Smaller chain ring or shorter cranks ... or won't it matter?

[wafter]

I don't disagree with that; what I disagree with is the statement that it changes the ratio. Out of interest, do you have a selection of bikes with different-length cracks?

It depends on what you're including in the "ratio" definition - restricting it to just the mechanical parts of the bike or the whole rider / bike system. The latter is ultimately the one that really matters, although as posted previously the range of crank length typically available is that little that it has minimal effect on effective gearing.

I currently have bikes with 165, 170 and 172.5mm cranks; while one of those with 170mm cranks came to me with 175mm... I'd like to replace the longest for unrelated reasons and if I ever find something suitable the default will be 170mm, although I'll consider shorter if necessary (availability etc).

It does not change the ratio, it may or may not change the effort required, a 52x13 is 108 inches on a 700c wheel I think, changing cranl length makes no difference to that equation.

It does change the required effort; that's precisely the point.

Consider a worked example with some extreme measurements for the sake of illustration.

Assume the most effort an 80kg rider can put into the pedal is their own body weight; we'll call it 800N of downward force / load for ease. Applying this to a 150mm crank at the point of greatest mechanical advantage (90 degrees past top-dead-centre of the crank stroke) gives a torque at the crank axle of 0.15*800 = 120Nm. Applying the same load to a 200mm crank arm gives a torque of 160Nm.

Based on a chain pitch of half an inch a 50T chainring has an effective circumference of 50*0.5" = 25" or around 635mm. This equates to an effective radius of 635 / (2*PI) = c.100mm.

The torque at the crank axle generated by the crank arm gives a pulling force on the chain of 120/0.1 = 1200N for the 150mm crank and 160/0.1 = 1600N for the 200mm item.

For the sake of ease let's say we have a 25T sprocket selected at the rear, which will have an effective radius of half that of the 50T job on the front; so 50mm. When subject to the pulling force from the chain this will generate a torque around the rear axle of 1200*0.05=60Nm for the 150mm crank, while the 200mm crank will give a rear axle torque of 1600*0.05=80N.

Finally, the rear wheel has an effective radius of 330mm, so for the 60Nm provided to the rear axle from the 150mm crank it generates 60/0.33 = 45N of force at the tyre's contact patch to propel the bike forwards. Conversely for the 200mm crank this force is 80/0.33 = 60N.

Hence, with the same gearing selection and all other things being equal the bike with the longer crank will accelerate around 1.3 times faster, or will be able to climb gradients 1.3 times steeper for the same amount of rider effort; biomechanical effects of the longer crank notwithstanding.

So if you wanted the two bikes to perform in the same manner with the different crank lengths the gear ratios would need to be changed to maintain the same relationship between force input at the pedal and force output at the tyre - which is the only reason bikes are fitted with gears in the first place..

 

[bobzmyunkle]

Shorter cranks or lower gears. I'd go for both, cause I'm a shortarse and a 10 stone weakling. Really 2 different things though.
Strikes me opinions on here need to be taken with a (large) pinch of salt.

 

[Alex321]

Technically, it does alter the gear ratio. As I said above, with shorter cranks your foot travels a shorter distance, and the gear ratio is distance travelled at the output divided by the corresponding distance travelled at the input.

No it doesn't, and no it isn't.

The gear ratio has a specific meaning, and it is the ratio between number of revolutions of the input and number of revolutions of the output.

https://www.collinsdictionary.com/dictionary/english/gear-ratio
https://dictionary.cambridge.org/dictionary/english/gear-ratio
https://www.merriam-webster.com/dictionary/gear ratio

The length of the lever driving the input gear has no bearing on the ratio, but it does affect the effort required to turn the input gear.

 

[Ming the Merciless]

More on why shorter cranks are better

https://www.pinkbike.com/news/why-shorter-cranks-are-better-according-to-science.html

 

[screenman]

It depends on what you're including in the "ratio" definition - restricting it to just the mechanical parts of the bike or the whole rider / bike system. The latter is ultimately the one that really matters, although as posted previously the range of crank length typically available is that little that it has minimal effect on effective gearing.

I currently have bikes with 165, 170 and 172.5mm cranks; while one of those with 170mm cranks came to me with 175mm... I'd like to replace the longest for unrelated reasons and if I ever find something suitable the default will be 170mm, although I'll consider shorter if necessary (availability etc).


It does change the required effort; that's precisely the point.

Consider a worked example with some extreme measurements for the sake of illustration.

Assume the most effort an 80kg rider can put into the pedal is their own body weight; we'll call it 800N of downward force / load for ease. Applying this to a 150mm crank at the point of greatest mechanical advantage (90 degrees past top-dead-centre of the crank stroke) gives a torque at the crank axle of 0.15*800 = 120Nm. Applying the same load to a 200mm crank arm gives a torque of 160Nm.

Based on a chain pitch of half an inch a 50T chainring has an effective circumference of 50*0.5" = 25" or around 635mm. This equates to an effective radius of 635 / (2*PI) = c.100mm.

The torque at the crank axle generated by the crank arm gives a pulling force on the chain of 120/0.1 = 1200N for the 150mm crank and 160/0.1 = 1600N for the 200mm item.

For the sake of ease let's say we have a 25T sprocket selected at the rear, which will have an effective radius of half that of the 50T job on the front; so 50mm. When subject to the pulling force from the chain this will generate a torque around the rear axle of 1200*0.05=60Nm for the 150mm crank, while the 200mm crank will give a rear axle torque of 1600*0.05=80N.

Finally, the rear wheel has an effective radius of 330mm, so for the 60Nm provided to the rear axle from the 150mm crank it generates 60/0.33 = 45N of force at the tyre's contact patch to propel the bike forwards. Conversely for the 200mm crank this force is 80/0.33 = 60N.

Hence, with the same gearing selection and all other things being equal the bike with the longer crank will accelerate around 1.3 times faster, or will be able to climb gradients 1.3 times steeper for the same amount of rider effort; biomechanical effects of the longer crank notwithstanding.

So if you wanted the two bikes to perform in the same manner with the different crank lengths the gear ratios would need to be changed to maintain the same relationship between force input at the pedal and force output at the tyre - which is the only reason bikes are fitted with gears in the first place..

As I wrote, it does not change the gear ratio.

 

[roubaixtuesday]

As I wrote, it does not change the gear ratio.

It does, however, change the ratio of force at the pedal to force atv the tyre.

Which could also be a relevant ratio.

And the angle at the knee.

Which could also be relevant.

 

[screenman]

It does, however, change the ratio of force at the pedal to force atv the tyre.

Which could also be a relevant ratio.

And the angle at the knee.

Which could also be relevant.

I have not disagreed with the force needed, only the gear ratio bit. For me I generate more power with shorter cranks and find them more comfortable.

 

[EckyH]

I'm aware that the cause of the problem is my fitness but at nearly 70 years of age and 108kg in weight (down from 136kg) that's not going to improve significantly so I'm looking for a mechanical way out.

Your weight loss is more than just remarkable. Well done.

But I'm afraid that there is no mechanical magic. Being in the same weight range as you are at the moment (down from 120something) and in the early 50s I can comprehend your experiences: keeping the cadence is similar difficult as pushing higher gears, but different. Probably it is a bit easier to work on the higher cadence, but with patience. Then shorter cranks could be helpful to spin lighter gears a bit faster. Assuming that your position on your bicycle is good, I'd try to deliberately choose a slightly lower gear on a section where you can comfortably ride and try to reach your usual speed - for example if your usually riding around 25km/h on 39:18, choose 50:24 instead. Over time it will become easier.

Hope that helps.

E.

 

[wafter]

As I wrote, it does not change the gear ratio.

But you do understand that the gear ratio as you refer to it is only part of a number of variables that affect the ratio of forces between pedal and tyre, and that crank arms of different lengths will require different gear ratios to maintain this relationship...?

 

[Bristolian]

Cheers everyone for your input. This has become far more technical than I imagined it would and I'm still not entirely sure of the answer

Whatever the science of shorter cranks, there are plenty of articles in the cycling press and from cycling coaches, both here in the UK and elsewhere, that suggest shorter cranks would help me with my problem. My very simplistic understanding of gear ratios says that is all it is - the ratio between the number of teeth on the chainring divided by the number of teeth on the rear cog and torque/force/rotational speed can't change that. In my case the top gear ratio on the bike is 4.545:1 (i.e. 50/11) so for every pedal revolution the rear wheel will rotate 4.545 times and that doesn't change whether I apply 1kgf or 100kgf to the pedals.

Of course, that's not my real problem; which is a lack of basic fitness and leg strength/endurance in particular which limits the amount of time/distance I can excerpt sufficient pedalling force before needing to change to a lower (easier) gear. Even as a youngster I wasn't able to ride at a high cadence - my average has always been in the 74-78rpm region - but back then I could overcome that by having the power in my legs to grind out high gears. Alas that is no longer the case

My days of racing bicycles are long gone - nearly 50 years have elapsed since my last race - and I have resigned myself to the fact I'm not as quick as I was back then so ultimate speed isn't important to me. What I do want to be able to do though is to overcome the result of decades of not riding by easing the effort needed to maintain my cadence on what are, to all intents and purposes, flat roads.

As a replacement chain ring is somewhat cheaper than a crank set I think I'm going to try that and see how it goes.

 

[screenman]

But you do understand that the gear ratio as you refer to it is only part of a number of variables that affect the ratio of forces between pedal and tyre, and that crank arms of different lengths will require different gear ratios to maintain this relationship...?

Force ratio, is that what you are talking about?

 

[screenman]

Cheers everyone for your input. This has become far more technical than I imagined it would and I'm still not entirely sure of the answer

Whatever the science of shorter cranks, there are plenty of articles in the cycling press and from cycling coaches, both here in the UK and elsewhere, that suggest shorter cranks would help me with my problem. My very simplistic understanding of gear ratios says that is all it is - the ratio between the number of teeth on the chainring divided by the number of teeth on the rear cog and torque/force/rotational speed can't change that. In my case the top gear ratio on the bike is 4.545:1 (i.e. 50/11) so for every pedal revolution the rear wheel will rotate 4.545 times and that doesn't change whether I apply 1kgf or 100kgf to the pedals.

Of course, that's not my real problem; which is a lack of basic fitness and leg strength/endurance in particular which limits the amount of time/distance I can excerpt sufficient pedalling force before needing to change to a lower (easier) gear. Even as a youngster I wasn't able to ride at a high cadence - my average has always been in the 74-78rpm region - but back then I could overcome that by having the power in my legs to grind out high gears. Alas that is no longer the case

My days of racing bicycles are long gone - nearly 50 years have elapsed since my last race - and I have resigned myself to the fact I'm not as quick as I was back then so ultimate speed isn't important to me. What I do want to be able to do though is to overcome the result of decades of not riding by easing the effort needed to maintain my cadence on what are, to all intents and purposes, flat roads.

As a replacement chain ring is somewhat cheaper than a crank set I think I'm going to try that and see how it goes.

I get my shorter cranks from Spa Cycles.

 

[Ming the Merciless]

But you do understand that the gear ratio as you refer to it is only part of a number of variables that affect the ratio of forces between pedal and tyre, and that crank arms of different lengths will require different gear ratios to maintain this relationship...?

The force that can be applied at the pedal will vary depending on the applicable angle of the legs. That angle will change over the period of a pedal stroke (and vary more for longer cranks) and is not a fixed value through the full pedal stroke. Plus the relative energy cost is lower for the shorter cranks. With shorter cranks it is easier to maintain a higher cadence. As per link above with shorter cranks you can put out higher power numbers.

 

[wafter]

Force ratio, is that what you are talking about?

Yes, which is what the gearing is there to control..

 

[Ming the Merciless]

Force ratio, is that what you are talking about?

Torque if you want to use the mathematical term. But remember that the maximum force that can be applied is also determined by the angle of the legs. Plus not a fixed value but varies through the pedal stroke. It is not necessarily the case that the average torque over the pedal stroke reduces when you use shorter cranks. We are also dealing with biology here.