Thanks a lot Jonny, Doug, and Gregor, for your usual excellent responses :-)
Hehe ;-) In time, in time... If it's good enough...
Ok, guys, I wrote up two big things earlier and didn't post either one. The
first one was too full of ramblings, and half way through the second one I
decided to look up and study stress, strain, and modulus of elasticity a bit
for clues. I've come to the quick conclusion that modulus of elasticity,
stress, and strain won't help much in my simplistic view right now (unless I
look at bending sidewalls, something that I'm not prepared for), because I'm
not talking about actually stretching a section of the tire to be a different
width (where strain could develop along that width), but merely displacing the
entire section sideways somewhat against the sidewall's resistance (and
whatever else).
Gregor, you wrote that the wider tire would be structurally stiffer. Meaning
that if you put it on a test stand, grabbed hold with 200 hands around the
perimeter of the tire and pulled as hard as you could, the tire wouldn't flex
as much as it would with a skinny tire with the same sidewall stiffness and air
pressure... Meaning the (I think this is the right term) "foundation stiffness"
should be greater in the wider tire. Right? If so, I wonder if it would
double when the width is doubled, to a point...?
I've tried things a couple ways here. First, if I assume that the lateral
force at one little sliver of the contact patch (extending through the width of
the patch) has a "spring rate" that does not change with tire width (foundation
stiffness is fixed), a skinny tire has a much steeper lateral force curve
(higher cornering stiffness) than a wide tire does. This happens because the
longer the contact patch is, the more lateral distortion there is at the
rearward area of the patch at any given slip angle. For instance, if the slip
angle was 45 degrees and the patch could not slip at all (not realistic, I
know), a skinny tire's patch at 0.2 ft long would distort 0.2 ft at the rear,
while a wide tire's shorter 0.1 ft patch would only distort 0.1 ft at the rear,
resulting in far less lateral force at any given sip angle in the linear
region.
Clearly, if this assumption is made, then a wider tire has very much less
cornering stiffness. The same happens in the slip ratio area too, but I don't
think this is right, hence the question :0)
If on the other hand, as Gregor said, the wider tire's "lateral spring rate" or
foundation stiffness would increase, then I wind up with almost exactly the
same force curve regardless of tire width; the shortened contact patch at a
given load is exactly cancelled out by the increased lateral strength if I
assume doubling the width causes the stiffness to double... Same slope, peak,
everything (well, maybe very slightly different.)
Intuitively, if I imagine getting a 1 inch wide tire and sticking it to a stand
of some kind and trying to pull the tire toward me, I'd think that it would
bend more easily than an 18 inch wide tire would, even if the construction was
pretty much identical. Lowering the profile I bet would increase this
stiffness even more. So it looks like this is more of a "bending sidewall"
problem, complicated by air pressure.
To me, this would mean that this article about why a wide tire usually has more
grip than a narrow one would seem to be rather right:
http://www.autospeed.com/A_0996/page1.html
If the compounds and everything else were identical, and the lateral/foundation
stiffness (spring, not the cornering stiffness slope on force vs. slip angle
graph) is really based on the width, then it wouldn't much matter how wide a
tire was at all. The force curves would be very close to the same in all
respects. The only reason why it might be steeper and peak higher is because
it allows you to use a higher coefficient of friction compound (and related
stuff) that isn't as heat resistant, which would let the cornering stiffness
and peak force both increase...
Any thoughts?
Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://PerformanceSimulations.Com
My little car sim screenshots:
http://performancesimulations.com/scnshot4.htm
