Wheel Circumference Physics
 

Hey guys,

Help me think through this please, I need a physics check.
I’m trying to set the wheel circumference for my Wahoo speed sensor for my Wahoo Bolt because I recently switched to a 32mm rear tire that I inflate to 63psi per the Silca calculator.
If I measure my inflated tire circumference with the roll out method and the wheel off method I get 2152mm BUT if I sit on the bike and do the roll out method I only get 2120mm… a 3cm difference!

My mind says that since my weight is compressing the low pressure, wide tire it results in a shorter rotating circumference but the other half of me says the same amount of tire material is being covered in the rotation.

Ran the test twice both ways, exact same results to the mm as noted above. Is the sit on test the most accurate and does it make sense that it is shorter? Just need a check because I haven’t found anywhere online that discusses this. Also at 3cm difference I don’t think I’m overthinking this, that can make a big difference over a day’s ride. Thanks!

The compressed tire has a smaller radius and smaller effective diameter. You can think of the outer diameter of the tire as folding up around the contact patch, using up the additional circumference.

Go with your loaded circumference for speed calibration.

Simply put, when looking at the tire perimeter, the tire is no longer round when loaded. So, it is not a true circle anymore and the equation for circumference is no longer appropriate.

Thanks everyone for the responses. Makes complete sense. I just got thrown when I found dozens of articles and videos showing measurement of unloaded tires and could find none loaded.
However, most of those were 8-12 years old and probably occurred when we were still pumping up to 100psi and the effects of loading were much less pronounced.

Can the Bolt calibrate the tire circumference automatically?

Well it kind of is, you just have to lose 5mm of ground-hub height (radius) with a compressed tyre to lose 3cm of effective circumference.

Isn't it used just when satellite signals are poor, or you're on the trainer?

It is usually a preferred source because GPS isn’t as accurate.

Yes, but it relies on the GPS and loses accuracy in low signal areas. The speed sensor is much more precise.

It only has to do the calibration periodically, and then it uses the speed sensor for better short-term readings. "Best of both worlds" kind of thing ...

Oh I see, I have used the Bolt without the speed sensor and it’s not very accurate but you’re talking about using it with the speed sensor set to auto.. that makes sense. I assume it uses the GPS in conjunction with the speed sensor to try and make an accurate size estimate.

The distance length of the circumference does not change when loaded, it stays the same, as when unloaded.
When going from an unloaded state to a loaded state, the radius changes at this contact point area, but the vital idea
to keep in mind is that one complete revolution equals one circumference distance length of forward travel distance.
Opinions welcome please thank you.

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.

Visualized, imagine cinching a belt around the circumference and tightening it to reduce the circumference uniformly around the wheel, can you do that? Yes, because the tire deforms outward. This is what is happening at the contact patch all the way around the revolution.

my opinion is that you’re only thinking in two dimensions

Pretty sure FL Gator and Choddo are right. ( and Sheldon Brown agreed with them).

there’s a simple way to confirm this. Just do a rollout with different weights on the bike.

It’s also why car speedometers almost always read low. The indicated speed of the car is going to depend on tire circumference, which will vary with the precise tire, inflation, vehicle load, tread wear, temperature.

Car Manufacturers know this, and the don’t want the indicated speed to read lower than actual, so they calibrate them to read a touch high.

You do realize that the 30 millimeters of difference between your two rollouts is only a 1.4% difference.

The odometer of your car isn't required to be that accurate.

That’s .75 miles off over 50 miles.. which is quite a lot on a bike.

Is there a practical reason why you need better accuracy?

That's plenty of accuracy. If you were to tell me you rode 20,000 miles a year, I'm not going to quibble if it was only 19,720 miles.

Interesting discussion. I don't know the first thing about a Wahoo Bolt is, so take this idea with a grain of salt. I think we agree that any of us would get similar results if we attempted the OP's two tests, and Wahoo likely knows this. Thus, I would be concerned about attempting to compensate for an effect that Wahoo has already compensated for.

No idea how Wahoo handles this, but with Gamin, you can have it auto-calibrate speed/distance. It uses GPS which works well for relatively larger distances that are flat. That is used to calibrate the speed/distance sensor. Which then is more accurate than GPS for short distance and hills.

And good god, anyone who thinks 1.4% accuracy is acceptable is just crazy ;)

Let’s talk physics. I want to hear more about the doppler effect and also wheel circumference vs speed and temperature and pressure.

First order or second order?