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Difference in gear ratios?

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Difference in gear ratios?

Old 06-17-19, 12:32 PM
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Difference in gear ratios?

Hey all,

I have kind of an academic question...

Let's assume you have a bike with a given set of wheels, cranks, and tires. Is there any difference in gear ratios, if the gear inches stay close to the same? So, for instance, 40x15 and 48x18 are both 72 gear inches (or a gain ratio of 5.4). Is there any functional difference between the two setups as far as acceleration and braking ability?
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Old 06-17-19, 01:03 PM
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No
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Old 06-17-19, 01:06 PM
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Originally Posted by mickey85 View Post
Hey all,

I have kind of an academic question...

Let's assume you have a bike with a given set of wheels, cranks, and tires. Is there any difference in gear ratios, if the gear inches stay close to the same? So, for instance, 40x15 and 48x18 are both 72 gear inches (or a gain ratio of 5.4). Is there any functional difference between the two setups as far as acceleration and braking ability?
If comparing two identical bikes, then effectively, no. A larger chainring/sprocket combination can reduce friction and technically make for a smoother more efficient drivetrain, by reducing the torque load on each individual tooth (spreading torque load out through larger number of teeth engaged) but the difference between these two combinations isn’t going to create any practical difference because they’re extremely similar in size. If you’re talking about a fixed gear setup and using the back-pedal ‘brake’, different size sprockets give varying number of contact patches on the tire. useful if you like to do skids, but otherwise inconsequential.
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Old 06-17-19, 06:44 PM
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I would imagine that drivetrains with a greater number of total teeth wear out very slightly less rapidly.

According to Sheldon sprockets with even numbers of teeth will reduce drivetrain wear and longevity as well so you could make a case for choosing a 48×16 over a 45x15 (both 78.9gi)

If your riding fixed and want skid patches, I guess then the most optimal drive train would be one with the most total teeth, an even toothed cog and a odd toothed chainring (?) So something like 49x18 would be just about perfect theoretically (I think...)
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Old 06-17-19, 10:55 PM
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Gear inches is just one of several ways of expressing how far the bike travels for one turn of the cranks. It is useful because it takes into account the diameter of the wheel.

The calculation is (Teeth on chain ring divided by teeth on the sprocket) multiplied by wheel diameter.

The term "gear inches" refers to the equivalent size of a wheel if it was directly driven by the cranks, like on a penny farthing or unicycle, rather than through a chain and gears. A bike with a 72 inch gear travels the same distance per turn of the cranks as a penny farthing with a 72 inch wheel.

If two bikes achieve the exactly same figure for gear inches, they will travel exactly the same distance for one turn of the cranks.

The mathematical variables are the number of teeth on the chain ring, the number of teeth on the sprocket, and the rolling diameter of the wheel. Change one and you will have to change one or both of the others to get the same number of gear inches.

You may find that a larger chain ring and sprocket will be slightly smoother and also result in less wear.

You may find that a larger chain ring and sprocket is slightly heavier and has slightly more aerodynamic drag. I doubt that most of us would notice the effect.

You may find that a smaller chain ring and sprocket gives more ground clearance if you are given to riding on rough terrain.

Of the three variables, the one that makes most difference to the ride is the wheel size. Set up a 700c bike for 72 inches, and a small wheel Moulton for the 72 inches and you will notice a difference, especially riding on an uneven surface.

The gear inches calculation does not take into account the length of the cranks. For modern bicycles, the length of cranks is fairly standard around 165mm to 170mm. Shorter cranks have less torque, but the rider's feet move a smaller distance per revolution. Short cranks mean you can spin faster (in a lower gear) but have to push harder (in a higher gear).

For comparison, unicyclists pay a lot of attention to crank length because unicycles are direct drive and the only variables they can play with are the wheel diameter and the crank length. (Geared hubs are available but are extremely expensive.)
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Old 06-17-19, 10:59 PM
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tl;dr see post 2
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Old 06-18-19, 08:22 AM
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Originally Posted by seau grateau View Post
tl;dr see post 2
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Old 06-18-19, 09:05 AM
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Yes. The difference may be marginal, but to say there is none is incorrect. Larger sprockets and cogs are more efficient.

  • Efficiency is higher when using larger sprockets because the chain benefits from a less extreme radius of rotation – chain links going around corners cause greater frictional power losses. The take away here is that if you can achieve the same gear using a large chainring + larger sprocket combination than a small ring + smaller sprocket combination it is a worthwhile consideration. The efficiency difference between an equal gear that involves the 24 sprocket and the 13 sprocket can be worth 1-2 watts when riding in the 200-400 watt range.
https://www.cyclingpowerlab.com/Driv...fficiency.aspx
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Old 06-18-19, 10:00 AM
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Not being descended form The Princess Who Could Not Abide the Pea, as some BF members seem to be, I freely admit that if someone altered my FG with a different sized chairing and cog that produced my favored 70 GI I could not tell the difference at all on my usual routes. Oddly enough, and perhaps even more astonishing, if the pressure in my tires were altered up or down by a couple of PSI, the chain was dried or given a drop or two of lube, my favorite socks were donned inside-out and an extra tire lever snuck into my flats kit I'd be oblivious to all of that as well on a rolling 20 mile ride.

Sometimes one just get on with riding the bike despite lacking the finest discrimination of the subtle minutia that creeping 41-ism provides, along with genetic Pea/Mattress Anaphylaxis of course.

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Old 06-18-19, 10:45 AM
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Originally Posted by AlmostTrick View Post
Yes. The difference may be marginal, but to say there is none is incorrect. Larger sprockets and cogs are more efficient.

https://www.cyclingpowerlab.com/Driv...fficiency.aspx
As much as 1-2 watts at a power level most of us don't ride at, when comparing cog sizes that are at the literal extremes of what is possible on a FG bike (I've never seen a fixed cog bigger than 24T). So it's correct to say that the efficiency difference is down in the noise, for all practical purposes.


I do try to use the biggest chainring and cog combination I can for my gearing, though. Chain wear increases with the angle the chain is forced to bend under load, and I'm pretty sure I can feel the difference in chordal action between a 13T and a 16T.
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Old 06-18-19, 10:55 AM
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Originally Posted by ThermionicScott View Post
As much as 1-2 watts at a power level most of us don't ride at, when comparing cog sizes that are at the literal extremes of what is possible on a FG bike (I've never seen a fixed cog bigger than 24T). So it's correct to say that the difference is down in the noise, for all practical purposes.
Right, so again, saying there is no difference is incorrect.

OP didn't ask if a particular rider could feel the difference.

And then there's this:

As power output increases efficiency increases because frictional losses become a smaller part of total input power. Typical best-case efficiency of a drivetrain in the 200 – 300 watt range is 96-97.5%. Above 300 watts typical best-case efficiency is 97-98%.


So any differences in efficiency are actually greater for cyclists of more modest power output than they would be for stronger riders.
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Old 06-18-19, 11:04 AM
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Originally Posted by AlmostTrick View Post
So any differences in efficiency are actually greater for cyclists of more modest power output than they would be for stronger riders.
I get about a 3 watt possible difference either way. Makers of ceramic-bearing bike parts and pricey chain lubes would certainly like us to believe that that's meaningful.
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Old 06-18-19, 11:11 AM
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Fixie Minds want to Know ..

Is there any functional difference between the two setups as far as acceleration and braking ability?


both are 2.6666666666.. :1 So, you really are asking others to judge your perceptions over the internet.








...

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Old 06-18-19, 11:11 AM
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Originally Posted by ThermionicScott View Post
I get about a 3 watt possible difference either way. Makers of ceramic-bearing bike parts would certainly like us to believe that that's meaningful.
Do you mean Pea-Products International makers of "Placebo Bearings" and "Wonder Lube"?

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Old 06-18-19, 11:22 AM
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@Bandera

*scoff*

Anyone who can't feel the massive drop in wattage with inside out socks isn't a serious cyclist
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Old 06-18-19, 11:27 AM
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You're talking about differences on a scale so small that they are imperceptible to the rider. If you think that qualifies as a functional difference, go off I guess.
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Old 06-18-19, 12:46 PM
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Originally Posted by AlmostTrick View Post
Right, so again, saying there is no difference is incorrect.

OP didn't ask if a particular rider could feel the difference.

And then there's this:



So any differences in efficiency are actually greater for cyclists of more modest power output than they would be for stronger riders.
2 watts is a functional difference in accelerating and braking to an average rider? Damn, I must be a scrub.
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Old 06-18-19, 01:55 PM
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Originally Posted by AlmostTrick View Post
Yes. The difference may be marginal, but to say there is none is incorrect. Larger sprockets and cogs are more efficient.
B-b-but larger rings and cogs are heavier!

Sure that has an effect as well?
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Old 06-18-19, 02:48 PM
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I don't understand gear inches; the concept is sound, but the formula is not logical. I'll use my Meridian for an example: I have a 60t chainring driving a 22t cog on the axle that spins a 26" wheel. So 60 / 22 ~= 2.73 (so every revolution of the crankset rotates the tire 2.73 times [2.73:1]). How far does my tire travel per rotation? Using basic geometry, the circumference of any circle is the diameter * PI (~3.14). So 26 x 3.14 = 81.64; therefore, that tells me my wheel travels 81.64" per revolution. When my drive wheel rotates 2.73 times per crankset revolution, I travel 222.88 inches per a single crank revolution.

Gear inches 70.91"?

Originally Posted by Mikefule View Post
Gear inches is just one of several ways of expressing how far the bike travels for one turn of the cranks. It is useful because it takes into account the diameter of the wheel.

The calculation is (Teeth on chain ring divided by teeth on the sprocket) multiplied by wheel diameter.

The term "gear inches" refers to the equivalent size of a wheel if it was directly driven by the cranks, like on a penny farthing or unicycle, rather than through a chain and gears. A bike with a 72 inch gear travels the same distance per turn of the cranks as a penny farthing with a 72 inch wheel.

If two bikes achieve the exactly same figure for gear inches, they will travel exactly the same distance for one turn of the cranks.

The mathematical variables are the number of teeth on the chain ring, the number of teeth on the sprocket, and the rolling diameter of the wheel. Change one and you will have to change one or both of the others to get the same number of gear inches.

You may find that a larger chain ring and sprocket will be slightly smoother and also result in less wear.

You may find that a larger chain ring and sprocket is slightly heavier and has slightly more aerodynamic drag. I doubt that most of us would notice the effect.

You may find that a smaller chain ring and sprocket gives more ground clearance if you are given to riding on rough terrain.

Of the three variables, the one that makes most difference to the ride is the wheel size. Set up a 700c bike for 72 inches, and a small wheel Moulton for the 72 inches and you will notice a difference, especially riding on an uneven surface.

The gear inches calculation does not take into account the length of the cranks. For modern bicycles, the length of cranks is fairly standard around 165mm to 170mm. Shorter cranks have less torque, but the rider's feet move a smaller distance per revolution. Short cranks mean you can spin faster (in a lower gear) but have to push harder (in a higher gear).

For comparison, unicyclists pay a lot of attention to crank length because unicycles are direct drive and the only variables they can play with are the wheel diameter and the crank length. (Geared hubs are available but are extremely expensive.)
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Old 06-18-19, 02:55 PM
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It's a relatively old sport with terminology going back a ways, but still very useful.

"Gear inches' is actually the diameter in inches of the drive wheel of a penny-farthing bicycle with equivalent gearing."

Read this:
https://en.wikipedia.org/wiki/Gear_inches

For comparison purposes, the whole point of GI, your set-up produces a 70.9 GI while my 48x18 700x25 is a 70.3 GI .
Two "different" ways to get very traditional and useful fixed gearing for riding on the open public roads., although per @JohnDThompson I'll stick with my well proven lighter set-up over yours.

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Old 06-18-19, 03:02 PM
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Development , OTOH, is gear ratio x circumference of the wheel in.. MM/CM/KM ...

how far you go with 1 crank rotation..
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Old 06-18-19, 03:49 PM
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Originally Posted by beach_cycle View Post
I don't understand gear inches; the concept is sound, but the formula is not logical. I'll use my Meridian for an example: I have a 60t chainring driving a 22t cog on the axle that spins a 26" wheel. So 60 / 22 ~= 2.73 (so every revolution of the crankset rotates the tire 2.73 times [2.73:1]). How far does my tire travel per rotation? Using basic geometry, the circumference of any circle is the diameter * PI (~3.14). So 26 x 3.14 = 81.64; therefore, that tells me my wheel travels 81.64" per revolution. When my drive wheel rotates 2.73 times per crankset revolution, I travel 222.88 inches per a single crank revolution.

Gear inches 70.91"?
60 t divided by 22 t = 2.72
2.72 x 26 inch wheel diameter = 71 inches. Approx.

That means that the distance you travel per single revolution of the cranks is the same as the distance you would travel with one revolution of the cranks on a penny farthing with a 71 inch wheel.

If you want to know how far you travel per revolution, it's (72 x pi) inches.

The history is that the directly driven wheel (cranks attached to the hub) pre-dated the chain driven bike. The penny farthing was known as the "ordinary bicycle". On an ordinary, the bigger the wheel, the faster you went, for a given cadence. Big wheels were impressive, fast, macho, etc.

When they invented bikes with smaller wheels, geared up, they were called "safety bicycles". In order to market the safety bicycles, they made the comparison directly relevant to the diameter of the equivalent ordinary.

The convention has persisted long after the safety bike has become the new "ordinary".
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Old 06-18-19, 06:59 PM
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Originally Posted by AlmostTrick View Post
Yes. The difference may be marginal, but to say there is none is incorrect. Larger sprockets and cogs are more efficient.
I am thrilled to "learn" this, but the "marginal gains" from riding the traditional 50 or 48 X 18 for the last 50 years could mean that I got home for lunch today a few seconds before my theoretical self on the same GI w/ smaller cogs on Total Time over several decades of riding.

I'm still at: No.

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Old 06-19-19, 09:29 AM
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Thanks for the logical info. About the history, a common result of big wheels were head injuries. Safety Bicycles are early modern bikes.

Originally Posted by Mikefule View Post
60 t divided by 22 t = 2.72
2.72 x 26 inch wheel diameter = 71 inches. Approx.

That means that the distance you travel per single revolution of the cranks is the same as the distance you would travel with one revolution of the cranks on a penny farthing with a 71 inch wheel.

If you want to know how far you travel per revolution, it's (72 x pi) inches.

The history is that the directly driven wheel (cranks attached to the hub) pre-dated the chain driven bike. The penny farthing was known as the "ordinary bicycle". On an ordinary, the bigger the wheel, the faster you went, for a given cadence. Big wheels were impressive, fast, macho, etc.

When they invented bikes with smaller wheels, geared up, they were called "safety bicycles". In order to market the safety bicycles, they made the comparison directly relevant to the diameter of the equivalent ordinary.

The convention has persisted long after the safety bike has become the new "ordinary".
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Old 06-19-19, 01:25 PM
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Originally Posted by Bandera View Post
I am thrilled to "learn" this, but the "marginal gains" from riding the traditional 50 or 48 X 18 for the last 50 years could mean that I got home for lunch today a few seconds before my theoretical self on the same GI w/ smaller cogs on Total Time over several decades of riding.

I'm still at: No.

-Bandera
Generally speaking I agree. That said.

It might be best to avoid extremes in both sprocket size and the resulting chain angles. but were talking 11 and 12 cog sprockets on a cassette, or chain angles exceeding 2 - 2.5 degrees. I doubt there is any appreciable efficiency loses with a 14T + sprockets or a 2 degree chain angle.

I choose 2 degrees on chain angle as that means all 7 freewheel sprockets on most bikes are good with the middle chainring, And with the small and large rings, I avoid using the farthest cassette sprocket when practical. But I have experimented with the most extreme combo's and have no problem using them from time to time. At the extremes the only problem I sometimes have is switching chainrings. I have to overshoot my small to middle shift for a smooth transition.
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