## Calculating a hard baseline for energy expenditure

PowerTap. After the immediate thrill of “how many watts can I do?” (answer: disappointingly few!), I moved on to the next most obvious question: “how fast will my bike(s) go for a given wattage?”

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! ðŸ™‚ ).

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).*

Fantastic post! I love the cavalier way you mix imperial, SI and “traditional” units ðŸ™‚ Your connecting kcal and watts is a great insight – thanks.

On my other computer (!) I have a spreadsheet formula that purports to convert watts of input into kph. The formula is complicated enough that I can’t remember or derive it, and it makes assumptions similar to yours about friction and aerodynamics. Presumably your power meter could provide actual values (for your set up) … could you give us a graph of watts v speed and some indication of the set up and conditions? It would be great to compare theory and practice.

I see you’ve already done the comparison I was looking for above :

Power (W) Roadie (mph) Midracer (mph)

100 13.4 15.9

150 16.5 19.4

200 18.1 21.7

250 19.6 24.0

300 21.3 24.6

I’ll stuff the numbers into the spreadsheet on my other computer, and get back to you …

Hi Joro,

Glad you enjoyed the article. I don’t have nice graphs (yet!) but it sounds like you’re probably interested in something like my Midracer vs Strava bike: power comparison test?

I should caution that my experimental technique does need refining! Much more like that to follow…

D.

Hi Dave

Here is the formula from my spreadsheet:

SQRT((2*WATTS)/(9.8067*WEIGHT*0.0053)+0.185)*60*60/1000*0.621371192

and here is my source:

http://www.americanroadcycling.org/thebook/PowerToWeightCalculatorExplained.aspx

Note the formula gives kph, the 0.621371192 converts to mph.

I have used a weight of 85kg and put the wattages you used into my spreadsheet. The theoretical results in mph seem quite promising …

Watts mph1 mph2 Formula ratio(F/mph1) ratio(F/mph2)

100 13.4 15.9 15.1 1.1 0.9

150 16.5 19.4 18.5 1.1 1.0

200 18.1 21.7 21.3 1.2 1.0

250 19.6 24.0 23.8 1.2 1.0

300 21.3 24.6 26.1 1.2 1.1

I hope that makes sense. The left three columns are your numbers. The Formula column uses the above formula with your weight as 85kg. The right two columns are the ratio of the theoretical speed in mph compared with the practical values you achieved on your two bikes. All values are rounded to 1 decimal place.

The Formula results seem biased towards racing as the values are closest to your fastest bike. A fudge factor could be introduced to get something more appropriate for utility or touring cycling.

We all know that there are diminishing returns for more effort on a bike. Your practical results are even more depressing than the values predicted by the formula (but not extravagantly different). It shouldn’t be too difficult to figure out a ‘DaveFactor’ and a ‘BikeFactor’ that makes the predicted results correspond almost exactly with the practical results you are getting from your Power Meter.

Great article. The only error is in the amount of FAT burned. Your energy is supplied by about 70% FAT and 30% CARBS. And there are only about 1550 calories per pound of CARBS. So lets say you burned 7,000 calories. You didn’t just burn 2 lbs of fat. You actually burned about 1.4 lbs of FAT (7000 * 0.7 / 3500) and about 1.4 lbs of CARBS (7000 * 0.3 / 1550). Or almost 3 lbs of body weight.

Hi Dave,

I’m no biologist but I don’t think it works that way. I understand the liver stores around 100g of glycogen while your skeletal muscles might store 500g – that’s only 1.5lbs in old money – and your body metabolises fat to replace the stored glycogen as required.

Say you ride until that carb store is completely burned up and sit around on an empty stomach… soon your body will reinstate the same 5-600g of glycogen from your fat stores.

I’d be happy for a correction here, but I’m pretty sure it works this way. The weight calculation simplifies things by ignoring the intermediate state where some fat is yet to be metabolised to replace depleted glycogen stores.

Hey Dave… I think your assumption is incorrect. But the main point was that your original comment seemed to suggest that a total calorie burn correlates to a weight in fat. I just wanted to mention that you lose more than that because you’re burning 25-40% carbs (depending on intensity) and carbs are not as calorie dense. So 7000 calories burned is more like 3 lbs (a mix of carbs and fat), not 2 lbs (pure fat).

But to your other comment. You’re right we store a limited amount of glycogen. And we burn that store of carbs as we exercise. If you don’t consume carbs, you’ll likely run very low after 2-3 hours of moderate cardio exercise, and then you bonk (hit the wall), which is when your metabolic demand has to rely almost entirely on fat, which is a less efficient energy source.

Smart athletes will prevent (or at least delay) this by consuming carbs from the start (if they desire to perform well beyond 2-3 hours) so they don’t run low on glycogen as soon.

The body can not regenerate glycogen from fat. It can, from a limited supply of triglycerides, and from a destructive and inefficient process by cannibalizing your muscle protein.

See Section 30.3.1:

http://www.ncbi.nlm.nih.gov/books/NBK22414/

This is also an interesting link:

http://www.unm.edu/~lkravitz/Article%20folder/limitations.html

Happy New Year!

Hi Dave,

Sorry, your comment got caught in a filter.

Thanks for the links. It clearly doesn’t work as I assumed: “fatty acids cannot be converted into glucose, because acetyl CoA cannot be transformed into pyruvate” but “muscle shifts almost entirely from glucose to fatty acids for fuel”.

So you don’t metabolise fat stores to free up glucose, you use a different pathway entirely to burn raw fat as a fuel.

I’m going to have to do some more background reading I think, as I’m now struggling to understand how low-carb diets work (sounds like we’re obligate “carbovores”), and exercise regimes promising to target fat (by, for instance, exercising in the fasted state) don’t seem so implausible.

From your links, however, it seems like reinstatement of the glucose stores is a metabolic priority after exercise. For the vast majority who are eating carbs, doesn’t this immediately replenish the “low-density” weight lost during the original exercise metabolism of carbs?

cheers,

Lots of people have got caught up in the low carb craze. The reason is because they think carbs just turn into fat, so now people think eating just fats and protein and eliminating carbs will make them less fat. Well, the truth is that carbs are very good for you, they provide energy better than other nutrients and without them you won’t be able to exercise efficiently. Without exercise you won’t be healthy.

When you are full of carbs you can exercise properly, and body fat burns whilst the carbs are used as energy. Just try and exercise without carbs, you will give up very soon, and how will your heart and lungs feel if you don’t exercise? Just dead tired that’s how.

How do I account for my metabolic rate based off this figure? I really am having trouble figuring out how much I should be eating after a ride. I always compensate with too many carbs for sure! Like at the gym when on the treadmill or whatever it has me punch in my weight. I weigh about 220lbs and am fairly lean <20% bodyfat so about 175lbs lean muscle so I'm sure I'm burning a TON of calories on say a 90 roundtrip minute bike commute! Considerably more than my 135 pound friend… The thing with commuting, at least for me, is that there are quite a few intersections to stop at. I think most bicycle computers stop computing when you stop riding. Don't they? Sorry to complicate things! Its what I do!

Just had to say that the discussion was even more enlightening than the article, and the article was great. Good work people! I’m much smarter than 20 minutes ago.