A Pedestrian's Guide to Harsh Winter

Date

November 2, 2025

Type

Phonon

Antecedent

No prior reading is required.

Emergence

Once, while running on the streets on a cold winter day, I recognized that the wind mattered significantly to how cold I felt. Then, I slowed down and started to walk. Walking slowly, however, meant I was outside for longer.

This was the point where I realized there might be an optimal speed to minimize body heat loss.

Stabilization

In order to build a model for a general walking situation, let me first clarify some key concepts.

1. How do we quantify how cold we feel in a strong wind?
2. Why measure the loss of heat?

There is a well-known concept called apparent temperature (also known as the 'feels-like' temperature). An experimental equation for it is stated below, which is called the Australian Apparent Temperature. It is related to the speed of the wind, which in this case is generated by your own movement. ($T_a, T_0, e, v$ are respectively apparent temperature and dry-bulb temperature in Celsius; water vapour pressure in hPa; and wind or movement speed in meters per second.)

Okay. How about the rate of heat we lose? The rate of heat flow will be proportional to the difference between the apparent temperature and your body temperature. This alone is not enough to determine the total amount lost.

The total time of exposure is inversely proportional to your speed, because the faster you walk, the faster you arrive at your destination for a given distance. ($Q, T$ are respectively total heat loss and body temperature in Celsius.)

Now, the complete function that must be minimized is established. It has become clear, hasn't it?

Thankfully, this model simplifies to a simple linear function of $1/v$. The coefficient of $1/v$ is positive due to the cold weather.Specifically, this coefficient is proportional to the difference between your body temperature and the apparent temperature.

This means your total heat loss decreases as you walk faster and faster (as $v$ increases, $1/v$ decreases).

Convergence

To sum up, based on this model, I recommend that pedestrians in harsh winter walk as fast as they can. But be careful! Slipping might be a big problem.

Descendant

No more related particles, yet.

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