Aside from changing your sprockets on a whim, just to change them,
or changing them by feel, to make your bike feel more or less tame when accelerating,
You can also change sprockets with a specific purpose in mind.
Pursuing that purpose with math, rather than by experience, can trade you precious Dollars to just a bit of your time researching, and going over the numbers.
Math can tell you a lot about what you need to know about riding with different sprockets, without having to cash up the cost of all these sprockets and installation time.
In the first example, we're going to change the sprockets, with the purpose to tune the bike for top speed:
The procedure is very simple; and mainly meant for a 125 to 350cc motorcycle; since bigger bikes usually have different speeds to ride them at.
All you need is the bike, access to buying the correct sprockets (eg: online), the right HP/Torque graph, and access to GearingCommander.com .
It works for bikes with chain drive.
Belt, or shaft driven motorcycles don't work like this.
First you'll have to download a HP/Torque graph from the internet of your bike.
This is an example of a Honda Rebel 250's HP and torque and HP curve:
What you see in the curve is pretty common for most sub 500cc engines.
They have a HP band, an area in which the bike performs at it's peak performance.
In this case, the Honda Rebel has it's powerband from 6600 to 8750 RPM.
As you can see from the graph, running the engine in RPMs lower or higher than this band, we will lower the HP output at those RPMs.
Since we're focusing on top speed, we would like to gain this top speed, within the powerband of the bike, rather than at the redline of the bike, where it makes less power.
So, next we do, is ride the stock bike on the interstate, as fast as we can.
Sometimes it takes a good, full 2 minutes before top speed can be gotten, as the engine and engine oil needs to warm up.
A totally cold engine vs a totally hot engine could differ 20MPH in top speed easily!
Once you're riding at top speed, you record the speed, and if possible also the RPM you're getting.
In this case it would be 83MPH at ~9k RPM.
We can verify RPM if we don't have a tach, with gearing commander:
Next, we go back to our HP curve, and notice that when we would gear our bike to do 83MPH at 7500RPM instead of at 9k RPM, that we can gain 1HP from the engine, and 2 LB ft of torque; power gained due to less friction losses, and less pressure losses on the oil pump.
We use gearing commander to get the right sprockets to match the top speed with the RPM we desire.
We also check our bike, to see if the sprockets would mechanically fit the bike, and order them.
Our rebel seems to host counter sprockets from 12t to 15t, with 14t being stock.
It also has 33T rear stock, and we can fluctuate from 25t all the way to about 50t I believe (when the chain guard is removed).
We fill out Gearing commander, 15/29t, and find that at 7500RPM the bike would be doing 84MPH.
We know that at 7500RPM the engine has more HP, and more Torque than at 9k rpm, which means it should go faster than 84MPH.
So we try a 28t instead, and test it out on the road, and find that the bike actually goes 87MPH top speed.
That would be 4MPH top speed gained, by the correct sprockets.
We now want to calculate our MPG gains.
If with our stock riding, we got 70MPG, mainly a mix of 3/4th city and suburbs, and 1/4th highway; our new MPG should come close to:
70MPG * 15/14 * 33/28 = 88MPG
The formula is derived from:
MPGstock * New front sprocket / stock front sprocket * stock rear sprocket / new rear sprocket)
We have gained an average of 18MPG compared to stock!!
You'll notice the more you ride at low speeds, in final gear, the higher this actual number becomes; and the faster you ride, the lower the MPG difference becomes.
When this number becomes lower than a previous gearing, we speak of lugging. A lugging engine, is an engine that is taxed beyond it's capabilities.
Mostly either at very LOW RPMs, or at top speeds; or, in the HP band but going up a hill and the bike is losing speed; can the engine start lugging, and might it be necessary to go into a lower gearing that can carry the load consistently.
We could go back to gearing commander, and try other sprocket combinations.
Suppose that a 27t or a 29t would have slower speed than a 28t; it would mean that the 15/28t is our optimal sprocket for top speed.
We now want to combine high top speed, with great MPG.
We can do this, by creating an extra overdrive; and by making our second to last gear, the same ratio as our last gear.
In the example above, our Honda Rebel's 4th gear would need to have the same speed per RPM as our modified 5th gear.
To start working on this, we go to Gearingcommander again.
We try to get the same speed results in 4th gear at 7500RPM as we had before.
It turns out that we'd need a 15/24t or a 16/25t to do so.
This is mechanically impossible to fit on the Rebel.
But should it have been possible, then we'd be able to run top speed in 4th gear, while maintaining great MPGs in 5th gear from 35MPH (2500RPM) to 60MPH (4400RPM).
In our above example, we could not fit the sprocket on the Honda Rebel.
So we can not gear it for top speed in 4th and great MPG in 5th.
Aside from just equipping it with a 15/25t, which is the maximum gearing the Rebel allows,
we can use a 3rd method to calculate, or aim for a good low speed sprocket.
When we're riding mostly in suburban roads, where the speed limit is 30-40MPH, our speed would be between 35-45MPH (since almost no one on a bike actually keeps the speed limit).
We will want to make sure that the engine will not be in a too low RPM range.
We ride with our current sprockets, in final gear, and slow down and accelerate, oscillating acceleration and deceleration at a constantly lower and lower RPM.
At a certain point in the RPM range, we find that the engine is no longer pulling the load very smoothly; say, 2500 RPM.
We now know we can't go below 2.5k RPM in stock gearing; so the engine won't start making odd noises.
We add 500RPM as a safety barrier, and change our gearing to suit our most optimal low RPM (3000RPM) at our most ridden speed (40MPH).
We use gearing commander again and notice that a 15/25t is getting pretty close to the gearing we desire!
It gives us 39 MPH at 3000 RPM.
We order the 25t sprocket, install it, and test ride it;
In this case, starts from a dead stop are a bit harder, but not impossible.
At 1400RPM, in 1st gear with the 15/25t sprocket setup, the speed is 5.9MPH.
At 1400RPM, in 2nd gear stock (14/33t), the speed is 6.6 MPH.
This means that our first gear is shorter than a stock 2nd gear, and if we can start the bike in second gear stock, we can much easier start it in 1st gear modified.
There's really a lot, lot, and lot more that comes to play in selecting the right sprocket. HP and Torque needs to be looked at, as well as wind resistance, to see if the bike has enough acceleration for regular traffic.