Is it better to walk or run in the rain??

Let’s assume you are stuck in the rain and want to get minimum wet then is it better run or walk or stand in the same place? Well let’s not fret about this question and do some math in arriving at the answer. Before we go ahead and solve this complex question let us make certain assumptions such as no friction and other wind constraints and also another assumption that the direction and speed of rain remain the same with space and time.

First let’s assume we are stuck in a meadow with no shelter nearby. Let’s represent the velocity of the rain as V_r. It has a vertical component (V_r2) pointing downwards and horizontal component (V_r1). The rain hits the person both from the top as well as sideways.

                     

If the rain is unlikely to stop and we have no shelter nearby then it is of no use running because the rain striking from the top remains same. Also if the person moves sideways then there is a chance that the person will be hit by more rain drops than standing still. So it is considered to be of no use to run in rain if the person doesn’t have a shelter nearby.

It is very unlikely in today’s world that the person stands in a meadow with no shelter nearby, so let’s see what to do if we are stuck in the rain with a shelter nearby and the rain is unlikely to stop before reaching the shelter. It is of no use to stand in the rain when we can reach the nearby shelter in lesser time.

From the above two points it is observed that the wetness due to vertical component of rain depends only on the time for which the person stays in rain and the wetness due to horizontal component depends on the distance from the shelter.

Therefore it can be written as

Wetness(top) α V_r2 X time spent in the rain ---(1)

Also

Wetness(side) α V_r1X distance travelled ---(2)

Thus the total wetness α (V_r2 X time spent in the rain)+ (V_r1X distance travelled) ---(3)

We need to minimize the total wetness in order to arrive at the optimum speed.

The distance travelled remains constant as we ll be approaching the nearest shelter. Hence it is important to minimize the only variable which is the time spent in the rain. As the time spent in the rain is inversely proportional to the speed, it is suggested to increase the speed as much as possible to minimize the wetness. Hence it is suggested to run as quickly as possible if a shelter is found nearby !!!