Simple Physics Question re SS Gearing

[ColonelJLloyd]

Wheels, tires, crankset, frame, etc all being the same, does a 53x21 gear (69.1 inches) require more, less, or the same amount of energy to move as a 43x17 (69.3* inches)?


*let's pretend they produce a gear with exactly equal gear inches.

[BdaGhisallo]

The 49x17 combo will produce more friction than the 53x21 will.

[Fat Cat]

Originally Posted by BdaGhisallo

The 49x17 combo will produce more friction than the 53x21 will.

But if you wax the chain ......

[BdaGhisallo]

Originally Posted by Fat Cat

But if you wax the chain ......

Then it'll have more friction than the waxed chain on the 53x21...

[robt57]

Originally Posted by BdaGhisallo

Then it'll have more friction than the waxed chain on the 53x21...

indeed...

[ColonelJLloyd]

Thanks. Aside from friction, I'm curious more about what the energy required to get them both rolling at the same speed. If I took this to the extreme and say a 63x25 or even larger gear.

[BdaGhisallo]

Originally Posted by ColonelJLloyd

Thanks. Aside from friction, I'm curious more about what the energy required to get them both rolling at the same speed. If I took this to the extreme and say a 63x25 or even larger gear.

If you throw out the frictional losses, I don't know that there'd be any difference large enough for you to measure.

[carpediemracing]

Generally speaking you want more teeth on the rear cog. They get less round as they have less teeth, and they get pretty inefficient. Think of a 1 tooth cog or a 2 tooth cog - that wouldn't be very efficient. Shimano dedicated an engineer to optimizing cog shape when they went to either 11 or 12t because at that point the cog was getting pretty out of round.

I'm sure there's a counter point where if you have a massive number of teeth, the inefficiency of the extra structure just makes it inefficient. For example, if instead of a 49x17 you had a 490 x 170 (ignoring ground clearance etc), there'd be so much chain (and relevant friction) that the extra "roundness" of a 170t cog wouldn't be worth it.

[Gabuyo]

Not specifically SS, but I have tried this with a fixed gear. I race at the local velodrome (Hellyer). I have participated in probably ~70 race nights, primarily mass start omniums.

I previously ran 51x14 (95.6), but have since switched to 58x16 (95.2). It was immediately noticeable how much smoother the system felt. The perceived effort to "get it moving" when responding to accelerations also felt seemingly easier and I could maintain my speed/cadence better once up to speed.

[bikinchris]

Originally Posted by Gabuyo

Not specifically SS, but I have tried this with a fixed gear. I race at the local velodrome (Hellyer). I have participated in probably ~70 race nights, primarily mass start omniums.

I previously ran 51x14 (95.6), but have since switched to 58x16 (95.2). It was immediately noticeable how much smoother the system felt. The perceived effort to "get it moving" when responding to accelerations also felt seemingly easier and I could maintain my speed/cadence better once up to speed.

This. The chain itself will have to articulate less and needs less energy to operate. Also, the chain pulling the rear cog will be much straighter when leaving the rear cog. Larger cogs and chainrings WILL allow the chain drive to be more efficient.
The ten tooth cogs on the modern systems is completely wrong in my opinion.

[dddd]

Originally Posted by bikinchris

This. The chain itself will have to articulate less and needs less energy to operate. Also, the chain pulling the rear cog will be much straighter when leaving the rear cog. Larger cogs and chainrings WILL allow the chain drive to be more efficient.
The ten tooth cogs on the modern systems is completely wrong in my opinion.

True, there is a proportional (to chainring size increase) reduction in the articulation of the links.

But, there is also a proportional increase in the number of links articulating per second.

The increase in swing angle of the links moving around smaller cogs is accommodated entirely under the condition of dynamic friction, while any increase in the number of links flexing incurs more in the way of static-friction threshold events (static friction being much higher than dynamic friction).

As I said earlier, the theoretical considerations are complex.

And I do think that the OP's suggested increase from 17t to 21t would perhaps have much less effect on efficiency than the aforementioned increase from 14t to 19t.
So, well less than 1 watt difference even at the relatively high output of 250W. How might that equate to the added weight and air resistance of the bigger sprockets and longer chain I wonder?

Still, I would expect the larger sprockets to increase the power transfer stiffness/resistance noticeably, seemingly giving this rider more efficient use of my muscles at higher force levels and cadences.

[.RJ]

Originally Posted by dddd

As I said earlier, the theoretical considerations are complex.

If you collect all of your marginal grains together in one basket, you can redeem them for valuable cash and prizes.

[Mark McM]

Originally Posted by dddd

True, there is a proportional (to chainring size increase) reduction in the articulation of the links.

But, there is also a proportional increase in the number of links articulating per second.

It is true that the total articulation is the same (angle of link articulation x number of links articulating). But the with the larger chainrings/sprockets, the chain tension force is lower for a given torque. The force in the articulatin links means the friction force is smaller, thus resulting in less friction loss with the larger chainrings/sprockets.

Originally Posted by benb

Doesn't the larger chainring/larger cog combination also wear out more slowly?

Yes, due to both the lower chain force, and the distribution of wear across more teeth.

[Mark McM]

Originally Posted by ColonelJLloyd

Thanks. Aside from friction, I'm curious more about what the energy required to get them both rolling at the same speed. If I took this to the extreme and say a 63x25 or even larger gear.

The energy of motion (also known as kinetic energy) is just dependent on the mass and speed:

Ek = 1/2 x Mass x Velocity^2

So if you assume no losses (such as friction), then the forces, torques, gear ratios, etc. don't matter - getting a given mass up to a give speed takes the same energy regardless.

But of course, there are losses, and that will affect the energy expended to achieve and maintain a given speed. As others noted, the sprocket/chainring sizes will affect the frictional losses, with smaller chainrings/sprockets having more losses than larger, all else being the same. So with the smaller chainring/sprockets, not only will it take more energy to get up to speed, but more energy will need to be continually applied to maintain that speed.

As a secondary matter, smaller chainrings/sprockets will have a little less mass, so a little less kinetic energy is required to reach a given speed. But the mass of the chainrings/sprockets is just a very small part of the total mass, and the benefit of the smaller mass will be much less than the extra losses from the extra friction with smaller chainring/sprockets, so that the larger chainring/sprockets will require less total energy.

[verticaldoug]

It isn't really worth thinking about. All the mass and wind resistance is with the rider. Worry about the big things first.

After I lose a few pounds, I will think about how I can shave some ounces from my bike.