Another technical question

[deian]

Ok, I've been doing some sums.

We all know speedo's are deliberately showing higher speeds (+10%ish) for the sake of safety and variables between manufacturers, and that GPS gives more accurate reading of speed (although it's not guaranteed as they also have a disclaimer about being accurate to the nearest 10m or whatever).

I've calculated my speed based on rpm and tyre size. Obviously speedo counts the odometer which some of us use to get mpg. Moving on...

How would I size a tyre up to correct a (for example) 10% error to something less like 5% or even 0%.

I've got the tyre sizes calculated, and I have MPH calculated from RPM's from given gear ratios and a final drive. So if I get two sets of these calculations, keeping the ratio's the same, but change the tyre sizes, how would i calculate the percentage difference of the new tyre size to the old tyre size.

So far, i've calculated that my car has tyres of 175 65 14, and 5th gear is 0.66:1, final drive is 3.94:1, so if my calculations are correct my car would be doing 60mph at 2300rpm.

Would the speedo be showing 66mph at 2300rpm if the calculated (true) speed is 60mph? (and a 10% error on the speedo)?

So my big question is: How would i calculate the percentage difference in circumference of the new tyre size to the old tyre size? And would those differences then relate directly to the calculated speed... i.e is it easy to correct the error in the speedo by changing tyre sizes?

It may be something simple, but it's midnight, and my brain needs massaging.

All this "fun" stuff stems back to my thoughts of fuels costs in the uk, to calculate true speed to get accurate odometer readings to get true mpg. And to get true mpg, i can then work out that it would cost roughly the same to run (fuel) my ZX 1.9td than it is to run a BMW e34 540i (LPG at 15mpg at worse, maybe gears/box/diff swaps). Naturally, the ZX would stay, it would be the runabout, backup car, wife's car etc, it will be a rare thing to have a veggie ready mechanically pumped turbo diesel non-cat ZX soon. And the BMW a toy/money magnet, obviously! But tuning the engine of 4.0 V8 will be fun, M5 is too much money for me.

Thanks for listening.

[Mandrake]

Hey Deian

Good grief, you've been giving that one a lot of thought haven't you. I have a couple of question though -

Why on earth are you considering changing tyre sizes to make your speedo more accurate ? Isn't that putting the cart before the horse ? Shouldn't the tyre size be determined by what is right for the car from a ride/handling perspective ? (Not to mention fitting the wheel arch and rim...)

What makes you think your speedo is so horribly out in the first place ? Have you had it accurately measured ? I've checked mine with the roadside digital "please slow down" signs, and my speedo at 50Km/hr agrees with the digital sign within the margin of error of the digital readout. (Eg +/- 1Km/hr)

The second problem you're going to run into is that you can't calculate tyre diameters to the degree of accuracy that you need to make a meaningful comparison - there is no magic formula where you can put in the tyre size figures and get out a diameter - because for the same "size" and "profile" figures, different brands and types of tyres can vary dramatically.

(For example I find michelins tend to look wider for the same width number than some other brands...)

Good tyre brochures will give you an approximate "rolling radius" figure for the specific tyre - but this can only be approximate because it takes into account a "nominal" amount of tyre footprint compression, which is obviously going to depend on the weight on the tyre and the tyre pressure, but the rolling diameter is also affected by the width of rim the tyre is fitted to. (as it effects the shape of the tyre)

Don't forget that the tyre diameter reduces significantly as the tread wears away too.

I went through all this over analyzing when I went from 185/65/R15 to 205/60/R15 and worried about the speedo being out of calibration but as long as you try to keep the rolling radius the same to the nearest tyre size its all just a big ado about nothing IMHO.

The amount of tyre size change to compensate for a potential 10% speedo error is rather large, and unsatisfactory from other perspectives - like having the tyre clear the wheel arch.

Relax.

Regards,
Simon

[jeremy]

You can calculate the theoretical circumference of a tyre quite easily.

To do s you need to know its diameter. This is 2 x the wall height + the rim diameter. This info is on the tyre itself in the familiar size marking.

For example - the tyres on my BX are 175. 65 x 14
The first figure (175) is the tread width in mm
The second figure (65) is the aspect ratio. This is the ratio the wall height has to the tread width - and for a radial tyre is 80% unless otherwise stated (crossply 90%) - So for my tyre the wall height is 65% of the tread width - 140mm

The 3rd figure is the rim diameter - in this (as most) in INCHES. Convert to mm by multiplying by 25.4 - for my tyre - 355.6mm

So the diameter is (140 + 140 + 355.6)mm - 635.6mm (or if you prefer 2ft 1.02in)

The circumference is the diameter x pi and in turn pi can be approximated to 22/7 if you don't have a scientific calculator. So the circumference of my tyre is 78.646 in (or 1997.58mm)

Odometers are generally more accurate than the speed reading on car instruments - and use a separate mechanism driven from the common cable. Common accuracy is about 3% - but of course this varies a bit with tyre sizes etc - and I doubt if you can measure everything else to much more accuracy.

None of this matters if you are making comparisons on the same car - which ideally should be expressed as a percentage. (For example change fuel - consumption is 3% worse)

(Imagine you are making a shelf to fit in your kitchen - the only measure you can find is simply a cheap rule you have always thought was inaccurate - your shelf will still fit providing you only use that rule (and its calibrations are even) Your problem will come if your brother says he'd like a shelf as well and tells you that he's measured the size for his shelf with an accurate measure - when the accuracy of the 2 measures will become of importance.)

[myglaren]

There is always a calculator in the accessories list but if you use Firefox there is an extension
Otherwise a spreadsheet has all the tools you need.

I may be wrong on this but I have always been led to believe that speedo's are non linear in response. i.e they read low at 30 and hight at 70.
Mine certainly reads low at around 30 as I occasionally trigger the 30 signs when the speedo reads exactly 30.

Apart from that all those calculations make my head ache. I'm off for a lie down.

[Stempy]

The other thing to remember is that the odometer isn't necessarily calibrated the same as the speedo, so if you use tyre size to correct the speedo then your mileage reading may well clock up 10% faster than it should! I had this problem with a motorcycle speedo that I recalibrated, the speedo was reading spot on but the miles were racking up more like km's.

[deian]

I do agree, there are some variables of course, even silly ones, which i have tried to avoid.

And in case you guys are wondering why on earth i am wasting time doing such stuff... it's cos i'm hopefully going to be doing an automotive links website, with technical stuff, pictures, links to downloads pdf's etc. And there are some geeky people (like myself), who do like to mess with numbers, to get typical figures.

I will post the link to the spreadsheets i've done in a bit. Should be interesting to some of the other geeks on the forum.

The 10% was just a assumtion from my imagination based on the fact that if u get caught speeding you get away with 10% over by law (correct me if i'm wrong), so if u drive past a speed camera doing 33mph on your speedo you should be ok.... likewise, you should be ok doing 75mph on the motorway.

Personally, I think those signs may have been calibrated to match most speedo readings and not the 'true' speed, to train drivers to slow down to 30mph on their speedo rather than the true speed.

The tyres sizes will change when they wear down, as does the tyre pressure, atmospheric pressure and altitude, weight of the car, forces of physics, tread patterns etc affect rolling resistance therefore speed and distance and finally fuel consumption.

The main question is... how do you calculate the percentage of tyre size difference if you want to change wheels?

Most people aren't aware that their speedo/odometer would be out by +/- when they change their wheels hence these tyre sites offering the tyre size difference service.

It's also why mileages are never guaranteed when a car is sold by trader.

Simon, i'm not considering changing my tyre to make my speedo more accurate, some people may do, and obviously there are pro's and con's. The last thing I want to do is make a site encouraging anything, i just want basic scientific fact proved through maths, no arguing then. Plus, the internet is full of resources contradicting each other, out of date etc.

Thanks for all your input guys.

[deian]

Tyre Size vs. RPM vs. Gears vs. MPH
https://spreadsheets.google.com/pub?key ... 3uMH4v4vHg

Fuel Consumption Comparison
http://spreadsheets.google.com/pub?key= ... IX6O7lVZTg

Problem is you can't edit them!!

[CitroJim]

Mine certainly reads low at around 30 as I occasionally trigger the 30 signs when the speedo reads exactly 30..

We have loads of the wonderful "Smily/Sad Face" ones around these parts that spend a day or so in one area before moving on to another on a regular if unpredictable cycle.

These are all set fast. Comparing them to a sat nav and my speedo, they read what my speedo says but the sat nav always claims I'm doing 4 or 5 mph less.

They work too. They lead you to believe your speedo is bang-on but actually get you to reduce your speed. Much more effective than any Gatso! Your kids will not like you if you make the face sad either. They always like to see happy faces...

[MikeT]

Same findings here Jim. A few S.I.D.'s have appeared locally and where my SatNav tells me the indicated 30MPH on my speedo is 27MPH, the SID tells me I should slow down.

[Mandrake]

Hi Jeremy,

You can calculate the theoretical circumference of a tyre quite easily.

Sure, you can calculate it - but will it bear any resemblance to reality ?

To do s you need to know its diameter. This is 2 x the wall height + the rim diameter. This info is on the tyre itself in the familiar size marking.

For example - the tyres on my BX are 175. 65 x 14
The first figure (175) is the tread width in mm

Ahhhh, but where is the tread width measured to ? If you've ever put a measuring tape on a tyre you'll find that a 205 tyre is not 205mm wide on the section that is actually touching the ground...the tread is usually counted as going up around to the edge of the sidewall to the invisible dividing line between tread and sidewall. This immediately throws simplistic formulas out the window.

Different manufacturers measure this differently and I've seen up to 20mm difference in usable tread width for the "same" spec size tyre before.

The second figure (65) is the aspect ratio. This is the ratio the wall height has to the tread width - and for a radial tyre is 80% unless otherwise stated (crossply 90%) - So for my tyre the wall height is 65% of the tread width - 140mm

But since I've just pointed out the tread "width" figure takes into account a significant amount of the tyre going up the sidewall, what portion of the "height" of the sidewall counts as far as the aspect ratio goes ?

The 3rd figure is the rim diameter - in this (as most) in INCHES. Convert to mm by multiplying by 25.4 - for my tyre - 355.6mm

So the diameter is (140 + 140 + 355.6)mm - 635.6mm (or if you prefer 2ft 1.02in)

You're glossing over the rim width here - fitting the same tyre to a different rim width will affect its profile, and therefore its diameter, and the rolling radius of a tyre in manufacturers spec sheets is usually listed when fitted to a specific rim width. (I'll admit that the effect is not much though)

The circumference is the diameter x pi and in turn pi can be approximated to 22/7 if you don't have a scientific calculator. So the circumference of my tyre is 78.646 in (or 1997.58mm)

You've completely neglected the flattening of the tyre under weight here, which is the biggest source of "error" between theoretical calculations like this and actual results. The rolling circumference of a tyre is not its actual circumference eg 2pi r the radius of the tyre, but 2pi r the distance from the centre of the tyre to the ground when the tyre is loaded, which is significantly less - something on the order of 20-30mm less.

The formulas you've given are right in describing the relationship of the tyre size specifications numbers, but they don't take into account the way that those numbers are measured on an actual real life tyre, and don't take into account the tyre compression, so they won't give the correct result within the margin of error that we're discussing here with all brands of tyres.

Now that you've calculated the rolling circumference of your own tyre - convert it back to a radius, and then go and measure from the middle of the wheel rim to the ground on your front tyres and tell us what the margin of error is

(I'm not trying to be a smarty pants here, just pointing out there is often a large discrepancy between calculations and measurements with tyre sizes...)

Out of interest I just went and measured the tread width on my 205/60/15 XM1's on the Xantia - 185mm across the tread to where the wear marks stop, (eg the contact width, which is actually slightly beyond the "square" width of the tread) so where did the extra 20mm go ?

This thread got me thinking, so I went out and measured everything properly. For my 205/60/15 I calculate with your formula a diameter of 627mm - radius of 313.5mm.

My tread is nearly worn down to the minimum so I would expect the radius to be slightly less. So what is it ? 305mm from the centre to an unloaded side of the tyre, but only 285mm from the centre to the ground. Thats a 20mm difference. (My earlier 20-30mm estimate was a good guess )

So the error in radius is 10% (taking into account some tyre wear) or 7% if you're just comparing the error due to tyre compression alone.

Regards,
Simon

[deian]

Well... can't we assume that the manufacturers size ratings, are an average for the lifetime of the tyre and the generic size... maybe the manufacturers have already thought about these issues. There must be industry tolerances they have to adhere to regarding the size.

Or to make things simple, can't we just mark the tyre at the bottom, mark the ground, move the car one wheel revolution until the mark touches ground again, mark the ground again, then measure with a measuring tape.

[myglaren]

Tyre Size vs. RPM vs. Gears vs. MPH
https://spreadsheets.google.com/pub?key ... 3uMH4v4vHg

Fuel Consumption Comparison
http://spreadsheets.google.com/pub?key= ... IX6O7lVZTg

Problem is you can't edit them!!

You can and you can't.
You can copy them then paste into a new spreadsheet but there is only data there, no formulas.

[Mandrake]

Or to make things simple, can't we just mark the tyre at the bottom, mark the ground, move the car one wheel revolution until the mark touches ground again, mark the ground again, then measure with a measuring tape.

Well you could, but you don't need to - just measure the distance from the middle of the wheel to the ground and multiply it by 2pi - perfectly accurate - for your exact tyre, with the exact load and tyre pressure you have at that time...

Regards,
Simon

[deian]

Tyre Size vs. RPM vs. Gears vs. MPH
https://spreadsheets.google.com/pub?key ... 3uMH4v4vHg

Fuel Consumption Comparison
http://spreadsheets.google.com/pub?key= ... IX6O7lVZTg

Problem is you can't edit them!!

You can and you can't.
You can copy them then paste into a new spreadsheet but there is only data there, no formulas.

I understand that. I know I can only publish it as data, not as an editable spreadsheet for everyone to experiment with... which is what i hoped google spreadsheet could have done.

[myglaren]

Tyre Size vs. RPM vs. Gears vs. MPH
https://spreadsheets.google.com/pub?key ... 3uMH4v4vHg

Fuel Consumption Comparison
http://spreadsheets.google.com/pub?key= ... IX6O7lVZTg

Problem is you can't edit them!!

You can and you can't.
You can copy them then paste into a new spreadsheet but there is only data there, no formulas.

I understand that. I know I can only publish it as data, not as an editable spreadsheet for everyone to experiment with... which is what i hoped google spreadsheet could have done.

The only way you can do that is to allow free usage to other gmail account holders, publishing locks it as an image.
There is a way around it - open a gmail account and allow all members to access it under a common username and password. One of the forums I use does this with music files so any member of the forum can upload/download to it.
The problem is excluding passers by. Anyone requiring access has to get the details from an admin.
Could be more trouble than it is worth for most. Simpler for anyone interested to get it direct from you as an attachment.