Measuring a tyre circumference for the computer.

[screenman]

I miss the guy who was our expert on pie.

 

[Ajax Bay]

Missed but not forgotten, @vernon.

 

[Ajax Bay]

Sensible portions of this pie would be slimming.

Here's one that I made earlier

View attachment 303600

The problem is is that's it's so more-ish.

 

[Aravis]

Things like average speed and maximum speed are of interest to some, but fundamentally, there is just one thing an old-school cycle computer has to do - count the number of times the wheels go round.

But strangely, they don't tell you what this number is. Not any of the examples I've used, anyway. The accuracy with which you can calculate it after a ride is limited by the number of decimal places your distance is expressed to.

Thinking of the device as a revolution counter would take the pressure off the apparent need to calibrate it with complete accuracy. Given the limitations of the technology, you'd have the purest possible measure of the distance of your rides, and if you decide at some point that your wheel circumference measurement wasn't quite right - and feel inclined to do something about it - you'd have all the data you need.

 

[I like Skol]

Here is the 'definitive' calibration method for old school wheel sensor computers (I have a GPS but don't believe its accuracy when compared to something that physically counts the wheel revolutions).

1. Find a smooth, straight length of tarmac.
2. Mark out a straight line of about 15m in length (a taut piece of rope is good enough).
3. Mark a start point on the line and using the wheel valve as a reference point roll your bike along next to the rope for 5 complete wheel revolutions until the valve is back at the bottom. Mark the valve finishing position on the ground.
4. Measure the distance between start and finish points in millimetres and divide the distance by 5
5. Enter the result into your computer as the wheel circumference (my Cateye micro takes the setting in mm )
6. Go out and ride a known distance to check the accuracy. I know from various mapping data that it is exactly 16 miles from my driveway to the square outside Sid's Café in Holmfirth so can ride 32 miles there and back then check if any adjustment is necessary.

The sum for the corrected circumference is this;

Corrected circ = set circ x true distance/measured distance

As an example, say I measure my wheel circumference using the above 5 revolutions method and get a figure of 2100mm. I then ride the 32 miles test route but when I get back the cycle computer is only displaying 31.8 miles. In this case the new setting would be;

2100 x 32/31.8 = 2113mm

That is a larger error than I have ever had using this method. usually only 2-3mm out at most. 3mm would only be 0.05 miles on this 32 mile ride which is a 0.15% inaccuracy!

 

[Ajax Bay]

The accuracy with which you can calculate it after a ride is limited by the number of decimal places your distance is expressed to.

My Cateye Velo2 displays distances to 2 decimal places (of km by my choice) even over 100km so that suggests 0.01% discretion. The major 'error' with the accuracy of cyclocomputers is the datum we've been discussing: as exact and accurate a dimension of the effective wheel circumference.
I understand the thrust of your point, but the impracticalities outweigh any benefit imo. The variety of screens mine gives me is fit for (my) purpose: speed (always displayed), average speed, distance (trip), distance (since last reset), whether current speed above or below current average, time.

 

[simongt]

My Cateye Velo2

I still have three of these great pieces of kit; why did Cateye 'improve' and get rid of this particular model - ?

 

[Milkfloat]

Go out and ride a known distance to check the accuracy. I know from various mapping data that it is exactly 16 miles from my driveway to the square outside Sid's Café in Holmfirth so can ride 32 miles there and back then check if any adjustment is necessary.

The mapping is entirely accurate and you are not using centre line geometry AND it is a totally flat 32 miles?

 

[presta]

"This is one thousandth of a per cent difference." My maths on this has been niggling at me (more off than on) for a few hours - it seemed much too low.

Thank you for getting it right. Negligible, then.

That would depend on your definition of negligible, but 0.16% was based on your assumed chord length of 40mm, which is too short. For my 700 x 35 Marathon, measuring the wheel development on the garage floor I get a circumference of 2188mm, Cateye list 2170 for my Enduro and 2168 for the Strada. Measuring against the kilometre posts I get 2150mm. That's 1.77%, a bigger difference than a lot of others on this thread are carping about. (Unless you're very careful, it's quite difficult to get a repeatable measurement rolling along the floor.) As the DoT haven't confirmed the accuracy of the posts, I hedge my bets with the computer set to 2160mm.

 

[Ajax Bay]

0.16% was based on your assumed chord length of 40mm, which is too short. For my 700 x 35 Marathon, measuring the wheel development on the garage floor I get a circumference of 2188mm, Cateye list 2170 for my Enduro and 2168 for the Strada. Measuring against the kilometre posts I get 2150mm. That's 1.77%, a bigger difference than a lot of others on this thread are carping about. (Unless you're very careful, it's quite difficult to get a repeatable measurement rolling along the floor.)

For those clickers who don't like maths, please move on.
My chord length estimate was based on 25mm tyres at 100psi and I assumed/estimated a width of tyre surface in contact at 20mm (A = 645mm2, A = Pi*ab) so length of ellipse 40mm.
For a 622-35 tyre like yours, I'd guess a pressure of 50psi (BQ Article/Frank Berto's graph) so (with same 100 lbs load) contact area twice the size, width of tyre in contact 30mm so a derived chord length of 55mm (not that much more). That suggests an effective wheel/tyre radius reduced by 0.3%.

 

[presta]

For those clickers who don't like maths, please move on.
For a 622-35 tyre like yours, I'd guess a pressure of 50psi (BQ Article/Frank Berto's graph) so (with same 100 lbs load) contact area twice the size, width of tyre in contact 30mm so a derived chord length of 55mm (not that much more). That suggests an effective wheel/tyre radius reduced by 0.3%.

For a load of 340N (~76lb), and a pressure of 65psi, I get a calculated error of 0.45%, and a chord length of 66mm, but for whatever reason, the error is much more than that measured on the road. Even Cateye's tables are based on a bigger error than that.

I assumed/estimated a width of tyre surface in contact at 20mm (A = 645mm2, A = Pi*ab) so length of ellipse 40mm.

If you drew a 40mm long chord through a 700mm circle, then with the same compression on the 25mm circle the chord on the other axis would be only 7.5mm. With a load of 340N on your tyre, I calculate chord lengths of 58mm and 10.7mm, but again that also gives a calculated error much smaller than allowed for in the Cateye tables.