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Assuming that we are using a fixed-gear bicycle and width of the wheels are the same, I wondered, does having bigger wheels mean I need to less effort to get from point A to point B in an urban setting? I'm thinking based on the formula for circumference:

enter image description here

Where r is the radius of a bike wheel. Additionally when looking at this gif for a vertical visualization of circumference:

enter image description here

It appears that having bigger wheels will get you from point A to point B in an urban setting with less rotations by the wheel, but does that also mean I need to work less to get there? What about uphill? Does having bigger wheels help/hurt biking uphill?

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Assuming a completely smooth road and neglecting the weight of the wheels, it makes no difference: you still need to do the same amount of work. Essentially, larger wheels give you a higher gear ratio, so doubling the diameter of the wheels would mean you'd only need to turn them half as many times, so you'd only need to turn the pedals half as many times, but you need to press twice as hard on them.

But, in reality, there are limits to what you can do. If you need to lift 100kg of wood, it's easier to lift 10kg at a time, even though the total work done is the same as when you lift the whole lot at once. Similarly, you'll be more physiologically efficent (and comfortable!) pedalling with certain ranges of cadence and force.

Bigger wheels roll over bumps better. As an easy thought experiment, consider a pit whose width is equal to the diameter of your wheel. Obviously, the wheel will fall right into the pit. But if you consider a wheel with twice that diameter, it will only drop a little way into the pit as it bridges over it.

In practice, though, there aren't a whole lot of wheel sizes to choose from. Either you get a folding bike with small wheels, or you get a non-folding bike with wheels about 62cm/29in in diameter (or about 56cm/26in for mountain bikes).

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  • To expand on the bigger wheel part, consider that as your tire falls into the pit the kinetic energy acquired by falling into Earth's gravity well will largely be absorbed by the tire, and pulling back out of it will reduce your speed. Conversely, hitting a convex bump will reduce your speed as you climb it, while as you descend you will incur losses there as well and won't completely reach your original speed.
    – Michael
    Commented Oct 20, 2017 at 22:59
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    Note in between the fairly standard 20" wheel size there's also 22" and 24" sizes, found on e.g. cruisers/bmx style bikes; 22" being the least common, 24" also used for on children's bikes.
    – stijn
    Commented Oct 21, 2017 at 15:56
  • @stijn Yeah, I left BMXes out of the equation since the question seems to me to be about cyling for transport, whereas BMXes seem to me to be more about cycling for the fun of cycling.
    – David Richerby
    Commented Oct 21, 2017 at 16:55
  • No problem, I was just mentioning it for the sake of (almost) completeness. Especially because the 22" size isn't widely nown.
    – stijn
    Commented Oct 21, 2017 at 18:31
  • What about up hills though? Surely one tire size is easier than the other? I would guess smaller tires are easier given they are lighter and you don't have to put as much effort into each pedal stroke. I guess your theory is right, but in reality it's like you say, it makes sense to go for the smaller 10 KG at a time, rather than try 100 kg in one go, the effort is the same, but you would struggle doing the latter.
    – KillerKode
    Commented Aug 16, 2020 at 15:25
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Work is force times distance.

A larger wheel doesn't spin as much, but instead you have to deliver more force to turn it. There is no escaping conservation of energy.

Additionally, I know you said fixed gear, but keep in mind that a multi-speed setup essentially does the same thing as you're hypothesizing about, but instead of changing wheel size it alters the torque-velocity relationship between the wheel and crank.

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Wheel size is only part of the equation which connect pedal cadence with road distance. Gears can change this ratio (almost) as well.

Even in a fixie you can get a lower or higher gear by changing the sprockets, thereby making the bike more suitable for flat or hilly terrains.

If you decide that you cannot modify the sprockets of a fixie, then the wheel size (which is actually much harder to change than the sprockets) will affect the cadence for a given speed.

Regarding work: at any pedal-to-road ratio the physical work is exactly the same. It can be just difficult (even impossible) to pedal very fast or very slow because of human limitations.

Gears ratios only allows one to keep the cadence where the human body can work better.

Given you set the preferred gearing, then the wheel size will only affect comfort (bigger wheels can go over road irregularities in a straighter path) and weight (bigger wheels are somewhat heavier).

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    Just to clarify: "at any pedal-to-road ratio the physical work is exactly the same" The work here refers to the net mechanical work that actually goes to helping the bike go. The work required to heat your muscles (which must happen due to human inefficiency, and does depend on gear ratio) and the transmission (also may depend on gear ratio) is also physical work in the literal sense of the word.
    – JiK
    Commented Oct 20, 2017 at 23:22
  • Uh, how do I get this "gear ratio" thing on my penny-farthing??
    – Daniel R Hicks
    Commented Jul 29, 2020 at 0:48
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No it depends on which gear your fixed gear is. Big wheels with a (fixed) low gear is similar to small wheels with a (fixed) high gear.

The (fixed) "gear" is the ratio of the number of cogs on the front to the number of cogs on the back (which, I guess, may vary from bike to bike).

Also I'd expect big wheels make it harder, not easier. Wheels an inch high are easy to turn (but don't go very far or very fast). Conversely, wheels a mile high would require a lot of effort to turn.

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Maybe it has something to do with momentum. Imagine the wheels like a fly wheel in a car. The larger the wheel, the more momentum it has, so maybe once you get the large wheel turning, it is easier to keep it going at high speed.

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    This effect exists, but is mostly undesirable because it costs energy to get it rolling and then you loose it when you brake. Cyclists strive to have light wheels - light alloys or even carbon.
    – Vladimir F Героям слава
    Commented Jul 29, 2020 at 5:52
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Two things to consider that are more important than wheel diameter in terms of bicycle efficiency.

Edit: on research my reasoning is very wrong on the weight ratio... Wheel weight discussion

  • tyre width

Wider tyres have increased rolling resistance, but will smooth out the imperfections in the road surface better than a thin tyre, leading to an overall better efficiency.

Tyre width discussion

Look at pro cycling teams' trend towards wider tyres.

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    I'd love to hear the reasoning behind 3.14.
    – ojs
    Commented Oct 21, 2017 at 7:24
  • @ojs: 3.14 is pi to 2 decimal places? circumference = Pi x diameter ?
    – Criggie ♦
    Commented Oct 21, 2017 at 8:40
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    @Criggie yes, the question is how it would occur to anyone that it would count as weight multiplier. Points for poster that he looked up the correct answer.
    – ojs
    Commented Oct 21, 2017 at 9:45
  • My reasoning originally was since Force is mass by acceleration, since you're accelerating the outside of the wheel 3.14 times more then you're accelerating the mass of the bicycle for every unit of forward motion. That had stuck in my head after reasoning it out, probably on a long bike ride! Flawed though. Funny how things you think of yourself become "something you read somewhere".
    – Michael O'Donnell
    Commented Oct 21, 2017 at 9:53
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    The problem is that actually the rotational velocity of tire equals the ground speed of the bike. So, if we simplify things so that entire mass of tire and wheel are at tire tread, we get the often quoted 2x number.
    – ojs
    Commented Oct 21, 2017 at 11:01
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If you think about all of the above reasonings about size and gear ratios etc. that say the energy needed will be the same, it makes sense. I agree. But if you're not on here to show how intelligent you are, and add gravity to the equation, smaller fixed wheels win, because both have it easy going down hill. Ok, I know you can go faster with bigger wheels, but you can freewheel with both, thus gravity is doing the work for you. On the other hand, gravity punishes bigger fixed wheels more going up hill. That's reality! Boyaka!

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  • In what way are smaller wheels faster down hill? Taken to the limit, something like 10mm wheels would just get stuck in bumps in the road (and larger wheels roll better over bumps in general).
    – David Richerby
    Commented Oct 23, 2018 at 17:49
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tl;dr: No, in fact bigger wheel may mean more effort

Answering a question similar to this allowed me to get an admission in my esteemed institute. I will try not to get too technical, here we go.

First of all (for sake of developing intuition), open the nearest window/door first with its handle, then close it, then open it again, this time use your palm keeping it as near to the hinge as possible. -->

You are very correct in saying that C (circumference) is in fact 2 times PI times r (radius taken of wheel) and if we hide the constants we can safely say that C is directly proportional to r.

In plain english, distance covered (irrespective of road conditions, be it urban, wavy, or even inclined road) varies directly as radius of wheel.

Now, think about it, you can cover 100s of miles with virtually no effort if you are sitting in a bus. You yourself realize going uphill will be difficult, why? 1 meter is 1 meter in all directions, clearly there's more to "work" than just distance covered.

So, when it comes to effort we must talk about force also and not just the displacement or the distance covered.

Now, work done is dot-product (think of it as regular multiplication with some added bells and whistles) of force and displacement. In our (slightly special) case the increased diameter/radius of the wheel implies that we need to exert more force to turn it (will edit n insert equations as soon as I learn MathJAX)

In plain english, big wheel implies more exertion to turn the wheel, even if we consider the wheel to be absolutely weightless.

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    This answer seems very unfocused. What's the relevance of buses? How do you conclude that it might be harder with a big wheel even though the physics you describe implies that the size of the wheel makes no difference?
    – David Richerby
    Commented Oct 21, 2017 at 13:29
  • By the way, this SE site doesn't have MathJax enabled -- not all sites do, since it takes time to process and users get confused when mentioning an amount of money in dollars causes the formatting to go all screwy.
    – David Richerby
    Commented Oct 21, 2017 at 13:30
  • Which institute? Name and shame!
    – ojs
    Commented Oct 22, 2017 at 15:48

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