# Bicycle gear ratios for maximum efficiency

1. Jun 14, 2010

### bill9999

We all know that there are several options of front sprocket/rear sprocket combinations that achieve the same gear ratio. i.e. A large front sprocket with medium rear or medium front with larger rear will produce the exact cadence at a given speed.
What I've always wondered, is there any advantage (in torque, efficiency, power or energy) in peddling using a medium front versus a large front sprocket assuming equivalent cadence-speed?

2. Jun 14, 2010

### phyzguy

I've wondered this, too. If the gear ratio and cadence are the same, I think a larger front sprocket means that the chain is moving faster. Since there must be small losses every time the chain links bend and straighten as they go around the sprockets and idler wheels, I would think that the larger front sprocket would be slightly less efficient. However, I think that the difference should be very small. What do you think?

3. Jun 14, 2010

### uart

Yes but you are neglecting another important difference. With the larger sprocket/cogs the velocity is larger but the force (tension) on the chain is correspondingly smaller. To a first order approximation with all other things equal these two effect should cancel out and the losses be similar.

There is yet another difference though, and that is that each link bends and straightens less (through a smaller angle) with the larger sprocket/cogs. So I think the efficiency advantage here would actually go slightly to the larger sprockets. Countering this however is that there would typically be a small weight penalty to the larger sprockets and corresponding slightly longer chain.

Regardless of efficiency concerns there is no doubt that there are smaller forces in both the chain and bottom bracket bearing in the case of larger sprocket/cogs. So that is definitely one advantage of this configuration.

Last edited: Jun 14, 2010
4. Jun 14, 2010

### jack action

Interesting question. I think there are only very small differences which must be practically unnoticeable, but here how I see it:

Like uart said, having the chain on larger gears means less deflection from each chain link which causes less friction to fight.

But having the chain on smaller gears means less inertia, as the chain's weight is closer to the center of rotation.

Since inertia is a problem only during acceleration, I would say that if you're at constant speed, use the larger gears to take advantage of the lower friction losses and if you have to accelerate frequently, use the smaller gears to take advantage of the lower inertia.

Again, it must be a really small effect.

5. Jun 14, 2010

### bill9999

Thanks for the replies. I agree with your analysis, the efficency change due to friction may be affected but the increased effort by the bicyclest would be practically unnoticable. However, when I first started thinking about this issue I was wondering if there is a more significant effect of using different diameter front sprockets that may cause a noticable change in torque delivery or work done to maintain a constant speed. Any ideas on torque and/or work?

6. Jun 14, 2010

### jack action

The torque output vs the torque input depends only on the gear ratio; the size of the gears have noting to do with it.

Work is a form of energy and energy (or even the power) must be conserve, so power in = power out, no matter what is the gear ratio (It is only "converted" from torque to rpm or vice versa).

7. Jun 14, 2010

### m.e.t.a.

So that I can refer to the various gearing setups more easily:

[SS] = small rear gear with (equal-sized) small front gear
[LL] = large rear gear with (equal-sized) large front gear
[ML] = medium rear gear with large front gear
[SM] = small rear gear with medium front gear
(etc.)

The combinations [ML] and [LM] do not result in the same bicycle speed for the same pedalling frequency. Did you mean, "A large front sprocket with medium rear or medium front with small rear will produce the exact cadence at a given speed"? This makes sense for the case when the gear ratios L:M and M:S are the same. Then, for a given pedalling frequency, your bike would travel at the same speed in either gearing combination. I think this was your question (?)

I couldn't possibly estimate the effects of the complex stresses, frictions etc. on the chain and gears in each of the two cases. For my opinion, I would say that riding "feels smoother" when using the largest pair of gears possible, i.e. [ML] seems to make for an easier ride than the equivalent [SM]. Similarly, when I'm riding I feel that [LL] gives me less friction than [MM] or [SS]. This is just the impression I get from my own, very subjective, experience.

8. Jun 14, 2010

### bill9999

M.E.T.A. Yes I did mean to say medium front with smaller rear...oops.
And the more I read the more I'm feeling that there will be no appreciable difference in torque or power. I will continue to use the mid and large front sprockets to minimize the "Stretching" that I've seen on the teeth of the small front sprocket due to the high torque placed on such few teeth.

9. Apr 9, 2011

### Sprogpole

Hi All,

I'm new to your forum, but I am an international BMX rider and I have a few questions on this topic that maybe you could answer.

The Bike Chain
The chain is under tension across the top of the chain line (from rear wheel to crank) and relaxed along the bottom. (From crank returning to rear wheel)
This exerts only a pulling force across the top of the chain line as the bottom line is only returning the chain links to the rear wheel for use again.
So, the main driving force is only ever a pull via a lever (the cranks).

If we compare two gear combinations, both with the same ratio, One will be pulling the chain from a position nearer to the bottom bracket and further from the pedals and the other ratio using say a larger front sprocket would be pulling the chain from a position nearer the pedals and further away from the bottom bracket.

What would be the better position for developing more torque pulling the chain?

Secondly.

A larger rear sprocket is further away from the rear wheel axel and nearer the tire. The sprocket is being pulled in the rotating direction towards the cranks. Would a larger or smaller rear sprocket provide more torque to the tire/road? I'm thinking how much easier it is to spin a wheel from it's outer circumference than it is from its centre pivot point.

If we can exclude friction in the chain line from this because although It will have an effect, it is always kept to an absolute minimum using the latest lubrication and if we can also exclude weight because it is not constant. E.g. a larger sprocket can weigh less than a smaller one because larger sprockets have space that can be hollowed without effecting strength. The space for drilling is simply not available on smaller sprockets so they are often heavier than larger ones.

Thanks guys
Any advice on this leverage effect is very much appreciated.

10. Apr 9, 2011

### mrspeedybob

The largest factor is that certain gears are more closely aligned with each other. Take 3 examples...

1. The large front sprocket with the large rear sprocket.
The large front sprocket on a bicycle is the most outboard sprocket, the largest rear sprocket is the most inboard sprocket. The tension of the chain pulls the chain against the outboard edges of the teeth on the front sprocket and the inboard edges of the teeth on the rear sprocket. In addition to the extra friction chain links will sometimes catch on the peak of a tooth momentarily before dropping onto it, this produces a less smooth operation.

2. The small front sprocket with the small rear socket.
This is a very similar situation to #1. The small front sprocket is the most inboard and the small rear socket is the most outboard. They don't line up well, therefore this combination does not work well.

3. The middle front sprocket with a middle rear sprocket. The sprockets are in line, there is less friction with the sides of the sprocket teeth and the chain rolls smoothly onto both sprockets.

I have ridden thousands of miles on 18 speed mountain bikes. My experience is that the mechanics work better if you use sprockets that are close to being in line with other.

11. Apr 9, 2011

### Sprogpole

mrspeedybob

I totally agree, if for nothing else than fatigue and premature failure of your chain.
Chains are not to good a going sideways especially under tension.

However, BMX Bikes are always single speed so the chain line is always straight.
We change gear ratio by actually removing chain rings and sprockets and fitting / refitting different sizes.

Also, I did ask if we could keep friction out of it.