Brian M Kennedy wrote:
> At 12:01 PM 10/27/99 , Todd Green wrote:
>>Mark Sipe sent some private email which got me thinking. GEEZ
>>appears to determine usage via:
>>
>> usage = max(current lat, current accel, current lat trans) /
>> max(peak lat, peak accel, peak lat trans)
>
> Hmmm. That would seem flawed. You could be right on the edge of the
> friction circle, at a 45 degree point, and get a usage in the 80's,
> assuming you normalized. If you didn't, it would be even more flawed.
>
> Ignoring the transition component, you'd want something like:
>
> g_usage = sqrt((cur_lat/peak_lat)^2 + (cur_accel/peak_accel)^2)
>
> where you use a different peak_accel depending upon the sign of cur_accel.
>
> Perhaps you would 'max' that g_usage with transition rate:
>
> usage = max(g_usage, cur_trans/peak_trans)
>
> Not sure the best way to incorporate transition rate, but don't you need
> one for lateral and one for acceleration? And perhaps even two for
> accel, one for throttle->brake and one for brake->throttle, taking into
> account the slower "spool up" of motors vs. brakes???
>
>Well, I am sure Byron will dazzle us well beyond the above. ;^)
Well, I'm not Byron, and I don't claim to be able to dazzle, but I will try
to explain how usage is computed based on my conversations with
Byron and my reading of the help files.
Before explaining usage, let me take a detour and explain how Geez
works with regard to longitudinal acceleration. This will become relevant
in a minute.
Geez doesn't use a friction "circle" but instead uses a friction "tube".
The friction tube is generated by taking friction circles and stacking
them on top of each other. Geez has a friction circle for each speed
quantum. The reason is a car could effect a much higher longitudinal
acceleration vector at one speed (say 25 MPH when the engine is
in the meat of its powerband) than at another speed (say 35 MPH,
right after the shift to 2nd gear when the torque at the rear wheels
is less than at 25 MPH because the gearing ratio change and the
fact that the engine is at an RPM which puts it lower in the powerband).
When a use the term "friction circle" below, I mean the friction circle
that corresponds to the speed you are currently traveling.
Now, usage at any point in the run is calculated as the highest of three
numbers.
1) Total G percentage - this number is the distance from the
origin (or center of the friction circle) of the total Gs that
the car is currently pulling divided by the distance from
the origin of the edge of the friction circle that touches
a line that runs from the origin through the total G point
that the car is currently pulling.
2) Maximum acceleration G percentage - this number is the
longitudinal acceleration that the car is currently pulling
divided by the maximum longitudinal acceleration that the
car can pull. If the friction circle for a given speed was
always a circle, then this percentage would always be less
than or equal to #1 above. However, the friction "circle" for
any given speed is actually a friction ellipse. This means
that although you might only be pulling 90% of total Gs,
you are accelerating at 95% of the maximum longitudinal
acceleration. Since Geez doesn't know whether you want
to pull max longitudinal Gs or max total Gs at this point on
the course, it gives you the benefit of the doubt.
3) Transition rate percentage - this number is calculated as
the current transition rate (Gs per second) divided by the
highest transition rate that you've pulled in your car. Basically,
Geez doesn't penalize you for moving through the middle of
the friction circle quickly.
I'm still a little unclear if there is a max longitudinal transition rate and
a max lateral transition rate that are used. Maybe Byron can enlighten
us about this.
John Engstrom
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