Comparing gears and the impact of wheel size

[Cudzoziemiec]

The stair analogy seems quite a good one, but I'm not entirely sure if it's an analogy for crank length or gearing. After all, riser height equates directly to distance covered. (FWIW, I'd usually find it easier and faster to climb on large steps than small ones if going up but short ones if going down; so maybe it's not much of an analogy after all!)

[tom_e]

But the length of the crank has no actual effect on the gearing, no more than does the length of your legs.

Semantics.  You can get more peak torque on a longer crank.  You can turn a shorter crank at higher rpm.  Call it 'leverage' if you like rather than gearing.  It affects what sprockets you want on the bike.  Though the conventional crank length variants are so similar the % is small.

In fact, if you go with the conventional (non-cycling) definition of gearing then you shouldn't be taking the wheel size into account either.

[Kim]

In fact, if you go with the conventional (non-cycling) definition of gearing then you shouldn't be taking the wheel size into account either.

Exactly.  You normally either care about the gears, or the whole system, depending on what you're measuring.  This gears-and-wheel measurement thing is odd.

[Cudzoziemiec]

You have to exert a greater force on the pedal to turn the same gear, because you've shortened the second order lever that is your crank. 

From what I've read and from my experience using shorter cranks over the last few months, short cranks make it easier to spin lower gears at the same speed. My theory is that they should also help me get lower on the TT bike without my knees hitting my nipples.

But the length of the crank has no actual effect on the gearing, no more than does the length of your legs.

Using an automotive analogy, changing the length of the con rod alters the engines ability to rev, or to deliver torque, but makes absolutely no difference to the final drive.

I think Sheldon Brown's idea is interesting in that it helps understand how crank length affects power delivery,  but as regards bicycle gearing I think it's inappropriate and just muddies the water. 

FWIW I've used cranks from 160 all the way to 175 and never noticed any difference. 

A few weeks ago I realised I had been riding one of my bikes with a 170 chainset and a 175 LH crank. I'd swapped over the chainset, got distracted and forgot to change the other side.  How would you work out the  "gain ratio" for that set up!   

It changes the distance your feet move through to move the bike X distance on the road, which is the point of gearing.  It does this not by changing the number of circles your legs move through to move the bike X distance, but by changing the size of the circles. 

If you halve your crank length, your feet will move at half the speed in order to keep the bike moving at a constant speed Y, and cover half the distance over distance travelled X.  In order to do this, you will have to apply twice the force Z.  This is exactly the same as happens if you double the size of your chainring, or half the size of your rear sprocket.

Thanks, Pharti, you've just explained it clearly (for my brain, at least).

[Morat]

Without knowing much (at all) about gearing, I tend to rely on this excellent little app
https://play.google.com/store/apps/details?id=com.gearcalculator&hl=en_GB
(Android)
which is free and seems to be able to convert between all the measurements mentioned in the thread so far.
It also makes very satisfying clicking noises

[Ningishzidda]

Metric measurements ( Base 10 ) became the sensible way of going about things because they worked in ONE base, base 10.

English measurements were quite ridiculous, with 12 inches to a foot, and 3 feet to a yard, and 220 yards to a furlong, and 8 furlongs to a mile, let alone rods, poles and chains.

1 metre had 1000 mm. The metre was subdivided into 10, which was 100mm; or 100, which is 10mm, or a centimetre.

English money was the same, multiple bases to add up, and then work out how much change from a Quid.
Once upon a time, there were three currencies operating in England concurrently. Marks, Libres and Groats.

The UK changed to decimal currency because at the time, computerised cash registers couldn’t handle multiple base calculations. Computers operate on base 2, and it’s a simple multiplier to operate in base 10 all the way.

Bicycles operate in base 2. Two legs, two wheels and two handlegrips.

[Highlander]

You have to exert a greater force on the pedal to turn the same gear, because you've shortened the second order lever that is your crank. 

From what I've read and from my experience using shorter cranks over the last few months, short cranks make it easier to spin lower gears at the same speed. My theory is that they should also help me get lower on the TT bike without my knees hitting my nipples.

But the length of the crank has no actual effect on the gearing, no more than does the length of your legs.

Using an automotive analogy, changing the length of the con rod alters the engines ability to rev, or to deliver torque, but makes absolutely no difference to the final drive.

I think Sheldon Brown's idea is interesting in that it helps understand how crank length affects power delivery,  but as regards bicycle gearing I think it's inappropriate and just muddies the water. 

FWIW I've used cranks from 160 all the way to 175 and never noticed any difference. 

A few weeks ago I realised I had been riding one of my bikes with a 170 chainset and a 175 LH crank. I'd swapped over the chainset, got distracted and forgot to change the other side.  How would you work out the  "gain ratio" for that set up!   

It changes the distance your feet move through to move the bike X distance on the road, which is the point of gearing.  It does this not by changing the number of circles your legs move through to move the bike X distance, but by changing the size of the circles. 

If you halve your crank length, your feet will move at half the speed in order to keep the bike moving at a constant speed Y, and cover half the distance over distance travelled X.  In order to do this, you will have to apply twice the force Z.  This is exactly the same as happens if you double the size of your chainring, or half the size of your rear sprocket.

I suspect we're not going to agree on this but I'll have another go at explaining why I don't consider crank length to be part of the gearing.

The point of gearing is not to "change the distance your feet move" to move the bike a given distance, it is to change the rate at which your legs move, ie your cadence.   Crank length makes no difference to cadence.

If you change the crank length yes your foot speed changes, but your legs, the power unit,  will be going up and down at the same rate.  The only thing that can affects the rate at which your legs move is the chainring size, the sprocket size, or the wheel/tyre size.   

The cranks are a lever to convert power through the gearing system.  A longer/shorter lever might affect the efficiency of the power delivery but you are not pedalling a higher gear when you use shorter cranks.

Apart from my own asymmetric crank example, what about a tandem with different crank sizes?  Are the captain and stoker pedalling different gears?

 

 

[Kim]

The point of gearing is not to "change the distance your feet move" to move the bike a given distance, it is to change the rate at which your legs move, ie your cadence.   Crank length makes no difference to cadence.

It's not about the distance or the rate per se.  It's about the force exerted on the pedals (and hence produced by muscles and inflicted on the joints) - that's what causes fatigue/damage.

If you change the crank length, the force changes. 

Apart from my own asymmetric crank example, what about a tandem with different crank sizes?  Are the captain and stoker pedalling different gears?

Yes, obviously.


See also an ordinary or unicycle with short cranks to increase the gearing.

[Morat]

Metric measurements ( Base 10 ) became the sensible way of going about things because they worked in ONE base, base 10.

English measurements were quite ridiculous, with 12 inches to a foot, and 3 feet to a yard, and 220 yards to a furlong, and 8 furlongs to a mile, let alone rods, poles and chains.

1 metre had 1000 mm. The metre was subdivided into 10, which was 100mm; or 100, which is 10mm, or a centimetre.

English money was the same, multiple bases to add up, and then work out how much change from a Quid.
Once upon a time, there were three currencies operating in England concurrently. Marks, Libres and Groats.

The UK changed to decimal currency because at the time, computerised cash registers couldn’t handle multiple base calculations. Computers operate on base 2, and it’s a simple multiplier to operate in base 10 all the way.

Bicycles operate in base 2. Two legs, two wheels and two handlegrips.

I don't think maths was a great consideration when Imperial units were dreamt up. I'd guess it was more a system designed to standardise everyday objects which were then defined in relation to each other in whatever ratio that would fit, near enough.
Counting, yes: Maths.. not so much.

If you turned up to a village in the Dark Ages and started talking about Base 10 and common factors you'd probably have been burnt for sorcery or pitchforked or something.

[Jurek]

I think this may be a contender for 'Most boring thread.
Ever'.

Really.
ETA - Albeit it didn't start out as that.

[quixoticgeek]

I think this may be a contender for 'Most boring thread.
Ever'.

Really.
ETA - Albeit it didn't start out as that.

I've found this thread very interesting.

Obviously we are all different.

J

[Jurek]

I think this may be a contender for 'Most boring thread.
Ever'.

Really.
ETA - Albeit it didn't start out as that.

I've found this thread very interesting.

Obviously we are all different.

J

That's fair enough 

[ElyDave]

I think the inherent issue here is the use of different ratios to mean the same thing with no real world context without another conversion factor to get to speed/distance etc whereas back in the engineering world there are loads of examples of trying to turn real world numbers into a dimensionless number to give us a universal measure.

REynolds number being a great example = fluid density x fluid velocity x pipe diameter / viscosity = can be applied to any fluid whether gas or liquid, if the value is >X its turbulent, good mixing, <X streamlined flow, not mixed and in either case we can use Re to help work out other real world problems like pump power requirements.

We need to put an engineer in charge of this.

[hatler]

I think gain ratio is the dimensionless answer you seek. Sadly its use ends up in non-convenient numbers.

[Ningishzidda]

Metric measurements ( Base 10 ) became the sensible way of going about things because they worked in ONE base, base 10.

English measurements were quite ridiculous, with 12 inches to a foot, and 3 feet to a yard, and 220 yards to a furlong, and 8 furlongs to a mile, let alone rods, poles and chains.

1 metre had 1000 mm. The metre was subdivided into 10, which was 100mm; or 100, which is 10mm, or a centimetre.

English money was the same, multiple bases to add up, and then work out how much change from a Quid.
Once upon a time, there were three currencies operating in England concurrently. Marks, Libres and Groats.

The UK changed to decimal currency because at the time, computerised cash registers couldn’t handle multiple base calculations. Computers operate on base 2, and it’s a simple multiplier to operate in base 10 all the way.

Bicycles operate in base 2. Two legs, two wheels and two handlegrips.

I don't think maths was a great consideration when Imperial units were dreamt up. I'd guess it was more a system designed to standardise everyday objects which were then defined in relation to each other in whatever ratio that would fit, near enough.
Counting, yes: Maths.. not so much.

If you turned up to a village in the Dark Ages and started talking about Base 10 and common factors you'd probably have been burnt for sorcery or pitchforked or something.

No. They'd think you was a Monk and knew Latin. Then fed you, give you beer and asked for a blessing.

[mrcharly-YHT]

I don't think maths was a great consideration when Imperial units were dreamt up. I'd guess it was more a system designed to standardise everyday objects which were then defined in relation to each other in whatever ratio that would fit, near enough.

Imperial units work well when all your maths is done in fractions.

[Morat]

Metric measurements ( Base 10 ) became the sensible way of going about things because they worked in ONE base, base 10.

English measurements were quite ridiculous, with 12 inches to a foot, and 3 feet to a yard, and 220 yards to a furlong, and 8 furlongs to a mile, let alone rods, poles and chains.

1 metre had 1000 mm. The metre was subdivided into 10, which was 100mm; or 100, which is 10mm, or a centimetre.

English money was the same, multiple bases to add up, and then work out how much change from a Quid.
Once upon a time, there were three currencies operating in England concurrently. Marks, Libres and Groats.

The UK changed to decimal currency because at the time, computerised cash registers couldn’t handle multiple base calculations. Computers operate on base 2, and it’s a simple multiplier to operate in base 10 all the way.

Bicycles operate in base 2. Two legs, two wheels and two handlegrips.

I don't think maths was a great consideration when Imperial units were dreamt up. I'd guess it was more a system designed to standardise everyday objects which were then defined in relation to each other in whatever ratio that would fit, near enough.
Counting, yes: Maths.. not so much.

If you turned up to a village in the Dark Ages and started talking about Base 10 and common factors you'd probably have been burnt for sorcery or pitchforked or something.

No. They'd think you was a Monk and knew Latin. Then fed you, give you beer and asked for a blessing.

Well, I know you shouldn't jump to conclusions about people on forums, but I didn't have you down as the monkish type. Forgive me, Father

[Karla]

If you change the crank length yes your foot speed changes, but your legs, the power unit,  will be going up and down at the same rate.  The only thing that can affects the rate at which your legs move is the chainring size, the sprocket size, or the wheel/tyre size.   

Incorrect.  The frequency at which your legs spin may change, but the distance they move through, the speed they move at and the force they need to apply - all the parts of 'rate they go up and down' that matter to the legs as a power-producing plant, change. 

Also, everything Kim said.

We need to put an engineer in charge of this.

Reporting for duty sir.

[Cudzoziemiec]

I think this may be a contender for 'Most boring thread.
Ever'.

Really.
ETA - Albeit it didn't start out as that.

I've found this thread very interesting.

Obviously we are all different.

J

I think it's descended into "Let's find as many ways as we can to use pedantically different definitions of gearing" which is in itself a version of a favourite yacf game, often played in pobi, "Let's find a way to disagree when basically we're saying the same thing".

[Ningishzidda]

Metric measurements ( Base 10 ) became the sensible way of going about things because they worked in ONE base, base 10.

English measurements were quite ridiculous, with 12 inches to a foot, and 3 feet to a yard, and 220 yards to a furlong, and 8 furlongs to a mile, let alone rods, poles and chains.

1 metre had 1000 mm. The metre was subdivided into 10, which was 100mm; or 100, which is 10mm, or a centimetre.

English money was the same, multiple bases to add up, and then work out how much change from a Quid.
Once upon a time, there were three currencies operating in England concurrently. Marks, Libres and Groats.

The UK changed to decimal currency because at the time, computerised cash registers couldn’t handle multiple base calculations. Computers operate on base 2, and it’s a simple multiplier to operate in base 10 all the way.

Bicycles operate in base 2. Two legs, two wheels and two handlegrips.

I don't think maths was a great consideration when Imperial units were dreamt up. I'd guess it was more a system designed to standardise everyday objects which were then defined in relation to each other in whatever ratio that would fit, near enough.
Counting, yes: Maths.. not so much.

If you turned up to a village in the Dark Ages and started talking about Base 10 and common factors you'd probably have been burnt for sorcery or pitchforked or something.

No. They'd think you was a Monk and knew Latin. Then fed you, give you beer and asked for a blessing.

Well, I know you shouldn't jump to conclusions about people on forums, but I didn't have you down as the monkish type. Forgive me, Father

You are forgiven, my son.
Do penance, ride your bicycle 200 kilometers with three rest stops each 50 km.

[Ningishzidda]

I think this may be a contender for 'Most boring thread.
Ever'.

Really.
ETA - Albeit it didn't start out as that.

I've found this thread very interesting.

Obviously we are all different.

J

I think it's descended into "Let's find as many ways as we can to use pedantically different definitions of gearing" which is in itself a version of a favourite yacf game, often played in pobi, "Let's find a way to disagree when basically we're saying the same thing".

The gearing question is within the top three topics of conversation for cyclists.

No. 1 "How much cake?"
No. 2 "Tubs or HPs?"

[mzjo]

I think this may be a contender for 'Most boring thread.
Ever'.

Really.
ETA - Albeit it didn't start out as that.

I've found this thread very interesting.

Obviously we are all different.

J

I think it's descended into "Let's find as many ways as we can to use pedantically different definitions of gearing" which is in itself a version of a favourite yacf game, often played in pobi, "Let's find a way to disagree when basically we're saying the same thing".

The gearing question is within the top three topics of conversation for cyclists.

No. 1 "How much cake?"
No. 2 "Tubs or HPs?"

Where I am it comes well behind:
No 1 Bordeaux, Bourgogne ou Beaujolais?
No 2 Combien de rillettes par baguette?