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If I had it immediately handy, I'd show them. That not being likely, I would definitely say/emphasize what I've heard every track session operator say when it's cold, "the track is cold/damp, go easy the first few sessions".
 

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Thanks for that. Your job must have had you knee deep in complex calculations far more difficult than this.
More like neck deep or higher occasionally. My earliest significant work was casualty estimates for the chemical attacks we expected during Gulf War I. About mid way thru my career, I was responsible for the analyses used to determine munition requirements for the entire Army, from 5.56mm to Patriot missiles and everything in between. After I retired from the military at 31 years and became a GS-15 federal employee, I was responsible for the simulations and data sets we used to estimate the effects of nuclear, biological, and chemical attacks, accidents, incidents, and natural emergences (Ebola in West African being the most significant on my watch). I was never bored with what I was doing.
 

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Discussion Starter · #23 ·
I knew people were running those models somewhere, and turns out you're one of those. Seeing stats and graphs on the news must be a totally different experience for you.
 

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True. What I've been seeing is best described by Kyle Reese in the first Terminator movie: "That Terminator (Coronavirus) is out there. It can't be reasoned with, it can't be bargained with...it doesn't feel pity of remorse or fear...and it absolutely will not stop. Ever." ...unless we stop it.

The basic models for this type of event are called SEIR which stands for the four subpopulation categories Susceptible - Exposed- Infected - Removed (Removed = Dead, Recovered/Immune, or Vaccinated). The crux of the kill-chain is each person's willingness or unwillingness to adopt mitigating behaviors that reduce the transition probabilities between these categories. Stay home or not? Wear a mask or not? Avoid maskless people or not? Get vaccinated or not? Once these decisions are made, it's just math from there.

If everyone adopts mitigating behaviors, you get results like those that New Zealand has been getting. Unfortunately for the U.S., vaccine deniers and science deniers set us up for failure. The price for this failure is the 550,000 dead so far plus another 60,000 predicted dead before we reach herd immunity, assuming that happens around July 1st. (Source: IHME | COVID-19 Projections)

But that's not what really scares me. What really scares me is that we don't seem to be learning from this one and eventually, there will be one that's much worse.
 

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oh boy, it is about to begin
Context? Enduring battle of wits?

For what it's worth, I'd like to see the manufacturers provide a table like this, for their track based tires. I can think of a multitude of reasons why they wouldn't, though. But knowing optimum tire temp and max lean on a easily understandable table would be handy.
 

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I'm thinking of a Dunlop Q3+ (dual compound, at 30 degrees lean you're off the center band) or Pirelli Diablo Supercorsa (single compound, medium).
My guess would be:

Modified scale with: Friction scale 0...1.1 and Lean angle 0...55
Those two (lateral force vs lean angle) have a very strong non-linear relation, that is why you can have bigish lean angles with poorish traction.

And even this table is strongly on the safe side.

On dry track:

Temp Traction LeanAngle
0C/32F 50% 33deg
10C/50F 55% 37deg
20C/68F 60% 40deg
30C/86F 65% 42deg
40C/104F 70% 44deg
50C/122F 75% 46deg
60C/140F 80% 48deg
70C/158F 90% 52deg
80C/176F 100% 55deg
90C/194F 100% 55deg
100C/212F 100% 55deg
 

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Discussion Starter · #27 ·
My guess would be:

Modified scale with: Friction scale 0...1.1 and Lean angle 0...55
Those two (lateral force vs lean angle) have a very strong non-linear relation, that is why you can have bigish lean angles with poorish traction.
Thanks for that.
And when you say lateral vs lean angle having a strong non-linear relation, can you expand on the non-linear part?
 

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Thanks for that.
And when you say lateral vs lean angle having a strong non-linear relation, can you expand on the non-linear part?
For example (without contact patch offset):
Lean angle 0->10deg Needed grip/friction grows 0.176
Lean angle 40->45deg Needed grip/friction grows 0.161
Lean angle 45->50deg Needed grip/friction grows 0.192
 

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As a new track rider, I didn’t know anything, but I learned how to high side on my second session of first day. Your graph could be augmented by temperatures of a couple tires types, new vs veteran riders, after one lap, two, and three laps. Then relate that to theoretical lean angle, brake and throttle application, etc.
My “one peso” marketing idea is a one page CSS “Your first track day” flier (available online, at the tracks you teach at, and BMW dealers) would save some knuckleheads leather and levers.
 

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Discussion Starter · #30 ·
For example (without contact patch offset):
Lean angle 0->10deg Needed grip/friction grows 0.176
Lean angle 40->45deg Needed grip/friction grows 0.161
Lean angle 45->50deg Needed grip/friction grows 0.192
Would you say that is related to the fact that the suspension needs to move farther for a bump as lean is increased?
 

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Would you say that is related to the fact that the suspension needs to move farther for a bump as lean is increased?
In a simplified model that comes directly from mathematics/ trigonometry/ tangent function.
That is why:
At small lean angles lateral force grows slower per each additional lean angle degree.
At big lean angles lateral force grows faster per each additional lean angle degree.

For example, lateral force calculated directly (without contact patch offset) from lean angle with tangent function:

At lean angle 25 lateral force is tan(25 degree) = 0.466 G.
So you need (at least) coefficient of friction 0.466 to keep that lean angle.
At lean angle 26 lateral force is tan(26 degree) = 0.488 G.
So you need (at least) coefficient of friction 0.488 to keep that lean angle.
Diff is 0.021 per one degree change in lean angle (from 25 to 26).

At lean angle 49 lateral force is tan(49 degree) = 1.150 G.
So you need (at least) coefficient of friction 1.150 to keep that lean angle.
At lean angle 50 lateral force is tan(50 degree) = 1.192 G.
So you need (at least) coefficient of friction 1.192 to keep that lean angle.
Diff is 0.041 per one degree change in lean angle (from 49 to 50).

As you see, at 49...50 deg lean angle the change rate of lateral force is almost double when compared to change rate at 25...26 degree.
 

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^ Good data!

What's coefficient of friction of a slick (let's say Pirelli) front 120 & rear 200?
At 50 lean angle, is coefficient of friction 1.192 on both wheels? If yes, how does that change with braking/accelerating at that lean angle?
 
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