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Reading Gear Ratios
Determining speed potential

By: James R. Davis



While reading my owner's manual a few days ago I came across a chart that listed my gear ratios in a section entitled: Power Transmission. It showed:

Primary reduction 1.708
Secondary reduction 0.973
Gear ratio, 1st 2.571
2nd 1.667
3rd 1.250
4th 1.000
OD 0.800
Final reduction 2.833

I also found that the engine in my bike redlines at 7,500 RPM and that my rear tire is a '150/90-15 74H'

From that information I was able to construct a pretty healthy understanding of shift points, speed ranges and maximum theoretical speed of the motorcycle. This article is designed to help you do the same with your own bike.

First, let's look at the power transmission. The primary and secondary reduction ratios mean that the revolutions made by your engine have been reduced by two sets of gears BEFORE it gets to your transmission. You must divide the engine's RPM by the product of these two ratios in order to determine how fast the input shaft to your transmission is turning.

For example, since the product you get by multiplying 1.708 and .973 is approximately 1.662, if the engine is making 2,000 RPM, then the input to your transmission is turning at the rate of 1,203 RPM (2,000/1.662).

The output of your transmission is then determined by what gear you are in. For example, if you are in 3rd gear, the output from your transmission is approximately 963 RPM (1,203/1.25).

And that output is reduced one more time by a set of gears in your rear-end so that the rear wheel will be spinning at the rate of approximately 340 RPM (963/2.833).

So? How fast your bike is moving at any particular engine RPM, I imagine, is what you are really interested in. That, of course, is a function of the radius of the rear wheel.

You could, if your bags were not in the way, simply measure from the center of your rear hub HORIZONTALLY to the tread to find the radius of the tire. (Note, this gets you a number close to the radius you would obtain from the information printed on the tire - and is accurate enough so long as you run with normal air pressure. If you run with low tire pressure then your tire will actually not be riding on the tread center-line at all but somewhere farther out. In other words, because of cambered design, the tread center-line will be sloughing against the pavement while the tire along the outside edges of the contact patch (which are closer to the hub of the wheel) will determine distance traveled.)

But from the information in your owner's manual you already have most of the information you need and, given normal air pressure in your tires, will be accurate enough to calculate speed from. The '-15' means that the rim the tire fits on has a diameter of 15 inches. The '150' means that the tire is 150 mm wide and the '90' means that its height is 90% of its width, giving a height from tread to bead of 135 mm. 135 mm is 5.31 inches. Thus, the radius of the rear tire is 5.31 inches plus 1/2 the wheel diameter of 15 inches, for a total of 12.81 inches.

From high school you remember a formula that determines circumference based on radius. You decide that you would rather ride a motorcycle instead of multiplying PI times twice the radius and converting the results from minutes and inches to miles and hours at this point in your life. So, I present you with a straight forward formula for converting engine RPM, final gear ratio and tire radius into MPH:


MPH = (Engine RPM * Radius) / (Final Gear Ratio * 168)

The 'Final Gear Ratio' is merely the product of all gear ratios involved. Thus, in our example it is 5.885 (1.708 * .973 * 1.25 * 2.833).

We can now use the formula:

MPH = (2,000 * 12.81) / (5.885 * 168)
MPH = 25,620 / 988.68
MPH = 25.91

At 2,000 RPM, in 3rd gear, your bike is moving at almost 26 MPH. It is just as easy to determine that if the engine were redlined (7,500 RPM) in 3rd gear your speed would be slightly more than 91 MPH.

The reason a tachometer is marked with a red band near its top end is that running your engine at those speeds yields a power falloff and may do damage to it! Further, your power curve tends to fall off as the engine RPM approaches redline. [You can damage your engine running it at lower than its redline - the redline is NOT a damage/no-damage point.] So, you are well advised to keep your engine RPM at less than about 80% of redline. In the case of my bike, that means at less than about 6,000 RPM.

Similarly, running an engine too slowly lugs it down because the power curve is not adequate there. Since most motorcycles idle at about 1,000 RPM, which is just barely sufficient to keep it from stalling, you know that you want to keep your motor running faster than that in order to accelerate. My preference follows the 80/20 rule. That is, just as I want to keep my engine running less than 80% of redline, I want to keep it running faster than 20% of redline while moving. That means that I want my engine running between 1,500 and 6,000 RPM except when out of gear.

Furthermore, it is my preference to try to keep the engine at 50% of my conservative redline. That is, at 50% of 6,000 RPM. At 3,000 RPM my engine should last forever. And, in the case of running in Overdrive, it is a high enough RPM that the power curve is sufficient to accelerate.

I leave it to the reader to take the formula I provided in order to determine the highest speed their bikes are theoretically capable of attaining. I might add, however, that the higher the gear, the less likely you are able to reach redline with your engine. But you should be able to reach my conservative redline (80%).

Copyright © 1992 - 2021 by The Master Strategy Group, all rights reserved.
http://www.msgroup.org

(James R. Davis is a recognized expert witness in the fields of Motorcycle Safety/Dynamics.)

     
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