Hypothetical gearing question.....

[Panter]

If you had two chainrings on the front, and exactly the same size rings on the cassette (a 10 & a 20 to keep it simple,) would the effort involved in pushing 10 front and 20 back be exactly the same as pushing 20 front and 10 on the back or is there a mechanical advantage to having the larger ring on the front?

 

[jimboalee]

I've got a 42 x 21 AND a 30 x 15.

Are they different?

 

[Bigtwin]

Here you are:

http://home.earthlink.net/~mike.sherman/shift.html

 

[jimboalee]

I've got a 42 x 21 AND a 30 x 15.

Are they different?

Sorry, misundertood.

20 ring to 10 sprocket is a 2:1 ratio, which on a 700C tyre is a 52" gear.
10 ring to 20 sprocket ia a 1:2 ratio, which on a 700C tyre is a 13.5" gear.

The 10 x 20 will be 1/4 speed for the same cadence and the 20 x 10 will be 4 x cadence for the same speed.

Power requirement is proportional to speed, and the equation is :-

kW = (Nm x revs) / 9549.3

Transpose the equation if you know revs and kW for a known speed, to get Nm force.

If you know your crank length ( and geartrain losses ) you can assess the force on the pedal in Newtons.
You know gravity, so then assess kg weight on the pedal.

 

[Panter]

Sorry, misundertood.

20 ring to 10 sprocket is a 2:1 ratio, which on a 700C tyre is a 52" gear.
10 ring to 20 sprocket ia a 1:2 ratio, which on a 700C tyre is a 13.5" gear.

The 10 x 20 will be 1/4 speed for the same cadence and the 20 x 10 will be 4 x cadence for the same speed.

Power requirement is proportional to speed, and the equation is :-

kW = (Nm x revs) / 9549.3

Transpose the equation if you know revs and kW for a known speed, to get Nm force.

If you know your crank length ( and geartrain losses ) you can assess the force on the pedal in Newtons.
You know gravity, so then assess kg weight on the pedal.

Thanks Jimboalee, why would the gear size be different though?

 

[Dan B]

If you had two chainrings on the front, and exactly the same size rings on the cassette (a 10 & a 20 to keep it simple,) would the effort involved in pushing 10 front and 20 back be exactly the same as pushing 20 front and 10 on the back

No, there'd be a 4x difference. The clue is is the name "gear ratio"

 

[Panter]

No, there'd be a 4x difference. The clue is is the name "gear ratio"

Ok, thanks for that

I still don't really understand though, if you have it in 20 front and 10 back it's harder to rotate the front but easier to rotate the back and vice versa.
Mind you, that's why I'm not an engineer

 

[jimboalee]

An 'Ordinary' bike, or a Penny farthing, had a 1:1 ratio. The cranks were solidly fixed to the hub.

These bikes were available in various wheel sizes to fit various stature riders.

The wheel size that fitted you was the size you got. The most popular was 52" wheel diameter.

John Kemp Starley ( and his dad ) had a brilliant idea of building a bike with the wheels the same size and putting the cranks in front of the rear driving wheel, and committing the front wheel to steering only.

The other disadvantage of the penny farthing was the saddle was high off the ground ( a 'High' bicycle ).

Starley's design had the saddle lower so the rider could hop off and stand on the ground. The crank axle was at a height which made the saddle height about pelvis height to the standing rider.

Starley decided upon a wheel size half of 52" and arranged a 2:1 gear ratio between crank axle and rear drive hub. Early bikes were a leather strap drive having the front pulley twice the radius as the hub pulley.

The resultant gear was the same as the 52" penny.

Then came the metal roller chain and toothed sprockets.

Take a trip to the Museum of road transport in Coventry to get the whole story.

In the Birmingham science museum, there once was a demonstration of a Rover Safety bike hooked up to a William Froude water brake dynamometer. Visitors were invited to light up a 100 Watt bulb from a dynamo connected to the water brake.
The bulb would light up when the needle on the dyno reached 0.1 kW at an equivalent road speed of 12 mph.

 

[Dan B]

Ok, thanks for that

I still don't really understand though, if you have it in 20 front and 10 back it's harder to rotate the front but easier to rotate the back and vice versa.

When you rotate the back you're pulling on the edge of the sprocket using the chain, so if you get a bigger sprocket you're pulling from a point that is further away from the axle. This means you have to pull more chain (i.e. pedal more) to make the wheel turn the same amount, but it's not as hard work to pull

When you rotate the front, though, it's not by pulling the edge of the chainring around but by pushing on the pedal, which is always a fixed distance from the axle in the bottom bracket. If you get a bigger chainring you will need to pedal fewer turns for the same amount of chain travel, but it will be harder work.

Does that make more sense?

 

[Panter]

When you rotate the back you're pulling on the edge of the sprocket using the chain, so if you get a bigger sprocket you're pulling from a point that is further away from the axle. This means you have to pull more chain (i.e. pedal more) to make the wheel turn the same amount, but it's not as hard work to pull

When you rotate the front, though, it's not by pulling the edge of the chainring around but by pushing on the pedal, which is always a fixed distance from the axle in the bottom bracket. If you get a bigger chainring you will need to pedal fewer turns for the same amount of chain travel, but it will be harder work.

Does that make more sense?

And the penny drops, thank you

 

[RedBike]

If you rotate a front chainring of say 20teeth around once the back sprocket also has to move 'by the same distance' ie, by 20teeth. If the rear sprocket only has 10 teeth in total then it has to rotate twice to move through a distance of 20 teeth. Therefore with this gear ratio every rotation of the crank causes the wheel to rotate twice.


Now if the front chainring only has 10 teeth then the rear sprocket only has to move by a distance of ten teeth. If the rear sprocket has 20teeth in total then it only needs to turn half a revolution to move this distance.
Therefore with this gear ratio one turn of the cranks will only turn the wheel 1/2 a revolution. A much lower (4x) gear.

The question you need to know is:
Is 30x15 and harder than say 42x21 (Both a ratio of 2:1)?

 

[Panter]

That makes perfect sense, anyone know the answer?

I guess where this all stems from is that sometimes, if I'm on a slight incline on the big chainring but finding it slightly hard going, I have a habit of flicking both gear change levers at the same time to drop a cog on the front and increase one on the back.
It always feels to be about the same gear size, but just a bit easier.

 

[tandemman]

Of course if you had asked if it took the same amount of energy to cover the same distance then yes it does it just needs a harder effort for a shorter period of time with a large front small rear configuration.This is where an understanding of gear inches comes in handy as wheel size also comes into the equation