25 replies to this topic

[Aubwi]

Does anyone have a real-world plot of Fy/Fz as a function of Fz? I'm having a helluva time finding anything like this. I'd really like to know if the curve is concave or convex. Does the Fy/Fz curve flatten at low loads or high loads? Or is it both (an S-curve)?

[Ben]

I've calculated a front and rear axle lateral force such that the total force equals the measured lateral G and it generates the yaw moment measured by a gyro. If you then divide these forces by the total front and rear axle loads you get axle mu. Plot that against load and you get the friction limit.

It actually turns out that with the front on the limit in the coasting phase you're actually measuring something that's mostly the outside front tyre. The data I have has a fairly (very) linear boundary.

Ben

[Greg Locock]

http://www.geocities...llery/f1_mu.png

That's a plot of Fy against slip angle for three values of Fz, for an F1 front tire, from Peter Wright's book.

[gordmac]

Would this be this any use? Avon 180/550/13, from data on their website, peak mu @-4deg camber vs vertical load.
I can't figure out how to insert the graph here, if it is any use tell me how to get it to you. Not sure if the data is on Avon site anymore, if not I can give you a copy.

[ben38]

Down to the grip of the tires, without any load it doesn't have grip.
Grip distribution over the tires is simply directed to the load on them.
The total latteral grip force that you have is equal to the mass of your car * latteral G force (*9.81 to get it in Newtons). How each tire contribute to it simply down to how much load you have on them.
Get the load either from too rare load sensors on the pushrods or by spring deflection*spring rate and compare how much each weel contribute to the total load. Multiplicate that rate by the total latteral force and you have your Flateral of each tire.
Pretty simple and usefull to compare different set up.

[Fat Boy]

Originally posted by ben38
Down to the grip of the tires, without any load it doesn't have grip.
Grip distribution over the tires is simply directed to the load on them.
The total latteral grip force that you have is equal to the mass of your car * latteral G force (*9.81 to get it in Newtons). How each tire contribute to it simply down to how much load you have on them.
Get the load either from too rare load sensors on the pushrods or by spring deflection*spring rate and compare how much each weel contribute to the total load. Multiplicate that rate by the total latteral force and you have your Flateral of each tire.
Pretty simple and usefull to compare different set up.

The problem with this is that it doesn't take into account car balance or driver performance. It does give you a lateral force for each corner, but ultimately, it doesn't tell you much more than load distribution. Since slip angle has such a huge effect on tire lateral force (and it's unaccounted for in this example), the actual information that you're getting is not terribly informative.

If you were able to use other information to determine slip angle at each tire and then tie it into FLat, then you'd be getting somewhere. Likewise, if you had hub lateral load to measure lateral force directly, you can make some big gains as well. I've never been able to play with either.

[exFSAE]

Do you mean PEAK Fy at a given load? As in max coefficient of friction vs load?

[Fat Boy]

Originally posted by exFSAE
Do you mean PEAK Fy at a given load? As in max coefficient of friction vs load?

Can you elaborate on these questions?

[exFSAE]

Can you elaborate on these questions?

Does anyone have a real-world plot of Fy/Fz as a function of Fz?

He is asking for a normalized lateral force, vs load. Doesn't say if that is at a given inclination angle, inflation, and slip angle... or if he means the peak Fy capacity (slip angle unconstrained) at a given inclination and inflation.. ie a "mu vs load" curve.

[Fat Boy]

Originally posted by exFSAE
or if he means the peak Fy capacity (slip angle unconstrained) at a given inclination and inflation.. ie a "mu vs load" curve.

This is pretty much what you can come up with, but even then, it's a little suspect.

Example:

Car cornering at a given later accel. and is showing whatever vertical loads. The inside tires run over ice. The car is still under it's cornering limit with primarily the outside tires producing the lateral load. The calculated lateral forces of the inside tires will be overstated and the outside tire contribution will be understated.

Again, all we're really looking at is tire vertical load and making a series of assumptions.

Regardless, it's a pretty good first guess at lateral loads for determining design characteristics.

[phantom II]

Just take a picture of it with your digital camara and then use Imageshack to post.

Originally posted by gordmac
Would this be this any use? Avon 180/550/13, from data on their website, peak mu @-4deg camber vs vertical load.
I can't figure out how to insert the graph here, if it is any use tell me how to get it to you. Not sure if the data is on Avon site anymore, if not I can give you a copy.

[Aubwi]

Yeah, I was looking for a mu vs load graph. I'll see if gordmac can set me up. I guess it is sometimes referred to as "peak mu" since it's the peak over the full range of slip angles. Confusing, that.

[Greg Locock]

That is what those curves I posted give you, if you divide through by Fz

[Aubwi]

No, that would be mu vs slip angle.

[Greg Locock]

?

[gordmac]

Put the spreadsheet on here:
http://www.megaupload.com/?d=6J1ZU5JO
Anybody know a better way of doing this? We used to use Moodle for student stuff and it was possible to allow anyone access but we have moved to Blackboard which seems a lot less flexible!

[Fat Boy]

Originally posted by Aubwi
No, that would be mu vs slip angle.

......at varying loads.

[Aubwi]

Hate to sound ungrateful, but I was hoping for more than 3 data points. The Avon data is interesting, though. mu of 2.25 at 100kg! I wonder if it goes even higher at lower loads.

[Greg Locock]

Yeah keep working on that first sentence. Why not define exactly what you need, for what sort of tire?

[Paolo]

Originally posted by Aubwi
The Avon data is interesting, though. mu of 2.25 at 100kg! I wonder if it goes even higher at lower loads.

Welcome to race tyres.

[exFSAE]

Keep in mind, tires tested on a flat track GENERALLY produce higher coefficients of friction than you will see on the track. The surface is very flat, very clean, and on tires that fall into the sportscar or open wheel category, they generate an insane amount of stick on that kind of surface.

You can test a tire on a FT that generates mu above 3.0, and on the track only generates 1.8 or so.

...which is why I'm fairly strongly against using flat track data for evaluating peak grip magnitude.

[gordmac]

I have put a zip file of all the Avon data here, I originally took it off the Avon website.
http://www.megaupload.com/?d=6QWE3ZZR
As has been said, you won't get these mu values on a real surface.
The characteristics and values will vary from tyre to tyre, temperature is also a significant factor.

[dentistTubster]

When a vehicle is turning, a force is created in a perpendicular direction to the direction the tyre is pointing, known as the cornering force. The slip-angle of a tyre is crucial to its cornering ability. During the cornering of a tyre, the tread is being pulled sideways due to the force of the cornering itself. In this situation, the front of the contact patch, or the front of the tyre, the deflection of the tread (the amount the tread is being pulled sideways, which is what causes the slip angle effect) is less than that at the back of the contact patch, or the back of the tyre. This means that the force of the tread being pulled during cornering will exceed the available friction at the back of the tyre first. When the cornering force exceeds the available friction of the tyre, the tyre begins to “slip” at an angle. The slip angle is simply the angle between the direction a tyre is pointing, and its actual direction of travel.

At a constant speed, an increase in the direction a tyre is pointing compared to 0° results in a greater cornering force, but at the same time this results in a larger slip angle. Once the direction the tyre is pointing compared to 0° creates a slip angle larger than a couple of degrees, the cornering force will recede. This is because during the slipping of the tyre, the front of the contact patch actually works harder and therefore can offer more grip, whilst the back is losing grip potential because it is not being work as hard. When the slipping of the back of the contact patch means more grip lost than is gained at the front of the contact patch, then the cornering force recedes.

The phenomenon of the slip angle being too great that the cornering force is not at its maximum is known as understeer – where the slip angle is greater than that which results in a high cornering force. In basic terms, this is where the driver of the vehicle turns the tyres to a greater angle than the tyres can grip the road at that speed, resulting in the vehicle describing a angle of turning greater than the tyres are describing.

This “breaking” of traction is more gradual the longer the contact patch is in comparison to its width – therefore, despite a wide tyre with a small circumference being able to offer larger lateral grip because the contact in this direction is greater, this is not always desirable because as soon as “the limit” is passed, the understeer will rapidly increase, which could result in the driver being unable to control the vehicle. To reduce understeer, the driver must reduce his speed to one that results in the tyres having a slip angle, resulting in the highest possible cornering speed. However, sometimes the limit of the cornering force can be within a range of speeds, due to the affects of downforce, because at higher speeds there is more downforce, resulting in the tyres having a higher grip capability (because there is more load on them).

[Aubwi]

Interesting stuff. OK, so you won't see a mu much over two under normal conditions. But is there any reason mu wouldn't approach infinity as load approaches zero? You can imagine a vehicle cornering over a bumpy surface with a wheel hopping over the bumps, getting light, at times experiencing zero load, but still generating cornering force because of the tacky, glue-like properties of the rubber compound. It sticks to the track, even with zero or slightly negative load. This is my "crazy" theory. I'm looking for something that will shoot it down. Granted, this really has very little to do with the maximum performance of any vehicle, but I think it's still an interesting question, even if all it demonstrates is how useless mu is.

[dentistTubster]

Originally posted by Aubwi
Interesting stuff. OK, so you won't see a mu much over two under normal conditions. But is there any reason mu wouldn't approach infinity as load approaches zero? You can imagine a vehicle cornering over a bumpy surface with a wheel hopping over the bumps, getting light, at times experiencing zero load, but still generating cornering force because of the tacky, glue-like properties of the rubber compound. It sticks to the track, even with zero or slightly negative load. This is my "crazy" theory. I'm looking for something that will shoot it down. Granted, this really has very little to do with the maximum performance of any vehicle, but I think it's still an interesting question, even if all it demonstrates is how useless mu is.

Don't forget that there is a very good reason that we use downforce to INCREASE the load on the tyres in Formula 1. The way to in practice get infinite mu is to have infinite load with NO MASS. As soon as you introduce mass, the tyres cannot deal with the lateral force, because the car is pushing it in the opposite direction to the cornering force (centrifugal and all that!). Increasing the load on the tyres makes them grip better, increasing the mass does not. Imagine a Lotus Elise and a 7-tonne Lorry using the same number of identical tyres - the Lotus would grip better because it has a much lower mass.

[exFSAE]

The phenomenon of the slip angle being too great that the cornering force is not at its maximum is known as understeer

Understeer is not driving a tire past its limit. Understeer is typically defined as the front axle operating at a higher slip angle than the rear (this can be in the linear range), or terminal understeer being the front axle saturating before the rear.

Mu would become very high at very low loads with a very sticky race rubber. This is why you want to build a car that's as light as possible. But at the same time you run into practical limitations as the footprint area will get smaller and smaller as load goes down, and you need some amount of load and deflection to get the tire hot and gluey.

Regarding bumps, in general load variation is bad. Whatever increase in friction level you get at low load is more than completely lost by decrease at high load. That's the whole thing that drives load transfer sensitivity. Beyond that there are dynamic effects at high input frequencies which cause the lateral force capacity to drop.