Umbrella Angle: 0°
Apparent Rain Speed: 0 m/s
This simulation demonstrates how the direction and speed of rain change from the perspective of a moving person. The key idea comes from vector subtraction: when a person moves, the apparent direction of the rain changes. This determines how they should tilt their umbrella to stay dry.
Vr is the actual velocity of the rain (with both horizontal and vertical components), and Vp is the horizontal speed of the person. From the person's point of view, the rain appears to come from a different angle based on these two vectors.
If the person is not moving (e.g., standing still), then Vrp = Vr. So the rain falls straight down (or at the same angle it originally fell). In this case, the umbrella should be held upright (no tilt).
Scenario: Rain angle = 30°, Rain speed = 10 m/s, Person speed = 0 m/s
Umbrella Angle: 30° (same as rain angle)
Apparent Rain Speed: 10 m/s
If the person runs fast enough that their horizontal speed exceeds the horizontal component of the rain, the rain will appear to hit them from the front. The umbrella must now be tilted forward significantly to keep the rain off.
Scenario: Rain angle = 30°, Rain speed = 10 m/s, Person speed = 15 m/s
Umbrella Angle: ~67.4° forward
Apparent Rain Speed: ~18.03 m/s
If the person walks slowly, the horizontal component of the rain is greater than the person’s speed. The rain seems to hit them from behind, so the umbrella should be tilted slightly backward.
Scenario: Rain angle = 30°, Rain speed = 10 m/s, Person speed = 3 m/s
Umbrella Angle: ~19.7° backward
Apparent Rain Speed: ~10.44 m/s
The umbrella angle shown in the simulation is calculated using trigonometry:
Where Vrp,x and Vrp,y are the x and y components of the apparent rain velocity relative to the person.