Projectile Motion with Air Drag Calculator

Summary

Simulate and plot a projectile trajectory with realistic air drag using numerical integration — adjust mass, drag coefficient, and launch angle to see the effect.

How it works

1. Enter the launch speed (m/s) and angle (degrees above horizontal).
2. Set the projectile mass (kg), cross-sectional area (m²), and drag coefficient (C_d).
3. Optionally adjust air density (default 1.225 kg/m³ at sea level).
4. Click "Simulate" — the tool solves the drag ODE with a 1 ms Euler step and draws the trajectory on a Canvas chart.
5. Key results (range, max height, flight time) are shown for both the drag and vacuum cases.

Use cases

• Physics students verifying drag effects on ballistic range.
• Engineers estimating projectile flight paths under aerodynamic drag.
• Comparing ideal vacuum trajectories to real-world drag-affected paths.
• Exploring how changes in drag coefficient alter flight distance.
• Understanding the effect of launch angle on range with and without drag.
• Sports science — modeling balls with known drag coefficients (baseball, soccer, golf).

Frequently Asked Questions