Will you get more wet walking in the rain or running in the rain?

If it rains one day and you don’t have an umbrella and have no place to shelter from the rain, would you choose to walk or run in the rain?

Image source: Tuchong Creative

This is an old question that has sparked several discussions at home and abroad. CCTV's "Go, Go, Go" program also conducted an experiment and concluded that running in the rain reduces exposure to rain. A foreign program "Mythbusters" also conducted an experiment, and did it twice, but surprisingly got the opposite result.

The reason is that there are many factors that affect this problem in practice, such as rainfall, wind speed, human speed, human surface area and shape, etc., which will affect the experimental results. Especially if the raindrops fall unevenly, the randomness will become greater.

01

Physical Model

Here I will make an analysis based on a simple physical model. The so-called physical model is to abstract the core content from a practical complex problem and ignore other unimportant influencing factors. For example, when we study the movement of the earth around the sun, we regard the earth as a point and ignore the mountains and rivers on the ground. This is the particle model. As a model, we must make some assumptions, although these assumptions may not be exactly the same as the actual situation.

Assumption 1: The rain is uniform, the raindrops are infinitely small and the density is uniform everywhere, and the mass of rain per unit volume is ρ.

Assumption 2: There is no wind and the raindrops fall at a constant speed of v.

Assumption 3: The person moves at a constant speed, and the speed of movement is u.

Assumption 4: Consider the human body as a cuboid, with the area in front of the body being S1 and the area on top of the head being S2.

Assumption 5: A person’s goal is to get from point A to point B, which is L away.

With the above assumptions, we can do the calculation. When a person moves forward in the rain, the rain will hit the top of his head and the front of his head. We need to calculate these two parts separately.

02

Fundamental analysis

The first thing we need to study is which raindrops fall on people in space. If we choose the ground as the reference system, people are moving and rain is also moving, and the problem will be more complicated. We can change the reference system - take people as the reference. In this way, people can be regarded as stationary, and the raindrops have a falling speed v in the vertical direction and a horizontal speed u relative to people in the horizontal direction. The raindrops move obliquely downward relative to people, as shown in the figure↓

When a person is moving from A to B, raindrops move in a straight line at a constant speed downward relative to the person, and the raindrops that can fall on the person (ignoring the small triangle on the top of the person's head) are all in a column in front of him, as shown in the ACDE part of the figure. These raindrops will run towards the person and eventually hit him.

This is an inclined cylinder, and its bottom area is the cross-sectional area S where people meet the raindrops, as shown in the AE part of the figure; and the height of the cylinder is the distance between AB and AB = L. According to the cylinder volume formula, the volume of raindrops is V = SL, and the mass of raindrops per unit volume is ρ, so the total amount of raindrops that finally fall on people is: m = ρSL.

03

How to avoid getting caught in the rain?

So, how can we avoid getting caught in the rain?

Obviously, no matter how fast you run, the distance L between AB is constant. When the running speed is different, the speed of the raindrops relative to the person is different, so the inclination of the column is different and the cross-sectional area S is different.

As shown in the figure above, if a person's running speed is relatively fast, the raindrops are closer to horizontal relative to the person's speed, so the cross-sectional area of ​​the person meeting the raindrops is part AF; if the person's running speed is relatively slow, the raindrops are more vertical relative to the person's speed, and the area of ​​the person meeting the raindrops is part AE.

Obviously, the height of the cylinder AFIH and the cylinder AEDC is the same, but the area of ​​the AF part is smaller, the volume of the cylinder is smaller, and the mass of rain in the cylinder is smaller, that is, when a person runs at a greater speed, he will be less rained on. If a person runs at an infinite speed, the raindrops will not fall on the top of the head at all, but all fall on the front side of the person's body.

04

Could you be a little more powerful?

So, if a person has reached the maximum running speed, is it possible to continue to reduce exposure to rain?

In fact, we have another solution. Because the area of ​​the top of a person's head is smaller than the area in front of the body, we can tilt our body to meet the raindrops, which can further reduce the area of ​​the person meeting the raindrops and make the rain column thinner.

If you want to get the smallest bottom area to receive the rain, you should use the top area of ​​your head to receive the rain. At this time, the degree of your inclination should be parallel to the direction of the rain relative to your speed. As shown in the figure, this angle can be expressed by trigonometric functions:

For example, when a person's running speed is the same as the speed of a raindrop falling, it is best for the person to lean forward at a 45-degree angle.

In summary, under certain model conditions, if a person runs as fast as possible and tilts his body forward, the number of raindrops that fall on him can be reduced. If we can finely adjust the angle of our body so that only the top of our head is always exposed to raindrops, then we only need a small lotus leaf to block our head to ensure that no water falls on our body.

END

Source: Mr. Li Yongle

The pictures marked as "from TuChong Creative" in this article are all from the copyright library, and the picture content is not authorized for reprinting