Does having bigger wheels mean less effort pedaling?

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).

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.

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.

tl;dr: No, in fact bigger wheel may mean more effort

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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.

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.

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!

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.