11 replies to this topic

[Greg Locock]

Being a sad bastard I spent a couple of hours turning Sakai's tire data (Milliken sec 2.4) into a friction circle graph.

Here it is

http://www.geocities...tion_circle.png

The plot on the top left is the total horizontal tire force. As you can see, max force is generated at 4,S4, which is 12 degrees of sideslip and 20% traction slip.
There are also optima at 12 degrees sideslip, 0% traction, and 0 degrees 10% braking.

So, the friction circle is not round. The plot on the right confirms this. Blue lines are constant slip angle, 0,4,8,12,16 degrees, and red lines are longitudinal slip, 0,.05,.1,.2,.4,.6,.8

It seems to me that for this tire under acceleration you can get a significant benefit in latacc by cornering at yaw=12 degrees, no steer, and 20% traction.

I'm not going to tell you why I'm looking at this, you'll laugh.

Milliken's plot of Fy vs Fz on p58 is essentially round.with max Fy at 1040, and max Fx at 1100. That is , he gets about 6 % out of round, with 17% traction and no sideslip as the optimum, I'm getting double that variation, with 12 deg sideslip and 20% traction as the optimum .

Has anybody else got this sort of data they can share?

[Engineguy]

I know dick about tires, but I'd think the length/width proportions of the friction ellipse would be heavily dependent on the ratio of tire circumference to tread width... as well as some carcus construction issues?

[Greg Locock]

Just had a dig around. Real world tires often have much more braking capacity than cornering, especially truck tires, where it can be a factor of 2. So my discrepancy of a factor of 6% between 2 unknown tires tested in unknown conditions is small beer.

When you add in the complexities of speed effects and so on then the approximations made in the friction ellipse method pale into insignificance.

[RDV]

Greg Locock- Real world tires often have much more braking capacity than cornering, especially truck tires

Racing tires too...thats why I always quote friction ellipse, and there are other factors which complicate the issue, such as the fact that you can generate much higher forces under braking than acceleration, as power availiable for accel about 1/3 of that availiabe for braking (at least on racing tires..).. noticed you didn't include the verical force(or load...) on the graph as per Sakai's data, which will be varying as car cycles through brake , turn in and power on...in other words the plot would have to be 3 dimensional , and as car cycles the lat and long grip values would be running up and down slopes....add varying aero forces and you have a right dogs dinner....
check your PM

[desmo]

I wonder if even the tire manufacturers' tech gurus have a real grasp of all the underlying subtle complexities or if they are just sitting on a big pile of hard won empirical data?

[RDV]

desmo-I wonder if even the tire manufacturers' tech gurus have a real grasp of all the underlying subtle complexities

As far as racing tires go some do, some are laughable....lets just say they are driven by other requirements, as most come armed with production tire needs...
The second reason is tire design and performance still a black art, very empirical and serendipitious, one of the biggest problems is having a rig to test tyres with all the variables. Calspan started doing some serious work early on, but the multiple variables of running surface temperatures, loads, pressures, and slip angles to accomodate on rig, plus analog measuring systems made life very difficult. It is improving but is a bit arcane still.
Considering tires are made of non-linear, anisotropic polymer of isoprene units, a hydrocarbon diene monomer, a neo-Hookian solid that can be described by the general Mooney-Rivlin solid model, and that stores strain energy thermally and electrostatically, over a textile or synthetic carcass, a true composite material...added to the fact that a the compressed gas also exhibits "elastic" properties inside the carcass and the surface is also dependent on thermal and chemical effects, and responsive to the Fletcher-Gent effect, the Mullins effect and behaves totaly differently from other materials; I find it amazing that Pacejka actualy came up with a way to describe mathematicaly its properties.... (its complexity is only exceded by the number of coefficients to input...also known as empirical adjust knobs or fudge factors )

After a huge amount of time in racing, I understand bugger all about it... even less than I can grasp about damping...

[phantom II]

This is an English forum, OK?

Originally posted by RDV

As far as racing tires go some do, some are laughable....lets just say they are driven by other requirements, as most come armed with production tire needs...
The second reason is tire design and performance still a black art, very empirical and serendipitious, one of the biggest problems is having a rig to test tyres with all the variables. Calspan started doing some serious work early on, but the multiple variables of running surface temperatures, loads, pressures, and slip angles to accomodate on rig, plus analog measuring systems made life very difficult. It is improving but is a bit arcane still.
Considering tires are made of non-linear, anisotropic polymer of isoprene units, a hydrocarbon diene monomer, a neo-Hookian solid that can be described by the general Mooney-Rivlin solid model, and that stores strain energy thermally and electrostatically, over a textile or synthetic carcass, a true composite material...added to the fact that a the compressed gas also exhibits "elastic" properties inside the carcass and the surface is also dependent on thermal and chemical effects, and responsive to the Fletcher-Gent effect, the Mullins effect and behaves totaly differently from other materials; I find it amazing that Pacejka actualy came up with a way to describe mathematicaly its properties.... (its complexity is only exceded by the number of coefficients to input...also known as empirical adjust knobs or fudge factors )

After a huge amount of time in racing, I understand bugger all about it... even less than I can grasp about damping...

[RDV]

phantom II- This is an English forum, OK?

...ok, lets quote Denny Hulme=
"They are round and black..."

[Lukin]

Originally posted by RDV
After a huge amount of time in racing, I understand bugger all about it... even less than I can grasp about damping...

Speaking of Damping, did you ever find those notes you were looking for?

[RDV]

Lukin-Speaking of Damping, did you ever find those notes you were looking for?

Arghhh... no, and haven't re-done search..... gimme a couple of days, when swoop past office will collect a couple of external hard-disks where it should be... and apologies..

[Paolo]

According to Claude Rouelle, even braking and traction capability are not the same; dragster tyres, he said, are much better in traction than in braking. I can imagine internal structure has something to do with that.
So friction circle apparently is not even an ellipse; it is a sort of egg.

[Lukin]

Thanks!!