BOTE #1 – Efficiency of running…?

I have always been interested in working things out roughly from first principles. These so called “back of the envelope” BOTE calculations are pretty good ways of a)making sure you understand how something is derived and b) good for checking what other people are claiming. I first came across this in high school science and the 80’s in an article working out how much it costs to get a bottle of wine to our nearest star, due to the wonders of the Internet here is the article. (It’s well worth reading as to why we will never have intergalactic space travel, the bottle of wine was \$11Bn in 1980 dollars)

With this in mind I might do a few articles in a series using this principle and so here’s the first and a caution: If you think the world is 6000 years old or that acupuncture actually channels Chi or that there is some conspiracy behind 9/11 you will probably have trouble with the following as it uses the language of science and assumes you are willing to understand and know basic science. In my experience people in the above mentioned groups and related woo-woo areas have incredible trouble with this stuff due to the mind control satellites put in orbit by the Illuminati that emit anti-science beams in an effort to confuse the human race. They are succeeding IMHO.

When checking out a company dealing with carbon offsets in Australia I came across the following information in their blurb.

” At 0.27 kg of CO2 per kilometre, air travel produces by far the largest amount of GHG emissions per passenger kilometre of any form of transportation. By comparison, a single-occupant vehicle produces 0.20 kg of CO2 per kilometre, and a bus produces 0.07 kg of CO2 per kilometre per passenger.

There’s a reference to the source of this but whoever does their blurb is apparently not a scientist as they don’t know how to cite references properly.

However, the question that formed in my mind is how much energy does a running human produce, perhaps these figures are not too bad in comparison? I doubt it but you never know. And this is where some idea of science comes in useful. How much CO2 do I produce when running a kilometre? I don’t want a super accurate answer, I only have a few minutes to find the answer. A quick search of the web is no use, the best I can get is energy burn but I already know that from my polar watch which I use when running. So given this data, lets see how much CO2 I generate when running.

When I run I burn about 60 to 70 calories per kilometre. (Sorry about mixing the units but this is BOTE, not some scientific paper). This corresponds to about 15-18 gram of sugar as we have 4 calorie per gram of sugar. When burning this sugar, we’ll assume it’s pure glucose, we get 6 molecules of CO2 for every molecule of glucose.

Glucose -> 6 CO2 + 6 Water + energy (assuming a perfect world)

The real equation is really complex ..and irrelevant to BOTE.

To work out quantity of glucose we need the molar mass of glucose (180.16 g mol−1)  and CO2 (44g mol−1). Wiki is a quick way to get this data. From here we work out the amount of glucose as 18 / 180.16,  so say 0.1 mol. After burning this will give 0.6 mol of CO2 and multiplying by it’s atomic mass we get 0.6 x 44 = 27 gram.

We now have our answer and in the units of the original article, about 0.03 kg of CO2 is produced when I run. So a bit under half what a bus uses. When walking I use about half that again but take over twice as long so that sort of balances out. This strikes me as pretty impressive for a bus which uses slightly more than twice as much energy per kilometre and is darn sight heavier, even when you spread it’s mass over each passenger.

And now I look at figures for  the car and plane and they are not that bad and I notice the car states for a “single-occupant vehicle” which instantly strikes me as the worst case scenario. Maybe a car with 3 people produces roughly 0.06kg per person, which is better than the bus! Perhaps further investigation of this quoted data is needed as things are starting to look rather fishy here but that’s a story for another BOTE day.

Today’s homework boys and girls is to get on the bike at the gym, remember the calorie burn for a kilometre and work out how much better wheels are than legs.. 🙂