Need help on precise RPM calculation regarding a car's tire size on a road

[antomabu]

Hello people! I really need a help with a Car project using Rpi 3 to measure RPM, distance etc... I already did the main part of it, but now I need help to know how much does the tire size can variate regarding its pressure variation on the road. For example I'm using a 305/30ZR19 tire, which has 19 in of diameter, and supponsing that it initiates with 33psi, 19.0 of diameter, and an ambient temperature, then on the road the tire heats, so the pressure increments to 40psi, how much can diameter be affected? For example from 19.0 inch to 19.5 when gets 40 psi.

I would really appreciate your replies, thanks!

[jamesh]

The tyre will indeed expand, but the amount it expands will depend on the make of the tyre and its construction. There is no equation to work it out because it various with every tyre.

I would suggest testing, then measure the tyre are various temperatures, and store the results for use later.

Failing that, fill with dry nitrogen which doesn't expand so much.

[Heater]

There are times when the only way to go is to do the experiments. There are so many variables here that I very much doubt you will get a realistically accurate calculation.

Hmmm....wait a minute. No matter what the pressure in the tire, no matter what the load on the wheel, no matter how squished down it gets (distance from axle to road) the distance around the outside of the tire remains constant (Ignoring a bit of thermal expansion) Even if it's not very round anymore. In order for the wheel to go around once, the outside of the tire has to get back to it starting point. If that were not the case the tire would get badly ripped up.

Ergo, the distance traveled by the car, per wheel revolution, is the same at all pressures and loads.

What is wrong with that argument?

See, unresolved, debate here: https://physics.stackexchange.com/quest ... -of-my-car

Like I said. Time to do some experiments and take measurements.

[jamesh]

There are times when the only way to go is to do the experiments. There are so many variables here that I very much doubt you will get a realistically accurate calculation.

Hmmm....wait a minute. No matter what the pressure in the tire, no matter what the load on the wheel, no matter how squished down it gets (distance from axle to road) the distance around the outside of the tire remains constant (Ignoring a bit of thermal expansion) Even if it's not very round anymore. In order for the wheel to go around once, the outside of the tire has to get back to it starting point. If that were not the case the tire would get badly ripped up.

Ergo, the distance traveled by the car, per wheel revolution, is the same at all pressures and loads.

What is wrong with that argument?

See, unresolved, debate here: https://physics.stackexchange.com/quest ... -of-my-car

Like I said. Time to do some experiments and take measurements.

What wrong with that statement is that it is wrong. Tyre circumference changes with temperature. Not by much, but it definitely changes. Probably not enough to affect a speedo as long as the tyre is in its operating range.

(ex. race kart driver, ex racecar driver, current kart mechanic. We put high pressure in wet tyres to expand them a bit, in order to spread the tread pattern out to give better water removal. Can also be done by putting on a narrower rim if you want to run lower pressures)

[Heater]

jamesh,

What wrong with that statement is that it is wrong. Tyre circumference changes with temperature. Not by much, but it definitely changes.

And what is wrong with that statement is that it totally ignores the part where I said "Ignoring a bit of thermal expansion".

And then goes on :

Probably not enough to affect a speedo as long as the tyre is in its operating range.

That is to say, ignore the small effect of temperature, and basically agree with me. That is to say I am wrong and right at the same time!

How do people ever get their software to work with logic like that?

[jamesh]

I'm going out with Rachel Riley. If you ignore the bit about going out with Rachel Riley.


You cannot ignore thermal expansion. P1V1/T1 = P2V2/T2 - Boyles law. And tyres get hot in use.

So basically, you statement was wrong because it ignores the laws of physics.

[DougieLawson]

That's Montgomery Scott's "Law" from Star Trek: The Naked Time.
http://www.imdb.com/title/tt0708473/quotes

Albeit that Albert Einstein changed some of Newton's "Laws" of physics with his general theory of relativity.

Someone needs to ask Pirelli, McLaren, Mercedes or Red-Bull Racing (other F1 teams are eligible). They'll know the rules of how tyre pressures affect the size of their wheels.

BTW, you're also old enough to be Ms Rachel Riley's dad.

[pootle]

The distance covered per rev varies with many things, and particularly with tyre wear as well as the type off tyre fitted, and the load on the wheel. Also the driven wheels will turn very slightly faster than the non-driven wheels at constant speed (and more so as the speed rises).

Some cars have the capability to recalibrate the speedo / odo based on data from the satnav to allow for these variations.

I would expect variation in the range of 1% - 5% at least. (diameter of the tyre varies by at least 2% from new to worn).

How precise do you need to be?

[bensimmo]

Tyre are a complex system, every part does a different thing.
Let alone the weight of the car will effect the tyres rotational circumference as would a bumpy surface compared to a flat one and of course wear and tear.
There is a good reason road cars speedometers measure slower than actual speed.

[klricks]

....... For example I'm using a 305/30ZR19 tire, which has 19 in of diameter, and supponsing that it initiates with 33psi, 19.0 of diameter.......

The R19 is the diameter of the metal rim NOT the diameter of the rubber...https://www.tirerack.com/tires/tiretech ... p?techid=7

[Heater]

jamesh,

You cannot ignore thermal expansion. P1V1/T1 = P2V2/T2 - Boyles law. And tyres get hot in use.

Please read what I wrote again.

I specifically opened by talking about the pressure in the tire: "No matter what the pressure in the tire...".

As you rightly point out that will depend on temperature, Boyles law, as well as how hard you inflated the tires and the load on the axle.

I then stated that "the distance around the outside of the tire remains constant (Ignoring a bit of thermal expansion)"

That is to say the thermal expansion of the perimeter of the tire. I think it is justified to ignore that tiny change in normal use.

So basically, you statement was wrong because it ignores the laws of physics.

Nope. I'm just doing what physicists do all the time. Try to identify the major contributors to some effect and ignore details that don't have much effect. Thus making it easier to reason about and the maths much simpler.

Of course such simplified models break down at some point...

We are just going to have to do the experiment, measure wheel rotations and distance traveled vs tire pressure. One, or both, of us might be surprised at the results.

[gordon77]

Tyre are a complex system, every part does a different thing.
Let alone the weight of the car will effect the tyres rotational circumference as would a bumpy surface compared to a flat one and of course wear and tear.
There is a good reason road cars speedometers measure slower than actual speed.

All speedometers l have used measure faster than actual speed, or maybe manufacturers are compensating to avoid too many speeding fines

[Heater]

I have found that too. I guessed the manufacturers just wanted you to feel better thinking you are going faster than you are. There is no way my old Citroen BX19 GTi hit 130 miles per hour on the M2. No way I tell you...

[JMK8]

I believe that to obtain type approval the vehicle's speedometer must not under-read. If the manufacturer does not get type approval they cannot sell the car to the public.

[thagrol]

All speedometers l have used measure faster than actual speed, or maybe manufacturers are compensating to avoid too many speeding fines

I've seen this too. I've also seen speed read from the ODBII port to be lower than that shown on the speedo.

Last time I checked, car speedos were only required to be accurate within 10%, at least in the UK. I'm guessing the speedo reads high so you don't accidentally break the limit if the sensors are out of calibration or erring on the high side. That 10% is also probably why the actual point you'd qualify for a speeding fine was reportedly speed limit + 10% + 2 mph. Not that I can verify this (and no, I'm not going to try that experiment )

Oh, and back in the days of mechanical speedos, they were driven off the gearbox not the road wheels (as were the odos).

[Burngate]

... no matter how squished down it gets (distance from axle to road) the distance around the outside of the tire remains constant. Even if it's not very round anymore

I then stated that "the distance around the outside of the tire remains constant"

I don't get it.
I start with a circle, radius r so circumference 2πr
Then I flatten a quarter of it.
The rest of it stays the same, so it's the same length, ¾ of 2πr or 3πr/2, but the flattened bit is the long side of a right-angled triangle, so r√2. That's shorter than πr/2 according to my calculator.

So the tyre's circumference has shrunk.
Unless British tyres work differently to/from American tires.

[Heater]

Why would the distance around the tread of your tire change just because you have let some air out and the axle moved down a bit? Where did that missing tire carcass go?

I look at it like this:

tires.png (23.22 KiB) Viewed 2207 times

On the left is a nicely inflated tire, circumference X, with the axle approximately in the center. When we let some air out, to a first approximation, we have the picture on the right. The axle is off center but the circumference Y is the same as X.

For every complete revolution of the hub, the length round the outside of the tire carcass also has to get back to its starting point. Else we have ripped the tire to shreds. The tire carcass has not changed length.

Ergo, distance traveled per revolution of the wheel has not changed.

[Burngate]

I've just been out to look at my car's wheels. The tyres are a bit flat - particularly so, with some bags of rubble in the boot (we're in Britain, so we have tyres 'n' boots rather than tires 'n' trunks)
As far as I can see, for the majority of the wheel - the part not touching the road - is concentric with the axle.
And the bit touching the road is a straight line.

If it were as you've drawn, two things would happen.
One is that the area of contact would be zero, and there'd be no grip.
The other is that (because the tyre has a steel carcass) the side-walls can flex so that the wheel-rim to tyre tread distance can shrink, but can't grow.
If what you've drawn happened, there'd be an air-gap between side-wall and rim.

That doesn't happen.
The tread flexes so that there's a large area in contact with the road (helps with braking as well as accelerating), and the tread grips the road as it flexes.

[bensimmo]

Tyre are a complex system, every part does a different thing.
Let alone the weight of the car will effect the tyres rotational circumference as would a bumpy surface compared to a flat one and of course wear and tear.
There is a good reason road cars speedometers measure slower than actual speed.

All speedometers l have used measure faster than actual speed, or maybe manufacturers are compensating to avoid too many speeding fines

Sorry, I meant faster. :Oops: As in you're going 28mph but it says 30mph.
Compensating for all sort and if it's VW who knows what it's really reading

[Heater]

One is that the area of contact would be zero, and there'd be no grip.

I did say "To a first approximation" of course there would be a contact patch.

By the way, why would there be no grip? As I reduce the contact patch area the load per square inch on the contact patch goes up to compensate. At zero area there is infinite pressure per square inch. What is the grip then?

The other is that (because the tyre has a steel carcass) the side-walls can flex so that the wheel-rim to tyre tread distance can shrink, but can't grow.

Not so. If I squish a tyres sidewalls together at some point around the wheel the tread will move further away from the rim at that point.

If what you've drawn happened, there'd be an air-gap between side-wall and rim.

I'm assuming our tyre bead is firmly in contact with the rim at all times.

The tread flexes so that there's a large area in contact with the road (helps with braking as well as accelerating), and the tread grips the road as it flexes.

Now we are talking about something else.

Consider this:

1) Every point around the tyre tread is connected to a point on the rim. Assuming there is no slippage of the tire around the rim that point to point mapping never changes.

2) The length of the tread round the outside of the tyre is constant. I will assume that because tyres have all kind of steal wires or whatever in there to make it so.

So, if the rim goes around a 100 times, the tread must go around a 100 times. Else we have broken the point to point mapping I describe above and the tyre is shredded.

If the tread has gone around 100 times the vehicle must have moved by a hundred times the tread length.

This must be true no matter if the tire is fully or partially inflated.

[antomabu]

The distance covered per rev varies with many things, and particularly with tyre wear as well as the type off tyre fitted, and the load on the wheel. Also the driven wheels will turn very slightly faster than the non-driven wheels at constant speed (and more so as the speed rises).

Some cars have the capability to recalibrate the speedo / odo based on data from the satnav to allow for these variations.

I would expect variation in the range of 1% - 5% at least. (diameter of the tyre varies by at least 2% from new to worn).

How precise do you need to be?

That's Montgomery Scott's "Law" from Star Trek: The Naked Time.
http://www.imdb.com/title/tt0708473/quotes

Albeit that Albert Einstein changed some of Newton's "Laws" of physics with his general theory of relativity.

Someone needs to ask Pirelli, McLaren, Mercedes or Red-Bull Racing (other F1 teams are eligible). They'll know the rules of how tyre pressures affect the size of their wheels.

BTW, you're also old enough to be Ms Rachel Riley's dad.

Thanks all for replying to this post. What I concluded is:

1. Test test test and more test. Without testing I now know it is almost impossible to get the the most precise values to get the most realistic values from RPM sensor(Hall effect).

2. It is possible that I might try with filling tires with Nitrogen.

3. For testing I might use a GPS to compare speed values between RPM sensor and GPS. Also monitoring at the same time the pressure (I have to add the new sensor) and the temperature. I think that could help.

4. I can contact the company tires provider, to know more information about how the pressure changes the size of the wheel. That could help too.

What I know for sure that there is a change when temperature and pressure increments, affecting the tire size at least at minimum, maybe 1 or 2% more. The same on the other side when gets colder.

Thanks everyone, I'll keep trying hard on this, I'll keep you updated.

Regards.

[Heater]

Please do let us know your results.

We have some conflicting theories here.

Well, at least conflicting hand waving

[DougieLawson]

The last time I filled a bike tyre with nitrogen (this was on a bike I bought in Los Gatos, CA) it was as flat as a pancake two days later (thankfully I found a kind American colleague with a pump I could borrow).

Bike came home with British Airways at zero extra luggage cost.

[rpdom]

1) Every point around the tyre tread is connected to a point on the rim. Assuming there is no slippage of the tire around the rim that point to point mapping never changes.

The tread is not a solid thing though. There are gaps in it (unless running slicks). The tread has the ability to flex in and out, so the effective circumference of the tyre can change.

[Heater]

True enough. The tread is not rigid. It can flex this way and that.

However, every point on the tread can be mapped to a single point on the rim. That mapping is fixed. If it were not your would have ripped the tyre apart.

The distance from one point on the tread round the tyre back to the same point is always the same. No mater how you have deformed the tyre. You cannot stretch, or shrink that by increasing or decreasing the air pressure in the tyre.

Enough hand waving, let's wait for the experimental results to come in.