This question is from a comment I got on my Calories Burned in Running vs Cycling post.

**Question:** If you double the speed you cycle will you burn more than twice the calories since air resistance increases exponentially with speed?

**Answer:** According to Dr. Edward Coyle of The University of Texas in Austin who did a study to determined the average values of oxygen consumption by cyclists at difference speeds, your position that if you “double the speed you cycle at, you will burn MORE than twice the calories” is incorrect. Here are the numbers Dr. Coyle’s tests came up with.

mph | calories/mile

10: 26

15: 31

20: 38

25: 47

30: 59

Here they are in metric.

km/h | calories/km

16: 16

24: 19

32: 24

40: 29

48: 37

You can see from these numbers that while at 10mph you burn 26 calories per mile but you don’t burn 54 calories per mile at 20mph but only 38 .

In metric at 16kmph you burn 16 calories per kilometer but at 32kmph you don’t burn 32 calories but only 24 calories per kilometer.

My typical average speed is 25kmph (15.5mph) so I am burning 19 calories per kilometer (31 calories per mile). Yesterday I managed to do 12.4km in 25:01 which is an average speed of 20kmph (18.6mph) which is close to my max.

While air resistance is an issue according to Dr. Coyle’s the effect is not doubled when you double your speed from 10mph to 20mph (16kmph to 32kmph).

When it comes to bicycle we are not dealing with the same speeds we are dealing with when it comes to cars. Wind resistance increases exponentially in higher speeds but not in lower speeds.

Biking on a non-professional level we are dealing with speeds below 30mph (48kmph) which are covered in Dr. Coyle’s numbers.

In cat 4 races, riders maintain an average speed of 18mph to 20mph (29kmph/32kmph), in cat 3 riders 24mph to 28mph (39kmph/45kmph), and in the US or EU pro circuit riders maintain 30mph to 35mph (48kmph/56kmph).

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July 6th, 2009 at 4:22 am

The question is not well-posed. The numbers clearly show that you do not double the number of calories/mile if you double your speed. However, you do more than double the number of calories/hour, which is the rate of burning calories, which is what most people want to know.

According to your numbers. 1 hour at 10 m.p.h. burns 260 calories (sounds low to me….) 1 hour at 20 m.p.h. burns 760 calories, which is much more than twice 260.

July 8th, 2009 at 5:37 pm

Hi John Yelton,

I thought the question was clear. The person wanted to know if you double your speed do you double your calorie burn per mile or km. In most cases the answer is no. While I don’t have numbers that go past 30mph or 48kmph it appears the way the graph is going in higher speeds this would be the case. How ever when you get into 30mph or 48kmph average we are then into the pro circuit. I can hardly do 32kmph average over 25km.

I would agree that calories/hour is the rate people want to know but calories per distance for a certain speed can be changed to calories per hour very easily. Again when you get above 30mph or 48kmph you are into the pro circuit and far above what a normal person can do.

I see you point about 1hr at 20mph would burn 760 calories. I think I will review my numbers as there seems to be something off in them. That’s for pointing this out!

July 16th, 2009 at 12:18 pm

It also depends how much you and your bike weigh. Moving 120lbs over 10 miles requires a good deal less caloric expenditure than 200 pounds.

Here’s an interesting link comparing calories per hour and rider’s weight.

http://www.nutristrategy.com/fitness/cycling.htm

Hope this helps.

February 1st, 2010 at 5:57 am

Wind resistance does not increase exponentially at all. The drag felt by an object is proportional to the square of the velocity at virtually ALL speeds relevant to a cyclist (only if you were cycling through treacle would viscous effects dominate and the relationship would be more linear). I suspect what Dr Coyle has done is measure some performance metric indoors ie. out of the wind (however see the qualification below).

The power required to overcome the drag increases proportionally to the velocity times the drag – ie. the cube of the velocity – and since energy is power times time the answer is YES you will burn more than twice the calories (actually 8 times the calories).

Now for the caveats: 1) it doesn’t really scale perfectly since you will only burn more than twice the calories you would have burned on top what you would have burned had you not been cycling thus there is an offset, 2) transmission losses and friction between the tires and road surface also scale with velocity, 3) in the results there is a cubic scaling present but given the sparsity of the data points it is hard to justify a particular fit, 4) it may be worth considering that cycling at lower speeds may be fairly inefficient and thus the lower speed data points could be mis-representative and 5) technically, for this to be true the rate of energy consumption must be constant.

So cycling at double the speed will theoretically use at least 8 times the calories – this is the minimum according to the laws of physics and to suggest otherwise one must present more than out of context data.

February 4th, 2010 at 8:13 am

Hi Tom,

Thanks for you good information.

I think we also have to take into consideration that there is a maximum speed a cyclist can maintain. For it is between 32 and 33kmph on a 12.5 distance that has a couple of nice hills and some other up and down grades.

So when it comes to running a person may be able to burn more calories when they try to run themselves out than if they try to cycle themselves out. Also depending on the fitness level a person is at it may be more possible to sustain running longer than cycling and hence do better in burning calories running than cycling.

Cycling has a lot to do with the fitness level of your legs where running seems to have more to do with cardio.

Thanks!

Bob.

April 27th, 2011 at 10:52 pm

Will I burn more calories cycling at the hardest gear speed (say level 8) for 10 minutes or cycling at the lowest gear speed (say level 1) for 20 minutes.

April 27th, 2011 at 11:05 pm

Hi Jaye,

You will burn more calories when you exert yourself harder. So you want to be efficient and in cycling you go by cadence. 88-95rpm is the sweet spot for using your slow twitch muscles. When you exert yourself harder you use your fast twitch muscles and these are not unlimited like the slow twitch muscles.

Bob.

April 27th, 2011 at 11:51 pm

Hi Bob,

So I am better to cycle using the hardest gear (at the fastest possible speed I can) for 10 mins as opposed to the lowest gear for 20 mins (at the fastest possible speed I can).

May 20th, 2011 at 3:57 pm

At the same speed you will burn pretty much the same calories whether you spin fast in low gear or mash in a high gear.

the work done is the same.

Spinning puts more demand on your heart and lungs, mashing puts more demand on your leg muscles, and joints.

As posted above around 90 rpm is the most efficient cadence, but that does vary with leg length, crank length etc.

May 21st, 2011 at 5:31 am

Hi Mark,

Yes I would agree to some degree. There is a most efficient rpm to cycle at and at that rpm you will travel farther using the same calories.

Bob.

May 21st, 2011 at 11:58 am

Spinning too fast will burn excessive calories.

EXAMPLE: if you spin as fast as your can, your power output is zero. Any load applied will cause you to spin slower.

So at max spin, you are burning a high rate of calories and doing no work.

There isn’t much talk about the acceleration and deceleration of limb mass when doing periodic motion. This involves Kinetic Energy which involves the square of velocity at constant mass. There is also Potential Energy which is related to the distance a mass is raised against gravity. This is another loss due to cycling motion but is not related to speed.

I suspect there is an efficiency curve of spin -v- load.

There would also be a burn -v- load curve.

Load can be calculated from the grade and velocity.

On the cyclist end there is output and recovery curves which determine the maximum output over time.

All that remains is to take this information and determine the load management that will produce the most miles given the characteristics of the cyclist.

This is definitely a non-linear analysis which must be solved by computer.

It is a fascinating problem.

Regards,

Tom

July 20th, 2011 at 1:03 am

Interesting comments!

Here are some additional facts and clarifications:

A corollary to the First Law of Thermodynamics, is simply that heat an work are interchangeable. Hence, the number of calories burned (i.e. heat liberated) is EXACTLY proportional to the amount of work done.

When counting calories for activities, we are really only interested in the number of calories extra we burn—we are not interested in the number of calories we are going to burn at the base metabolic rate.

Therefore, when doing most activities, time is irrelevant, only the amount of work being done. In other words, if you hike up a mountain in 2 hours, you are going to burn up exactly the same number of extra calories you would if you hike up the same mountain in 4 hours. If you run 1 mile and burn 120 calories, you will burn off 1200 if you run 10 miles, no matter how long it takes you. This is true for cycling also, except someone did raise the issue of wind resistance, which is definitely a factor for cycling (not so much for hiking). Therefore, on a per mile basis, the number of calories you burn will be directly proportional to the distance you go at any given speed, but that faster the speed the greater number of calories per mile will be burned.

However, the notions of wind resistance being exponential or linear are both incorrect. Wind resistance is proportional to the square of the speed. In other words it is a second order polynomial (or quadratic) function, not an exponential. In the case of a vehicle, the best gas mileage is usually obtained at around 60 miles per hour, although it might be higher for a corvette and likely lower for dump truck due to each vehicle’s respective drag co-efficient (which for each vehicle is a constant but higher for a dump truck than a corvette). At slow speeds, the wind resistance is negligible (for the keeners, this is due to a relatively large drag coefficient in relation to the speed: at slow speeds the drag coefficient is dominant and at high speeds the quadratic wind resistance is the dominant factor) , but not much above 60 Mph, the slope of the quadratic curve starts to exceed 1 (i.e. 1:1) and mileage starts to plummet because the power required to overcome wind resistance becomes enormous. However, in the case of an automobile, the improved mileage in spite of the initial increases in wind resistance is largely do increased engine efficiency.

In the case of the human body, which is horribly in efficient to start with this might not be much of a factor but I have no facts to back it up but lets stick to Dr. Coyle’s observations:

10 mph –> 26 calories/mile

20 mph –> 38 calories/mile

30 mph –> 59 calories/mile

This means that are most efficient at much slower speed and way less than half as efficient as at 30 mph as at 10 mph. However, if we accept these numbers, then at 10 mph, we would burn 260 calories (10 miles/hour x 26 calories/mile) in an hour and at double the speed we would burn 760 calories (20 miles/hour x 38 calories/hour). Therefore, based on this data, we would conclude that doubling the speed definitely requires more than double the calories per hour.

The question of human body efficiency and variability might also be a factor, but unfortunately the data is inconclusive on this point, and the conspicuous difference of calories\hour between 10 mph and 20 mph (12 calories/hour) and between 20 mph and 30 mph (21 calories/hour) raises some interesting questions. Efficiency probably plays a factor but I’m not a kinesiologist, so I’ll defer that to some other expert. However, I am a cyclist and I know that even a small head wind on a flat surface creates more work for me than a small hill on a calm day. So my gut is definitely in line with the physics (for which I have some expertise), which indicates that wind resistance is a huge factor. Furthermore, Dr. Coyle’s research would seem to support this although there may be a few other factors at play also. Looking at his graph, this could quite easily be a quadratic and the smaller difference between 10-20 mph as compared to the difference between 20-30 mph could easily be explained by a suitable drag coefficient.

Also note that the difference between the calories per mile at 15 mph and 30 mph. This is almost double, so if one were presuming that wind resistance is the dominant factor at 30 miles per hour, then just over 15 mph will be the speed at which doubling the speed will also require over double the calories per mile.

In summary, the one conclusion we should be able to draw with a high degree of confidence, is that you definitely burn more than twice the calories at double the speed! Secondly, based on irrefutable physics, the wind resistance will become the dominant factor, if not already at fairly low speeds. Here is how it effects the question and its responses:

Question: The question was okay except that it stated that wind resistance increases exponentially with speed, which is incorrect—the increase proportional to the square of the speed

First response: Claimed that it is false that if you double the speed you cycle at, you will burn more than twice the calories. This is incorrect; you do burn more than double the calories at double the speed.

To John Yelton: Same incorrect conclusion as the first response.

To Bob Mulch: The question did not state calories/mile should be more than doubled. It also did not state calories per hour should be more than doubled, but the latter is the only one that makes sense for lower speeds. However, at slightly higher speed, the former will also be true.

To Tom: You were correct about resistance being proportional to the square of velocity and about that function being multiplied by the drag coefficient. However, the drag coefficient does not have velocity as a factor, so it is not a cubic (i.e.not X*X*X) but more like A + K*X*X, where A and K are constants associated with drag. Consequently, doubling the speed will result in a factor of 4 times increase in wind resistance, not a factor o 8. Also, note that at the reported speeds, wind resistance accounts for only part of the work being done so the caloric factor attributed to wind resistance is much less than 4 times, although it will get much closer to a factor of 4 at higher speeds when the wind resistance is completely dominant. At the lower speeds, the A and K factors will be dominant , which results in only modest multiples at low velocity (especially if A is relatively large). However, kudos for also noticing that we don’t know much about the lab conditions–that accounts for a lot. Road resistance is one just one of several other factors (body resistance, body efficiency, mechanical efficiency of the bicycle, etc), which is directly proportional to distance traveled.

To Jaye: You should burn the roughly the same number of calories either way since you are doing roughly the same amount of work. Technically, you are burning slightly more calories pedaling faster because you are moving your body more and you are incurring some additional mechanical overhead in the bicycle.

To Mark/Bob: Seems reasonable but need to note that efficiency is sometimes more of a qualitative feel than anything else. Certainly, we all have our own sweet spots that seem to take us farther faster or at least enable us to go the distance. However, the actual number of calories burned may not be reflected in how burned out we are or how great we feel.

To Tom: Huh?

A Final thought: Riding on cold days will burn off a lot more calories than riding on warm days (assuming similar dress). The cooler you are the faster you will burn calories, and this can be a non-trivial amount so climate can be a huge factor.

July 20th, 2011 at 1:08 am

Chris,

Thanks that comment post. Lots of good stuff there.

Bob.