Calculating a hard baseline for energy expenditure
However, there’s another side to measuring power output which I hadn’t really considered until some time after I built up my PowerTap. You actually know how much energy you put into the road over the course of a ride (or part of a ride).
Turning watts into calories
If you know duration and average power you already have energy, it’s just not expressed in good old-fashioned calories. It turns out there’s a suprisingly simple formula to turn the wattage from a power meter into kcal though:
energy (kcal) = avg power (W) X duration (hours) X 3.6
As with so many surprisingly straightforward looking formulae, there are assumptions built into the constant.
When you multiply power by duration you get energy (a joule is 1 watt for 1 second). 100W for an hour (3600 seconds) is thus 360,000 joules, or 360kJ. Since we lose a factor of a thousand turning joules, or calories, into kcal, you can see where the 3.6 comes from in the simplified formula.
However, like any machine the human body isn’t perfectly efficient – it has to burn more than 1 joule of real energy to output 1 joule of *measured* energy through a power meter. In fact the efficiency of cycling humans is between 20-25% (so your body’s many systems and inefficiencies burn 4-5J of energy for every 1J you deliver to the pedals).
This means we should divide any “measured joules” figure by 0.2 to 0.25 to get it expressed as “real joules”.
By a happy coincidence, a calorie is ~4.18 joules, so to turn the “real joules” into calories we’re about to do broadly the opposite (a joule is 0.24 of a calorie).
For a human with 24% efficiency, you can cancel the last two steps exactly, so that measured joules = real calories. Since the range is 20-25% efficiency this is an underestimate (lots of people will burn more calories than the calculation suggests, but few will burn less).
See it worked out both ways below:
100W X 1h X 3.6 = 360kcal
or in full:
((100W x 3600s) / 4.18 ) / 0.24 = 358,851cal = 358.9kcal
There are a other few bits and pieces to consider, but they’re all further reasons why this is an underestimate (like drivetrain efficiency – your dirty chain means you might be working harder to get that 100W than Joe Spotless).
Running on spare tyre
Using the formula above, we can see that a watt-hour is worth 3.6kcal. By a convenient coincidence, the energy density of fat is ~3500kcal per lb, so a kilowatt-hour of effort from a cyclist will burn off a good pound of fat.
If you commute at an average of 100W, every ten hours you will burn a pound of fat. Let’s suppose your commute lasts half an hour, so it takes 20 journeys (two weeks) to lose that pound of fat.
Assuming the standard five weeks paid holiday a year, you’ll lose 23lbs of fat a year from that modest 30 minute commute (assuming you don’t increase your food intake to compensate – evidently most do since cyclists aren’t all emaciated! 🙂 ).
Based on my early PowerTap tests, 100W on my road bike is good for ~13.5mph on the flat in no wind, so it’s probably fair to guess that most regular commuters are managing 100W.
If you commute at 200W (18mph for me, again on the flat in no wind) you’ll burn more (although a half hour commute at 13.5mph only takes 23 minutes at 18mph, so your actual increase is on the order of 50% rather than doubling – 100*.5*3.6=180kcal, 200*0.375*3.6=270kcal).
Allows some interesting thoughts on “food as fuel”. A portion of Weetabix (my breakfast of choice) contains 134kcal, so even adding 100kcal for a generous serving of milk I’m still running a deficit from my morning ride *even after breakfasting on arrival*.
Certainly not the way I thought it would be!
P.S. Depending on where you live, you may have kcal on food packaging (like the UK) or just “calories”, which is always really kcal (there’s some mumbo-jumbo about Calorie = 1000 calorie, not that people capitalise like that in real life, but see Wikipedia).