Maths Question

[imadoofus]

My bargain-bucket Volvo 850 just sailed through its MOT (with only an advisory for a slight puff from the downpipe) :bannana:

But: The tester said to me that he'd noticed I have been rubbing the inner arches on full lock, but he couldn't replicate it on the ramp, so he couldn't fail it.

Apparently, my car should run 195/60 15"s all round, but it's got 65 profiles on the front.

So the question is: What effect does that have on my speedo accuracy, and if the trip computer says I drove 1,780 miles in France last summer, how many miles did I actually do?

Too lazy/dopey to work this out myself.

TIA

PJ

 

[BTB 500]

Rolling radius calculator:

http://www.torquecars.co.uk/Tuning/alloy-wheels.php

Your front wheel circumference should be 1932.08 mm, but it's actually 1993.34 mm. So your actual mileage was 3.17% more than you thought i.e. 1,836. Your speedo under-reads by the same percentage, so 80 mph indicated is actually 82.5 mph.

 

[Satch]

Too lazy/dopey to work this out myself.

PJ

For shame

 

[PJH]

... Your speedo under-reads by the same percentage, so 80 mph indicated is actually 82.5 mph.

Assuming it was accurate in the first place which it probably wasn't. Under-reading speedos are illegal.
Compare it to a GPS if possible.

 

[imadoofus]

Compare it to a GPS if possible.

I did. I used my Navman in France in the Volvo over that 1,800 miles, and it seemed pretty well spot on. Which presumably means my speedo was over-reading, and the bigger tyres corrected it

I think I'll get some new 60's on the front, and put the 65's on the back. And just hope that I don't get a puncture in one of the 65's...

PJ

 

[Nibbo]

It’s quite simple really.

Given the following:
PI is 3.142857143
To convert inches to mm you multiply them by 254.

Therefore the following aspect ratios will produce the following conferences.

A/r 65 = ((15 * 254) + (195/100)*65) * 3.142857143 = 12372.64286mm
A/r 60 = ((15 * 254) + (195/100)*60) * 3.142857143 = 12342mm

This means that the tyre with the larger aspect ratio will travel an extra 30.64285714mm per rotation.

As a percentage this is about 0.2476662% which means that the 1,780 miles your odometer registered it could have been as much as an extra 4.408458754 miles (roughly)!

You may wish to note also that if your speedometer is registering 50mph you are probably nearer 51mph so watch those speed cameras.

 

[BTB 500]

Assuming it was accurate in the first place which it probably wasn't. Under-reading speedos are illegal.
Compare it to a GPS if possible.

Yes, most speedos over-read at the high end. But I thought under-reading at the low end (30-ish) was actually fairly common ... which is why the 'zero tolerance' policy that was proposed for 30 zones rapidly got dropped?

Think I remember reading that GPS speed is typically accurate to within about 0.5 mph, however it's 'smoothed' (not instantaneous) so you do need to travel at a constant speed for a little while to get a correct reading. On cruise control my VW is very close indeed to the GPS speed, my OH's Audi A4 over-reads a lot (about 5 mph at 'motorway speed').

 

[BTB 500]

It’s quite simple really.

Given the following:
PI is 3.142857143
To convert inches to mm you multiply them by 254.

Therefore the following aspect ratios will produce the following conferences.

A/r 65 = ((15 * 254) + 65) * 3.142857143 = 12178.57143mm
A/r 60 = ((15 * 254) + 60) * 3.142857143 = 12162.85714mm

This means that the tyre with the larger aspect ratio will travel an extra 15.71428572mm per rotation.

As a percentage this is about 0.129198966% which means that the 1,780 miles your odometer registered it could have been as much as an extra 2.299741602 miles (roughly)!

You may wish to note also that if your speedometer is registering 50mph you are probably nearer 51mph so watch those speed cameras.

Any questions?

It's not as simple as you thought

The section height of a 195/65 tyre is 195mm * 65% = 126.75mm. You need to double that and add to the rim diameter in mm to get the rolling diameter.

 

[stats007]

Yes, most speedos over-read at the high end. But I thought under-reading at the low end (30-ish) was actually fairly common ... which is why the 'zero tolerance' policy that was proposed for 30 zones rapidly got dropped?

Think I remember reading that GPS speed is typically accurate to within about 0.5 mph, however it's 'smoothed' (not instantaneous) so you do need to travel at a constant speed for a little while to get a correct reading. On cruise control my VW is very close indeed to the GPS speed, my OH's Audi A4 over-reads a lot (about 5 mph at 'motorway speed').

By law all speedometers have to overread between 0 (wholly accurate) & 10% - they are illegal if they underread. Most manufacturers it seems average on a 3% overread which may fluctuate in either direction as speed increases. Tolerances on components are +/- so increased revolutions can have an effect in both ways.

I remember reading an article about an Audi owner that discovered his speedo was on the limit at 10% overread which theoretically meant at 50k miles he'd only done 45k and therefore the overread was devaluing his car. Audi weren't that interested IIRC.

 

[stats007]

It’s quite simple really.

Given the following:
PI is 3.142857143
To convert inches to mm you multiply them by 254.

Therefore the following aspect ratios will produce the following conferences.

A/r 65 = ((15 * 254) + (195/100)*65) * 3.142857143 = 12372.64286mm
A/r 60 = ((15 * 254) + (195/100)*60) * 3.142857143 = 12342mm

This means that the tyre with the larger aspect ratio will travel an extra 30.64285714mm per rotation.

As a percentage this is about 0.2476662% which means that the 1,780 miles your odometer registered it could have been as much as an extra 4.408458754 miles (roughly)!

You may wish to note also that if your speedometer is registering 50mph you are probably nearer 51mph so watch those speed cameras.

Your value for Pi is also way out in mathematical terms

Pi = 3.1415926535897etc etc

 

[Dieselman]

By law all speedometers have to overread between 0 (wholly accurate) & 10% - they are illegal if they underread. Most manufacturers it seems average on a 3% overread which may fluctuate in either direction as speed increases. Tolerances on components are +/- so increased revolutions can have an effect in both ways.

I remember reading an article about an Audi owner that discovered his speedo was on the limit at 10% overread which theoretically meant at 50k miles he'd only done 45k and therefore the overread was devaluing his car. Audi weren't that interested IIRC.

The mileometer shouldn't over-read as that is an exact measurement and is a simple ratio issue, i.e for each wheel revolution the mileometer gears turn an exact amount. The speedo over reads as it has to account for the spring pressure against the needle.
Mechanical speedos use a magnetic flux to drive the needls boss so are not accurate, hence are set to over read.

 

[stats007]

When did you last see a mechanical odometer? Even so they are inaccurate because of tyre size - even inflation pressure and tyre temperature has a noticeable effect when you're dealing with that many revolutions - not to mention tolerances in parts. Most mechanical odometers are lucky to be within 5% accuracy.