Ok, I was getting a bit carried away with the specific details of F1
race cars. In some cases, 1st gear is "undergeared" so the cars can
exit pits, but 2nd gear is "better" once the car is moving.
Ok, I was getting a bit carried away with the specific details of F1
race cars. In some cases, 1st gear is "undergeared" so the cars can
exit pits, but 2nd gear is "better" once the car is moving.
Regarding the formula itself, as mentioned in the web site below:
"don't try to find any physics in here: it's just a convenient formula that fits the data reasonably well."
http://www.miata.net/sport/Physics/Part21.html
Slip ratio generating force does seem strange at first, but that's how
it works. If you imagine 4 elements in a contact patch starting at
the front and progressing toward the rear, here's essentially what
happens:
If the contact patch is 1 unit long, under a free rolling condition
our evenly spaced elements are located at these positions:
0.2
0.4
0.6
0.8
If we add in 10% slip at the rim and assume there's enough friction to
keep all the elements stuck to the ground so there's no sliding, the
position that each element wants to be will move 10%. The "deformed
positions" have now stretched away from the 0.2, 0.4, etc., to this:
0.22
0.44
0.66
0.88
Each of those elements is like a spring. Granted, in a real tire this
is generating shear, but it's fundamentally the same thing as far as
you need to be concerned. The elements have deformed the following
amounts
0.22 - 0.20 = 0.02
0.44 - 0.40 = 0.04
0.66 - 0.60 = 0.06
0.88 - 0.80 = 0.08
The force is getting larger and larger toward the rear and at some
point will slip. However, the percentage of the contact patch that is
actually slipping has nothing to do with the slip ratio and is not
important for you. "20% slip" does not mean that 20% of the contact
patch is sliding. It just means the rim is rotating 20% faster than
it would be if it were free rolling just as the slip ratio equation
says.
Conceptually, however, once these elements have left the contact patch
they eventually return to their (perhaps nearly) undeformed position,
so it's perhaps not too unreasonable to accept that this occurs with
something deformable like a tire. It's indeed what happens.
In my simulator I am modelling the contact patch directly and the end
result is quite similar to the Magic Model as far as force vs slip
ratio or slip angle go (although the low speed/stopping issues are
solved much more easily with my approach; you'll have to cross that
bridge when you come to it: Search for "relaxation length" when it
falls apart at low speed).
One other thing: The slip ratio here has nothing to do with the
vertical tire squash. It's free rolling angular velocity versus
current angular velocity *at the current vertical displacement.* 0
slip ratio ought to give you 0 or very near 0 force. That's what free
rolling means. The tire is rotating just as you imagine it. Don't
worry about 10-15% slip ratio and the effects on rendering. It's
imperceptible unless you want to look really closely under slow
motion.
But hey, it looks pretty wierd in reality too: ;-)
http://youtube.com/watch?v=V3yj_OGezWc
Getting back on topic, I would assume that low profile tires, like a 345/30/19
tire (the 30 being the profile percentage) would have a lower optimal
slip ratio than a higher profile tire.
Also, what about the hysteresis effect mentioned earlier (the transition
from dynamic friction back to static firction)?
Lastly there's the classic case of car stopped on a hill or banked track
where the Pacejka model because actual velocity is zero. Has your
approached solved this problem?
Nice video link to those wrinkle wall tires.
Hi Jeff,
RAS used to be about the only place I ever posted. Really it was my
first spot on the internet I think. I don't come around here too
often nowadays.
Low profile tires: Generally speaking it's probably a safe rule of
thumb to assume that that's indeed the tendency if you look at all
tires overall. The cord angles and construction (# of plies, etc)
have a lot to do with this too though, so it's not a hard and fast
rule. You can make 2 tires that are identical dimensions in this
regard that vary considerably in stiffnesses in different directions.
Hysteresis: I'm not sure I'm following what you mean on that one.
Static versus dynamic friction go right out the window when it comes
to *** and I'm not sure of the connection you're implying with
hysteresis there.
Classic low speed problem/hill stopping: Yes, my approach solves this
(finally) and there's a perfectly smooth transition between all
states. There is no separation between low and high speed (it's all
just 1 model; no switching equations around at x speed). I have this
running in the RC simulator (Virtual RC Racing), but not in my big car
sim thingy but it should work just fine.
A relaxation length addition to Pacejka's Magic Model solves it nicely
enough too. When I was playing with those models I didn't really know
all that much about tires and never got the approach to work. Since
I've not used it forever there isn't any reason to go back and make it
work, but anyone using the Magic Model should definitely look into
it. It's one of those big problems every sim guy runs into, often
unexpectedly.
I think most of our locking of horns stems from you addressing things
from a roadholding (what the tires can transmit to the road) issue,
whereas I was presenting it from a driving torque issue (i.e. when are
the tires least likely to develop the high rates of slip that caused
Benoit's orignal concern).
Brings to mind a story from Jackie Stewart's old book ("Faster!"?)
where he and Ken Tyrrel hit upon using a high first gear that they
thought would be ideal for the chicanes installed at Monza, I think,
but didn't practice a start with it on full tanks, and ended up being
done at the drop of the green flag...
I suppose I was a bit quick to have flashbacks of bygone days at the
Papy forums. Could be worse; I could tell folks I won't share my
ARCA sim setups with them and REALLY get the **** kicked out of me.
speedmd
I really don't mind being kicked around if it brings some action to
RAS :)
Pat Dotson
Yeah, I just got myself a copy of SAE950311 on the subject. Still
missing Milliken&Milliken's bible though.
So all in all, I'm convinced now, and I have learned something, so I'm
happy :-)
Thanks,
Benoit.
amazon.com, or direct from the SAE. It ain't cheap no matter where you
buy it, though.
speedmd
My copy is signed by Mario Andretti and Doug Milliken. Whoot! :-)
We had Doug in the shop a few years back, and he signed the team
owner's copy, but I didn't think to have him sign mine.
speedmd