# General Cycling Discussion - Yes, it is bicycle science.....

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View Full Version : Yes, it is bicycle science.....

Blue Order
09-03-06, 05:32 PM
OK, a physics question for all you science types.

I would argue that a 700c wheel is more efficient than a 26" wheel, because given two cyclists turning their cranks and traveling at the same speed, the 700c wheel travels a farther distance with each revolution of the crank. The extra distance traveled may be small with only one revolution, but eventually, over miles, it would add up. The only way for the cyclist on the 26" wheel to travel the same distance at the same speed would be to pedal at a faster cadence.

So at first glance, it appears that the 700c wheel is the more efficient wheel.

However, I'm wondering about 2 things:

1) Have I neglected to account for wheel and tire diamater? I.e., a 26" tire generally has a higher profile than a 700c tire, so when you factor in the diameter of a 26" tire and wheel compared to a 700c tire and wheel, does that higher profile on the 26" tire compensate for the smaller diameter of the 26" wheel?

2) Is there some extra amount of energy that the cyclist on the 700c wheel is using to turn the crank one revolution due to the greater circumference of the 700c wheel?

One last question... Please try to convert your conclusions into lay English. ;)

Jerseysbest
09-03-06, 05:48 PM
I'm only a lay person who struggled to get a B in college physics. For the other person to travel at the same speed with a smaller wheel, yes, he would have to pedal faster, but he would have a mechanical advantage with the smaller wheel, just as you would being in a lower gear... So yeah, the person with the 700c wheel has to exert an extra amount of energy to travel at that speed, as if you were traveling in a higher gear.

asgelle
09-03-06, 06:22 PM
I would argue that a 700c wheel is more efficient than a 26" wheel, because given two cyclists turning their cranks and traveling at the same speed, the 700c wheel travels a farther distance with each revolution of the crank. The extra distance traveled may be small with only one revolution, but eventually, over miles, it would add up. The only way for the cyclist on the 26" wheel to travel the same distance at the same speed would be to pedal at a faster cadence.
Very good, you figured out gearing from the age of the high wheeler where the pedals turn the drive wheel directly. For those of us riding chain drive bikes with one or more gears, the gearing in the drive train removes the diameter from the wheel as a factor in how far the bike moves with one pedal revolution.

Nachoman
09-03-06, 06:23 PM
Here are a couple of articles addressing the issue.

http://www.precisiontandems.com/artdwanwheelsize.htm

http://www.precisiontandems.com/artbillwheelsize.htm

Falkon
09-03-06, 06:25 PM
fastest bicycle ever?
http://www.metzbicyclemuseum.com/sitebuilder/images/bike2-459x346.jpg

Cyclaholic
09-03-06, 06:32 PM
You are ignoring gearing. You can gear your 700c and 26" bikes so that at the same speed you're pedalling at the exact same cadence. Even if you're talking about the same gearing, the slightly higher cadence in turning the 26" wheel may actually be more energy efficient. Either way if all other parameters are equal, i.e. weight, frontal area, rolling resistance, etc. then your efficiency won't change.

DieselDan
09-03-06, 06:38 PM
If both the 700c and the 26" bikes were using the same chainring and rear cog, the 700 would go further. Rides using smaller wheels tend to need a larger big chainring.

Blue Order
09-03-06, 06:39 PM
Well, I assumed equal gearing in my question. If both bikes are traveling at the same speed, in the same gear, then the 700c bike should travel farther with each revolution. Of course the 26" can gear up or down, but so can the 700c cyclist. Therefore, assuming that they're in the same gear, and traveling at the same speed, the 26" cyclist would have to use a faster cadence to travel the same distance at the same speed.

My question really gets to the two questions I asked-- if the higher tire profile of the 26" is a factor, and if the 700c cyclist is burning more calories to travel the extra distance a 700c wheel travels.

asgelle
09-03-06, 06:52 PM
Well, I assumed equal gearing in my question. If both bikes are traveling at the same speed, in the same gear, then the 700c bike should travel farther with each revolution. Of course the 26" can gear up or down, but so can the 700c cyclist. Therefore, assuming that they're in the same gear, and traveling at the same speed, the 26" cyclist would have to use a faster cadence to travel the same distance at the same speed.

My question really gets to the two questions I asked-- if the higher tire profile of the 26" is a factor, and if the 700c cyclist is burning more calories to travel the extra distance a 700c wheel travels.
Well if they're in the same gear combination (front/rear) then isn't one (if not both) in the wrong gear? Why wouldn't the rider just shift into the proper gear? That is what they're there for. But moving on, if the 26" rider is using a faster cadence to match speed, as you say; then the 700C rider doesn't go any further, does she, and your final question doesn't make sense. But to answer the question as best I understand it, if the 700C rider rides further of faster, she will burn more calories than a slower rider on 26" wheels. Of course that has everything to do with the fact that she's riding faster or father, and nothing to do with the diameter of the wheels. Should you ask the question is a 26" wheel faster or slower than a 700C wheel, the answer of course is it depends.

TrackSmart
09-03-06, 07:33 PM
Hello there. I'm sure that if you had thought more carefully before posting, you would have put a much more exciting (and sensical) question forward. Here are some questions that you possibly meant to ask:

1) Are narrow tires more efficient than wider tires, given both have a smooth tread and are at full inflation pressure?
A) The wider tire may have similar rolling resistance to the narrow tire assuming both tires are pumped to proper inflation and have smooth tread. Some studies have even shown that 25mm and 28mm tires tend to have lower rolling resistance than 23mm tires However, for a bicyclist traveling at high speed, the largest force opposing them is AIR RESISTANCE, so the small difference in rolling resistance will be less important. The factors resposible for lower rolling resistance in tires are less understand than they should be (tire deformation, etc), but actual measurements of rolling resistance have shown that 23mm tires do not generally have less rolling resistance than 25 and 28mm tires. The evidence also shows that very little (if any) decrease in rolling resistance is gained on a good quality road tire by pumping it up past its rated inflation pressure. Might as well leave the tire at the intended pressure and have a better quality ride.

2. Followup to question one: Will a tall, skinny tire have less air resistance than a shorter, fatter tire? The skinny tire has less girth, but the shorter tire has less height.
A: ? All other things being equal, I suspect the skinner tire would be better than the shorter one given a 26 x 1.5" slick versus a 27 x 1" road tire. But I have not done the math or calculated the rotational movement or drag etc (My physics is rusty...). This presumes similar spoke types and similar tire construction.

3) Is wheel weight, or the weight of spinning components (cranks, chains) really dramatically more important than stationary weight on a bicycle?
A: http://www.diablocyclists.com/pauldec00.htm
Their conclusion (link above) is that at relatively constant speeds, wheel weight is not significantly different from other bike weight. The main advantage is during quick acceleration, which mostly happens during the first meters of a race. Over longer distances, it would not be as important. Certainly not 2-3 times more important than stationary weight, as the "myths" told by some on this website would have you believe.

Sorry for the long post, but those are wheel questions that are really interesting and that have always fascinated me. I presume you were going for some similar comparisons.

xlntRider79
09-03-06, 07:39 PM
lets say you had two bikes, one with 26" wheels and one with 700C wheels with no drivetrain and started riding them down a long, straight hill (emiminates the effect of drivetrain input, and gravity affects both riders the same): If the tires have have identical profiles, the guy on the 26" wheels wins because his tires have smaller frontal areas and shorter spokes, resulting in less air drag. (its also possible that the shorter wheel results in a shorter fork, which lets the rider get into a more aero position. Then he REALLY wins big. that's why Tri and TT guys run 650 instead of 700C in the front). However if the 26'er had fatty mountain bike tires, he would lose because those tires would generate more air drag.

asgelle
09-03-06, 07:41 PM
3) Is wheel weight, or the weight of spinning components (cranks, chains) really dramatically more important than stationary weight on a bicycle?
A: http://www.diablocyclists.com/pauldec00.htm
Or better http://www.biketechreview.com/archive/wheel_theory.htm

asgelle
09-03-06, 07:45 PM
lets say you had two bikes, one with 26" wheels and one with 700C wheels with no drivetrain and started riding them down a long, straight hill (emiminates the effect of drivetrain input, and gravity affects both riders the same): If the tires have have identical profiles, the guy on the 26" wheels wins because his tires have smaller frontal areas and shorter spokes, resulting in less air drag. (its also possible that the shorter wheel results in a shorter fork, which lets the rider get into a more aero position. Then he REALLY wins big. that's why Tri and TT guys run 650 instead of 700C in the front). However if the 26'er had fatty mountain bike tires, he would lose because those tires would generate more air drag.

You're also oversimplifying the effect of small front wheels. They make little difference when the there is no wind or the wind is directly head on. They only start to matter in crosswinds. This makes sense since it's easy to get a flat back with dual 700C wheels and dropping the shoulders below this point doesn't reduce frontal area but just exposes more of the back. With a crosswind, however, the lower position makes the body look more like an airfoil and drag is reduced.

TrackSmart
09-03-06, 07:55 PM
Or better http://www.biketechreview.com/archive/wheel_theory.htm

Yes, that's another great reference. Their conclusion:
"In summary, wheels account for almost 10% of the total power required to race your bike and the dominant factor in wheel performance is aerodynamics. Wheel mass is a second order effect (nearly 10 times less significant) and wheel inertia is a third order effect (nearly 100 times less significant)."

At speed it's all about wind resistance. Of course, the steeper the climb, the slower you will be riding and the greater the forces of gravity that need to be overcome, and hence the greater importance of overall weight (doesn't matter if the weight is on the bike or the rider). Mt Washington comes to mind. 7.6 miles up an 11% average grade at about 8 mph for the fastest riders. That's one of the few races where weight is truly king. In normal races, being aero takes priority.

MORAL: If you are going to shave weight, do it as cheaply as possible. It does not matter where the weight comes from. So first take it off the rider! Then off the cheapest bike components. Lastly, worry about those super-expensive and fragile wheels...

Blue Order
09-03-06, 08:10 PM
Hello there. I'm sure that if you had thought more carefully before posting, you would have put a much more exciting (and sensical) question forward. Here are some questions that you possibly meant to ask:Er, no.

...

Sorry for the long post, but those are wheel questions that are really interesting and that have always fascinated me. I presume you were going for some similar comparisons.Er, no again. But it's all good to know...

TrackSmart
09-03-06, 09:20 PM
Er, no.

...

Er, no again. But it's all good to know...

Sorry I was trying to be nice. I should just be cruel and wickedly honest. You asked a silly question. You might be ********. :D Kidding of course. But gearing makes your number-of-pedal-revolutions argument invalid. So...

1) You clearly wanted to know if a 700c wheel was more efficient than a 26" wheel.

2) The questions that I posed are the reasons that the two wheel sizes might be different (tire width, wheel height, wheel weight, rolling resistance, overall aerodynamic differences).

So, if these are the things that make the wheels different, wouldn't that naturally be what you'd want to learn about to decide which wheel size is more efficient and why? Maybe my reasoning in this is wrong and I'M the ******** one!? :D

Ha ha. I do like a good tech talk though. Of course I don't care a whit about this stuff in real life. Luddite that I am, I ride a 25-year-old steel touring bike with all original drivetrain and wheels.

xlntRider79
09-03-06, 09:43 PM

The OP asked for a simple answer! Once you take into a account contact patch size and sidewall deflection it gets complicated fast. I supposed (somewhat incorrectly) that the smaller tire (at equal inflation pressure on a smooth road) would deflect more and have higher resistance, but this is a constant factor, but I assumed air drag wins out every time because it varies as the square of velocity.

Interestingly, in Bicycling Science, 2nd ed. by Whitt and Wilson (a cool book, but pretty dated) There is a graph (Figure 5.10) showing that small wheeled bicycles (16 inch) are at a significant disadvantage vs. larger wheeled bikes (27 inch) at low speed (20% slower for the same power input at 10 mph), but that advantage exponentially decays as speed increases (it's about 4% at 25 mph)...so for 26 vs 700c, the difference is probably even smaller. So to follow up on my previous post, you'd have to be going down a really long hill to notice any difference.

Now on a rough road, the ratio of "roughness" to wheel diameter makes a huge contribution to the rolling resistance. But for that discussion, I'd check out the 29er vs 26er threads in the MTB forum

Blue Order
09-03-06, 09:54 PM
Sorry I was trying to be nice. I should just be cruel and wickedly honest. You asked a silly question. You might be ********. :D Kidding of course. But gearing makes your number-of-pedal-revolutions argument invalid.Gearing would only make it invalid if the rider on the 26" wheeled bike had gearing and the rider on the 700c geared bike had no gearing. Assume that both bikes have the exact same cranksets (same number of teeth on each chainring, same number of chainrings) and the exact same freewheels/freehubs (same number of cogs, same number of teeth on each cog). Each rider is able to gear up or gear down to the exact same gear combinations the other rider is able to gear up or down to. If that is the case, then the gearing is irrelevant, because as soon as the 26" wheeled rider gears up, or gears down, the 700c rider can and will do the same.

So...

1) You clearly wanted to know if a 700c wheel was more efficient than a 26" wheel.

2) The questions that I posed are the reasons that the two wheel sizes might be different (tire width, wheel height, wheel weight, rolling resistance, overall aerodynamic differences).

So, if these are the things that make the wheels different, wouldn't that naturally be what you'd want to learn about to decide which wheel size is more efficient and why? Maybe my reasoning in this is wrong and I'M the ******** one!? :D Your responses regarding resistance are good ones, and I didn't consider those factors, although they certainly figure into the equation. However, they do not address the questions I raised. I am not wondering what makes one wheel more efficient than the other; I am wondering if calories burned vary depending on wheel size (assuming that all other factors are equal)-- i.e., does it take more calories to push a 700c wheel than it does to push a 26" wheel, due to the extra distance traveled. If it does take more calories, then it would be a factor to consider in the efficiency question. On the other hand, if it takes exactly the same number of calories to push a 26" wheel as it does to push a 700c wheel, then the 700c wheel would be the more efficient (not accounting for resistance). I am also wondering if the higher profile of the 26" tire creates a tire/wheel diameter that is so close to the 700c tire/wheel diameter as to make the question moot.

Ha ha. I do like a good tech talk though. Of course I don't care a whit about this stuff in real life. Luddite that I am, I ride a 25-year-old steel touring bike with all original drivetrain and wheels.Hey, me too!

DieselDan
09-03-06, 10:07 PM
BTW: it's not about the bike.

DCCommuter
09-03-06, 10:57 PM
Assume that both bikes have the exact same cranksets (same number of teeth on each chainring, same number of chainrings) and the exact same freewheels/freehubs (same number of cogs, same number of teeth on each cog). Each rider is able to gear up or gear down to the exact same gear combinations the other rider is able to gear up or down to. If that is the case, then the gearing is irrelevant, because as soon as the 26" wheeled rider gears up, or gears down, the 700c rider can and will do the same.

I think this is the answer that you are looking for: If two riders are pedaling at the same cadence, and one is going faster than the other, the one who is going faster has to be pushing harder on his pedals -- and thereby burning more calories.

Having a bigger wheel is no different from shifting into a harder gear. If you shift into a harder gear, and keep up the same cadence, you go faster, but you have to work harder.

Wheel design is much more important than wheel size. The reason that most road bikes have 700c wheels is that most wheels designed for road use come in that size. Ken Kifer has a great riff on the subject:

One of the oddest tales, and also clear proof of how us cyclists let ourselves be pushed around, is the story of tire sizes. When I started riding as an adult, all the bikes had 26-inch tires. My first "10-speed" (6 useful gears) came with 27-inch tires, forcing me to buy tires at bike shops (which are hard to find on a tour). A dozen years ago came a "great" improvement created by shifting from 27-inch to 700 cc tires. Article after article raved about the improvement. The only difference I can see is the need to stop at a bike shop rather than Kmart. Then came a new shift, where to? -- the 26 inch bike; only the tires on this bike are a different size from the old 26 incher.

Since he wrote that, 29-er tires for mountain bikes have come along, and 650c tires for road bikes have been introduced, which are about the size of the other two type of 26" tires, but different.

TrackSmart
09-03-06, 11:06 PM
Assume that both bikes have the exact same cranksets (same number of teeth on each chainring, same number of chainrings) and the exact same freewheels/freehubs (same number of cogs, same number of teeth on each cog).

Your responses regarding resistance are good ones, and I didn't consider those factors, although they certainly figure into the equation. However, they do not address the questions I raised. I am not wondering what makes one wheel more efficient than the other; I am wondering if calories burned vary depending on wheel size.

The number of watts should be almost the same. So the answer to your question will, again, have only to do with 1) the gearing (i.e. mechanical advantage not the physical gears on the bike) that results from the wheel change and 2) what cadence our engine (aka the rider) is most efficient at pedaling.

Changing wheel size, while keeping all other factors equal, is the same thing as changing gears.

If we take a bike with 700c wheels and ONLY change wheel diameter to 26" - but nothing else - it just means that you have lowered all of your gears on the bike by the difference in wheel circumference. In this case, you have about 4 less gear-inches on the 26"-wheeled bike across your entire gear range.

Will the number of calories the rider burns change, even though the amount of work (watts) remains the same regardless of wheel size or gearing? Well, if a "human motor" is most fuel efficient at a cadence of 90 rpms, then the bike whose gearing allows them to stay within that cadence more often will be the most efficient in terms of calories per distance. Again, actual work (force x distance, measured in Watts) will be exactly the same. However, if the "engine" is more efficient at a particular cadence, it will burn less fuel at gearing allows it to pedal at 90 rpm - or whatever the ideal cadence is.

(PS: The most efficient cadence for a particular rider will vary. For some it will be 80 rpm. For those who have trained to ride at a higher cadence, it might be 120 rpm. Individual body physiology will also play a role in this.)

Blue Order, does that make sense? Do you understand the relationship between wheel size and gearing (aka mechanical advantage - not physical gears)?

Blue Order
09-03-06, 11:08 PM
I think this is the answer that you are looking for: If two riders are pedaling at the same cadence, and one is going faster than the other, the one who is going faster has to be pushing harder on his pedals -- and thereby burning more calories.

Having a bigger wheel is no different from shifting into a harder gear. If you shift into a harder gear, and keep up the same cadence, you go faster, but you have to work harder.That's what I suspected, but wasn't sure about. That answers the question. So when considering efficiency, in addition to distance traveled per revolution, one must also consider things like resistance and calories burned.

So the reason i was wondering all this is because I've decided to convert a mountain bike into a commuter, but I wasn't sure about the efficiency of those 26" wheels; when I started to think about it, I realized it was a more complicated question than just "distance traveled per revolution."

I wonder which wheel size is more efficient... :lol:

TrackSmart
09-03-06, 11:15 PM
I'm glad you used the laughing emoticon. Otherwise I might have taken you seriously and started to cry ;)

So you get it now. Wheel size = gearing. It's the reason why those guys back in the day (before chain drives) kept putting bigger wheels on the front of their bikes - you could get a higher gear with a bigger wheel!

Now you know why I thought this post by Falkon was HILARIOUS!:

Falkon: fastest bicycle ever?
http://www.metzbicyclemuseum.com/sitebuilder/images/bike2-459x346.jpg

Blue Order
09-03-06, 11:18 PM
The number of watts should be almost the same. So the answer to your question will, again, have only to do with 1) the gearing (i.e. mechanical advantage not the physical gears on the bike) that results from the wheel change and 2) what cadence our engine (aka the rider) is most efficient at pedaling.

Changing wheel size, while keeping all other factors equal, is the same thing as changing gears.

If we take a bike with 700c wheels and ONLY change wheel diameter to 26" - but nothing else - it just means that you have lowered all of your gears on the bike by the difference in wheel circumference. In this case, you have about 4 less gear-inches on the 26"-wheeled bike across your entire gear range.

Will the number of calories the rider burns change, even though the amount of work (watts) remains the same regardless of wheel size or gearing? Well, if a "human motor" is most fuel efficient at a cadence of 90 rpms, then the bike whose gearing allows them to stay within that cadence more often will be the most efficient in terms of calories per distance. Again, actual work (force x distance, measured in Watts) will be exactly the same. However, if the "engine" is more efficient at a particular cadence, it will burn less fuel at gearing allows it to pedal at 90 rpm - or whatever the ideal cadence is.

(PS: The most efficient cadence for a particular rider will vary. For some it will be 80 rpm. For those who have trained to ride at a higher cadence, it might be 120 rpm. Individual body physiology will also play a role in this.)And cadence will need to rise or fall, depending on wheel size, to maintain speed when mechanical advantage rises or falls, correct? So if I'm understanding this, a rider maintaining a cadence of 90 rpm on a bike with a higher mechanical advantage (bigger wheel) will ride farther (or faster) than a rider maintaining the same cadence on a bike with a smaller wheel. Therefore, the bike with the larger wheel will travel farther on the same output of energy, and is therefore more efficient. Is that correct?

EDIT: I think my conclusion is wrong. The energy output is not the same...

Blue Order, does that make sense? Do you understand the relationship between wheel size and gearing (aka mechanical advantage - not physical gears)?Yep! thanks!

vulcan
09-03-06, 11:25 PM
work in = work out

energy cannot be created nor destroyed

TrackSmart
09-03-06, 11:42 PM
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.

TrackSmart
09-03-06, 11:45 PM
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.

Blue Order
09-03-06, 11:46 PM
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?

TrackSmart
09-03-06, 11:57 PM
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 "extra" energy to travel the farther distance that the wheel travels on one revolution, while the motor that turns the smaller wheels will apply "extra" energy to turn the cranks at a faster cadence. In other words, both cyclists are expendintg 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!"

DannoXYZ
09-04-06, 12:19 AM
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?"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....

asgelle
09-04-06, 01:39 PM
work in = work out
How do account for steam engines?

vulcan
09-04-06, 06:48 PM
steam engines...

energy in = energy out

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

asgelle
09-04-06, 07:04 PM
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.
http://www.grc.nasa.gov/WWW/K-12/airplane/thermo1.html

TrackSmart
09-04-06, 07:07 PM
"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:

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...

vulcan
09-04-06, 07:10 PM
change in internal energy of the system = mostly heat loss, heat absorbed by the system that will later be dissipated.

DannoXYZ
09-04-06, 09:04 PM
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...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.

cooker
09-04-06, 10:34 PM
I am also wondering if the higher profile of the 26" tire creates a tire/wheel diameter that is so close to the 700c tire/wheel diameter as to make the question moot.

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.

geo8rge
09-05-06, 10:56 AM
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.

MMACH 5
09-05-06, 11:46 AM
All of this hub-bub makes me glad I still ride 27" tires. :p

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?

asgelle
09-05-06, 12:18 PM
The theory is that your heart rate correlates to your power output.
This is a very weak correlation even if all rides are done on the same day.

WorldWind
09-05-06, 01:10 PM
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”

diff_lock2
09-05-06, 04:45 PM
If both bikes are traveling at the same speed, in the same gear, then the 700c bike should travel farther with each revolution.
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