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While we were in Antarctica, we experienced some pretty extreme temperatures. The very coldest that it got was one day in the Ross Sea where the temperature dipped to -19°C and we had 111 km/h winds (equivalent to -2°F and 69 mph winds). These were nearly hurricane-strength winds, and so were not actually allowed to go outside that day. Not only could we have been blown overboard, but there was immense danger of frostbite. In fact, there were times when I got so cold that people's facial hair had frozen solid!
During one of the onboard lectures, we were shown a table that gave the wind chill based on the air temperature and wind speed. It also gave the risk of frostbite, from "Low risk of frostbite for most people" to "High risk for most people in 2 minutes of exposure or less." And we had been told stories of explorers who had lost fingers or toes due to frostbite. It definitely made us be more thoughtful about how well we covered up and how much time we spent outside. Sometimes we took our gloves off to operate cameras, and it when the weather was bad, we had to make sure we went inside after 5-10 minutes. There were multiple times when I couldn't feel my fingers!
The thing that interested me, though, was the math behind the table. What was the relationship between air temperature, wind speed, and wind chill? I could tell that wind didn't affect wind chill in a linear way: if you look at the numbers in any column, they decrease more slowly as the wind gets faster and faster. So the relationships was more complicated than that. But what could it be?
When I got off the ship, I did some research, and I found the following formula for wind chill (WC) based on temperature (T) and wind speed (V):
WC = 13.12 + 0.6215T - 11.37(V0.16) + 0.3965T(V0.16) (for V ≥ 5)
I found it quite interesting that the relationship included an exponential component. But while I was researching wind chills, I learned something even more fascinating: the wind chill formula was developed using a bizarre experiment where volunteers walked on a treadmill in a cold wind tunnel, and sensors on their faces and inside their cheeks were used to calculate rates of heat loss. Sadly, we were told that similar experiments were done to determine the danger of getting frostbite based on air temperature and wind speed. But luckily for you, we can rely on the table and formula for use in the sample problems below.
Sample Problems
Sample Problems
1. On February 27th, we had an air temperature of -5°C and a wind speed of 45 km/h. Find the wind chill in the table, and then calculate the wind chill using the formula. How long would it take for the average person to get frostbite on exposed skin in these conditions?
2. On March 1st, we had an air temperature of -10°C and a wind speed of 70 km/h. Find the wind chill in the table, and then calculate the wind chill using the formula. How long would it take for the average person to get frostbite on exposed skin in these conditions?
3. On March 3rd, we had an air temperature of -19°C and a wind speed of 111 km/h. This falls outside the range of the table. Calculate the wind chill using the formula. How long would it take for the average person to get frostbite on exposed skin in these conditions?
4. Suppose during the winter air temperature dropped to -30°C with a wind speed of 120 km/h. This falls outside the range of the table. Calculate the wind chill using the formula. How long do you think it would take for the average person to get frostbite on exposed skin in these conditions?
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