Run or walk in the rain? (Orthogonal projected area of ellipsoid)

New conclusions about this problem in the paper.

√main parameters-speed of rain and body. angle of rain and body(new). body size.

and density and volume of rain drops, distance and time.(new)

New conclusions about this problem in the paper.

√main parameters-speed of rain and body. angle of rain and body(new). body size.
and density and volume of rain drops, distance and time.(new)

New conclusions about this problem in the paper.

√main parameters-speed of rain and body. angle of rain and body(new). body size.
and density and volume of rain drops, distance and time.(new)

(1) When going the same distance

1. When it rains from the front

1-1 When the shape of your body is a box-cube,

1-1-1 Angle of body leaning forward > Critical angle
Run as fast as you can!

1-1-2 Body tilted forward = critical angle
Above a certain speed, the number of raindrops hit when running at the speed of light is exactly the same as the number of raindrops hit when running at the speed of an airplane.

1-1-3 Angle of body leaning forward < Critical angle
Lean forward and run slightly faster than the speed of the rain. Running at the speed of light doesn't mean getting less rain.

1-2 When your body is oval or cylindrical,
To get the least amount of rain, you should lean forward and run slightly faster than the speed of the rain.

2. When it's raining from behind

2-1 When the shape of your body is a box-cube,

2-1- 1 If you run with your body upright, you must run at the horizontal speed of the rain.

2-1-2 To get the least amount of rain, you must lean forward and run a little faster than the horizontal speed of the rain.

2-2 When your body is in the shape of an oval,
To get the least amount of rain, you have to lean forward and run a little faster than the horizontal speed of the rain.

(2) When you have to travel the same amount of time (for example, when you have to travel in the rain for 10 minutes)

1. When it rains from the front
You should lean in the direction of the rain and not move.

2. When it's raining from behind
Interestingly, regardless of the shape of the object, you have to stand upright and move at the horizontal speed of the rain for the fewest number of raindrops to hit you (the difference from walking the same distance is that when you walk the same distance and when the rain falls from behind, you To get the least amount of rain, you must lean forward and run a little faster than the horizontal speed of the rain.)

3. In a three-dimensional space, for example, when rain is pouring out sideways, the optimal speed according to the angle of the body is slightly different from that in a two-dimensional space. Interestingly, however, when you should move at any given time and when the rain falls backwards, regardless of the shape of the object, as in two-dimensional space, the least amount of raindrops will be hit by keeping the body upright and moving at the horizontal speed of the rain.

4. In this paper, not only moving at a constant speed but also moving with acceleration were considered.