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This page is provided to provide you a convenient method to access all the gearing and gear ratio formulas.
When you complete one computation, please remember to write it down as the results may be necessary for another formula.
We will not be computing internal transmission gear ratios as these are normally available either in the service manual or from the manufacturer of any aftermarket transmission.
Primary Ratio Seconary Ratio Final Drive Ratio Overall Gear Ratio RPM Lost After Shift Sprocket Size
The Primary Gear Ratio is simply the ratio between the number of teeth on the engine sprocket and the number of teeth on the clutch basket.
This one's an easy one. All you have to do is count the number of teeth on your engine sprocket and the number of teeth on your clutch basket. Then you divide the number of teeth on your engine sprocket into the number of teeth on your clutch basket.
For example, on our '71 Triumph TR6, we have 29 teeth on our engine sprocket and 58 teeth on our clutch basket. When you divide 29 into 58 you get a 2:1 primary ratio.
Of course this gets a bit harder if these numbers aren't in your service manual (you DO have a service manual don't you???). If you don't have a service manual (which you should), you will have to pull your primary cover and physically count the teeth on each component. This really isn't to difficult. Use a colored grease pencil to mark the tooth you start on so you don't lose count. And don't forget, USE A NEW GASKET WHEN YOU REPLACE THE COVER!
The Secondary Gear Ratio is simply the ratio between the number of teeth on the transmission sprocket and the number of teeth on the rear wheel sprocket.
Let's assume that you have a transmission sprocket with 20 teeth and a rear wheel sprocket with 40 teeth. We are also assuming that you do not have a transmission, that the tranny sprocket is attached directly to the engine's crankshaft. This means that each time your engine makes one complete revolution, the tranny sprocket will also make one complete revolution. That way we will not have to deal with the transmission's internal gear ratios at this point.
Let's also assume that you have a tire that has a CIRCUMFERENCE of 3 feet or 36 inches.
Let us also assume that your top RPM is 7000.
We will be dealing with a distance of 1320 feet (Surprise!!! That's a quarter mile).
With 20 teeth on the tranny sprocket and 40 teeth on the rear wheel sprocket, you will have a final drive ratio of 2:1 (40 divided by 20). This means that each time your tranny sprocket makes one full turn, your rear wheel sprocket and rear wheel will make a half a turn or 18 inches (36 divided by 2).
If you increase the number of teeth on the tranny sprocket to 25 teeth, you will have a new ratio of 1.6:1 (40 divided by 25). This now means that your rear wheel will move forward about 22.5 inches (36 inches divided by 1.6). Now your engine has made one revolution, but that one revolution has made your bike move forward 4.5 inches MORE, IN THE SAME AMOUNT OF TIME, with the addition of 5 teeth on the tranny sprocket. Hence, less work for the engine for you to go further per revolution. This is why you'll hear racers say that more teeth on the tranny sprocket will give you a higher top end speed.
Also, please remember that it takes so much power to turn the engine that one revolution.
Let's take the same scenario but this time DECREASE the rear wheel sprocket by 5 teeth to 35 teeth. You now have a ratio of 1.75:1, (35 divided 20). Under these conditions, your bike will move forward 20.57+ inches (36 divided by 1.75) for each individual single revolution of the tranny sprocket. This is 2.87 inches MORE than the orginal 20 tooth/40 tooth arrangement. Again, less engine revolutions to make your bike go farther. Again, this means less strain on your engine.
So, in summary, if you INCREASE the number of teeth on the tranny sprocket or DECREASE the number of teeth on the rear wheel sprocket, your top speed will increase. Also, changing the number of teeth on the rear wheel sprocket does not cause as much of a change as changing the number off teeth on the tranny sprocket.
Now we will look at the opposite instance.
Let us DECREASE the number of teeth on the tranny sprocket from 20 to 15 teeth. Your final drive ratio will now be 2.667:1. For every one revolution of the tranny sprocket, your rear wheel will travel 13.498 inches (36 divided by 2.667). Hmmm, so now you're using the power of a single revolution of the engine to turn the rear wheel and go a SHORTER distance than with the stock sprockets. 18 inches versus 13.498 inches. BUT to travel that 13+ inches you have all the power available in one revolution of the engine.
OK, now lets add teeth to the rear wheel sprocket. You now have 20 teeth on the front sprocket and 45 teeth on the rear sprocket. That gives you a final drive ratio of 2.25:1. For each single revolution of the engine, your rear wheel will travel 16 inches (36 divided by 2.25). Again, your tranny sprocket (on the engine) will turn LESS than one revolution to make your rear wheel move that 16 inches.
One other point we'd like to stress at this point. During that one revolution that the crankshaft is making, the FORCE that it generates in analogous with TORQUE. Now, if you take that revolution, do it more than once, you now have RPM or revolutions per minute. Once you add the element of TIME, to the element of FORCE, you now have HORSEPOWER which is basically FORCE OVER TIME.
We will revisit this page at a later date and, using the above data and calculations, extend it to calculate what effect the various ratios will have on your 1/4 mile times and ET's.
The Final Drive Ratio is the Primary Gear Ratio times the Secondary Gear Ratio. This ratio is not used very often, but we have included it here so that you can use it for reference.
We hope that you have been writing down the results of other calculations. For this page, you will need to know the Primary Gear Ratio and the Secondary Gear Ratio. If you haven't figured these yet, go back to the top of this page and compute those two items.
The Overall Gear Ratio is simply the transmission internal gear ratio times the final drive ratio.
I don't know how I missed this formula and info the first time around. It is very important.
Every time you change gears, you lose a certain amount of RPM. Ideally, you should shift at about peak horsepower RPM (hopefully at some point you have had your bike dynoed). After the shift, you should be at peak torque RPM or on the upslope side of the torque curve, not on the downslope. If your bike is not always accelerating, you are losing the race.
An interesting fact occurred to me while I was working on some formulas for weight transfer. By this time, you should all be aware of what torque is. If you have a lever one foot long, and you apply 100 pounds of pressure to that lever, at the pivot point you have 100 lbs/ft of torque.
torque = force (in pounds) times lever length (in feet)
I was trying to figure the amount of force or thrust at the rear wheel to calculate the forces at launch. After several false starts, the answer was right before my eyes!
torque
force = -----------------------------
lever length
It then dawned on me that the driveline is not one component but a system of several components. For example, at the tranny sprocket you have "x" torque being applied at the shaft. That torque can then be divided by the radius (or 1/2 the diameter) of the sprocket to find the force being transmitted to the wheel sprocket. You can then compute the torque being applied to the rear wheel sprocket by knowing the radius (or 1/2 the diameter) of the rear wheel sprocket. Then the next step becomes computing the amount of torque transferred to the rear wheel via that sprocket. The last step is then computing the amount of force generated at the contact patch of the rear wheel.
What this means is that if you are happy with a certain gear ratio, you don't have to change that ratio to increase the amount of force being applied at the rear wheel. By simply changing the sprocket sizes, while maintaining the same ratio, you can increase that force. Running several calculations, I have found that decreasing the sprocket sizes results in an increase in force.
Bear in mind that these calculations do not take into account frictional losses, the size of the contact patch, inertia, tire to road friction, etc. However, what these calculations will provide you is an idea of how much that force at the rear wheel will increase given a certain sprocket size change.
When you enter the values in the following calculation, if you don't know the exact torque figures, don't worry. Simply compute the percentage change from one sprocket set to another. And also don't worry about calculating the radius of the sprockets. You will be asked to enter the diameter and the program will figure out the radius for you. You will have to run the calculations twice, once to figure the amount of force for your current sprocket setup and once to compute the value for a new sprocket set. Make sure you write down the value produced for the first calculation so that you can compare it with the second.
Now I'm sure that others have already thought of this before but to me, it was a bit of a revelation and it may be one of those little tricks you can use to beat your opponent.
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Last revision : August 30, 2009
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