3D Relative Velocity: Rain and Bicycle
Interactive simulation of optimal umbrella angle for bicycle rider
Results:
Optimal umbrella angle: θ = 19° from vertical
Calculation: tanθ = vbicycle/vrain = 12/35 ≈ 0.343
Physics Explanation:
When riding a bicycle in the rain, the apparent direction of the rain changes due to your motion. To stay dry, you must tilt your umbrella forward to account for your horizontal velocity.
Relative Velocity Concept:
The velocity of rain relative to the bicycle is:
\[ \mathbf{v}_{rain/bike} = \mathbf{v}_{rain} - \mathbf{v}_{bike} \]
How to Use This Simulation:
- Adjust the sliders to change rain and bicycle speeds
- Observe how the umbrella angle changes automatically
- Use the view buttons to see the scenario from different angles
- Drag to rotate the view, scroll to zoom, right-click to pan
- Click "Start Bicycle Movement" to animate the bicycle
