# Calculating the TPM of your Speedometer Cable

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2 on-line at It is not the scope of this article to describe how to repair or recalibrate an instrument. As an aside, this was Jon Levine s original question (edited slightly for clarity): Does there exist a chart or equation for the conversion of the rate of rotation of the speedometer gear pinion to the MPH on the speedometer? After destroying 2 speedometer cables I removed the speedometer and lubricated the clock works, then spun with an electric drill using the remnants of the cable. I would like to check calibration of the speedometer i.e at 300 rpm x MPH I wrote back: The speedometer turns 1600 turns per mile. At 60 mph, that's one mile in a minute, so it would require 1600 turns in a minute (rpm) at 60 mph shown on the face. 300 turns in a minute would be mph, which is not a very accurate portion of the speedometer dial. Here are some other numbers: 20 mph is 533 rpm 30 mph is 800 rpm 40 mph is 1066 rpm 50 mph is 1333 rpm 500 rpm is 19 mph 750 rpm is 28 mph 1000 rpm is 38 mph 1250 rpm is 47 mph 1500 rpm is 56 mph Method one: Suitable for dealing with changing the rear axle gearing and using your original tires. If you are already happy with the accuracy of your speedometer system and its response, you can be relatively certain that the car s tires, through the current axle, are providing the TPM output your speedometer head needs. In that case you simply need to provide the rear axle change to your technician for recalibration, or if you know your current TPM you can provide your new expected TPM. Needed are the current axle ratio, the new axle ratio and the current TPM. On most of our TDs the axle as delivered by the factory has 41 crown wheel teeth and 8 pinion, or 41:8, which is often stated as 5.125:1, by dividing 41 by 8. A common improvement is to give the car more comfortable high speed cruising by lowering the engine RPM required at a given road speed by raising the rear axle ratio. The common ratio is from the MGA and is 43 crown wheel teeth and 10 pinion teeth. That gives a ratio of 4.3:1. Notice that the ratio is always some kind of odd number so that the same gear teeth must make many revolutions before they contact each other again. This helps to create even wear and promotes a quiet rear end. To calculate the new TPM of the speedometer cable, you simply have to take the new over the current axle ratio and multiply it by the current TPM. In our case that would be 4.3 / x 1600 TPM = 1342 TPM Copyright 2008 Dave Braun 2

4 On my car, the measurements yielded 13.5 turns over 1/100 of a mile, or 1350 TPM. With my new rear axle, this was very close to the 1342 TPM I was expecting. My conclusion is that my new radials are ½ of 1% smaller than the original bias plies. Method four: Suitable for providing a TPM value when you don t know anything about your speedometer system. This method is one that Bud Krueger tossed out which I like for several reasons. First, it allows a rolling start without comparing the frame of the car to the ground, so it is easier to yield an accurate result. Secondly, you probably won t have to push the car as far! And finally, it requires more fun math, and optionally allows for a good tire radius calculation without measuring the radius directly. The description is for rear wheel drive. Just use a front tire on front wheel drive. You need a nice chalk mark on one of the rear tires, your speedometer cable disconnected from the speedometer head, a flag on the speedometer cable, like a piece of tape or a hairpin, and either the rolling radius of your tire, or optionally, the distance the tire traveled in the six rotations (and so a measuring device long enough to measure the distance traveled.) The formula involves a Magic Number i.e. 1680, and N, the number of turns of the speedometer cable while the rear tire turns six revolutions and R the rolling radius of your rear tire. The formula is TPM = 1680 x N / R When Bud offered this formula, I couldn't find a derivation of it on-line so I thought about it for a bit. It comes from: TPM = Turns/mi = Turns of Cable / (6 tire rev x Tire Circumference) x Conversions Where Turns is turns of the speedometer cable in revolutions and is dimensionless Tire Circumference is in inches (2*pi*R) and the R or radius is in inches, and Conversions are 12 in/ft and 5280 ft/mi This yields: TPM = Turns/mi = (Turns of Cable / (6 tire revs x 2*pi*R) in) x 12 in/ft x 5280 ft/mi The inches and feet cancel, leaving miles, and the 6 and 2 cancel with the 12 leaving only 5280/pi which is closer to 1681 than 1680, but according to Bud, truncating to 1680 makes sense as it seems to be an industry standard; and in practical terms, except for digital folk, their resolution is limited by the gear sets available to them. Getting back to the formula: TPM = 1680 x N / R where N is turns of the speedometer cable in six tire revolutions, and R is the radius of the tire in inches. Again, It would be important to measure the radius of the tire on a fully loaded car with proper air pressures, from the center down to the ground, to account for the squish. Or we can eliminate squish as Bud suggested by noting the distance traveled by the car in six tire revolutions. To do this we need to note the ground where the mark on the tire passes the first time during our rolling start, and as we count our tire revolutions and our turns of the speedometer cable (including fractions of a turn), we need to note on the ground where the sixth revolution of the tire ends. If we measure that distance for six tire revolutions, we can determine the rolling radius in inches by: Copyright 2008 Dave Braun 4

5 Distance traveled in feet / 6 revolutions / 2 / pi x 12 inches / feet = R inches Also, you don't have to have the car in gear as the prop shaft will still be turning the gearbox output shaft, and the speedometer gears, in neutral as you push the car (thank goodness!) So in my case, the distance traveled in six revolutions of the tire was /16, while the speedometer cable turned 10 times. R = ft / 6 / 2 / pi x 12 in/ft R = in Which agrees closely with the actual measurement when I try to measure it statically of 12-15/32. My TPM using Bud s formula is TPM = 1680 x 10 / TPM = 1347 The downside to this method is that it is difficult to measure in less than 10 th s of a turn, But it does show that the 1350 TPM number I gave to APT was reasonably accurate! Using the 1342 TPM available by calculation of gear ratios and my tire radius, my possible turns in six tire revolutions is 9.96 turns. It would be hard to measure the difference between 10 turns and 9.96, but I hope this helps you in your own measuring and decision-making! One last reminder for you T-Typers from Bud: Be sure that the nut on the gearbox output shaft is snug. Early gearboxes depend upon this snugness to prevent the speedometer gear from slipping on the output shaft. Later gearboxes incorporate a woodruff key in the gear and shaft. Slippage can give you an erroneous N figure. Don t ask how I know! Copyright 2008 Dave Braun 5

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Page (1 of 14) CONTENTS I. Why Align Rotating Equipment? II. Defining Shaft Misalignment III. Alignment Methods Poor, Fair, Good and Best IV. Pre-Alignment Considerations V. Alignment Methods A. Rim and