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Here, in the Quebec state of Canada, there was a class action legal suit against Honda because it became known the speedometer was inaccurate by showing higher than true speed and that ended up in having the odometer higher than the real mileage and people wanted to have the warranty to be adjusted accordingly. I'd trust the GPS speed over the speedometer...
Joined: 24/06/2003 00:22:12 Posts: 2946 Location: Escaped to the Antipodies! 36.83°S 174.75°E
Posted: Wed Jan 16, 2008 8:51 am Post subject:
GilbertQC wrote:
the odometer higher than the real mileage and people wanted to have the warranty to be adjusted accordingly. I'd trust the GPS speed over the speedometer...
Interesting comment about the odometer! I haven't compared many cars but I noticed that my odometer is pretty accurate when I've compared it to the GPS trip computer. I guess they have learned their lesson and the calibrate them separately now...
Andy_P2002 wrote:
Right angle triangle 1 by 5 gives length of hypotenuse= sqrt26=5.099 .... making speed error -2%
The other thing to remember is that anything more than a 1 in 5 gradient is quite steep and you wouldn't be doing a high speed down it anyway. _________________ Gone fishing!
Joined: Aug 22, 2007 Posts: 211 Location: Peterborough
Posted: Wed Jan 16, 2008 11:03 am Post subject:
tgold wrote:
dhn wrote:
Snudge wrote:
My point is that for one revolution of the wheel the vehicle travels a distance equal to the circumference. It's nothing to do with the radius.
Except Circumference = 2*pi*radius
I suggest you forget circular geometry and instead consider a tyre to behave much like a tank track. Each revolution will result in an equal distance of travel no matter what shape a tank track (or a car tyre) takes.
Tony
Yes I agree and that is exactly my point! My previous post about using a piece of string to represent the circumference makes the point that despite the shape of the circumference changing with tyre pressure the length of the circumference stays the same and so the distance travelled per rev of the wheel does not change.
Other posters are using the word 'radius' as the distance from the centre-line of the axle to the ground which is why I said it was irrelevant. The tyre does not have a true radius when in loaded condition so the distance from the axle to the ground is useless.
If you mean use the formula c=2*pi*r when the tyre is in the unloaded condition then that's ok.
Joined: Jun 04, 2005 Posts: 19991 Location: West and Southwest London
Posted: Wed Jan 16, 2008 11:46 am Post subject:
Well, I just spoke to our resident genius at work, and he agrees the rolling radius is the important factor and the circumference is irrelevant.
When I asked how we could convince you, he suggested "let his tyres down!"
I can see we are never going to agree, but here's my final attempt:
1. Using your tank-track analogy...Imagine the track (i.e. the tyre circumference OR your piece of string) rolling nicely over the ground, being driven by a 2-foot diameter wheel. Now imagine what happens if you drive the same track at the same speed over the ground with a much smaller wheel. It has to rotate faster doesn't it? Well it's those revolutions that are effectively being counted by the speedometer isn't it?
2. Or imagine a wheel made of sponge rubber. Like an ordinary tyre, the outside circumference wont alter, but if you pushed down on the axle as you rotated it, you would travel less far for every complete revolution.
Joined: Aug 22, 2007 Posts: 211 Location: Peterborough
Posted: Wed Jan 16, 2008 12:54 pm Post subject:
No, no, no Andy! The tank track example is wrong(but it wasn't mine) and what you've said about it is correct but you've missed the point about the string. Mark the point on the circumference of the tyre in line with the valve and, assuming the tyre is not completely flat and there is slippage, the mark will always be in line with the valve. Now run the tye at 15psi and then at 50psi - the circumference of the tyre will be a different shape but the same length (as proved by the string) so the vehicle will move forward a distance equal to the circumference for each rev of the wheel. This means that the gear ratio is not altered and so the speedo' reading will not be affected.
(I've had trouble with you before over that pythagoras stuff and equal triangles. )
Joined: Dec 06, 2007 Posts: 30 Location: Brighton, MA, USA
Posted: Wed Jan 16, 2008 2:53 pm Post subject:
GilbertQC wrote:
Here, in the Quebec state of Canada, there was a class action legal suit against Honda because it became known the speedometer was inaccurate by showing higher than true speed and that ended up in having the odometer higher than the real mileage and people wanted to have the warranty to be adjusted accordingly. I'd trust the GPS speed over the speedometer...
In most systems I'm familiar with, the speedometer and the odometer work off the same data source but use it differently, so that an error in one doesn't necessarily imply the same error in the other.
Joined: Nov 07, 2004 Posts: 98 Location: UK or USA from time to time.
Posted: Wed Jan 16, 2008 3:02 pm Post subject:
Andy_P2002 wrote:
1. Using your tank-track analogy...Imagine the track (i.e. the tyre circumference OR your piece of string) rolling nicely over the ground, being driven by a 2-foot diameter wheel. Now imagine what happens if you drive the same track at the same speed over the ground with a much smaller wheel. It has to rotate faster doesn't it? Well it's those revolutions that are effectively being counted by the speedometer isn't it?
I can't visualise your example or where this wheel is, but in the case of the tank track I was just pointing out that each revolution of the track will have the same distance of travel. A belted tyre tread is about as inelastic as a track.
Quote:
2. Or imagine a wheel made of sponge rubber. Like an ordinary tyre, the outside circumference wont alter, but if you pushed down on the axle as you rotated it, you would travel less far for every complete revolution.
If the outside circumference does not change length and if there is no slippage such that one revolution of the axle causes one revolution of the outside then again each revlolution of this sponge wheel will have the same distange of travel.
Tony
Joined: Nov 30, 2007 Posts: 649 Location: Doncaster
Posted: Wed Jan 16, 2008 4:24 pm Post subject:
Andy_P2002 wrote:
we're going to have to agree to differ on this one!
I will agree to that Andy as when we are going into ABS and things sending speed signals to the speedo etc. I have 14 years experience to say that is not true to a certain extent but thats as far as i will go with it as i did'nt really want to go that far into it allready. _________________ NEW Tomtom GO 500 (hope it is good)
iphone (running all day, doesn't like it)
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...This is the only thing you said that I disagree with. You postulate a slope of 1 in 5, which is 20%. A 20% slope is 11.3 degrees (arctan(0.2)). Taking the cosine of 11.3 degrees, I get 0.9805806757.
100*(1.00 - 0.9805806757) = 1.94193243
or less than 2%.
Jon
You're absolutely right, of course. I'd started with a 1 in 3 slope before deciding that was unrealistic, but the original calcs got posted by mistake (either 5% or 6% is for 1 in 3, depending on which way you interpret "1 in 3").
Well, I just spoke to our resident genius at work, and he agrees the rolling radius is the important factor and the circumference is irrelevant.
Sorry, the resident genius has not looked deeply enough - both are relevant.
A. The circumference is what is in contact with the road and will cover the same ground as before per revolution, so the tyre revs will (in theory) stay exactly the same.
B. With the reduced rolling radius, the wheel will (in theory) need to turn faster for the same road speed.
Both statements are correct and are mutually exclusive. In the tank tread analogy the inner wheel rotates faster than the tread itself. However in a car tyre, the two are forced to rotate at the same speed because they are connected by the sidewall, and the tyre bead locks the tyre onto the wheel itself. So, something has to give!
In reality the tyre bead may be forced to slip round the wheel rim and the tyre's tread may be forced to skid somewhat on the road surface, depending on which has the greater grip. The conflicting forces are huge which explains why flat tyres overheat and destroy themselves very quickly.
Joined: Nov 24, 2003 Posts: 1441 Location: Swansea
Posted: Wed Jan 16, 2008 6:39 pm Post subject:
Gnomeface wrote:
..... So, something has to give!
In reality the tyre bead may be forced to slip round the wheel rim and the tyre's tread may be forced to skid somewhat on the road surface, depending on which has the greater grip. The conflicting forces are huge which explains why flat tyres overheat and destroy themselves very quickly.
and also explains why driving a 4x4 with different tread depth on either side will quickly wreck the transmission
Robin _________________ TomTom One v3 Europe, Navcore 7.903, Western Europe 835.2420
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Joined: Apr 04, 2006 Posts: 10118 Location: Bexhill, South Sussex, UK
Posted: Wed Jan 16, 2008 7:49 pm Post subject:
All terribly interesting, with some really good analogies, including sloping roads. BUT.... Which is the more accurate - GPS speed reading or car speedometer??? Given the short term RELATIVE positional accuracy (NOT the absolute accuracy) and the accuracy of the several atomic clocks to which your GPS device must be locked to give a sensible positional lock, I know which I would prefer over a device that relies on either tank tracks, bits of string, circumferences, rolling radiuses, ABS sensors, flat tyres, over inflated tyres etc. even if any or all are irrelevant.
That is unless of course the GPS manufacturer has really screwed up some fairly simple spherical geometry calculations, and incorrectly calculated the distance between two adjacent fixes.
Joined: Nov 07, 2004 Posts: 98 Location: UK or USA from time to time.
Posted: Wed Jan 16, 2008 8:08 pm Post subject:
M8TJT wrote:
I know which I would prefer over a device that relies on either tank tracks, bits of string, circumferences, rolling radiuses, ABS sensors, flat tyres, over inflated tyres etc. even if any or all are irrelevant.
That is unless of course the GPS manufacturer has really screwed up some fairly simple spherical geometry calculations, and incorrectly calculated the distance between two adjacent fixes.
We agree on the choice even if I believe your reasons (the geoid is not spherical and anyway GPS speed measurement is not even based on position fixes) are suspect.
Tony
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You're absolutely right, of course. I'd started with a 1 in 3 slope before deciding that was unrealistic, but the original calcs got posted by mistake (either 5% or 6% is for 1 in 3, depending on which way you interpret "1 in 3").
Given the short term RELATIVE positional accuracy (NOT the absolute accuracy) and the accuracy of the several atomic clocks to which your GPS device must be locked to give a sensible positional lock, I know which I would prefer over a device that relies on either tank tracks, bits of string, circumferences, rolling radiuses, ABS sensors, flat tyres, over inflated tyres etc. even if any or all are irrelevant. 
