Oh my god!!! He still doesn't get it!

Blue Order, if the rider can output exactly 100 Watts of energy, then he will HAVE TO SWITCH TO A GEAR THAT IS LOW ENOUGH TO KEEP PEDALING AT 90 RPM. If the wheel is bigger, that just means he'll have to drop to a lower "cog" on the drivetrain to stay at 90 RPM. He won't be strong enough to push the big gear (or big wheel) that quickly.

That's why the Big Wheel bicycle is a joke! It's making fun of your logic from the start of the post. By your logic, we'd all be riding bikes with 10-foot-high wheels. No, a bigger wheel is not more efficient. It changes nothing but the gearing. Higher gearing equals lower cadence. The rider can only push the pedals so hard.

I'm going to bed. Read the posts carefully and consider the logic. You'll see what everyone is trying to say...

Best of luck mr Blue Order.

OK, here's what I'm getting from the various responses. Although the larger wheel travels farther on one revolution, the energy required to turn that larger wheel one revolution is greater. On the other hand, in order to travel at the same rate of speed as the larger-wheeled bike, the human motor must turn the cranks on the smaller-wheeled bike at a faster cadence.

If you have two bicycles with differently-sized wheels traveling at the same rate of speed, the motor turning the larger wheels will apply energy to push that large wheel one revolution, while the motor that turns the smaller wheels will apply energy to turn the cranks at a faster cadence. In other words, both cyclists are expending the same amount of energy to perform the work of traveling a certain distance at a certain rate-- one to turn a larger wheel, the other to turn at a faster cadence.

is that correct?

Yes! Perfecto! I knew it would eventually hit you and you'd go "whoa - it makes sense!"

"Although the larger wheel travels farther on one revolution, the energy required to turn that larger wheel one revolution is greater. "

No, the energy (power) required will be exactly the same if the speed is the same. Part of your confusion is understanding that force is not the same as power. From basic physics:

POWER = (force * distance) / time

We can simplify some of the terms out, like "distance" which is the distance your feet moves. If the crankarm lengths are the same between the two bikes, we can cancel it out and we end up with this for cycling applications:

POWER = PedalForce * RPM

That's where gearing comes in. If you have identical gearing on both BigWheel and SmallWheel bikes, they BOTH will require EXACTLY the same power to go at the same speed, assuming same aero-drag and rolling-resistance. However, the BigWheel bike rider will be at lower-RPM and will require more pedal-force to generate the same power and speed as the SmallWheel bike at higher-RPM and lower pedal-force. Like this:

BigWheel @ 25mph = 300w = 60lbs * 60rpms
SmallWheel@25mph = 300w = 40lbs * 90rpms

Note that the guy on the BigWheel bike has to push on the pedals A LOT harder (+50%) just to create the same power and speed.

If you modify gearing such that both BigWheel and SmallWheel bikes are matched to same RPM at same speed, then power and pedal-force and RPM for both will be exactly the same.



Imagine this extreme case, you have a bike with 72t front-chainring and a 8t rear cassette cog. You'll be able to go 64ft with a single crank of the pedal... is this more efficient? How about combining this monstrous gearing onto TrackSmart's bike and go 150ft with a single rotation of the crank, would this be even more efficient? Nope, it'll require an extraordinary amount of strength to push that gear and get the bike moving....

How do account for steam engines?

steam engines...

energy in = energy out

chemical energy in = mechanical energy out + losses due to friction and heat loss

Thanky you for acknowledging energy is not the same as work. But for the same trouble let's just get it right. The first law of thermodynamics says for a system in equilibrium, the difference between the heat transfer into the system and the work done by the system will be the change in internal energy of the system.
https://www.grc.nasa.gov/WWW/K-12/airplane/thermo1.html

DannoXYZ, while your strict analysis of what he wrote is correct, "we get what he means". He just did not use the technically correct language. Remember, in our scenario the drivetrain of the two bikes are the same, they are in the same "gear" on their shifters, the only difference is wheel size. He clearly gets that the two bikes will require the same amount of energy to move a given distance. And he clearly gets that the bike with lower gearing (the smaller wheel) will require a greater cadence to stay at the same speed as the bike with the higher gearing (the big wheel).

He gets it! And that's great! Let's not beat up the guy about the technical correctness of his language. Although, it might be good for Blue Order to understand the correct way to express the concept that he most clearly understands...

change in internal energy of the system = mostly heat loss, heat absorbed by the system that will later be dissipated.

Yeah, I think he partly got it, but I wanted to clarify since we had two difference scenarios discussed that were collapsed into one. Identical-gearing must be differentiated from identical-cadence examples of two difference wheel-sizes.

A little calculus also really helps to understand this as power is the integration of force with respect to distance and time.

Quite the opposite. If the 26" wheel has a fat enough tire to give almost the same wheel diameter as a 700 c wheel, it will likely be far slower. That fat tire can't hold the high pressure a thin tire can, so it will deform more as it runs along the ground and will have a much higher rolling resistance. It will also be a lot heavier.

I read somewhere that you can determine this experimentally. Get a heart rate monitor. Ride both configurations over the same course keeping your heart rate constant. See which configuration gets you further. The theory is that your heart rate correlates to your power output.

I have never done this but always wondered if it really works.

All of this hub-bub makes me glad I still ride 27" tires.

I haven't looked for it, but hasn't anyone ever just hooked up two bikes to an engine and measured the power/speed/rotation of the output?

This is a very weak correlation even if all rides are done on the same day.

The funniest part of this is that the OP refuses to acknowledge the most significant aspect of the difference between a 700c and a 26” wheel. (post 18)

“I refuse to accept your reality and will substitute my own”

If there traveling at the SAME speed, there gona cover the SAME distance over the SAME time.

A 20" bmx traveling at the SAME speed as the other two would aslo cover the SAME distance...

so how can you ask "if there both going the same speed"? if there going the same speed, guess what, there going the same speed, so how would the 700c bike cover MORE distance?

EDIT: wait, i read that wrong. yeah thats right lol. oops