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Technical FAQ: Why is riding in the cold so hard?

This week, I’ll take a look at why, exactly, riding in cold temperatures feels so much harder than in warm temperatures. The topic ties back to a VeloNote I wrote in the March 2013 issue of Velo magazine. After hearing feedback from a number of aerodynamics experts and others in the cycling industry, the topic deserves a little more examination. It turns out the resistance we feel when the mercury dips isn’t all mental, not even close.

Dear Lennard,
Living North of the 45th parallel, I find myself riding a good portion of the winter season at temperatures at or below 25 degrees Fahrenheit. Having a general understanding of the relationship of temperature and density, I was wondering if there is any measurable effect on a rider’s effort as the temperature decreases from, let’s say, 75 degrees Fahrenheit to 25 degrees Fahrenheit? My personal observation is that it sure seems harder in the cold than in the warm, but this could be my mind telling me I’m crazy for being out and to get inside and enjoy the fire.

Dear Eric,
I answered this question in a recent issue of Velo magazine. Since many readers of this will just be coming off a lot of cold-weather riding, and some are still in it for some time, I’m going to run a few more answers to this question, as well as the one that I put in the magazine.

Aerodynamicist Len Brownlie wrote:

You raise an interesting question and you’re observations are correct. The drag force on a cyclist is provided by the following equation: D = ½ p V2 Ap Cd where D is the drag force (N); p is the air density (kg/m3); Ap is the frontal area of the cyclist (m2) and Cd is the drag coefficient (dimensionless).

As you mentioned, air density is affected by temperature, pressure, and also by humidity. Temperature has a much more pronounced effect on air density than humidity: cold air contains more molecules per cubic meter. If the air pressure is constant at 1000 kPa, then the air density at 25 degrees Celcius (77 degrees Fahrenheit) will be around 1.169 kg/m3 while at -5 degrees Celcius (23 degrees Fahrenheit) the air density will be 1.3011 kg/m3 — about 10-percent higher, and the drag would also be increased by 10 percent.

So, on a cold day, you would need to work harder to maintain the same speed because the air density is higher than on a warm summer day. Additionally, if the relative humidity in the summer is 50 percent and near zero percent in the winter, then the air density would be increased by up to an additional 0.5 percent in the dry air of winter.

Using the Ap (0.43 m2) and Cd (0.54) of an amateur time trialist and assuming the cyclist would complete a 40km time trial in 58:37 in the summer, the same cyclist, generating the same power, would take 60 minutes to complete the race in the winter. Thus, the 10-percent increase in air density would equate to a 2.77-percent decline in performance.

If you wear additional clothing in the winter, then your increased frontal area will also increase your drag and slow you down.

Physiologically, depending on the distance of the ride, clothing worn, and wind chill, it is possible that your leg muscles may not be operating at an ideal temperature — a one-percent decline in local muscle temperature may reduce muscle force generation by up to 10 percent, which would also make the winter rides feel harder. The decrement in muscle force generation occurs despite an increase in energy cost as biochemical reactions within the muscle slow down and nerve conduction and fiber recruitment of the muscle also take longer, so that additional motor unit recruitment is required to generate the same force — leading to higher perceived strain for a given workload.

So, overall, winter rides are tougher, but, if you can handle them, they also provide additional training stimuli and are excellent training sessions.

As an aside, if you ride in an indoor velodrome where the air temperature is relatively constant, variations in the atmospheric pressure may affect race times. Atmospheric pressure normally varies between 980 and 1050 mbar (kPa). A 4km Individual Pursuit that required six minutes to complete on a bright, sunny day (high atmospheric pressure) might only take 5:54.7 to complete if there were a storm outside (low atmospheric pressure).
—Len Brownlie, Ph.D, www.aerosportsresearch.com

Cycling icon Georgena Terry wrote:

The March issue of Velo’s Tech Talk had a question from a reader wondering why riding in cold weather feels hard.

In addition to the reasons you cited, another is vasoconstriction, the constricting of blood vessels in cold weather. Cycling Weekly recently ran an article about cold weather riding and quoted to Dr. Mark Garcia, who noted, “your heart will be working very hard to pump the blood round your body due to this increased vascular resistance and the subsequent increase in blood pressure. The knock-on effect is fatigue.”

And this is the answer that I ran in Velo, from aerodynamicist Chet Wisner:

You have my admiration for having the fortitude to ride in these conditions. The drag you experience at 25 degrees Fahrenheit is about 10-percent greater than you would experience at 75 degrees Fahrenheit. This is approximately equivalent to the difference between riding at 20 mph and increasing your speed to 21 mph. Making things even more challenging is the wind chill of -22 degrees Fahrenheit your body is experiencing as you cruise along at 20 mph. I’m sure you’re already aware that protecting all exposed flesh under these conditions is imperative to preventing frostbite during even short exposures.

The physics behind this is based on the fact that aerodynamic drag is proportional to air density, and, in turn, air density is inversely proportional to absolute temperature. For a temperature in Fahrenheit degrees, the absolute temperature is calculated in Rankine degrees by adding 460 degrees. So, 25 degrees Fahrenheit is 485 degrees Rankine. Similarly, 75 degrees Fahrenheit is 535 degrees Rankine. The ratio of these Rankine temperatures is 1.10, which means the air on your cold rides is 10-percent denser than on your 75-degree rides. Since drag is proportional to air density, the drag you experience is also about 10-percent greater on the cold rides.

Drag is also proportional to the square of the speed with which the air passes by you and your bike. If there is no wind and you are traveling 20 mph, then increase your speed to 21 mph (or pick up a 1 mph headwind), the drag increases by the square of the speed. The ratio of the squares of 21 mph and 20 mph is about 1.10. So, this increase would have the same effect on the drag you are pedaling to overcome as the 50-degree Fahrenheit temperature difference.

So, you can take some consolation on your cold rides that it really is harder for you to pedal than your more fortunate cohorts in warmer climes.
—Chet Wisner, Ambient Air Technologies, LLC

Editor’s Note: Lennard Zinn’s regular column is devoted to addressing readers’ technical questions about bikes, their care and how we as riders can use them as comfortably and efficiently as possible. Readers can send brief technical questions directly to Zinn.