That represents the shortening of the circumference. I think you are saying the shortened circumference is constant.
A seperate the question came up of what the speedo would indicate. It's probably best calibrated empirically rather than trying to determine its reading with any accuracy.
Very true. Along similar lines, at which point along the contact patch (chord AQB) does most of circumference size shrinkage occur.
It works better than anything you have come up with so far ...
Hey, I believe we have a climate?
And as my Dad used to say (probably about you), 'Most of the harm done in this world isn't done by people who don't know but by people who don't know they don't know'.
It will be interesting to see how you finally get out of this one.
'That's what I meant / have been saying all along' is my best bet. ;-)
With a correctly inflated car tyre on the car and parked on a smoothish / flat surface ... jack a wheel up and measure the circumference with a tape measure. Lower the car back onto it's wheel, keeping the tape in place and once back on the ground, check the tape again.
Lower the tyre pressure a reasonable percent and measure again.
I presume when you say "flat" you mean a tyre that is below the rated pressure but still maintains roughly the same profile. I tend to think of that as "low", and "flat" to mean a tyre that has bugger-all air in it, so the wheel rim is rubbing on the inside of the tread surface, doing untold damage to the tyre.
Having driven on a low tyre (to get me to a garage that I knew was only half a mile away, to save the hassle of changing the wheel in heavy traffic) I have no idea by how much the speedo may or may not have been overreading. Short of checking it with a GPS, it's very difficult to tell.
I have once driven on a totally knackered tyre for about a hundred yards, when a car pulled out and I had to swerve to avoid it, hitting the kerb harder than I would have liked. The sidewall burst. As it was immediately before a roundabout, with no way of traffic getting me round me, I decided that since the tyre was buggered, I couldn't do any more damage. Once I'd stopped safely beyond the roundabout, my fun really began because I discovered that the wire cage which held the spare tyre had seized up: there was a long bolt that went through the floor of the boot into a nut on the cage: and that was rusted up. I actually had to call out the RAC for help with changing a wheel, simply to get at the spare. The pillocks who made that car had out a very broad semi-cylindrical nick in the head of the bolt which you were supposed to turn with the flattened end of the wheelbrace - utterly useless for getting any purchase if the bolt had seized. If only the bolt head had been a proper hexagon the same size as the wheelnuts, it would have been trivial to undo it.
That's why 'most people' that know what they are talking about use the terms 'rolling radius' (effective loaded radius) and have done for years, and all without your understanding or permission!
From this dynamic value you can extrapolate the rolling circumference or even measure it (as it's a real thing of course).
Plug an OBD reader into your ABS equipped car and pickup one of the sensor ring outputs.
Measure the unloaded circumference of the tyre.
Use the output of the ABS ring to count the wheel revs, calculate the theoretical distance traveled and compare that with a GPS or road marked value. Report back here with your findings. ;-)
I think that is unlikely given that you don't see that effect with a steel radial although it is certainly possible that Tim's parallelogram effect means that it isnt as rigid as you might think.
I believe the circumference gets shorter by APB - AQB relative to the tyre in free air. The circumference of the natural tyre is compacted by upward pressure from its contact patch.
Do you think he has worked out that tyres aren't flat even when at zero pressure if the wheel is spinning. Maybe he has never swung a weight on a bit of string?
Its all different when its on a car rather than say a rolling road. On a car as you go faster the load tangential to the contact area increases with speed due to air resistance.
Also the tyre will become more circular as the speed goes up.
There is almost perfect correlation between people who believe in the european Union and people who beleive a flat tyre speeds up by the change in apparent radius.
I bet thr is a strong correlation s ell with peopple who believe in catastrophic man made climate change.
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