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-   -   Wheel Circumference Physics (https://www.bikeforums.net/road-cycling/1298552-wheel-circumference-physics.html)

njkayaker 08-16-24 08:51 AM


Originally Posted by tomato coupe (Post 23323788)
Your initial post was about calibrating a speed sensor. If your concern is about accurately determining distances during a ride, the speed sensor is not offering any advantage -- just use your GPS computer without it.

Ignoring the contradiction of using the GPS to calibrate the distance, the rider's path is generally going to be longer than what the GPS can measure. One also doesn't always get sufficient GPS reception.

njkayaker 08-16-24 08:56 AM


Originally Posted by choddo (Post 23323552)
Can just about read that. A higher quality image would have helped.

Yes, it's a mess (and a day late).


Originally Posted by choddo (Post 23323552)
What’s the definition of the “effective radius” there? Cos based on the image alone it’s “distance from hub to an arbritrary dotted line”. Does PC=CA? And if so, why?

The "effective" radius is the radius for horizontal travel with a full wheel rotation. It's the radius "you want". Exactly what the value of that radius is is complicated (and it varies).


Originally Posted by choddo (Post 23323552)
Cos based on the image alone it’s “distance from hub to an arbritrary dotted line”. Does PC=CA? And if so, why?

These distances vary depending on a bunch of things. The image isn't saying PC=CA. It's just showing the spatial relationships of these things (not their sizes).





tomato coupe 08-16-24 09:22 AM


Originally Posted by njkayaker (Post 23323800)
Ignoring the contradiction of using the GPS to calibrate the distance, the rider's path is generally going to be longer than what the GPS can measure. One also doesn't always get sufficient GPS reception.

GPS is far more capable of the accuracy the OP is interested in, over the distances that the OP is interested in, than any distance measurement based on the circumference of a tire.

njkayaker 08-16-24 09:30 AM


Originally Posted by tomato coupe (Post 23323836)
GPS is far more capable of the accuracy the OP is interested in, over the distances that the OP is interested in, than any distance measurement based on the circumference of a tire.

He's apparently interested in differences of 1.4%. It's possible that the wheel sensor would be better generally than the GPS in practice.

https://www.dcrainmaker.com/2019/04/...th-review.html


Of course, the main reason you’d use this sensor is to display speed and distance on your bike computer, most likely off-road. For the most part, GPS is more than accurate and stable enough these days on-road for most cyclists. Whereas off-road mountain-biking in dense forest or with switchbacks, that’s where you’d probably want a speed sensor to give you better distance accuracy and better pace stability.
The wheel sensor also works better for instantaneous speed.

tomato coupe 08-16-24 09:38 AM


Originally Posted by njkayaker (Post 23323844)
He's apparently interested in differences of 1.4%. It's possible that the wheel sensor would be better generally than the GPS in practice. (I'm not going to say what the OP is interested in.)

The OP did state what he was interested in -- roughly .01 mile accuracy over distance of approximately 50 miles. GPS can do that, but measurements based on tire circumference would almost certainly not be capable of that.

On edit: oops, it wasn't the OP that stated the above requirements.

The wheel sensor also works better for instantaneous speed.
Yes, that's what they're designed to do. But, the OP is interested in distance -- that's not what speed sensors are designed to do.

downtube42 08-16-24 09:40 AM


Originally Posted by tomato coupe (Post 23323788)
Your initial post was about calibrating a speed sensor. If your concern is about accurately determining distances during a ride, the speed sensor is not offering any advantage -- just use your GPS computer without it.

That was my initial post, injecting myself in the midst of physics and geometric debates, on the very specific question of why one might need more accuracy than a cyclocomputer can offer. This is a multithreaded and largely pointless conversation, as these things tend to become.

tomato coupe 08-16-24 09:50 AM


Originally Posted by downtube42 (Post 23323864)
That was my initial post, injecting myself in the midst of physics and geometric debates, on the very specific question of why one might need more accuracy than a cyclocomputer can offer. This is a multithreaded and largely pointless conversation, as these things tend to become.

Sorry, I posted a question for the OP. When you quoted my question and answered it, I mistakingly thought you were the OP.

njkayaker 08-16-24 10:01 AM


Originally Posted by tomato coupe (Post 23323859)
Yes, that's what they're designed to do. But, the OP is interested in distance -- that's not what speed sensors are designed to do.

??? They are clearly designed for distance too. That's their primary (historical) purpose. They started out to measure distance (they couldn't do speed at all).

They aren't "speed" sensors anyway. They are "rotation" sensors. The speed and distance have to be provided by the head unit (there are a few that do this calculation in the sensor but that's a recent thing).

tomato coupe 08-16-24 10:05 AM


Originally Posted by njkayaker (Post 23323880)
??? They are clearly designed for distance too. That's their primary (historical) purpose..

No. Speed sensors that are meant to be used with GPS computers offer better speed measurements at short times/distance where GPS doesn't work as well. At longer distances, GPS computers rely on GPS positions to determine distance more accurately.

njkayaker 08-16-24 10:44 AM


Originally Posted by tomato coupe (Post 23323885)
No. Speed sensors that are meant to be used with GPS computers offer better speed measurements at short times/distance where GPS doesn't work as well. At longer distances, GPS computers rely on GPS positions to determine distance more accurately.

I've found nothing that indicates distance from a well-calibrated rotation sensor is less accurate (for the usage being discussed). Using GPS is easier (no calibration) and it's clearly "good enough" (generally).

The early GPS units might not have been that good at measuring distance. (They still aren't great at measuring short-term speed.)

The distinctive thing GPS provided was the location of where you were riding (and recording data). GPS didn't improve much on the results (distance and speed) of using rotation detectors and were more expensive.

GPS has improved such that it might now be fine or better for distance generally. There are still situations where GPS doesn't work well at all.

==========================

https://support.garmin.com/en-US/?fa...623Z535geTx2e9


The Garmin Speed/Cadence Sensor (GSC10), Bike Speed Sensor (BSS), and Speed Sensor 2 override the speed and distance data from the GPS satellites when used during an outdoor timed activity.

The GSC10 uses a magnet on the wheel and the bike profile's wheel size to calculate distance and speed with improved accuracy, while the BSS and Speed Sensor 2 use a magnetometer and orientation to accomplish the same thing.

These sensors are useful when traveling through tunnels, areas with heavy tree cover, and on rides with substantial changes in elevation where GPS is limited. When the device is recording distance with GPS, it is recording the distance from one point to the next, and may not be factoring in the elevation ascent or descent. The sensors give a more accurate reading by recording distance based on wheel rotation.

tomato coupe 08-16-24 02:51 PM


Originally Posted by njkayaker (Post 23323932)
I've found nothing that indicates distance from a well-calibrated rotation sensor is less accurate (for the usage being discussed). Using GPS is easier (no calibration) and it's clearly "good enough" (generally).

The most accurate way to calibrate a rotation sensor is to use GPS to determine tire circumference. As a consequence, distance measurements based on the sensor will not be as accurate as those based on direct GPS measurements, if the distance is greater than that used for calibrating the sensor.

njkayaker 08-16-24 03:08 PM


Originally Posted by tomato coupe (Post 23324147)
The most accurate way to calibrate a rotation sensor is to use GPS to determine tire circumference.

This is easy to do but it might not be correct at all (it depends on getting a good signal). One might get a better number riding in a straight line.


Originally Posted by tomato coupe (Post 23324147)
As a consequence, distance measurements based on the sensor will not be as accurate as those based on direct GPS measurements, if the distance is greater than that used for calibrating the sensor.

Garmin says otherwise. The GPS distance doesn't include the effect of elevation and the GPS might not get a good signal and the GPS distance likely smooths out some of the movement of the bike.

The rotation sensors are not inaccurate (as long as a good roll out number is obtained).

=============================

Given the variability of GPS tracks, it's not clear that distance from a well-calibrated rotation sensor would necessarily be different in accuracy.

https://media.dcrainmaker.com/images...6/image-49.png

tomato coupe 08-16-24 03:35 PM


Originally Posted by njkayaker (Post 23324161)
Garmin says otherwise.

Yes, Garmin says that in their one sentence blurb. But, when you dig into it, it's a lot more complicated. You have to understand the nature of sensor calibration errors, the various contributions to GPS error, and how all those errors accumulate over multiple measurements.


Originally Posted by njkayaker
The rotation sensors are not inaccurate (as long as a good roll out number is obtained).

You're missing the point. The most accurate way to get is good number for the roll out is with GPS. That's why the sensor cannot be better than GPS at distances greater than the distance used to determine the rollout.

znomit 08-16-24 07:08 PM

A good exercise might be to put a sensor on the front wheel and compare front to rear. Fronts generally travel further I believe from looking at wheel tracks.

njkayaker 08-17-24 06:38 AM


Originally Posted by tomato coupe (Post 23324182)
Yes, Garmin says that in their one sentence blurb. But, when you dig into it, it's a lot more complicated. You have to understand the nature of sensor calibration errors, the various contributions to GPS error, and how all those errors accumulate over multiple measurements.

All that doesn't make what Garmin said incorrect.


Originally Posted by tomato coupe (Post 23324182)
The most accurate way to get is good number for the roll out is with GPS.

You don't know whether there's really any difference between using that and other methods. It's certainly easier.


Originally Posted by tomato coupe (Post 23324182)
That's why the sensor cannot be better than GPS at distances greater than the distance used to determine the rollout.

Again, this is wrong. The GPS can have drop outs and doesn't account for elevation. And it might cut corners too. And Garmin says otherwise.





njkayaker 08-17-24 06:59 AM


Originally Posted by znomit (Post 23324344)
A good exercise might be to put a sensor on the front wheel and compare front to rear. Fronts generally travel further I believe from looking at wheel tracks.

I'm not sure if the Garmins let you use two rotation sensors. (You could use two head units.)

spclark 08-17-24 07:48 AM


Originally Posted by FL_Gator (Post 23321626)
I think the proposed explanation is that the deformation of the tire under weight is consistent for the entire revolution, thus the reduced radius is consistent for the entire revolution and therefore the effective circumference loaded is less than an unloaded circumference.

To my mind it's kinda like calculating ERD when building wheels. Hard to measure directly w/o some sophisticated tools but the concept is fundamental to getting spoke length right.

With tires on wheels, when tires aren't loaded the effective circumference is greater (corrected thanks to Choddo for calling me out on my error) than when the tire is loaded. It's not the distance traveled so much as the lever arm of the wheel's effective radius when loaded that affects calculations when that variable's plugged in.

Sy Reene 08-17-24 08:33 AM

Wheel rollout measurements are only valid for the tire pressure, tire wear, road surface, plus weight of rider and equipment used at time of measurement.

tomato coupe 08-17-24 09:13 AM


Originally Posted by njkayaker (Post 23324616)
All that doesn't make what Garmin said incorrect.

It's a short, simplified answer in an FAQ. It doesn't get into the details of how these devices work.


You don't know whether there's really any difference between using that and other methods.
It is the most accurate way to calibrate tire circumference.


Again, this is wrong. The GPS can have drop outs and doesn't account for elevation. And it might cut corners too. And Garmin says otherwise.
Elevation error is already very small AND it can be corrected using readings from a barometric altimeter. Errors from cutting corners can be an issue mountain biking, but they're pretty insignificant when road cycling.

This subject has been discussed at length in several other threads. Anyone interested should just search for those threads.

choddo 08-17-24 10:15 AM


Originally Posted by spclark (Post 23324645)
To my mind it's kinda like calculating ERD when building wheels. Hard to measure directly w/o some sophisticated tools but the concept is fundamental to getting spoke length right.

With tires on wheels, when tires aren't loaded the effective circumference is less than when the tire is loaded. It's not the distance traveled so much as the lever arm of the wheel's effective radius when loaded that affects calculations with that variable plugged in.

Hang on - say that again slowly?

njkayaker 08-17-24 11:06 AM


Originally Posted by tomato coupe (Post 23324719)
It's a short, simplified answer in an FAQ. It doesn't get into the details of how these devices work.

Which still doesn't make it incorrect.


Originally Posted by tomato coupe (Post 23324719)
Errors from cutting corners can be an issue mountain biking, but they're pretty insignificant when road cycling.

It's not just cutting corners that are a problem with mountain biking. Mountain biking is an extreme case ("worst case scenario") but similar issues can happen when road riding or gravel riding.

Rotation sensors using a separate magnet can have issues with the magnet not being picked up (alignment issues). Likely more of an issue with mountain biking. The newer hub rotation sensors should eliminate that issue.


Originally Posted by tomato coupe (Post 23324719)
Elevation error is already very small AND.it can be corrected using readings from a barometric altimeter.

No one does this.

spclark 08-17-24 12:49 PM


Originally Posted by choddo (Post 23324776)
Hang on - say that again slowly?

Right... should have proofed what I'd drafted before hitting 'save'. Thanks!

(Does my edit (to correct my error) help any?)

merlinextraligh 08-17-24 03:40 PM


Originally Posted by znomit (Post 23323311)
Does the tyre compress less at speed? There is work done deforming the tyre.

Is the contact patch compressed horizontally due to the torque exerted by the rider?

Yes, if you’re a top fuel dragster. At 200 watts or so, I doubt it’s significant, maybe not even measurable, within an available margin of error

znomit 08-17-24 03:56 PM

Now go around a corner. What happens to the effective circumference?


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