A few months ago I posted a piece on Usain Bolt. It's interesting to consider his physical limits. Not considering his metabolic efficiency, only about eight percent of the energy he uses goes into moving his body down the track. The the remainder is used to overcome air resistance. That's his speed limit. 100 and 200 meter sprints largely use anaerobic metabolism which can produce enormous amounts of power (over three horsepower). The problem is it only lasts for a short amount of time. Its "fuel" runs out and his core body temperature soars. Trying to run 25 or 30 seconds at that rate might be lethal. Fortunately humans have ways to regulate core body temperature.
Bicycle racers are at or near the top of human power output endurance. A world class rider can generate about 6 watts per kilogram of body weight. A seventy kilogram racer could generate about 420 watts of power on average for periods over an hour.1 The spinning motion of riding a bike is one of the most efficient mechanisms of turning energy from food into motion. It varies with people and training, but 25% efficiency is close to average. So for every watt delivered to the pedals, three are lost as waste heat.. that heat has to go somewhere. Our bike racer would need to get rid of 1260 watts - not far from the 1500 watts the burner on an electric range pumps out. Usain Bolt had to get rid of much more heat, but only for a short period of time.2
In humans one of the most important mechanisms for getting rid of heat is sweating. It takes a lot of energy to evaporate water .. just think of the extra heat as waste energy. For fun consider a three cases: a normal person at room temperature, a normal person on a hot day in Arizona, and a Tour de France racer attacking an uphill segment in the French Alps.
Evaporation of sweat, radiation, convection and conduction are the four mechanisms we use to transfer heat. To simplify matters imagine our people are naked so we don't have to worry about the impact of clothing. Conduction and convection are usually lumped together in these calculations and aren't major factors in these three cases. (We'd have to study them if you were in the water or holding a block of ice against yourself.)
Room Temperature
Sitting around in a room at 23°C (73°F) a 70 kg person generates about 100 watts. The details will be in the footnotes, but here's the gist of it. Radiation transfers about 130 watts to the surrounding environment at 23°Ç.3 This is why our most comfortable temperature range if we're not exerting ourselves is in the low 20°C s. We don't crack a sweat unless we're exerting ourselves. That changes dramatically with rising air temperature and/or physical exertion.
Arizona in the Summer
Consider a 45°C day - not uncommon in the Phoenix area. Now the body is absorbing heat from the surrounding environment. Now the body receives about 150 watts from the air adding to the 100 watts it generates just sitting around. You start sweating when the air temperature nears body temperature. You need to sweat about 400 grams of water an hour to keep your core body temperature stable.4 Move around and that soars and don't even think of getting out of the shade. Note if you wipe the sweat off, you need to sweat even more as it must evaporate on the skin to be effective.
Tour de France mountain stage leader.
Sweating dominates heat removal. The racer is generating over 1300 watts of waste heat corresponding to the need to sweat out about two liters of water an hour. A normal adult in average physical shape can sweat about 1.5 liters per hour. Endurance athletes can increase this to over three liters per hour.
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1 Aside: this is insane. If you have an exercise machine calibrated to show watts delivered, see what you can do. Figures over 5.5 watts/kg make one suspect doping. A few people seem to have bodies that can do it naturally, but 7 watts/kg would almost certainly indicate doping.
2 There are estimates of around 10% efficient .. so he had to get rid of well over ten thousand watts of waste heat .. his body couldn't sweat it out in real time, so his core temperature soared.
3 To calculation the radiative power transfer you need to convert to degrees Kelvin and use the heat transfer equation:
P = eσA(T4hot - T4cold)
where σ is the Stefan-Boltzmann constant, A is your skin area .. about 2 square meters for an adult male, and e is the emissivity of skin - in the infrared human skin is nearly a perfect radiator and 0.97 is commonly used. We'll go with 1.0 for a quick back of the envelope. Your skin temperature is about 34°C or 307°K and 23°C is 296°K. Plugging this in gives about 133 watts .. say about 130 for a simple number.
If you want to estimate the surface area of your skin the Du Bois formula is generally considered to be the best approximation for most people.
A ~ 0.007184 * W0.425 * H0.725
where W is body mass in kilograms and H is height in centimeters and A is in square meters. My guess is very few people know the surface area of their skin, but it's an important number when you're trying to work out heat flow.
4 For the sweating component note a 70 kg person sweats that the rate of 25 grams an hour at rest. It takes 2428 Joules to evaporate a gram of water at 34°C (note it's almost 10% higher than the amount needed at 100°C).. so the cooling power is approximately 25g/h * 2428 J/g * 1/3600 s/h ~ 17 watts. You can use the same equation to calculate how much sweat per hour is needed to transfer a given amount of heat away from the body.
This is in dry air. It's much more difficult to evaporate sweat in humid air. Tokyo in late July through August is hot and humid - it promises to be a real challenge for many athletes and it seems unlikely records will fall in endurance sports.
Note sweating chills blood just under the skin by transferring heat to water on the skin causing it to evaporate. The chilled blood then moves to the body's core where it picks up heat and drops the core temperature a bit. It's just like a radiator in a car.
making obsolete tech sing and beyond
Over the past few weeks I've been playing around trying to repurpose old hardware. Mostly CD and DVD drives and they're chock full of useful parts - lasers, motors, lenses and so on... That and a bit of Arduino prototyping to come come up with a bag of junk that could be sent to undergrads next year. Motivation came from the COVID-19 teaching experience. At least in physics online classes proved difficult and labs unworkable. Some folks at Caltech suggested a different lab experience where the student assembles or even invents a piece of experimental apparatus to use to make some measurements. The fact that most students have smartphones - basically computers with a number of interesting sensors and a network connection - makes this even more appealing. It probably isn't appropriate for 101 non-major courses, but it may make a better lab experience for more advanced physics and engineering students. The potential for real learning rather mechanically following directions is great - assuming you have good instruction to go along with it. There's also the possibility of creating inexpensive lab kits for high schools. High school lab experiments are ridiculously expensive and inflexible. There are a number of interesting directions. It's been fun and several of us are in exploration mode.
I need to add I'm a privileged white male with the ability to take a bit of time and focus on this kind of craziness during an epidemic. Too many people aren't in that position.
The project reminded me of some attempts to help my mother when she was dealing with dementia. She became forgetful, so we'd make lists. Then she lost the ability to read so picturegrams. All along the way glasses, remote controls, almost anything that wasn't nailed down managed to get misplaced. And then there was medication. She went into a managed care facility. Life was less stressful, but she was constantly misplacing things and forgetting how to operate the style telephone and TV remote. I started building gadgets to help out, but by the time one sort of worked, she had lost more capability.
I've thought about it a fair amount since. The facilities are expensive - at least $80,000 a year and usually more. What could you change to allow someone stay at home a few years longer? Even if it cost ten or twenty thousand dollars, it could save a lot of money and be better psychologically. (Greg Vesonder has done thinking along these lines)
Om and I were talking about where the local and personal application of "intelligence" is a big thing, perhaps the biggest thing, for Apple going forward. With their sensors and local connectivity outside of the cloud, the iPhone and Apple watch have great senior citizen potential. The iPhone has machine learning hardware. Combine this with ultrawideband location and a dozen applications immediately leap to mind.1 Fertile ground indeed.
Of course the trick is to stay healthy and sharp as you get older. It turns out there's a wonder drug which, taken regularly, doesn't have negative side effects. The AMA now considers physical exercise a powerful drug - often with superior results than conventional drugs. It has been shown effective in lowering the probability of several types of cancer, heart diseases, many forms of dementia, and is even associated with "happiness". You don't need a lot. Walking enough counts and you get it for free if you use a bicycle. But you have to do it.
Many people use smartphones , watches or dedicated fitbit type devices for motivation.It turns devices aren't universally motivating over time, but if they work for you it's money well-spent. The sensors and processing can be useful for athletes training at the amateur level, but not at the elite level. That's a separate and fascinating story at the frontier of sports science these days.
Finally it's becoming clar that certain types of mental stimulation help push back the onset of dementia. Forget the memory games marketed for the purpose - they've been shown to be ineffective. What you want is something that challenges you - something you've never done that you have really work at. Anecdotally creatives who constantly push boundaries are in good shape. I suspect it doesn't matter how creative you are - just the fact that you're forcing a lot of new neural connections. The brain stays plastic for a long time.
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1 Current generation iPhones have the U1 ultrawideband chip. They haven't done much with it, but it makes a lot of sense for augmented reality, ID verification and object location. I wrote a bit on UWB a few months ago.
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