>> Your acceleration to the centre of the corner (i.e. G force) is
>> proportional to the grip of the car.
>> If you have NO downforce, the only force keeping you on the road is the
>> weight of the car.
>> The maximum cornering 'force' is therefore the same ammount.
>> F=ma
>> Hence, only ever 1 g.
F=ma doesn't prove that a vehicle can't accelerate at more than 1 g. Let's
look at a real tire test for an Indy 27x14.5-15 rear tire here, from the same
source Matthew Jessick was referring (Race Car Vehicle Dynamics, Douglas and
William Milliken):
With 1000 lbs vertical load (that's your "F", or Force, in F=ma)---- A bit
over 1700 lbs lateral force is generated. Really, you want A=F/m here. If the
1000 lbs downforce on the tire is all from weight of the car, what's the mass
of the car? 1000/32.16=31.09 slugs.
Acceleration=Force/Mass
Acceleration=1700/31.09
Acceleration=54.68 ft/sec^2
54.68/32.16 = 1.7 G lateral acceleration
By golly, that's the same thing as:
1700/1000=1.7G
If the coefficient of grip/friction can never exceed 1 as Doug said, a quarter
mile dragster could never do any better than about 9 seconds at 200 mph
(roughly). We know that's not true, even cars with no downforce beat that
these days by a long shot. Top Fueler dragster tires show a grip /friction
coefficient of about 4 when they're hot.
G and F are "relatively constant"? I doubt the acceleration of gravity changed
much during the above tire test. :-) Also, I was referring to skidpad testing
in the earlier post, where everything is as constant as you can get it.
You're right about that. Coefficient of grip/friction changes with the load
on the tire. For instance, the Indy tire from the example above shows about
1.7 at 1000 lbs load, while the same tire shows a little over 2500 lbs of
lateral/sideways force with 1800 lbs pushing down on it.
That's 2500/1800 = 1.38. That's quite a change in grip coefficient from the
1.7g's in the other example. Tire engineers call this effect "load
sensitivity." You're right about there being no simple relation between the
two, Michael, but in both cases, the coefficient of grip is well above 1, as
Matthew Jessick pointed out. (Thank you, Matt, BTW, for posting those
numbers.) The numbers he quoted are at one particular load and are not
constant, but the really sticky ones will stay above 1 pretty much no matter
what ya do!
Cheers,
Todd Wasson
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Performance Simulations
Drag Racing and Top Speed Prediction
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http://PerformanceSimulations.Com
**No tires were injured or killed in the production of this post.
