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Extreme tyre-road mu values under certain conditions
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#1 - axus
Extreme tyre-road mu values under certain conditions
This thread is based on some analysis tristancliffe and myself have been doing based on extreme values that looked very out of place on a alpha version of a programme that estimates the traction budget. (The programme is not yet available to anyone not involved in its development). MonkOnHotTinRoof has been doing some programming and we got some grip values that looked way out of place - most plotted values looked in the right place but some were just way too far out. Mu values in the region of a 6g+ got us wondering weather there is a glitch in our code. This is when Tristan and myself extracted data from the RAF into a spreadsheet and did the same calculations on it. Basically what we are trying to do is work out the coeficient of friction between the road and each tyre. We are using RAF files to get vertical tyre load and lateral and longitudinal force exerted by each tyre. The grip is basically the coeficient of friction.

f_mu = mu * normal reaction

where f_mu is the force exerted by the tyre, mu is the coeficient of friction and normal reaction is the force with which the road is pushing back on the tyre (also equal to the vertical load). From here:

mu = f_mu/normal reaction

f_mu is the total force exerted by the tyre. From simple Phythagoras' theorem we can work out the total force from the lateral and longitudinal tyre force:

Total tyre force = SQRT[(Lateral tyre force)^2 + (Longitudinal tyre force)^2]

Dividing the total tyre force by the vertical tyre load will then give you the coeficient of friction and hence the grip.

We added a few extra columns to the spreadsheed into which we extracted the RAF file for the grip of each tyre and put the appropriate formulea in each. Some mu values even jumped to ~3200. We then investigated when such mu values occur. It apperas that they occur when you are bouncing over curbs, as the tyre is leaving the ground and then making contact with it again. Attached is a graph that Tristan made from the spreadsheet which shows a world record lap at Blackwood with the FZ50 (road version). The speed - distance graph is in pink with the scale on the right. The blue is the mu between the left front tyre and the road against distance. The strange grip values seem to coinside with curb use. The tyre load becomes negative at times which is also very strange - presumably when the tyre is in the air because mu becomes negative over the curbs and then seems to spike dramatically as the tyre comes into contact with the road again, exerting more force than it presumably should and making the car behave strangely. It also seems to be quite high before it drops to a negative as the tyre lifts so it is possible that this behaviour makes tyres exert more force than they should over bumps which may cause instability of light RWD's over bumps in the road.

I am not sure if this behaviour is correct or incorrect, but it certainly sounds strange to me. Any thoughts?

EDIT: Forgot the attachment
Attached images
To follow on from Asux's post:

Using the raf file data, I limited the max mu's to 500 to get rid of the REALLY silly ones which were messing up some other stuff. Then I plotted mu (the resultant tyre force/tyre load) against a few different things.

The notable one is mu against load. Here it shows the highest values of mu are at the lowest loads, probably as a result of kerb hopping judging by the other graphs.

Regarding the tyre load values going negative: Does that mean the springiness of the tyre is greater than the 'weight' of the car acting at that moment? i.e. the force is upwards, making the car bounce, or is it a glitch somewhere?

Edit: Updated the graphs to show negative loads. I have inverted all negative mu's so that every value is now positive, which makes the graph easier to read.
Attached images
muagsainstload_log scale.jpg
#3 - w126
Vertical load from RAF is not really tyre normal load but rather vertical part of the force acting between the suspension (including arb) and the wheel. This part is probably vertical in car coordinate system, so it's not always perpendicular to road surface.

See the attachment for comparison. It contains rear tyre normal loads from the same wr lap and was generated with RAFTyreExtract. Of course this part is calculated, not taken directly from RAF. It looks reasonable, so I hope it is correct.
Attached images
Just off the top of my head, i seem to remember that the load values are not tyre loads, but the load in the suspension (when measured at the wheel).

So a 20 kg wheel hanging from a car which is suspended in the air, would report a load of -20 kg * 9.81 N/kg = -196.2 N

So... make sure you have added the wheel weights to get the correct loads. Also note that there can be rapid oscillations in the loads at the contact patch, which don't show up in the RAF data, because the RAF data comes from suspension measurements.

EDIT : w126 explained it well, thanks.
Are the tyre forces merely produced by friction? Or could some of the forces be generated by elastic contact-patch effects? Just guessing here, it is quite some time ago I read some stuff about tyres. Or maybe by the side-wall of the tyre?
#6 - axus
Thanks for the informative replies, Scawen and w126

@w126: How did you get the actual vertical tyre load? We need it to make the programme work - we will be doing the tests on the skidpan which means it is flat anyway.

@Frankmd: As I understand it, it does get more complicated than this but an apparent coeficient of friction of 3000+ was enough to make me think something might be wrong.
I think LFS has a problem with simulating friction values of the tyre when you are driving on the tyrewall. This is exactly what happens here, after hopping over a curb. Instead of decreased friction because of the much lower contact area, it increases a lot (the peaks in your graph) and causes the high g values or a flip in the worst case. I've already tested this behaviour quite some time ago and got similar results.
#8 - w126
Quote from axus :How did you get the actual vertical tyre load? We need it to make the programme work - we will be doing the tests on the skidpan which means it is flat anyway.

It's basically what Scawen said. To the load from RAF I add wheel mass (1/4 of (mass - sprung mass)) * 9,81. I also add wheel acceleration in the vertical direction multiplied by its mass (these oscillations), but maybe it's not needed for flat surface.
#9 - axus
Where can one find the unsprung mass of all the different cars in LFS though? EDIT: And how do you calculate vertical acceleration? I see it is not part of the RAF files. EDIT: Found the sprung and total mass so we can work out the unsprung from there - it is in the RAF file. It would be preferable if we could add vertical acceleration to it too.
#10 - w126
Masses are in RAF header. For wheel accelerations you have car positions for time steps, neutral relative positions of wheel centers, suspension deflections for time steps, body orientation for time steps (right and forward vectors). From these you can calculate positions of wheel centers in world (circuit) coordinates for time steps and then calculate its 2nd derivative and take its vertical part. As you can see it can get interesting.
This is good :up:

The next problem I have is how to find the wheel acceleration. Now, how to find that. The RAF file has this:
"1 float 0 suspension deflect : compression from unloaded"

Can I use that to calculate the wheel acceleration (as a function of the rate of change of suspension deflection)? As far as I know, Excel can't differentiate a list of numbers And does the suspension ratio have an effect (I guess it does), because 1cm of wheel travel won't necessarily be 1cm of suspension travel.

Hope this makes sense to other people. In my mind it makes perfect sense.

Edit: Hadn't spotted the last two posts Forum Noob :S
What does that mean w126? How can I turn what you wrote into an equation?
#12 - axus
We will be able to do the differentiating ourselves but I have no idea what you are talking about with the wheel center co-ordinates. You lost me on that one. BTW, I'm pleased to report a much better looking traction budget diagram after adding the 1/4 unsprung mass * g to the suspension loads at the wheel on a skid pan. I'm sure that we can make the tool useful for track RAF analysis if you helped us out a bit with the wheel positions.
I have made this graph. It shows the forces exerted by the left front wheel against the vertical load on it (on the FZ50 WR at BLGP).

As you can see it's linear (which I think is expected, but perhaps it isn't in reality), but it crosses the y axis and goes to negative loads. So when the tyre/suspension has a negative load on it, the tyre still generates a force against the road. How can this be? If there is a negative load then the tyre can't be touching the track.

I currently have as my load:

RAF reported tyre load
Unsprung mass * 9.81
Unsprung Mass * Wheel Accel (see below)

To find wheel accels (well, actually suspension accels but for the time being it will do). I took the difference in suspension positions (and converted it from mm to m) and divided that by 0.01 seconds. I then took the difference from each of these suspension speeds and divided them by 0.01 seconds. This should give me wheel accelerations in m/s/s. I get peak values of 32m/s/s.

But I'm still getting tyre forces (and therefore grip) at negative loads. What have I missed? I must have missed something! Am I right in thinking that a negative load means the wheel is hanging?

Also, if the load is almost zero, then I should get low forces, meaning the coefficient of friction would still be in the region of 0 - 2. But I'm frequently finding values of 5.5, 8, and one or two right up at mu=56, which clearly isn't right, especially as that occurs at a vertical load of just 8N.
Attached images
Rubber does actually give very high mu figures under very low loads. I played around trying to model tyre load sensitivity a while back and did a lot of reading on it. At about the same time there was also a thread about it on RSC, JeffR had a good video of soft rubber.

Edit: attached the spreadsheet I was playing around with... I doubt it's particularly accurate...
Attached files
tyre load - 4.9 KB - 191 views
Hmm from the grip vs load graph it seems clear that it is a straight line..

I've been letting Google loose and found this at the catheram official site:

Quote :When cornering, the wheels on the outside of the turn get more heavily loaded than the inside pair. Load is 'transferred' to the outside. It is natural to think that the outer tyres, being under higher load, produce more grip and the inner tyres produce less grip. This is true, but the total grip produced by the axle pair is in fact less than if the tyres were evenly loaded - Honest! This effect is often referred to as the load sensitivity of the tyres. One way to minimise this load transfer is by generally using a softer suspension system.

I never really knew if load sensitivity was minor or major but this indicates that it is fairly major. The sim "Racer" (Ruud van Gaal) uses the Pacejka tyre model and someone (Alpine at RSC) found some actual coefficients including load sensitivity. With the Pacejka Player supplied with Racer, you can vary the load and see how big the effect of load is on available grip based on some real measurments!

Of course I don't have the real pacejka data on my drive anymore to check..

Edit: source:
I don't know any details about Scawen's tyre model. I know he said he was thinking of programming a tyre testing rig to perfect it under certain circumstances. I wonder if our fiddling will uncover LFS's low speed tyre physics shortcomings, or whether the problem lies elsewhere. I also wonder is Scawen knows where the problem lies, but that's not the aim of this project anyway.

I very much doubt the next tyre physics update will be the definitive version (Scawen would be a fool to say it was finished, no offence intended), but I think a lot of people would like to see nice graphs to do with the tyres, if only so we can compare them to real life published data and show off how good LFS is/will be.

Anyway, I've watched enough David Attenborough for one evening, so I bid ye goodnighte.
Quote from tristancliffe :
But I'm still getting tyre forces (and therefore grip) at negative loads. What have I missed? I must have missed something! Am I right in thinking that a negative load means the wheel is hanging?

The tire isn't hanging in the air until the negative load is notably less than zero. The suspension can be exerting negative load while the tire is still in contact with the road, because the weight of the wheel itself pulls it downwards. Until the upward (negative) load from the suspension is great enough to overcome the weight of the wheel itself, the tire will stay touching the ground.

Unless I'm misunderstanding what you mean by negative load...
#18 - axus
Shouldn't adding (suspension acceleration * unsprung mass) to the tyre loads along with (1/4unsprung mass * 9.81) give you ideal results on a flat surface but still possibly inaccurate results on a track?
Keep up the good work guys, Its a shame I dont have much time for this stuff these days.

I have a PHP script which extracts everything out of raf files and can be edited to work out any custom extrapolations of data from the basic raf data. Its not public because obviously it would enable easy reading of the setup data in a raf file, but if you would find it useful, PM me and I'll chuck it over.

Just a note about the unsprung mass calcs, I doubt that the total unsprung mass/4 = unsprung mass at each wheel, as unprung mass tends to be different at each end, depening on the drive train of the car. Scawen has never confirmed it this is modelled or not, but its on the big-old-list-o-cardata we asked him for a while back.

Also, me and bob have got tables of raf extracted car data for S2 cars, so you shouldnt need to go rummaging through all the raf files too much. ... =2747487&postcount=79

That post has a zip with a spreadsheet with everything we've got so far, might be of some use.
A few notes after reading this post (If I have missed the point slighty then please feel free to shoot me . . fire me. I mean. Not shoot. That hurts to much)

Unsprung mass also can include axles, brakes, assorted gubbins that are in contact with the vehicle below the Springs. Indipendant suspension you yould just have the swing arms and brake assemble etc, but with a live axle (any in LFS?) you are adding a hell of a lot more weight to the unsprung mass. Just a thought.

Wheel Travel will not correlate to the suspension travel. Unless you are using a double wishbone system, you might get close. But even then you have to assume that the damper/spring assemble is lining up exactly with the tyre. Rarely they are, they will cant off inbound by some degrees to the extreme of the Single seaters where the damper assemble sits horizontally, perpendicular to the tyre. On more traditional cars expecially the more road going version the tyre will sit on an axle which in istelf will be sprung. This means the tyre will move over an arc when it moves up and down. This means that the tyre movement will be (I am so sorry if my maths is way of here, hopfully my point will get across and a real mathematician can correct me) a square of the suspension travel. you know that thing you have to do with a circle and a point in the middle with a line joining the two. You can't just double the figure to get the movement, you have to times it by four. Or something . . HELP! *Wipes brow*

Also, again I might have got the wrong end of the stick here, but with these negative numbers you are getting. You mentioned that you assumed it was after contact with a kurb or whilst the tyre was in the air . . . A tyre is a pnuematic device. It activily reacts to its surroundings in so much as whislt a tyre is in contact with the ground it is under pressure. A force is excerted by the air inside the tyre to push against the force given by the ground. But when teh tyre lifts of the ground it will react accordingly and push against air . . . Air is less dense than the ground (sic) so the tyre can expand outwards. It will flex and rebound untill brought back in contact with the ground again. Could this be providing some of you negative numbers? I might not have got your maths very well, it was just an idea that occured to me.

*Edit*Doh. Didn't see Colcobs post . . . I tak eto long to write my own . . .
#21 - w126
I see things progressed a little and there are more questions. I'll try to answer wherever I can.
Quote from tristancliffe :And does the suspension ratio have an effect (I guess it does), because 1cm of wheel travel won't necessarily be 1cm of suspension travel.

I assumed suspension deflect (RAF) is wheel travel, I don't remember why now. Maybe because spring constant (RAF) is wheel rate and not spring rate. I'm not sure, it must be still verified.
#22 - w126
Quote from tristancliffe :To find wheel accels (well, actually suspension accels but for the time being it will do). I took the difference in suspension positions (and converted it from mm to m) and divided that by 0.01 seconds. I then took the difference from each of these suspension speeds and divided them by 0.01 seconds.

Suspension deflect (RAF) is already in meters, so there is no need to convert them. But in this way you get wheel acceleration relative to car body. I think you should rather calculate wheel acceleration in track (world) coordinates, because in fact to find tyre normal load we use F = m * a equation so we must be in an inertial system. We consider only linear movement of the wheel so we take into account all the forces acting through the suspension and forces at tyre contact patch. Through the suspension there are vertical load, X force and Y force (all in RAF dynamic wheel info). I believe these forces are aligned with car body, not road surface. So in fact when there is body roll (cornering even on completely flat surface) part of X force affects tyre normal load. Similarly for body pitch (braking or acceleration). BTW, now I see I have to improve RAFTyreExtract a little. The other part of forces, one acting at the contact patch, which we want to calculate, is usually expressed in 'tyre-road' coordinate system and thus divided into tyre normal load, tyre longitudinal force and lateral force.
For now remaining part is calculating wheel positions in world coordinates, necessary to get linear wheel accelarations. We start at X, Y, Z (RAF data block) which is the position of car's CoG. Also in RAF data blocks there are right-vector and forward-vector, which define car orientation in world coordinates. We can also get up-vector, which is cross product of right-vector and forward-vector. They must be all normalized (their lengths must be equal to 1). Then to CoG of car we add:
X (static wheel info) * right-vector
Y * forward-vector
(Z + suspension deflect) * up-vector
The result should be the position of a given wheel in world coordinates at a given time step.
#23 - axus
But surely with suspension travel varying camber, you would get an inaccurate result as the wheel goes along an arc...? Atleast your X and Y co-ordinates will be inaccurate and the Z too on an uneven surface or am I misunderstanding the RAF output? And I assume those vectors come from the CofG, but is the CofG position (ie, height, distance from front axel and rear axel) in the RAF files?
#24 - w126
Quote from axus :as the wheel goes along an arc...? Atleast your X and Y co-ordinates will be inaccurate

Yes, but it is a very small error, especially when the position is then used to calculate accelaration.
Quote :but is the CofG position (ie, height, distance from front axel and rear axel) in the RAF files?

Yes, it's all there, but maybe it's better to think of it the other way around. X, Y and Z in static wheel info is a position of a given wheel relative to car's cog. So Y is really the distance from a given wheel's axle, X is track for a given wheel's axle, height of cog would be equal to - Z - suspension deflect (with no car movement) + wheel radius.
#25 - axus
Thanks a lot for the help! We will come back with the results as soon as we have a better version of the programme and keep you guys posted! Looks like we will soon have this cracked and with any luck it will be a great tool for setup analysis as well as driving analysis (ie. weather you are using all the grip available to you) that should help fast drivers in finding where they can get the last little bits of time out of their laps.

Extreme tyre-road mu values under certain conditions
(33 posts, started )