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.

[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.

[dddd]

I'm not aware of any study that supports larger cogs being more mechanically efficient in the size range we are talking about.
There are complexities to the theoretical study of this topic.

Smaller chainrings induce greater total yield in the drivetrain as felt at the pedal, and it's a second-order (X-squared) sort of relationship since the chain, chainstay and axle firstly flexes more in proportion to any chainring size reduction, while the smaller chainring then secondarily multiplies the added flex distance seen at the chainring teeth out to the pedal due to the leverage relationship there.

The added flex changes the feel and alters the relationship between the muscle's contraction and resultant force response felt at the pedal.
I've always noticed the added "power transfer" stiffness when riding hills in the big ring, the small ring always giving a softer feel that I don't feel jibes well with spirited efforts.
I have gone to some efforts to improve the chainline so as to better optimize my preferred use of the big ring for this very reason, and that includes moving the cogs a bit further toward the dropout where possible and moving the chainrings inward to the limits of clearance and of the front derailer's ability to retract sufficiently. I just don't like the rubber-bandy feel of the chain pulling against smaller sprockets, but it's not a smoothness thing, it's a flex thing.

I'm only a 140# lightweight in case anyone was wondering, but I usually ride steel frames having older-style hubs and bottom brackets that can be set up to alter the overall chainline picture, unlike most of today's rigs.