Ratios, sprocket diameter, and acceleration

[Frankster]

In this scenario, the only values that change are the sprocket sizes, weight and the number of teeth. My question relates to efficient use of available power. On a motorcycle, I have a front sprocket with 14 teeth and a rear sprocket of 48 teeth. The chain length is 120 links and it is a 520 gauge chain. The power at the drive shaft is 'constant' as is the size and weight of the rear wheel and the unsprung weight. We can assume that each sprocket has half of its teeth in contact with the chain at all given times.

What I am keen to determine is the effect of changing the sprocket sizes while still keeping the same ratio. As an example, if I use a 28 tooth front sprocket and a 96 tooth rear sprocket or a 7 tooth front sprocket with a 24 tooth rear sprocket. What will the effect be on acceleration, force exerted on the drive shaft and wear on the chain and sprockets. Obviously, the weight of the sprockets will change as they get bigger or smaller and the number of teeth in contact with the chain will also change as will the length of the chain needed to maintain the same distance from the drive shaft to the rear axle.

Assume the weight of the sprockets changes with the number of teeth e.g. 7T sprocket is half the weight of 14T and 28T will be doubled the weight of 14T sprocket. Chain weight will increase slightly when used with larger sprockets and decrease with smaller sprockets. My brain tells me there will be no effect on acceleration regardless of size of the sprockets, but I am curious to hear what the forum members think.

 

[Baluncore]

My brain tells me there will be no effect on acceleration regardless of size of the sprockets, but I am curious to hear what the forum members think.

With bigger diameter sprockets, the speed of the chain will increase, while for the same wheel torque, the chain tension will be proportionally reduced.

It comes down to the strength of the chain, and that is decided by the dimension of the rollers and pins in the chain.

Stronger chains have bigger links, which must be longer. Bigger links need less teeth on the same diameter sprocket. But geometry makes roller chains engage and disengage cleanly, and more quietly, when they have more than 12 teeth on the sprocket. To be weight optimised, the minimum sprocket, in the system, should have 13 or 14 teeth.

 

[jrmichler]

There are a number of variables involved in chain drive design. Search roller chain catalog, then dive into the engineering sections. The U.S. Tsubaki chain catalog is a (not the only) good one. The chart below is from page 253 in the Tsubaki Roller Chain Drive Selection Process section of the catalog.

Read the introductory section starting page 1 of the catalog first, then the engineering section starting on page 251. Study carefully the parts about lubrication vs chain speed.

On a motorcycle, the inertia of the chain drive (inertia of sprockets plus chain) is a very small portion of the total inertia. That being the case, the size and weight of the chain drive has negligible effect on acceleration. Then the drive design criteria is the minimum cost drive that delivers acceptable life and reliability. BTW, a 28 tooth sprocket is four times the weight of a 14 tooth sprocket, and has 16 times the inertia.

 

[Lnewqban]

Welcome, @Frankster

The limitations are in the front sprocket: the diameter of the output shaft (minimum number of teeth for certain chain pitch) and the available clearance outside the transmission case (maximum).

Chains with 1/2" pitch have more teeth to play with than 5/8" and 3/4" ones.
Smaller sprockets work harder: more frequent tooth engage-disengage and greater centrifugal force, which makes more difficult keeping the lubrication on the chain.

The differences you are looking for are not huge, as you are geometrically restricted (impossible to make 7 and 28 teeth front sprockets to fit).
Even if you could, for your 520 chain, the diameters will be within the range of 1.15 to 4.45 inches.

 

[Frankster]

Thanks Baluncore

I am of the opinion that the weight of the chain and sprockets will also have an effect on acceleration. I'm only really interested in accelerating quicker using the same ratios. I can go from a 520 gauge chain to a 420 gauge and change the sprockets to suit; the rollers are the same size, but the links are closer together (4/5th of the distance). If the drive shaft produces 50HP and drives through a 520 chain using 14T/48T sprockets, I wonder if using a 420 chain with an 18T/62T sprocket set will 'allow' more of that power to get to the rear wheel. Again, unsprung weight being the culprit; less weight in the drive train means more efficient use of the power...yes? I know we're talking about fractions, but I am about to build another bike for salt racing and I am looking for any options to pick up power and/or acceleration/speed.

 

[Frankster]

On a motorcycle, the inertia of the chain drive (inertia of sprockets plus chain) is a very small portion of the total inertia. That being the case, the size and weight of the chain drive has negligible effect on acceleration. Then the drive design criteria is the minimum cost drive that delivers acceptable life and reliability. BTW, a 28 tooth sprocket is four times the weight of a 14 tooth sprocket, and has 16 times the inertia.

That's interesting to know. What formula do you use to arrive at that?

The limitations are in the front sprocket: the diameter of the output shaft (minimum number of teeth for certain chain pitch) and the available clearance outside the transmission case (maximum).

Let's pretend there are no physical (bike) limitations. For the sake of the exercise, assume there is 50HP coming through a drive shaft and the only other constant is the distance from the centre of the drive shaft to the centre of the rear sprocket. Everything else is changeable. I can certainly gain a little by going from a 520 gauge chain to a 420 chain. I can also reduce the weight of the sprockets by using lighter material. The main question is what size should the sprockets optimally be to gain the least amount of power loss when driving the rear wheel. What variables do I need to factor in to my equation.

 

[Baluncore]

Welcome to PF.

Minimise the weight. If you know the RPM and HP, use the chart shown in post #3 to select the size of chain required.

Next find an acceptable chain drive ratio, p/q, where p and q are integers.
Make sure that p and q are as small as possible, while both have more than 12 teeth.

The weight of a sprocket is proportional to the area of the circle, which is a square law function. A heavier chain will run on a thicker sprocket plate that weighs more.

 

[Ranger Mike]

Every pound you can take off a race car or bike in rotating weight is like you reduce the weight of the race car or bike by 10 pounds when accelerating. The stock chain and sprockets you are using are meant to go 50,000 miles so the manufacturer does not have warranty issues. Screw that in racing. Cut down the weight of the rotating mass and gain a real advantage over the competition. Go with the narrower number 35 chain versus the number 41 chain if the power does not hinder you. Be advised that if you do this, more cost as you must replace the lighter chain more often.