This article is from the VW Performance FAQ, by with numerous contributions by Jan Vandenbrande others.
A:There is no straight answer! There are really three main
factors that determine handling (disregarding suspension
changes for now): 1) Frictional coefficient between the
tire and the road, 2) Contact patch size and geometry, 3)
Tire sidewall stiffness. If you keep the frictional
coefficient constant as well, you have two parameters to
play with: Width and Sidewall stiffness. Wider tires will
change the contact patch from an oval to a more elongated
oval, which generally improves handling, but increases
steering effort, and makes the car more prone to
aquaplaning (hydroplaning) in wet weather and in snow it
never gets to through the snow. In snow conditions the
best way to go is small rims (13" for A1 & A2) with a 165-
175/70/13 tire on it.
However, another, perhaps more important factor is
sidewall stiffness. The stiffer the sidewall, the less
the tire will flex sideways which improves turning,
transients, steering accuracy Therefore going from a
175/70-13 tire to a "plus 1" 185/60-14 or a "plus 2"
195/50-15 tire will elongate the contact patch, reduce
the sidewall height ==> increase side wall stiffness and
therefore improve handling. However changing from 185/60
to a 195/60 may or may not do much good: The contact
patch is more favorable but the sidewall is also
increased in height ==> more flex. Test by VW and EuroCar
have shown that an A2 GTI with 185/60 tires handles about
the same as one with 205/55. Note that they were using
the same car for this test, with the same suspension. (VW
sold the A2 GTIs with wider tires purely for looks and
customer demand despite the fact that it did little or no
good in handling). To make use of wider and lower profile
tires the suspension needs to be matched to the tires.
But there is more to it as well! Tires, even within one
type & size, may have different sidewall stiffness (e.g.
HR vs VR), and compound! A softer compound will grip
better, but wear faster.. Wider rims make a big
difference due to a better lateral support, effectively
increasing sidewall stiffness. NEVER use 5.5" on a 185/60
or wider tire; the wider the better, at least within
reason. A 7" rim would probably be ideal for a 195/50R15
tire for the street.
From Roy Kao: wider tires may make a marginal improvement
in transient cornering responses, but how often do you
make radicalattitude changes on the street?
In summary [From Mark S]:
Cost: worse
Ride quality: worse
Tramlining: worse
Handling quickness: better
Handling limits: better
Safety in standing water, mud, or snow: worse
Looks: better (imho)
Steering feel: probably worse
Braking: can't say for sure
Power application: probably worse
A lot of the above depend on tire choice, too. Note that
choice of tire will have a much much larger effect than
changing wheel size on handling. Alignment also has a
huge effect, as does tire pressure.
 
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