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Discussion Starter · #1 ·
Longer is better for SS. (Starting the crank wars again :) )

I start with the idea that there are two modes of using the cranks on an SS. One is the usual sitting and pedaling on the flats to an interesting destination. The other is standing and applying greater force to the cranks - usually climbing, but maybe just for acceleration.

When standing one applies body weight and more force by pulling the handlebar up. One then tries to apply this maximum force to the "sweet spot" of a nearly level crank. Let's designate the sweet spot by an angle through which the crank moves, the actual angle could be different for each rider but just for argument say it's 45 degrees.

The arc length through which the crank moves increases as the crank length increases. If the rider applies his usual maximum force then the total energy transferred to the bicycle is greater with a longer crank. Energy (Work) = Force * Distance.

This energy has to show up as greater distance climbed per stroke or greater acceleration per stroke. The rest of the pedal stroke is wasted energy, just an effort to return the pedal to a position for another push down. If the rider with shorter cranks increases the RPM to catch up in terms of Energy (Work) transferred then he will have more wasted strokes and therefore be less efficient.

Knee damage is brought up in context of applying force (maximal?) throughout the pedal's travel. I am self-regulating in that respect, I don't try to pull hard.

There is another possibly secondary effect of smaller cranks and higher RPM's. Knee damage occurs when maximal force is applied to an immovable object. A crank at the bottom of the stroke is immovable. With higher RPM's the rider's timing to "left off" the force becomes critical. Equally important is to not apply force too soon at the top, higher RPM's are a problem here too.

What about "spinning out" on the flats? Yes it does occur, yes I can ankle it to make my foot move less than the pedal. But on most slopes I find that a full aerodynamic tuck beats pedaling (especially a spinning SS with shorter cranks) and it takes no energy. :)
 

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Sure, you'll be in that "sweet arc" for a longer period of time, but it will also take a longer period of time for the pedal to come around into that sweet spot again - so you'll able be out of the sweet spot for a greater period of time.

And as for your knees, longer cranks mean lower seat height in order to reach the bottom of the stroke, which means your knees need to bend even more at the top of the stroke.

I'm only building my first SS MTBike, so I don't really have a preference yet, just playing devil's advocate. I do plan on using 175mm though. (Actually, I did race BMX for quite a few years and my last bike had 180mm cranks, but when I built that bike I was only 14 and the only reason I put on 180mm cranks (Redline Flight cranks) was because I thought it would be "cooler" than 175mm)

Later,
Greg
 

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Discussion Starter · #3 ·
Gregzilla said:
Sure, you'll be in that "sweet arc" for a longer period of time, but it will also take a longer period of time for the pedal to come around into that sweet spot again - so you'll able be out of the sweet spot for a greater period of time.
Why would you assume it takes a longer time? Same RPM's means the same time for the pedal to come around. The sweet spot could come around faster for a more efficient rider who can sustain higher RPM's.

Gregzilla said:
And as for your knees, longer cranks mean lower seat height in order to reach the bottom of the stroke, which means your knees need to bend even more at the top of the stroke.
Two modes of pedaling.

Standing: The seat height is irrelevant. I could reach the ground if necessary. :D

Seated: "I can ankle it to make my foot move less than the pedal." that limits the knee flex.
 

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I had a long response typed up and then the server ate it....

So what I was trying to say, is look at your physics again, but don't look at RPMs - you need to look at the actual linear speed of the pedal. To hold a certain RPM with a longer crank you need to move your feet faster, since for each revolution it will have to travel a greater distance.

Also, you've got it backwards - you should hold work constant. Right now you thinking is plagued with "free lunchism".

There's really no free lunch with crank lengths. Your cranks and drivetrain are just a system of linked lever arms. You can make changes to any part of the system and get the same net effect. In other words, increasing your crank length 10% is pretty much the same as decreasing your chain ring size 10% or increasing your cog 10% or decreasing your wheel size 10%.

There will be a minor change in tempo, but that is offset by the amount of power stroke. So if I'm on 170's and you're on 180's, but we have the same overall gain ratio (in other words my gear is 5% lower), the force we both apply on the pedal will be the same. For every 100 pedal stokes you do, I'll do 105, however each one will be shorter in duration.
 

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I've ridden both and I laugh everytime someone thinks 180mm is some quantum leap better. It's 5 friggin milimeters, big deal, I didn't notice a difference, but I don't seem to obsess over equipment like most in this forum.
 

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university physics 211, classical mechanics

you only talked about energy/work in your post--this my friend is not correct. if in two separate occassions you ride on the same trail surface under the same conditions at the same speed on two different bikes, then you are keeping a constant POWER (energy output per unit time), not merely doing the same amount of work.

power = torque around BB * angular frequency/RPM

where torque = (force on pedal)*(crank arm length)

your mistake is that you assumed the force on the pedal to be the same regardless of crank arm length. that means if the rider changed to a crankset of 180mm from one of 170mm, with other things unchanged, his power must increase to 180/170 times his original power in order to achieve the same RPM. in layman terms he has to work harder.

in other words, for the same rider, the power of the rider is the same when he rides two bikes with different crank arm lengths. that means (force on pedal)*(crank arm length)*(RPM) is constant. given the same RPM, as you assume, force*length is constant. that means the force on pedal is NOT the same when length changes.

if you assume the sweet spot is about 45 degrees, the fraction of power output that is optimized is simply 1/8 of the total (because in each complete cycle 1/8 of the cycle is optimized)--independent of crank arm length.
 

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P.S. the difference between power and work is,

if in two separate occassions you ride on the same trail surface under the same conditions **at the same speed** on two different bikes, then you are keeping a constant POWER (energy output per unit time)

if you ride on the same trail surface under the same conditions **for the same distance regardless of speed** on two different bikes, you are doing the same amount of WORK.
 

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Discussion Starter · #8 ·
weather said:
you only talked about energy/work in your post--this my friend is not correct. if in two separate occassions you ride on the same trail surface under the same conditions at the same speed on two different bikes, then you are keeping a constant POWER (energy output per unit time), not merely doing the same amount of work.
The big if is "same speed". I claim the gain means that longer cranks climb faster.
Put the same force on these setups:

175mm with 32x20
180mm with 33x20 (change is ~3% longer crank with ~3% higher gearing)

The changes cancel out so the same force on each crank will produce the same torque on the cog. But for each revolution the 180mm 33x20 moves the bike more, and the energy model agrees because the same force is applied to a longer stroke.

weather said:
your mistake is that you assumed the force on the pedal to be the same regardless of crank arm length. that means if the rider changed to a crankset of 180mm from one of 170mm, with other things unchanged, his power must increase to 180/170 times his original power in order to achieve the same RPM. in layman terms he has to work harder.
The force is the same regardless of crank length. When standing the rider is putting his entire body weight on the crank. Gravity doesn't care what the crank length is. Look at it in terms of converting potential energy to kinetic energy. The rider "falls" a greater distance with each stroke, imparting more energy to the bicycle. The rider builds up the potential energy on the idle part of the stroke..
 

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pacman said:
The big if is "same speed". I claim the gain means that longer cranks climb faster.
Put the same force on these setups:

175mm with 32x20
180mm with 33x20 (change is ~3% longer crank with ~3% higher gearing)

The changes cancel out so the same force on each crank will produce the same torque on the cog. But for each revolution the 180mm 33x20 moves the bike more, and the energy model agrees because the same force is applied to a longer stroke.
So you have a 3% longer stroke to go 3% farther. Net gain is nothing. You're just doing more work, less often. A longer power stroke at a slower cadence. A longer crank doesn't magically give you more energy.

Or look at it another way. The same force on the cog means the same propulsive force on the ground. That's the force moving the bike over a certain distance. Or in other words, over a given distance, with the same force propelling the bike, the energy needed to move them that distance is the same.
 

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pacman said:
The big if is "same speed". I claim the gain means that longer cranks climb faster.
Put the same force on these setups:

175mm with 32x20
180mm with 33x20 (change is ~3% longer crank with ~3% higher gearing)

The changes cancel out so the same force on each crank will produce the same torque on the cog. But for each revolution the 180mm 33x20 moves the bike more, and the energy model agrees because the same force is applied to a longer stroke.
you said the force on pedal is the same, let's call it F. the torque around BB is (F*180mm) so that at RPM w, your total power is (F*180mm*w). for 175mm crank, your power is (F*175mm*w). of course you are going faster---you are upping your power! it's not the crank but rather yourself. under the same power, with an increased crank arm length, either your RPM will be lower or force on pedal will be lower.

pacman said:
The force is the same regardless of crank length. When standing the rider is putting his entire body weight on the crank. Gravity doesn't care what the crank length is. Look at it in terms of converting potential energy to kinetic energy. The rider "falls" a greater distance with each stroke, imparting more energy to the bicycle. The rider builds up the potential energy on the idle part of the stroke..
when force is the same (assuming you are standing and NOT pulling on the bar), your RPM is slower. simple energy conservation--you won't get more than what you put in.
 

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pacman said:
Longer is better for SS. (Starting the crank wars again :) )...
All circles are comprised of 360 degrees. A longer crank covers more ground to turn 1/8th of a circle and that's just another way of saying leverage is increased. But so is torque, which seems to be the ignored aspect that is left out of the "long cranks have the same effect as lowering gearing" argument -- long cranks are not the same as running a lower gear, not the same at all.

Pacman, personally I agree with you, as evidenced by the fact that I run 195mm cranks on my singlespeed. (On my gearie, too, for that matter.) But then, I have long legs. A couple of my other bikes are equipped with 202mm cranks.

I say, "Run whatever cranks feel best for you." Trouble is many folks are too close-minded to consider anything outside their comfort zones, or to consider anything that threatens their dearly-held confidence in the investment they've already made in whatever they currently own.

Whatever. Frame and component manufactures really don't want the world trying to find a way to include one more sizing factor in the bike-fit equation anyway. That's more work and expense for them.

--Sparty
 

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pacman, if you are still confused, go to your local university (california lutheran university?) and ask a physics or engineering professor. they'll tell you the same thing (and make sure you post here after you ask). longer crank arms won't magically give you more power, otherwise we won't need all those nuclear power plants. we only need a million pairs of 20-ft long cranks.

ED: longer cranks might be beneficial--but not for the reason pacman stated.
 

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Discussion Starter · #15 ·
weather said:
when force is the same (assuming you are standing and NOT pulling on the bar), your RPM is slower. simple energy conservation--you won't get more than what you put in.
Energy is always Force*Distance regardless of speed (RPM). If I put in a longer stroke I supply more energy, and the result is a greater speed at the end of the stroke. Yes, I put in more and get more. :)
 

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you do the same thing with a shorter crankset too. you supply more energy in the same amount of time (larger force on pedal or higher RPM) , you speed up. in this aspect a 110mm crankset and a 220mm crankset perform exactly the same.

so far you only proved that longer cranks motivate you to crank harder.
 

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Discussion Starter · #17 ·
weather said:
pacman, if you are still confused, go to your local university (california lutheran university?) and ask a physics or engineering professor. they'll tell you the same thing (and make sure you post here after you ask). longer crank arms won't magically give you more power, otherwise we won't need all those nuclear power plants. we only need a million pairs of 20-ft long cranks.

ED: longer cranks might be beneficial--but not for the reason pacman stated.
They would tell me to run a thought experiement. How well would I pedal with 50 mm cranks. I would say that I would waste a lot of energy just moving my feet around for the next mini-stroke and that stroke would be pitiful due to the short stroke length. So obviously something longer than 50mm is needed, or even longer than 75mm etc. , longer until the losses outweigh the gains.
 

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sorry, "i would say" is not a proof. if you think energy is wasted by pedaling 50mm cranks, show how it is and where the loss goes to--you have not done it so far. please also show why pedaling 180mm cranks is not wasting the energy for the same reason--you have not done this either.
 

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Chaos theory?

Sparticus said:
All circles are comprised of 360 degrees. A longer crank covers more ground to turn 1/8th of a circle and that's just another way of saying leverage is increased. But so is torque, which seems to be the ignored aspect that is left out of the "long cranks have the same effect as lowering gearing" argument -- long cranks are not the same as running a lower gear, not the same at all.

Pacman, personally I agree with you, as evidenced by the fact that I run 195mm cranks on my singlespeed. (On my gearie, too, for that matter.) But then, I have long legs. A couple of my other bikes are equipped with 202mm cranks.

I say, "Run whatever cranks feel best for you." Trouble is many folks are too close-minded to consider anything outside their comfort zones, or to consider anything that threatens their dearly-held confidence in the investment they've already made in whatever they currently own.

Whatever. Frame and component manufactures really don't want the world trying to find a way to include one more sizing factor in the bike-fit equation anyway. That's more work and expense for them.

--Sparty
I think the problem with trying to figure crank length using physics is there are too many variables. You have the frame design, seat position, seat height, femur length, fibula/ tibia length, fast/slow twitch muscles, age, cardio conditioning, blah, blah, blah. Now let's throw in some physics and personal preferences and ...my head hurts. I have a track bike with 166.5 mm cranks, a tandem and a couple of geared mountain bikes with 175mm cranks and a SS mountain bike with 180's. As I have mentioned before, I used to use one of my geared MTB to pull an Alley Cat (read, third wheel kid trailer) up the local heartbreak hill (I pretty much stay in a 36:28 gear) and found the 175's easier to spin than the 180's (yeah I know, no surprises there). Anyway, I figure there are so many variables that using pseudo physics to justify 5 mm seems pretty silly. I am the local bike expert at work, so everyone asks me, "What bike should I buy?" My answer, go to the bike shops, ride the bikes; when you find one you like take it were you are going to do most your riding, if you still like it pay as much as you can afford for the better components. I'll leave the physics (read, custom frame design) to Paul Sadoff at Rocklobster.

Missed you at the Otter, Sparty :(

1G1G, Brad
 

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pacman said:
They would tell me to run a thought experiement. How well would I pedal with 50 mm cranks. I would say that I would waste a lot of energy just moving my feet around for the next mini-stroke and that stroke would be pitiful due to the short stroke length. So obviously something longer than 50mm is needed, or even longer than 75mm etc. , longer until the losses outweigh the gains.
Why are you wasting energy pedaling small circles and not big ones? What is intrinsically wasteful about a small circle? Where is that waste going? You said earlier that you use your ankles more with long cranks? Why are you wasting all of that ankle motion?

And anyway, this is a straw man argument. We're not talking about running cranks completely outside of reasonable biomechanics. You should be doing the thought experiment of "If I double my crank length, which by my theory will double the energy output, how will my body supply that energy?"

You still haven't explained where this energy is coming from. Are you just getting tired faster?
 
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