Biking In the Rain

Growing up in the Netherlands and Oregon, biking through the rain was a fact of life. However, I never quite figured out how exactly I should go about minimizing how soaked I would get in the process.

My first instinct was to assume that if you bike faster, you'd be out of the rain sooner. However, in doing so the rain hits you more from the front, exposing a greater surface area to the incoming rain, and at a greater speed than it would if you biked slowly. I've tried both, and either method usually resulted in getting soaked to the skin in a heavy downpour, so it wasn't quite clear to me which was superior in minimizing how soaked I would be upon reaching my destination. The question thus posed is:

In order to minimize how soaked you get when traveling through the rain, should you go fast, slow, or is there some optimum mid-range speed?

Before we start, let’s make some basic assumptions:

We'll ignore aerodynamic effects:
Since rain droplets are roughly 1,000 times as dense as the air they are traveling through, the effect the air moving around your body has on the trajectory of the raindrops can be assumed to be negligible.
All rain drops that intersect with your path are absorbed:
Rain drops are assumed not to stream off your jacket or clothes, or spatter upon impact.
Rain drop terminal velocity = 10 m/s
Your vertical-projected area (head and shoulders) = .1 m^2
Your forward-projected area = .6 m^2
Rain density = .001 kg/m^3

Here is a plot that shows how much rain your body intercepts (in kg per km) as a function of speed through the downpour.

It turns out that in order to minimize how soaked you get, you should bike as fast as you can! This makes sense when you break the down the relative vertical and horizontal components of the incoming rain. The vertical component of the incoming rain is solely due to its terminal velocity, and remains unaffected by your speed. This component would therefore clearly benefit from the shortest possible trip. The horizontal component on the other hand, is solely due to your speed. This may prompt you to think that the horizontal component would benefit from a slower forward speed, but your body sweeps out the same volume of air (.6 m^2 * 1,000 m) regardless of your speed, meaning that the front of your body will absorb the same amount rain regardless of your speed (.6 m^2 * 1,000 m * .001 kg/m^2 = .6 kg). This is evident in the chart: the faster you travel the less the vertical component of the rain will contribute to the overall amount absorbed, and the problem becomes dominated by the fixed .6kg of rain; this is seen as the asymptotic limit as speed increases. At low speeds the problem is dominated by the inverse relationship between speed and rain absorbed (this is due to the vertical component of the rain); this is seen as the linear portion toward the left in the log-log plot.

So we've established that the faster you go, the less rain you are likely to absorb. You can further reduce the amount of rain absorbed by reducing your forward facing area. you can easily do this by leaning forward on your bike (which as far as I'm aware is a natural instinct when biking in a downpour).

Additionally, because a normal biking speed is around 5 m/s, the sensitivity of rain absorbed to the speed at which you're traveling is quite low when compared to walking speeds (1 m/s). This explains the difficulty in establishing whether it was better to bike slow or fast through the rain compared to facing the same dilemma when walking, where the effect of each is more pronounced.

Interestingly enough, the Mythbusters performed the same experiment as it applied to walking, and determined that that it was best to walk slowly. After apparently some criticism of their methods by viewers, the test was performed again a few episodes later in a more rigorous manner, and they came to the same conclusion as that determined in this exercise: it is better to travel as fast as possible in the rain if you want to minimize how soaked you get. See below for the two segments. Unfortunately there is no YouTube video of the revisited edition, so try and dig it up online if you can.

Further complication to this model can come into play: what happens when there is a strong headwind? What about a tailwind? In order to model this, headwind component must be added to the biking speed. Care must be taken to ensure that in the case of a tailwind, water absorbed on your back rather than your front is not considered a negative quantity, so the absolute value of the flux of rain through your projected area is calculated instead. Below is a plot showing the effects of wind:

In the case of a headwind (red line), the same remains true, it is better to travel as fast as possible in the rain if you want to minimize how soaked you get. In the case of a tailwind, for low wind speeds, nothing changes, you still benefit form moving along as fast as possible. However, beyond a certain wind speed, it is best to bike along at exactly the same speed as the wind, which fortunately is easy to qualitatively determine, you just speed up until you feel no wind anymore!

Attachments:

MATLAB script used to generate the plots above: Biking_in_rain.m

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