dragoscscc

Recently took a trip around town, the bike computer registered 100.7 miles. Looked it up on google maps and the same trip was 98.8 miles. Right now I have the tire circumference set at 2173mm. To correct the error, the new tire circumference would have to be set at 2132mm. (100.7/98.8=1.019230, in order to get the same ratio with the tire circumference it would have to be 2132) However 41mm difference is huge, I could understand a 4 or 10 mm error but 41mm per revolution? I remember, to get the original tire circumference of 2173mm I actually measured the tire. I doubt I was off by that much (1.6"!)

So clearly my math must be wrong somewhere.

Or there's a 2% error between real world and google...

Interested to hear some ideas

Cheers
D

Bill Kapaun

Back when I used to care about such things, when my apparent mileage increased by .5% it meant it was time to air up the tires.

Wanderer

The chance of you, and Google, using the exact same geometrics is hard to fathom!

10 Wheels

What size and brand of tire is it.

Google miles are NOT accurate.

ThermionicScott 

Is 2173mm based on an accurate roll-out?

FBinNY 

There's a difference between theoretical (map) distance and distance actually traveled. Part of the reason is that you don't ride a straight line.

To take an extreme example, imagine you climbed a steep hill by slaloming. The actual distance as measured by your front wheel would be much greater, possibly double the straight line op that hill.

Also, I'm not sure whether google's algorithm uses flat distance based on GPS coordinates, or accounts for the longer distances that going up and down hills involves.

Lastly, steering always has the front wheel taking a longer path than the rear which rolls in a straighter line as the front wheel wiggles, and takes a smaller radius on all turns. You can see this by buying two computers, calibrating them precisely, mounting one each of the front and rear wheels. The front wheel unit will always read higher.

When I used to bother with that nonsense, (no computers on any bikes any more) I used to set the computer by theory, then adjust it based on a 10 mile stretch with NY's mile markers along the road. I've found that the adjusted computer is accurate where the state has measured (3) miles.

njkayaker

Where did you get this number from?

That number gives R = 345.84 mm.
C = 2132 mm gives R = 339.32 mm

A difference of 6.52 mm.

The google path is going to be smoother. That is, your measured path is almost always going to be larger.

dragoscscc

Wow, thanks for all the replies. Lots of things to chew over...

The tire is a Kenda Kwick Trax K1053-003 700x32C

The 2173mm I think I got it by rolling a piece of masking tape around the tire and then measuring it. I guess a roll out measurement would be more accurate or even measuring 10 miles distance or so...
Also, all the things mentioned make sense. Front tire goes a longer distance, subtle differences in route, etc.

"Back when I used to care about such things".... maybe that's the best way to go. I'm not that obsessed with it to be honest, just did my first 100 miles the other day I was extremely pleased with myself. Traced my route on Google and that's how all this came about. I guess more curious than anything.

D

Bill Kapaun

So, which bike computers use tire radius?

curbtender

I've used this https://sheldonbrown.com/cyclecomputer-calibration.html and keep pretty close to my GPS buddies, a couple of hundredths per 20 miles.

bobotech

A man with 2 watches never knows what time it is.

gsa103

Your tire compresses due to the weight of the rider. This results in the effective rolling diameter being less than the unloaded rolling diameter, hence a smaller circumference.

Basically, you have a couple of options:
1) Use a generic value from a table somewhere (usually gets within 2% for average riders)
OR
2) Dedicated calibration using a roll-out or straight road segment

Remember that this is a function of tire pressure and wear. The more accurate you want to measure, the more often you need to re-calibrate.

Also, don't assume that GPS will be more accurate. GPS is usually less accurate than a sensor, because the GPS clips corners. The faster you ride, the worse GPS tends to be.

RubeRad

All interesting stuff. I agree with some that it doesn't really matter a whole lot, but I'm a bit OCD and would feel compelled to "get it right".

I would recommend searching out a road with tenth-of-mile markings, coast "exactly" 0.1mile (choose the downhill direction) as arrow-straight as possible, and you will have accounted for tire deformation and wandering route as much as possible. Then recalibrate your computer's circumference using the adjusted calibration technique you describe, and you can sleep well at night.

Asi

There are better methods for roll-out circumference settings.

I've marked accurately 200m of straight road and planted two nails into the asphalt. (by measuring with a 50m tape measure four times)
Set the valve stem down on the 1st nail. Ride straight and stop right on top of the 2nd nail 200m away. Complete the roll up where the valve stem is down again and mark it. Do this several times and average the marks where the valve stem is down after the 200m mark, and drive another nail in the asphalt.
Now for the math: between the 1st and 3rd nail there are a complete number of revolutions, and those revolutions happened into 200m+whatever distance is between 3rd nail and 2nd nail (a few centimeters easily measured by a normal tape measure)
Now we need to find how many complete rolls are there: measure the approximate circumference of one roll and divide those 200m+something meters to the approximate value and round the value to integer (it should be fairly close)

study case: I measured loosely 2250m as the circumference of tire. The mark was set at 200.365m (200m + 365mm). Now 200.365/2.250=89.051111 => we can clearly state there were exact 89 complete revolutions, and there are pretty much exact 200.365m of rollout for 89 revolution => 200.365/89=2.2512921 meters of circumference of the tire in normal riding mode.

Now there are concerns about precision: how accurate are those 200m? (I'd guesstimate 10mm tolerance), how accurate did I set the 3rd nail? (out of 20+ rollouts both ways with consistent speed**.. i'd say it's pretty accurate with 5mm).
**Disclaimer: it was rolled out very straight as the wheel was mounted to a car (see below) that was driving straight following a set line, so the valve is ending up consistently ant the same mark every time.. on a bike, the shakiness of that line ridden on a bike is a major error inducer and most likely there will be a wide spread of data.

So based on estimated errors if I fail with 5+10mm in one direction means i'd measure about 200.365 plus or minus 15mm that is between 200.380m and 200.350mm=> the lowes value for circumeference i could get is 200.350/89=2.25112m and highes is 200.380m/89=2.25146m
That is well under half a mm tolerance for that circumference.

The study i made was involved finding the rolling circumference for a 5th wheel measuring device for speed and distance needed for braking tests and other drive performance tests of cars. The transducer (the encoder that counts revolution of the wheel) has 1000 impulses per turns with a gear ration inside of 3 to 1, that gives 3000impulses per turn of the wheel, so it give a fine accuracy provided that the circumference of the wheel is well known to properly calibrate the measuring equipment.
So given the circumstances, i did bother measuring the circumference of that bicycle wheel in lots of ways as that was needed for proper calibration.

Now, for a normal bike such accuracy is overkill, but those nails are planted in the parking lot and did the same for my bike (and planting another fixed marker for my rollout, this time a cross head screw )

So for recalibrating from time to time (due to wear, and air pressure) it's needed only a few steps: strat stem down on 1st marker, roll out to the 3rd marker and see where the valve stem is.. it should be down again, if not complete the revolution either way closest to the set marker and eyeball the distance from the previously set marker. If it's less than 80mm off there is no need for change, as at about 80mm intervals you can add another millimeter to the cyclocomputer (smallest division i have on my crappy cyclocomputer, and in contrast, for the real deal: the 5th wheel speed and distance transducer, we can set whatever value as it's a calibration value inside a labview program that is live and hooked via data acquisition system - another story).

Yet the strive for perfection is not needed for biking, i mostly ride fixed gear and do not have a cyclocomputer for most of my bikes (except for my road bike).
But for those keen on numbers this might be useful info

Have fun crunching numbers, or just go ride

dsbrantjr

"Have fun crunching numbers, or just go ride"

Just go ride.

njkayaker

All of them do, indirectly, (the ones that count wheel rotations). The radius (the height of the hub center from the ground) is the thing directly affected by load and air pressure. It would seem that his difference is close to the difference you'd see between a loaded and unloaded tire.

Bill Kapaun

And they all pretty much use circumference DIRECTLY!
I don't know why you want to go off on a tangent? Did you just learn about PI?
2% is 2% no matter what method you use!

njkayaker

It's the radius (the height of the hub center from the ground) that is affected by the load on the tire (and the air pressure).

More-weight/less-pressure means a smaller radius (the hub center is closer to the ground).

It's the radius, at that one place, that causes the difference in the apparent circumference.

The radius is key to understanding why measuring the circumference of the tire isn't really a good approach and why the roll-out measurement is.

Bill Kapaun

Apparent circumference?
My coffee almost went up my nose on that one.

njkayaker

This method will produce a number that is too large (by a small amount).

ThermionicScott 

njkayaker

You do like digging holes!

A circumference is a property of a circle. There isn't any real circle in a loaded tire.

The tire (in use) is a circle with a flat area under the hub touching the ground. The circular tire is deformed in use (so it isn't a circle any more).

What you are measuring is the radius of an imaginary circle.

FBinNY 

Someone mention something about tangents? Like is the road on a tangent to the wheel, or is it more like a secant?

If you get within 1-2% on a bike computer, or any odometer, be happy and move on with your life.

HillRider

A fairly good approximation to the rolling circumference of a bike tire is to assume the tire has a circular cross section. If the named width is correct the circumference can be calculated by (rim diameter+(2* tire width))* Pi

For a 700-32 the estimate is (622+(2*32)* 3.14159... = 2155 mm or about 99.2% of your current value. Realistically a lot of "32" tires are a bit smaller so a true roll-out measurement is still the most accurate method.

AnkleWork

"Arithmetic is hard!" -- with apologies to Barbie