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Old 08-05-10, 07:41 PM   #1
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why the variation in speedometer charts on tire size --> circumference

so the user's guide to every speedometer has a little chart giving the circumference for common tire sizes.
But the exact circumference (almost always listed in millimeters) for a given tire size is not consistent across the various speedometer user's guides that I have.

What I'm wondering is, is the variation actually meaningful? For example, say I have two bikes with identical 700x25c tires. One speedometer says to program 2124mm circumference, another says 2146mm. Is this meaningful? that is, does the speedometer have something else going on in its programming that I should plug in the number specified?
Or are all speedometers just multiplying wheel circumference by the number of rotations to get distance?

I assume the latter, and the differences in listed circumference are just because of variations in the tires that the manufacturers measured, or because they were just sloppy in producing the chart. But I'm curious to hear if others share my assumption.


Just for the record, here's an example of the existing variation. Circumference measurements for 700x25c tires from the various speedometer user's manuals I have...

2100 (Cateye Mity 2, from about 1995)
2105 (Filzer wireless)
2110 (Cateye Mity 8 and Cateye Velo 2)
2120 (Planet Bike Protege)
2124 (Ascent wireless)
2146 (E3 and Axiom, which I think are both Performance in-house sub-brands)

Last edited by TallRider; 08-05-10 at 07:51 PM. Reason: add data
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Old 08-05-10, 07:46 PM   #2
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The variation is due to rim width. the wider the rim, the less tall the tire will be and that will affect the overall diameter.

i would the the blame of laziness goes with the owner, who should be measuring their own rolling circumference for the most accurate reading.

For the most accurate measurement you should also sit on the bike as your weight will deflect the tire and change the circumference. Also you should ensure that your tire is always at the same identical pressure, otherwise the circumference will drop and your readings will be affected likewise.
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Old 08-05-10, 07:52 PM   #3
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Those are just rough estimates. Actual tire sizes vary from brand to brand even though the nominal sizes are the same.
There is an area near my home with section line roads that have survey pins in the center of the intersections. Pin to pin is exactly one mile. In the past when I wanted a lot of accuracy I would calibrate my speedometers with those survey pins. But I quit worrying about it and no longer bother to do that.
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Old 08-05-10, 07:53 PM   #4
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glad to hear that others share my assumption. I just wanted to make sure that this all points back to "measure your own wheel circumference."
And also "speedometer makers are lazy or at least not careful when putting together their guides/charts."
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Old 08-05-10, 07:53 PM   #5
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AFAIK they just multiply the wheel rotations. And every tire manufacturer is different, and every bike and rider weighs a different amount, and everyone inflates their tires differently. The problem is that the circumference measured is not the circumference that one would tape with the wheel off the bike. Rather it is pi*D, where D is twice the radius from the hub center to the road in the center of the contact patch, the bike being loaded. So at best, the manufacturer is offering an approximation.

To get it closer for the initial installation, stretch out a tape on the floor next to a wall. Get on the bike and push yourself along the wall, while measuring valve-to-valve on the wheel with the magnet. That should be close for that tire and inflation. Then the next time you're out on a long measured course, see how your mileage matches up with that of the course designer. You can use ratio and proportion to tune it closer. Every time you fit a new brand or size of tire, you'll have to do it over if you want it to be accurate.
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Old 08-05-10, 08:05 PM   #6
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The problem is that the circumference measured is not the circumference that one would tape with the wheel off the bike. Rather it is pi*D, where D is twice the radius from the hub center to the road in the center of the contact patch, the bike being loaded. So at best, the manufacturer is offering an approximation.
Correct, measuring the circumference with a tape will not give you the right answer.
If you do a roll out measurement it will be better to measure several rotations and then average those.
And do this for the wheel with the magnet and computer sensor. The rear wheel carries a much larger proportion of the weight.

Last edited by Al1943; 08-05-10 at 08:08 PM.
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Old 08-05-10, 08:08 PM   #7
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Calibration numbers given in mm or cm are the estimated circumference of the tire so the bike's travel distance is just that number times the number of revolutions. Avocet used to express the circumference in inches and others may use an arbitrary number.

Cat Eye, among others, uses the circumference in mm or cm as their calibration values. From their charts it appears they assume the tire is circular in cross section. Therefore, the wheel diameter is the rim's bsd +2* (tire width) and the circumference is pi times that number. For a 700x23 tire the diameter would be 622 + 2*23 = 668 mm and the calibration number would be 668*3.1415..... = 2099 mm or 210 cm. And, in fact, that is the value their chart gives for a 700x23 tire.

Variations in calibration number from manufacturer to manufacturer are possibly due to many bike tires not running true to their marked size. I've seen tires marked 700x23 as small as 21 mm in width and I have some tires marked 700x32 that actually measure 26 mm both wide and high.

Also, loading the tire and doing a rollout can give slightly different distance than the assumed circumference so that may be another source of difference. Actually, a carefully done rollout is the most accurate way to determine the true calibration for your particular tire and weight.

Your example values of 2124 and 2146 is a difference of 1% or 1 mile in a century. I personally want better accuracy than that but many riders don't care.

Last edited by HillRider; 08-09-10 at 05:32 PM. Reason: Corrected a typo in the value of Pi.
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Old 08-09-10, 12:24 PM   #8
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Your example values of 2124 and 2146 is a difference of 1% or 1 mile in a century. I personally want better accuracy than that but many riders don't care.
In the data I report above, it's worse than 1%. The difference between 2100 (low value) and 2146 (high value) is 2%. That's an even bigger deal, and as you say, below the level of accuracy I want in measurement.
Now, I could arguably throw out the 2146 from analysis (since it's such a far outlier, we could just say it's erroneous, and even though it showed up in two user's manuals, those are both Performance in-house brands so they presumably were working from the same chart). And we might also throw out the low value (2100) since it is from the mid-90's whereas everything else is mid-2000's and since. Then the low value is 2105 and high value is 2124, which is still a variation of 0.90%

In the past I've ridden a lap or two on a running track (400m or 800m) with the speedometer set in km, to try to nail exactly 0.40km or 0.80km. As long as I'm not weaving, that's about the best roll-out measurement I could hope for. (unless the tire behaves differently on a rubberized track than it does on pavement)
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Old 08-09-10, 01:39 PM   #9
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I measure a course with google maps, then adjust the wheel size setting by the percentage that the speedo is off. Setting it this way over 20-25 miles is as accurate as google maps at 3x the distance so that's close enough for me.

I always wondered about weighting the bike for rollout tests - I don't see how the circumference would change. (Tire squish ~= contact patch size != circumference). I started to test it once, but I got sidetracked thinking about the difference in effective torque from the shorter effective radius of a loaded/squished tire, then I saw a cool butterfly... and then I quit worrying about rollout measurements and went for a ride.
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Old 08-09-10, 01:51 PM   #10
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A single rollout with or without a bit of weight on the bars is sufficient to be within less than 1% accuracy. All the other time one would spend is better done on the road, riding.
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Old 08-09-10, 01:56 PM   #11
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Originally Posted by TallRider View Post
What I'm wondering is, is the variation actually meaningful? For example, say I have two bikes with identical 700x25c tires. One speedometer says to program 2124mm circumference, another says 2146mm. Is this meaningful? that is, does the speedometer have something else going on in its programming that I should plug in the number specified?
This is a 0.1% difference. That's 0.1 miles per 100.

Since all 25mm tires are not all the same and things like pressure and load produce different effective circumferences, the best thing to do is measure your setup (with you and your load on the bike). People might prefer entering a number from a chart rather than doing the real measurement.

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Or are all speedometers just multiplying wheel circumference by the number of rotations to get distance?
Yes. Speedometers (other than GPS) detect wheel rotations and compute the speed/distance from the circumference entered.

Last edited by njkayaker; 08-09-10 at 02:02 PM.
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Old 08-09-10, 02:00 PM   #12
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I always wondered about weighting the bike for rollout tests - I don't see how the circumference would change. (Tire squish ~= contact patch size != circumference).
The patch size is related to the effective circumference.

The more load you put on the tires, the wider the patch gets and the closer the hubs get to the ground. The effective radius (the distance between the center of the hub and the ground) decreases (which means the circumference decreases as well).
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Old 08-09-10, 04:49 PM   #13
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As already suggest...don't waste time on this. Do a couple rough rolls with inflation and some weight...input a "close enough" estimate and ride.

If you are going to agonize over every little 10th of a MPH or 100th of a mile - I question why you have a bike to begin with.

To be honest, most folks I have setup for are happy with the generic references in the manuals.

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Old 08-09-10, 05:02 PM   #14
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This is a 0.1% difference. That's 0.1 miles per 100.
Wrong! The original calculation was correct at 1% or 1 mile per 100. Check your math.
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Old 08-09-10, 05:41 PM   #15
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In the data I report above, it's worse than 1%. The difference between 2100 (low value) and 2146 (high value) is 2%. That's an even bigger deal, and as you say, below the level of accuracy I want in measurement.
Now, I could arguably throw out the 2146 from analysis (since it's such a far outlier, we could just say it's erroneous, and even though it showed up in two user's manuals, those are both Performance in-house brands so they presumably were working from the same chart). And we might also throw out the low value (2100) since it is from the mid-90's whereas everything else is mid-2000's and since. Then the low value is 2105 and high value is 2124, which is still a variation of 0.90%)
I have no idea where the 2146 could have come from but, as you say, it's probably an outlier or a typo. All of the Cat-Eyes I've seen use 210 - 211 cm for 700x25 tires and that's calculated from the circular cross section assumption I mentioned above. If the tires are true 25 mm then the actual rolling circumference will be very close to that if the tires are inflated to say 100 psi or thereabouts as the deflection is pretty small.

BTW, I use 209 cm (Cat-Eye says 210) for 700x23 tires and once rode a 10K TAC certified race course on my bike and it agreed with the course distance (6.214 miles) within a few feet. Good enough. Various model tires differ more than that.
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Old 08-09-10, 06:11 PM   #16
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The range from the smallest to the largest (including the 2146) is about 2%. When you inflate your tires are you consistent to within 2%?

Sometimes close enough is close enough.
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Old 08-09-10, 06:32 PM   #17
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If my speedometer say's I'm going 19.2 mph, I expect that I'm actually traveling at 19.2 mph and not 19.0!

I get really pissed when I find out it's wrong. (really, I do).

So now let me describe how I calibrate my computer. Tell me if this is accurate or not.

I set it according to the instructions, Sheldon Brown's numbers or even the default number it comes at. Just to get a baseline.

Then I ride the bike for a few miles over a course that I've measured on Google Earth. I generally use the Yolo Causeway because it's almost perfectly flat and straight and 3.11 miles from levee to levee. It's also on my way to work. As I ride, I try to stay as straight and centered as I can.

Then I take the distance my computer reads and divide that number by the distance I rode. Then I multiply that number by whatever number I told my computer was the size of my tire.

I did this today, actually. I had entered 2136 as my tire size. I rode the causeway. At the other end, it said I rode 3.15 miles. 3.11/3.15=0.99 .99x2136=2115 (my new wheel size).
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Old 08-09-10, 07:45 PM   #18
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The patch size is related to the effective circumference.

The more load you put on the tires, the wider the patch gets and the closer the hubs get to the ground. The effective radius (the distance between the center of the hub and the ground) decreases (which means the circumference decreases as well).
Nope, radius is tied to circumference only for a circle. Once you put the tire on the ground it is no longer a circle. I'm not saying there is no "stretching" of the outer part of the tire, because in practice there is a very slight amount - with a flat steel tape around a tire I can feel it but not measure it. But for the most part the deflection is in the cross section getting wider, and the outer circumference of the tire does not change.
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Old 08-09-10, 08:28 PM   #19
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Originally Posted by MrCjolsen View Post
If my speedometer say's I'm going 19.2 mph, I expect that I'm actually traveling at 19.2 mph and not 19.0!

I get really pissed when I find out it's wrong. (really, I do).

So now let me describe how I calibrate my computer. Tell me if this is accurate or not.

I set it according to the instructions, Sheldon Brown's numbers or even the default number it comes at. Just to get a baseline.

Then I ride the bike for a few miles over a course that I've measured on Google Earth. I generally use the Yolo Causeway because it's almost perfectly flat and straight and 3.11 miles from levee to levee. It's also on my way to work. As I ride, I try to stay as straight and centered as I can.

Then I take the distance my computer reads and divide that number by the distance I rode. Then I multiply that number by whatever number I told my computer was the size of my tire.

I did this today, actually. I had entered 2136 as my tire size. I rode the causeway. At the other end, it said I rode 3.15 miles. 3.11/3.15=0.99 .99x2136=2115 (my new wheel size).
Ow! My head hurts...........
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Old 08-09-10, 08:32 PM   #20
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I removed the computers off my bikes years ago.

Who really wants to know how slow they are?
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Old 08-09-10, 08:45 PM   #21
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I'm curious about how you folks that are using Google Earth know that it's accurately calibrated? Let alone the fact that a three figure working distance implies at best a limited accuracy. For example 3.11 miles plus or minus .01 miles implies an error of plus or minus 53 feet. And that's only good if you can actually trust that Google Earth is accurately calibrated to that level. It's also allowing for up to a possible 3% error over that distance even if you CAN trust it to be accurate to the two decimal places. If we want to be truly anal about our input setting for these things then I'm sorry but that is not good enough.

At that point I'd rather trust someone marking my valve position, roll for three revolutions while sitting in the saddle with my weight in the usual riding position and regularly used tire pressure and then use a steel tape to measure the distance to the nearest 1/16 inch. At that point I'd be working with roughly a 3360mm distance plus or minus the allowable 1.6 mm (1/16 inch) error. That's a possible plus or minus error of only .05% and I've got far more control over the results. Now THAT is being suitably OCD about the whole exercise....
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Old 08-09-10, 08:54 PM   #22
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Nope, radius is tied to circumference only for a circle. Once you put the tire on the ground it is no longer a circle.
I agree with njkayaker. As the wheel rolls the distance traveled is the effective circumference of circumscribed by the radius from the center of the wheel's axis and the weighted wheel's contact patch on the road. On a smooth road this is a perfect circle, 2 r pi, where r is the effective (weighted radius).
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Old 08-09-10, 09:07 PM   #23
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I'm curious about how you folks that are using Google Earth know that it's accurately calibrated? Let alone the fact that a three figure working distance implies at best a limited accuracy. For example 3.11 miles plus or minus .01 miles implies an error of plus or minus 53 feet. And that's only good if you can actually trust that Google Earth is accurately calibrated to that level. It's also allowing for up to a possible 3% error over that distance even if you CAN trust it to be accurate to the two decimal places. If we want to be truly anal about our input setting for these things then I'm sorry but that is not good enough.

At that point I'd rather trust someone marking my valve position, roll for three revolutions while sitting in the saddle with my weight in the usual riding position and regularly used tire pressure and then use a steel tape to measure the distance to the nearest 1/16 inch. At that point I'd be working with roughly a 3360mm distance plus or minus the allowable 1.6 mm (1/16 inch) error. That's a possible plus or minus error of only .05% and I've got far more control over the results. Now THAT is being suitably OCD about the whole exercise....
I don't put a lot of faith into Google Earth being deadly accurate, either.

When I measured a tire's rollout recently, I made sure to only do one revolution, so as not to display OCD behavior.
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Old 08-09-10, 09:11 PM   #24
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If my speedometer say's I'm going 19.2 mph, I expect that I'm actually traveling at 19.2 mph and not 19.0!

I get really pissed when I find out it's wrong. (really, I do).

So now let me describe how I calibrate my computer. Tell me if this is accurate or not.

I set it according to the instructions, Sheldon Brown's numbers or even the default number it comes at. Just to get a baseline.

Then I ride the bike for a few miles over a course that I've measured on Google Earth. I generally use the Yolo Causeway because it's almost perfectly flat and straight and 3.11 miles from levee to levee. It's also on my way to work. As I ride, I try to stay as straight and centered as I can.

Then I take the distance my computer reads and divide that number by the distance I rode. Then I multiply that number by whatever number I told my computer was the size of my tire.

I did this today, actually. I had entered 2136 as my tire size. I rode the causeway. At the other end, it said I rode 3.15 miles. 3.11/3.15=0.99 .99x2136=2115 (my new wheel size).
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Ow! My head hurts...........
Actually it's easier, I think, than having somebody hold you on your bike while you do a rollout test.

Basically, I just stop, reset my computer, ride the set distance, remember the number at the other end of the course and then sit down with a calculator and do the math when I get to work. No more complicated than what everyone does at the gas station after they fill up and want to know what mpg their car is getting.
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Old 08-09-10, 09:13 PM   #25
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I removed the computers off my bikes years ago.

Who really wants to know how slow they are?
That's a good point but I like to know how far I've been, and how many miles my chain stays within tolerance.

Last edited by Al1943; 08-10-10 at 04:30 PM.
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