Best gear for moderate progress

[Pale Rider]

Trundling along cinder tracks on my Cannondale MTB I've been using the middle ring at the front and cogs two to four at the back.

Recently I've been trying the granny ring and cogs five and upwards at the back.

It seems to me the latter is a bit easier to pedal for approximately the same speed across the ground.

Is this likely, or am I imagining it?

The bike is a 29er with standard three X 10 gears.

My usual cadence is about 60-70rpm.

It may be I spin a bit faster in the granny ring, but it feels about the same.

 

[ChrisEyles]

What are your gear inches in those gears?

For open roads with a nice surface, the 52/20 and 42/20 gears on my ten speed see by far the most use - with 27" wheels that's around 70 and 57 gear inches. This is with 165mm cranks (shorter cranks are better to spin faster in a lower gear at a given speed, if I understand correctly), which gives roughly 17-19 mph and 14-15 mph at around 80-90rpm.

On my commuter I tend to use a slightly higher gear for a given speed (and corresponding lower rpm). I guess this must be due to the difference in geometry - the seat is positioned further back from the BB due to the slack seat tube angle, which means the back of the leg does relatively more work compared to on my ten speed.

To come to the point: yes, higher cadences in a lower gear might well be a more efficient way of maintaining a given speed, but this will depend on the bike (geometry and crank length), and on your personal cadence preferences!

I am definitely guilty of this, but I think it's possible to over-think this too... just pedalling a little harder seems to work equally well a lot of the time!

 

[Pale Rider]

Not sure about gear inches, but the two gears I'm using feel about the same.

As you know, there are some near duplicate gears on a 30 speed bike.

I am wondering for a pair of such gears, if it's easier to push the granny ring at the front and the smaller cog at the back, or the middle ring at the front and the bigger cog at the back.

If it makes any difference, I am talking about relatively slow speeds, about eight to 10mph.

 

[User16625]

What are your gear inches in those gears?

For open roads with a nice surface, the 52/20 and 42/20 gears on my ten speed see by far the most use - with 27" wheels that's around 70 and 57 gear inches. This is with 165mm cranks (shorter cranks are better to spin faster in a lower gear at a given speed, if I understand correctly), which gives roughly 17-19 mph and 14-15 mph at around 80-90rpm.

On my commuter I tend to use a slightly higher gear for a given speed (and corresponding lower rpm). I guess this must be due to the difference in geometry - the seat is positioned further back from the BB due to the slack seat tube angle, which means the back of the leg does relatively more work compared to on my ten speed.

To come to the point: yes, higher cadences in a lower gear might well be a more efficient way of maintaining a given speed, but this will depend on the bike (geometry and crank length), and on your personal cadence preferences!

I am definitely guilty of this, but I think it's possible to over-think this too... just pedalling a little harder seems to work equally well a lot of the time!

Dont longer cranks provide more leverage? I always though that a longer crank is better than a shorter one for this purpose assuming you can still pedal properly.

 

[ChrisEyles]

Aha, I get you - sorry for teaching you to suck eggs there!

If you're talking about two equivalent gear inch gears (e,g, 50/20 and 30/12) I'd be very surprised if there'd be a measurable difference in efficiency under realistic riding conditions. Granny ring and a small sprocket will probably wear the chain and teeth quicker though?

 

[ChrisEyles]

Dont longer cranks provide more leverage? I always though that a longer crank is better than a shorter one for this purpose assuming you can still pedal properly.

As I understand it a longer crank does provide more leverage for when you're over-geared (e.g. climbing a hil and grinding up at 40rpm). Since you don't get as much leverage from a shorter crank you have to use a lower gear and higher cadence, and the shorter crank makes the motion of spinning quickly a little easier (I definitely find this to be the case anyway).

 

[Pale Rider]

Aha, I get you - sorry for teaching you to suck eggs there!

If you're talking about two equivalent gear inch gears (e,g, 50/20 and 30/12) I'd be very surprised if there'd be a measurable difference in efficiency under realistic riding conditions. Granny ring and a small sprocket will probably wear the chain and teeth quicker though?

Nothing to apologise for.

Common sense suggests efficiency would be about the same, but bicycles are strange contraptions which don't always behave as expected.

My best guess is that of my chosen pair of gears, the granny ring one is slightly lower and I am spinning a bit faster without noticing.

Plus I accept there's not much scientific measurement going on here, it could be my speed is a bit slower in what I find to be the easier gear.

 

[Yellow Saddle]

All things being equal, the bigger the sprocket the less energy lost to friction. A chain articulates when it enters a sprocket at an angle defined by 360/sprocket teeth qty.
On a 36 tooth sprocket (I like my math easy), the chain articulates through ten degrees and on a 28 tooth sprocket, through 13 degrees, There is more energy required to do the latter. However since you are fiddling with both front and rear, your sums become more complicated, but not impossible. I would just add front degrees to rear degrees and come up with a "factor", to calculate which gear is the most efficient. There is nothing else in the system that requires consideration so the decision is mathematically precise.

 

[ChrisEyles]

I would have thought the angle the chain is running at would also be important, if you are going to attempt a "proper" physics based solution. A small-small sprocket combination would have a tighter angle (perpendicular to the plane the chain is running in) than a medium-medium combination, requiring a second factor to be guesstimated/assumed.

I would also have thought that any systematic difference between the two combinations is orders of magnitude less than the statistical variation due to weather/rider etc variables. Not to say that it's not an interesting one to try and solve anyway though!

 

[Citius]

Crank length differences are negligible although ironically, some studies show that fractionally more power can be produced with shorter cranks. And as YS says, for the same gear ratio, a big/big combo will be more efficient.

 

[Yellow Saddle]

I would have thought the angle the chain is running at would also be important, if you are going to attempt a "proper" physics based solution. A small-small sprocket combination would have a tighter angle (perpendicular to the plane the chain is running in) than a medium-medium combination, requiring a second factor to be guesstimated/assumed.

Sketch the various scenarios you envisage and see if you still agree with yourself afterwards.

 

[Fab Foodie]

I find that the best gear for moderate progress is the one I feel happiest pedalling ....
Sod the maths.

 

[ChrisEyles]

Sketch the various scenarios you envisage and see if you still agree with yourself afterwards.

I think I still agree with myself!

Surely a chain line like this (sprockets at left, chainrings at right, or vice versa, top down view as if you were looking down at your chain line while riding)

___________________

is more efficient than one like this
............. _______
______/

which is in turn more efficient than one like this?
...................._____
.........._____/
____/

The ascii diagrams above are a bit rubbish, but you get the idea. If the skew angle becomes too great eventually the drive chain would cease to function. Obviously between there and a perfectly straight chain-line won't be a linear response, but even at small skew angles some resistance must creep in*.

Not saying there would be any noticeable difference when riding! Just being pedantic in the spirit of things If I'm wrong, I'd be interested to know why - since I see you've written an entire book about bicycle chains I guess you are the man to ask!

*less than or equal to the resistance encountered by riding head first splat into a big bug but (arguably!) greater than the amount overcome by upgrading a wheelset

I'll stop digging now!

 

[Yellow Saddle]

I think I still agree with myself!

Surely a chain line like this (sprockets at left, chainrings at right, or vice versa, top down view as if you were looking down at your chain line while riding)

___________________

is more efficient than one like this
............. _______
______/

which is in turn more efficient than one like this?
...................._____
.........._____/
____/

The ascii diagrams above are a bit rubbish, but you get the idea. If the skew angle becomes too great eventually the drive chain would cease to function. Obviously between there and a perfectly straight chain-line won't be a linear response, but even at small skew angles some resistance must creep in*.

Not saying there would be any noticeable difference when riding! Just being pedantic in the spirit of things If I'm wrong, I'd be interested to know why - since I see you've written an entire book about bicycle chains I guess you are the man to ask!

*less than or equal to the resistance encountered by riding head first splat into a big bug but (arguably!) greater than the amount overcome by upgrading a wheelset

I'll stop digging now!

Aha! The Tower of Babel strikes again and I slap my forehead.

I understand you now, but the misunderstanding would have been prevented if you described it as parallel (not perpendicular) to the plane the chain is running in. I was envisaging some sort of scenario where one sprocket is higher than the other when viewed from the side of the bike.

What you are describing is cross-chaining. Yes, cross-chaining is inefficient. Nice ASCII art BTW.