Gear ratios

[SpeedMattersNot]

Hello all,

I'm scratching my head regarding gear ratios on bicycles.

Having a good grasp of gear ratios in other platforms, such as cars, racing cars, r/c cars and (go) karts I'm struggling to understand why in the cycling community they calculate ratios differently. In the other platforms I understand that to calculate the ratio it is very simply; DRIVEN / DRIVER = GEAR RATIO

DRIVER = Gear attached to motor
DRIVEN = Gear driven by the driver gear (on the axle)

So when applying this logic to bikes, I would call the DRIVER cog to be that of the chain-ring and the DRIVEN cog to be that on the rear cassette. However, from all the information I can extract online from various blogs, articles and company websites they calculate the gear ratio by dividing the chain ring number by the rear cassette ring number - To me this is back to front.

What's the reason for this?

P.s. this is my slimmed down version of this, cutting equations, examples of kart and car ratios with torque/rpm differences with ratios etc

[Roman]

This explains all along with an excellent gear calculator:

http://sheldonbrown.com/gears/

Bike gearing is commonly measured in inches (of forward motion per crank revolution).

[gazza285]

Bicycles don't have cogs.

Except for the hub geared ones that is.

[RGambo]

It must also come down to outher factors with cars. With a bike then it's just 1 rotation of the crank = x number of rotations of wheel, which is pretty much a standard size, so calcs are easy.
With a car, you have gearbox input shaft rotation ( between 1000 and x000 rpm) vs gear box out put rotation . But it then clouded by the final drive ratio on the diff, then that is factored into the wheel diameter, which is hugely different.
But I think the main thing is bikes are geared to increase the crank rotations to wheel rotations, but cars are using gearboxes to reduce the engine rotation speed. If you see what I mean.

[Gizmoish]

Bike gears are the other way around to car gears. A car gears step the engine's 1000-8000 rpm down to fewer rpm at the wheels; bike gears multiply 60-120rpm up to more rpm at the wheels.

[SpeedMattersNot]

Roman said:

This explains all along with an excellent gear calculator:

http://sheldonbrown.com/gears/

Bike gearing is commonly measured in inches (of forward motion per crank revolution).

Thanks for your input, but this doesn't answer my question, I don't think.

gazza285 said:

Bicycles don't have cogs.

Except for the hub geared ones that is.

Ok, sprockets is probably a more suitable term, if not, gears.

RGambo said:

It must also come down to outher factors with cars. With a bike then it's just 1 rotation of the crank = x number of rotations of wheel, which is pretty much a standard size, so calcs are easy.
With a car, you have gearbox input shaft rotation ( between 1000 and x000 rpm) vs gear box out put rotation . But it then clouded by the final drive ratio on the diff, then that is factored into the wheel diameter, which is hugely different.
But I think the main thing is bikes are geared to increase the crank rotations to wheel rotations, but cars are using gearboxes to reduce the engine rotation speed. If you see what I mean.

Like I said, it was a slimmed down version, I was a mechanic for 12 years and now a student studying motorsport and have a great understanding of the effect of differing gear ratios, wheel diameters and even calculations of tyre carcus distortion at varying speeds - and how they all mate together with the final drive ratio.

But I entirely agree, the bike ratios are designed to do what the 'overdrive' gears do in road cars. Therefore they rotate the wheels faster than the engine is spinning as I assume torque input from the human isn't the limiting factor in cycling, but rather rpm...! Either way, they are calculating the gear ratios (by ignoring DRIVEN / DRIVER) which is GCSE physics whereas torque is multiplied and rpms are divided. If you have a positive number for your gear ratio your speed output will be less than input - which just isn't the case in the cycling community as you say so yourself.

Gizmoish said:

Bike gears are the other way around to car gears. A car gears step the engine's 1000-8000 rpm down to fewer rpm at the wheels; bike gears multiply 60-120rpm up to more rpm at the wheels.

I agree and understand this. Hence why I question the reason why in the cycling community they seemingly incorrectly use the driven / driver rule.

A cars gearbox ratios could be described as such;

1st = 3:1
2nd = 2.1:1
3rd = 1.4:1
4th = 1:1
5th = 0.85:1

Since torque is multiplied with gear ratio but rpms are divided, if an engine developed 100Nm @ 2000rpm its figures would be like so;

1st = 300Nm @ 667rpm
2nd = 210Nm @ 952rpm
3rd = 140Nm @ 1429rpm
4th = 100Nm @ 2000rpm
5th = 85Nm @ 2353rpm

This makes sense to me, since we can pull more G (traction permitting) with 1st gear than we can in 2nd and why it's required to change down a gear to go up a steep hill. It also shows how the output rpm is much more suited to top speed the further up the gears you go. Another similarity is in a car, or bicycle I can spin the driven wheel/s easier than I can the higher gears - This is again because torque is increased with gear ratio not reduced.

I do the same on my mountain bike. If I want to climb a steep hill, I will select the lowest front chain ring (pinion) and the larger rear cog (spur)...and the opposite if I want to go down hill, of course.

Very confusing.

Edited by SpeedMattersNot on Wednesday 10th September 23:41

[gazza285]

SpeedMattersNot said:

Hello all,

I'm scratching my head regarding gear ratios on bicycles.

Having a good grasp of gear ratios in other platforms, such as cars, racing cars, r/c cars and (go) karts I'm struggling to understand why in the cycling community they calculate ratios differently. In the other platforms I understand that to calculate the ratio it is very simply; DRIVEN / DRIVER = GEAR RATIO

DRIVER = Gear attached to motor
DRIVEN = Gear driven by the driver gear (on the axle)

So when applying this logic to bikes, I would call the DRIVER cog to be that of the chain-ring and the DRIVEN cog to be that on the rear cassette. However, from all the information I can extract online from various blogs, articles and company websites they calculate the gear ratio by dividing the chain ring number by the rear cassette ring number - To me this is back to front.

What's the reason for this?

P.s. this is my slimmed down version of this, cutting equations, examples of kart and car ratios with torque/rpm differences with ratios etc

It is only driven/driver because they are reduction gears, for multiplying gears it is the reverse.
So an 18t driving a 36t is a 2:1 reduction, and a 36t driving an 18t is a 2:1 multiplication.

The confusion arises in vehicle transmissions where the top gear is usually an overdrive gear to allow the diff to be kept at a sensible size, but it is still expressed as a reduction gear ratio, such as the Ford Type 9 top gear being 0.82:1.

However, cycles still use the distance traveled by one crank revolution as this also incorporates the wheel size into the equation.

[SpeedMattersNot]

gazza285 said:

[b]It is only driven/driver because they are reduction gears, for multiplying gears it is the reverse.
So an 18t driving a 36t is a 2:1 reduction, and a 36t driving an 18t is a 2:1 multiplication.[/b]

The confusion arises in vehicle transmissions where the top gear is usually an overdrive gear to allow the diff to be kept at a sensible size, but it is still expressed a reduction gear ratio, such as the Ford Type 9 top gear being 0.82:1.

However, cycles still use the distance traveled by one crank revolution as this also incorporates the wheel size into the equation.

But this would mean to get accurate torque/rpm figures you would also have to do the opposite; Divide torque by the ratio and multiply the rpm!

In racing cars, say a Formula 3 they typically don't have an 'overdrive' gear because the aerodynamic resistance and low rpm limit means they still need that torque multiplication to punch through the air.

I guess this is just the first discipline I've come across where they don't run gear reduction

[gazza285]

Same rule applies, torque times reduction ration and torque divided by the multiplication ration equals the same.

18t driving 36t = 2:1 reduction ratio = 0.5:1 multiplication ratio.

Say torque is 200lb/in, that gives us either 200x2 or 200/0.5. Same answer, 400lb/in.

36t driving 18t = 0.5:1 reduction ratio = 2:1 multiplication ratio.

200x0.5 or 200/2. Same answer.

Torque is multiplied by reduction ratios and divided by multiplication ratios.

The relationship to rpm does not change.