Physicists; Rolling Radius - How to Assess?

[innocent_bystander]

OK, you're a pretty smart lot; how do you assess the rolling radius, effective circumference, or working diameter of a wheel for speedometer calibration purposes?

 

Now, you'd think it was easy, wouldn't you. But it aint!

Scenario No.1 :- The circumference is the total distance around the centre of a properly inflated tyre.

Scenario No.2 :- Because the bottom of the tyre is slightly flattened by the weight of the car, the real radius is that which is measured at the radius perpendicular to the ground.

Scenario No.3, the pragmatic one :- Mark the rim of the tyre with chalk at the point that it touches the ground, roll the car along for, say, ten turns of the wheels, and measure the distance travelled which, divided by ten, is the effective circumference.

Scenario No.4 :- Go to the http://www.tyresave.co.uk/ website where the rolling radius of all readily available tyre sizes is listed. Question for the older members: knowing, as you do, that the majority of people are incompetent, do you believe the figure shown?

 

I haven't done all these things because that level of accuracy is largely irrelevant but as an academic puzzle I AM interested. If you use No.2, where does the excess rubber at the point of contact go? To take an hypothetical extreme, if the system were a tank track the jockey wheels would rotate several times more quickly than the track. But, in the case of a tyre where there is no slippage twixt rim and bead, how can the wheel avoid rotating at exactly the same speed as the tyre. That being the case, surely the actual circumference as measured in No.1 is the proper one?

 

Answers on a postcard....

[Tight fart]

If your that fussed get a GPS unit someone else has done the maths for you.

 

T.F@O.F.

A7 RDP

Pics here

[Nov-07]

You may be confusing the issue ❗ The wheel/tyre assembly is not round, so radius has little bearing on the answer, other than to calculate the circumference of the tyre. If there is no slip between the tyre and the road (never, in a Caterham 🤔) then the circumference of the tread in contact with the road determines the number of revolutions of the wheel. As the tyre wears the "length" of the tread will marginally decrease, causing the wheels to rotate faster for a given engine speed. Any speedometer connected to the gearbox is always going to indicate, in effect, prop-shaft revs, not the actual speed of the car. But then, I'm not a Physicist - only an Engineer 😬

 

TonyK

[Joe 90]

If you want an actual answer, use method 3. The radius to ground method #2 is distinctly inaccurate as the carcass at the contact point is deformed. The footprint pressure pushes the "missing" circumference around, either to the front or the back.

 

SEP field working not spotted in 100,502 miles. Photos here

[innocent_bystander]

November7:

The "physicists" bit was a hook to get attention. 😳

 

I am clear about the irrelevance of the term radius but Speedycables are not. I wanted my VDO mechanical speedometer recalibrated and they insisted on the distance from hub centre to ground being measured with the car on the ground, plus the number of turns of the speedo cable for a certain number of wheel revs - 6, actually. They forbade, and that's not too strong a term, jacking up and rotating the wheel off the ground even if you did it twice the number of times to allow for the diff - non-LSD. Not having done the pragmatic check of measuring the actual distance travelled with ten revs, I am simply exercised (as a fellow engineer but specialising in polymers, the moulding design and physical properties thereof) by the theory. The loss of circumference due to tyre wear is another factor, of course. Thanks for your interest, though.

[innocent_bystander]

Oliver Sedlacek: Thanks also. I am instinctively of that opinion too.

 

As I said in my reply to November 7, I like the niceties of the theory - it keeps the brain ticking over of a Sunday afternoon.

[Strangely]

When I initially set up my bike computer I did method 3, but for only one revolution. When I later test it over a measured mile it was accurate to well within 1%.

 

See here if you want more info:

http://www.strangely.org/owned/bikecomp/index.html

[frankyknuckles]

When I setup my Stack I reaised a wheel off the ground, carefully placed masking tape around the centre of the tyre to get a length of masking tape exactly equal to the circumference, removed the tape and measured it. I then tested the speed with a following vehicle keeping to exactly 60mph with cruise control and we both held station perfectly.

 

Like you have said, the speedo will change as the tyres wear down.

 

Build Diary

[Myles]

I've always used method 3... Agrees very closely with GPS.

 

I did try using more than one revolution once, but I got *exactly* the same result, so haven't bothered since.

 

Franky - I'm dubious about the accuracy of your method - the cruise control is likely to be only as accurate as the chase cars speedo - and that's probably running 7-10% over the actual speed.

 

The rolling circumference (i.e. with weight compressing the tyre) will always be less than that of an unloaded tyre - so you are effectively overstating the speed of your 7 (the Stack thinks you're travelling further per revolution than you really are), and this is consistent with the usual overreading of the chase car speedo/cruise...

 

You'll be slightly safer from speedcams though

 

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