From: mark@wdcwdc.sps.mot.com (Mark Shaw)
Subject: Re: Tyre pressure vs circumference vs speedo accuracy!
Organization: Motorola Western MCU Design Center, Chandler Arizona
Date: Sat, 5 Sep 1992 00:44:43 GMT

In article <1992Sep2.233313.1@wombat.newcastle.edu.au>, sysnet@wombat.newcastle.edu.au (David Morrison) writes:
|> I have observed that my speedo (and odometer) are wrong by about 3%.  I 
|> normally keep the tyres 3-4 psi greater than recommended (for good reasons)
|> and wondered whether this may have explained the error. 

|> 1. Is there a theoretical method of determining the circumference for a given 
|> tyre pressure?  Or at least the difference in circumference for a difference 
|> in pressure?

There is nothing wrong with you method.  The problem is that you have assumed that the
speedo/odo was accurate at the correct inflation pressure.   A good reference on the subject
of speedo/odo accuracy is SAE Information Report J862.   Back when I road rallyed alot
I looked closely at odo error since it can really foul up mileage (and navigation).

The most dominant factors are tire contruction, size, and wear.  That all assumes that
your car has the right gear drive ratio for your speedo/odo.  Most US makers follow SAE
recommended practice and design their speedo/odo for 1000 rev/mile at the input shaft. 
The European typically use 1500 revs/mile, the rest of the makers use whatever strikes their
fancy.   Unfortunately it is difficult to precisely hit this ratio since there are few gears
in the chain and gears can only be made in finite steps.  The recommended SAE practice (J678)
allows +4%/-4% variation from actual on odometers and either +4%/-4% OR +6%/-0% on speed. 
I have found that GM cars (US) are notorious for indicating LOW by as much as 10% since they
are usually designed for smaller tire sizes than they are shipped with.  

The J862 data shows about 0.1% for a 6 psi change (close to your data).
It also shows an increase in mileage of up to 3% for tire wear (new to old).
It also shows an increase or decrease of up to 1.7% for differences in tire construction.
Radials are more accurate over speed than bias ply tires, which tend to grow with speed.

Tire size is also really dominant - For your 13 inch rims you could get the following tires:
(these are for Yokohama A008RS tires):
  185/60/13 - 957 revs/mile
  175/70/13 - 914 revs/mile
  185/70/13 - 882 revs/mile
  205/60/13 - 873 revs/mile
That's a variation of +4.5%/--4.7% from your 175/70/13 size!

The best way to determine the effects on you odometer is to measure the tire's static rolling
radius, which is from the center of your axle (use the axle connected to the odo) to the
ground and then multiply by 6.28 (2 pie) to get the distance per revolution.  This is quite
adequate, though difficult to measure for some axle designs.

My guess is that your odo/speedo is off due to the manufacturing tolerance of matching the
speedo cable gearing to your tire size.  You are basically stuck with it unless you want to
go to a different tire size.  But even then your accuracy will vary over the life of the tire.
You didn't state whether the reading was low by 3% or high by 3%.

Anybody who swears my their odo/speedo in making MPG, top speed, or mileage measurements
had better calibrate their tires on a daily basis.  The more serious rallyists do -- hence
the need for a 10-mile odo check at the start of an event.

regards,
Mark                (mark@wdc.sps.mot.com)   Tempe, AZ, USA