rec.autos.simulators

Let's say Q (read theta) is the bank angle, v is speed, M is total
mass, r is radius, g is gravity and mu is friction.

Resolving forces relative to the track surface, I get

M (v^2/r cos Q - g sin Q) needed down the slope, and
M (g cos Q + v^2/r sin Q) download on the tyres

Check at Q = 0 => sin Q = 0, cos Q = 1 leaving

Mv^2/r across and Mg into the ground.  Sound good.

So adding tyre friction, to corner at the limit we have

mu M (g cos Q + v^2/r sin Q) = M (v^2/r cos Q - g sin Q)

Since I can now see a trig identity coming on, and I don't like
those ;-), cheating and using Excel gives me a bank angle a little
under 19 degrees for mu = 0.9 and the data you've already given.
Less, obviously, if the tyres are stickier than 0.9.

See if that sounds plausible!

Jonny

Ah ha! yes, that would explain all!

Have fun!

    Paul

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First, I spent an afternoon measuring the race track.  The actual radius
of the turns is 95 feet, so the lateral G's are a little more than 1 G.
There is 2-4 degree banking on the track.

Second, what I really wanted to know is, how much left side static
weight bias do I need so that during cornering the weight transfer evens
out to a 50/50 split between the right side and left side of the kart.

Jonny Hodgson came to the rescue with the following
equation:

x = h (v^2/r cos Q - g sin Q)
      -----------------------
      (v^2/r sin Q + g cos Q)

Where x is the offset distance of the static CG from the center of the
kart, given,

h=VCG
v=velocity
r=turn radius
Q=track banking
g=gravity

Then the percentage of weight on the inside is just:

        100* (x + 0.5t) / t

The results are that close to an 80% left side weight bias is needed to
balance the weight transfer between the right and left side of the kart.

So I'd like to see if there are any comments on the validity of these
calculations.  Not necessarily whether or not a LTO kart will work with
80% LS weight (though thoughts on that are welcome), but is the formula
correct for predicting the weight transfer?

Thanks,
Pat Dotson

  That formula looks familiar, although I haven't used it (writing it down now
:0)).  If it came from Jonny Hodgson, I'd trust that it's right.  How did you
find the center of gravity height with yourself on the cart?  

My little car sim screenshots:
http://performancesimulations.com/scnshot4.htm

There are kart setup programs that include a worksheet to
calculate VCG.  The typical range for VCG is 11" to 14".

What you do is first scale the kart to measure the weight
at each wheel.  Then tip the back end of the kart up and
record the new front wheel weights.  The programs will
calculate VCGb based on the transferred weight, kart
wheelbase, and the distance the rear tires are raised.

What is intersting is that oval track racing kart setups
never use much more than 60% left side bias - usually
more like 56%-58%.  Yet, to balance the weight transfer
between left and right, you need more than 70% left bias.
I think I can gain an advantage by running higher left
side bias which will work the left tires more.  Whether
or not the kart will work right or handle well remains
to be seen, since they are designed for less left bias.
--
Pat Dotson

 That's odd that they don't usually run more than 60% left side bias, I wonder
why that is.  Maybe it's not practical for some reason, although I can't
imagine why it wouldn't be..  It seems like you're on the right track there
anyway (no pun intended) :-P.  

Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://PerformanceSimulations.Com

My little car sim screenshots:
http://performancesimulations.com/scnshot4.htm

http://www.nacoma.cc/kartsmart.htm

Yes, that's with the driver.  You only have to tip the kart
up as little as 6", though the higher it is the more accurate
the result should be.
--
PD

Don't do that!  I was famous at uni for my silly mistakes and
factors-of-2... :-)

Jonny

  Hehe :-)  Alllllllll-righty then!  

Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://PerformanceSimulations.Com

My little car sim screenshots:
http://performancesimulations.com/scnshot4.htm

For CG height calcs--these are usually very sensitive to any small
inaccuracy with the scales.  The few times I've done it, I've taken weights
at a number of different heights, plotted the results, then fit a good
line through the scatter in the data points.

I've heard from a friend that the short track cars ("super modifieds"?)
that used to run at the Oswego, NY paved oval had up to 80% left weight.
There must have been one guy that figured out (by trial and error, and by
being clever) what it took to get the car to drive reasonably with that
much offset...  and then I suppose every one else copied him.  The big
block V-8 engines were set between the F and R wheels on the left side of
the car, drive shaft passed just inside the left rear wheel, rear axle had
an offset pumpkin, driver sat next to the driveshaft.  These cars were
banned some years ago (I'm not clear on the full history).  They were very
fast.  Also very easy to roll over if you spun 180 deg...or maybe even if
you had to turn right (up the banking) to miss something in front of you??

It will be interesting to hear how this works out for you.

-- Doug Milliken

That's scary.  I wasn't actually going to start out at 80%,
more like 70% or so.  The key is how low I can get my VCG.
The lower it is the less left I have to run.

I'll probably just end up scuffing my shiny Simpson
Super Shark! :)

Kart people are very skeptical about high left side
weight.  Everyone has a stock answer - too much left
bias will cause a four wheel drift.  With normal
setups, cornering at 1 G, 75% of the total weight of
the kart is on the right side tires.  If you suddenly
go to 50% of the total weight on the RS, but still
have the same tire setup, of course all the grip is
gone.    My answer to that is use softer tires and
less air pressure until they start gripping.

--
PD

Ruud van Gaal
Free car sim: http://www.racer.nl/
Pencil art  : http://www.marketgraph.nl/gallery/

<g> I was fine with the off-by-ones; my answers almost always came
to a factor of 2, whenever they were wrong!  I think it's actually
something to do with my inability to operate a calculator...

Jonny