> Sorry, I wasn't being very clear... by more grip I meant higher coefficient
> of friction, not actual friction force. I guess what it boils down to is
> the behavior along an axle (let's assume a single-axle rally car for
> convenience on a flat road.)
> Let t be the fraction of lateral load transfer, then the normal forces at
> the wheels are
> mg*(1-t) and mg(1+t). For simplicity, let's normalize everything to mg, so
> this becomes
> (1-t) and (1+t)
> Let the coeff of friction be a linear function of load, f(x) = ax + b, which
> will be accurate for these purposes since we're just looking at the behavior
> at a given load +/- a small delta.
> then the max lateral grip should be:
> (1-t)*f(1-t) + (1+t)*f(1+t) =
> uhmmmm..... (really, I have a point here, bear with me.... ;)
> (1-t)*(a(1-t)+b) + (1+t)*(a(1+t)+b) =
> a-at+b - at + at^2 -bt + a + at + b + at + at^2 + bt =
> 2a + 2b + 2at^2 = 2(a + b + at^2) (whew, stuff cancelled out!)
> So this shows that when "a" is negative (which is true of tires on asphalt,
> or at least of every tire data I've ever seen), the maximum cornerering
> force is at t=0, or no load transfer. This, of course, explains why
> increasing front roll stiffness causes understeer and increasing rear roll
> stiffness causes oversteer: because the total grip at the stiffer end has
> more lateral load transfer, and thus loses more grip.
> So if on dirt, "a" would have to be positive to have the effect of lateral
> load transfer increasing grip, which would also have the effect of flipping
> the understeer/oversteer of a car, which is the behavior I'm having trouble
> with imagining or matching up to what I've seen. I think I can imagine this
> being true for really wet tarmac, as you say, because increasing the load
> would decrease hydroplaning. I suppose the same argument could be made for
> a tire on dirt making a "furrow" in the ground, this could cause a "digging
> in" effect, which could result in positive "a"...
> What we really need is a tire dyno for dirt. I'm thinking of an old school
> bus driving down a dirt road with a tire mounted on an arm sticking off the
> side bolted to some bathroom scales... throw in some C-clamps and a lot of
> duct tape for good measure. I'm still pretty sure that the peak is at a
> wide slip angle, although until one of us actually coughs up some real data,
> we're just ... (insert colorful aphorism of your choice here)
> -Dave P.
> PS. I'm actually only *mostly* joking about the bus thing. I just may try
> it some day... ;)
> > On Sat, 20 Apr 2002 17:00:39 -0500, "Dave Pollatsek"
> > >I'm guessing the "more load = more grip" thing, if true, is nonlinear; if
> it
> > >were strictly true, than this would mean that the load sensitivity is
> > >inverse to asphalt, which would imply that a typical RWD sedan (e.g., 55
> %
> > >front weight, same tires front and rear, more roll stiffness in front to
> > >make it "safely" understeer) would be oversteer on gravel, while an
> > >oversteer car would become understeer.
> > Well, no. In Asphalt you also have more lateral force with more load.
> > Just look at the pacejka formula. However that's true that for very
> > strong load the lateral force start to decrase.
> > >In my experience, production cars
> > >still understeer in loose surfaces unless the handbrake or some sort of
> > >throttle technique (left-foot brake on FWD, or dipping the clutch on RWD)
> is
> > >used to degrade rear grip.
> > That's true, the car always loose lateral force on the driven wheels
> > because those wheel tends to slip more.
> > >Also, I wouldn't expect removing ARBs to change steady-state total
> lateral
> > >load transfer--isn't that merely a function of lateral force, CG height,
> and
> > >track width? I would, however, expect removing ARBs to reduce wheel-hop
> on
> > >bumpy surfaces.
> > Rally driver usually removes the ARB on wet tarmac because it's a
> > really slippy surfaces. Nothing to do with bumps. It's, again, to
> > increase the lateral load transfert.
> > >I think the biggest factor is that the friction peak on loose surfaces is
> at
> > >an extremely wide slip angle, probably due to a quasi-viscous behavior of
> > >dirt building up on the outside edge. I think there's also some
> threshhold
> > >where for very tight turns, it's faster to rotate the car by sliding than
> to
> > >actually take the turn "properly"--hence autocrossers use the handbrake
> even
> > >on asphalt.
> > >Whatever is true, there's no doubt that there isn't enough stuff written
> > >about offroad tire behavior!!!
> > I think the optimum slip angle on slippy surfaces is tighter, because
> > the contact patch on loose surfaces has less friction
> > so it's deformation is smaller on slippy surface.
> > IMO, regards,
> > Sebastien TIXIER - Game Developer
> > Dynamics and Car Physics
> > http://www.eden-studios.fr
> > GPLRank Normal:-44.24 Monster:-124.44
