction through keyboard controls.

Features

• Realistic gravitational motion using Newton's second law
• Drag force modeling based on Reynolds number and fluid dynamics
• Ball type classification based on mass input
• Ground collision with energy loss (coefficient of restitution)
• Real-time graphical display with height, velocity, and timer
• User controls for pausing, resuming, and resetting the simulation
• Adjustable mass (0.001–100 kg) and height (1–10 m)

Example

Physics model

Gravitational force

F_gravity = m * g
g = 9.81 m/s²

Air resistance

Drag is computed using the standard drag force equation:

F_drag = 0.5 * ρ * v² * C_d * A

Where:

• ρ = air density (1.225 kg/m³)
• v = velocity
• C_d = drag coefficient
• A = cross-sectional area of the sphere

Reynolds number

Re = (ρ * v * D) / μ

• D = ball diameter
• μ = dynamic viscosity of air

Drag coefficient calculation

Regime	Condition	Equation
Stokes flow	Re < 0.1	C_d = 24 / Re
Intermediate	0.1 ≤ Re < 1000	C_d = 24 / Re * (1 + 0.15 * Re^0.687)
Turbulent	1000 ≤ Re < 300,000	C_d = 0.44
Post-critical	Re ≥ 300,000	C_d = 0.1

Collision model

Ground collisions apply a fixed coefficient of restitution (COR = 0.7):

v_after = -COR * v_before

The simulation ends when the bounce speed falls below 2.0 m/s.

Integration

Euler integration is used to update velocity and position:

acceleration = force / mass
velocity += acceleration * dt
position += velocity * dt

Controls

Key	Action
Enter	Start / Resume
Backspace	Pause
0	Reset
Escape	Exit

Ball type classification

Gravr assigns a label based on the selected mass:

Mass Range (kg)	Ball Type
0.001 – 0.003	Ping pong
0.003 – 0.05	Racquet ball
0.05 – 0.065	Tennis ball
0.065 – 0.16	Baseball
0.16 – 0.5	Soccer ball
0.5 – 0.7	Basketball
0.7 – 8.0	Bowling ball
8.0 – 20.0	Light medicine ball
20.0 – 50.0	Heavy medicine ball
50.0 – 100.0	Industrial ball

Project structure

gravr/
├── src/
│   ├── main.cpp                       # Application entry point
│   ├── Simulation.cpp/.h              # Main simulation loop and logic
│   ├── Particle.cpp/.h                # Physics calculations and particle state
│   ├── UIManager.cpp/.h               # User interface and rendering
│   └── InputHandler.cpp/.h            # User input processing
├── assets/fonts/
|   └── RobotoMono-Regular.ttf         # Font used
├── build/                             # Build directory (created by CMake)
├── CMakeLists.txt                     # Build configuration
└── README.md

Build instructions

Requirements

• C++17-compatible compiler
• CMake 3.10 or higher
• SFML 3.0.0 or higher

Linux

Debian/Ubuntu

sudo apt update
sudo apt install build-essential cmake libsfml-dev

Arch Linux

sudo pacman -Syu
sudo pacman -S base-devel cmake sfml

Compile and run

git clone https://github.com/chitvs/gravr.git
cd gravr
mkdir build && cd build
cmake ..
make
./bin/main

VS Code build

1. Open the project in VS Code
2. Run CMake: Build from the Command Palette (Ctrl + Shift + P)
3. Execute the built binary from the build/ directory

Configuration

const float PIXELS_PER_M = 57.78f;
const float GRAVITY = 9.81f;
const float AIR_DENSITY = 1.225f;
const float AIR_VISCOSITY = 1.81e-5f;
const float BALL_RADIUS = 0.04f;
const float DRAG_MULTIPLIER = 8.0f;

License

This project is licensed under the MIT License. The included Roboto font is licensed under the Apache License 2.0.