Tyre forces vs speed

[silente]

Hi all,

since i found so many interesting references with my previous question, i will ask another one!

This time more vehicle dynamic related.

I read that tyre forces (both longitudinal and lateral) for a given slip angle, a given vertical load and a given camber angle reduce as speed increases. But honestly i was not able to find any reference explaining why and how much this phenomenon is influencing tyre force at contact patch. I can guess it is connected with centrifugal force acting on tyre structure which reduce the contact patch dimensions when speed grows, but i didn't find any link to proper studies about this matter.

I know some of you are very deep into vehicle dynamics and tyre behaviour, so maybe they could help me to understand this tyres feature that, if i remeber correctly, is not included in any of the most used tyre modeling tecniques (pacejka MF, for example).

Thanks for your help!

[Lycoming]

Wheel speed was mentioned as a variable (independant of aerodynamic effects) that affects tyre behavior in Racecar Vehicle Dynamics. I don't recall any detailed explanation, but I've only skimmed though it. Try looking there for a more detailed explanation.

[Jersey Tom]

I read that tyre forces (both longitudinal and lateral) for a given slip angle, a given vertical load and a given camber angle reduce as speed increases.

Says who? I call BS. Or if it were to, it would be by a very small amount. Load, camber, slip angle, and slip ratio sensitivities are the big ones. There's a reason why tire models have those as variables with generally no direct speed parameter.

[strad]

Have to agree with J.T....I don't know where you read that but I think they were wrong.

[munks]

It is briefly mentioned in RCVD with no explanation or supporting data.

Although I don't recall ever having seen any data myself, a few possible influences would be:

1) The static friction of rubber increases the longer it sits in one place in some sort of logarithmic fashion, but the paper I saw on this measured in minutes and hours, not tiny fractions of a second so any effect would likely be too small to measure.

2) Temperature, of course. The sliding part of the contact patch can heat up quite quickly which will have some influence, but in some cases this will help, others hurt. But most any tire at 15 degree slip angle at 200mph is going to get awfully hot awfully quick. The same slip angle at a lower speed might be better for "grip" for a much longer period of time (parentheses for JT's sake). Measuring this effect might be difficult: my understanding is that most tire testing records the "steady state", but that's going to be a fleeting moment if you're destroying the tire.

3) The contact patch force distribution is going to change and move forward with higher speeds. This is demonstrably true based on rolling resistance vs. speed curves. Whether that will be better or worse for overall side force generation, I'm not sure, but my hunch would be worse in general.

As for the OP's original suggestion of reductions in contact patch size due to the effects of the centrifugal force on the tire shape, perhaps ... but modern tires really don't grow that much because of the strong belts.

And then we didn't even get into driving in the wet, where the effect is clear but the reasons are different.

[Jersey Tom]

To go further here... like anything with tires, it can go either way. On certain bias ply tires you may get a lot of tire growth with speed. On other tires with some extra growth-limiting components in them this becomes a non issue. Tires will run hotter as you increase speed... maybe that makes some forces go up, some go down. You can easily have both happen.

More importantly, what I alluded to before is that it's either small, out of your control, or both. At a given point on the track, you can change tire Fz, camber, slip, and inflation pressure through setup changes. Speed pretty much just is what it is.

I bin this as "one of those small things you shouldn't let distract you from the important stuff."

[silente]

thanks for your answers guys.

I understand this is a small effect compared to others, like load sensitivity, camber sensitivity, slip curve shape etc, but i was anyway curious to understand how and why this happens and its magnitude.

Moreover i was working on a tyre model that, although simple, give to the user the possibility to include such an effect. Of course, it's hard to look at it separately from the others, like speed effect on temperature as JT said. But i was curious anyway!

[Jersey Tom]

As I'm a fan of saying... making tire models is easy. You can make it whatever you want. But all models - physical or empirical - still need hard data of one sort or another to drive them. That's the hard part.

[xpensive]

...
You can make it whatever you want. But all models - physical or empirical - still need hard data of one sort or another to drive them. That's the hard part.

"Physical or empirical", I had no idea that the two were contradictions in terms?

[Jersey Tom]

...
You can make it whatever you want. But all models - physical or empirical - still need hard data of one sort or another to drive them. That's the hard part.

"Physical or empirical", I had no idea that the two were contradictions in terms?

Empirical model being one driven by experimental data collected regarding system inputs and outputs. A Pacejka model is pretty much the standard reference for an empirical tire model - it is nothing more than a curve fit (and a good one at that). Or use the example that engineering students learn the Hooke's law empirical spring model of F = -kx... a linear empirical model that's about as simple as it gets.

Whereas a physical or analytical model is more about solving the internal "physics" behind what's going on and predicting outputs accordingly. A finite element tire model would be the ultimate example here. Or to use the spring analogy again, a finite element model of the geometry of all the coils.

Doing a meaningful empirical model is contingent on getting representative data regarding the system inputs and outputs and then fitting the relationship through some relatively arbitrary set of equations. Doing meaningful physical / analytical modeling relies on having information on the physical properties of things. F = -kx is meaningless if you can't experimentally arrive at 'k' but you have the advantage of not needing to know anything about the physical entity. A FEM for a spring is meaningless if you don't have elastic modulus, etc of the steel - though you don't need to rely on experimental results to find 'k'.

[xpensive]

...
Engineering students learn the Hooke's law empirical spring model of F = -kx.
...

This is the first time I have heard Hooke's Law mentioned in connection with a viscoelastic material, neither would I refer to it as "empirical", you sure you don't have it mixed up with Maxwell's model, not that I would call that "empirical" either?

[Jersey Tom]

...
Engineering students learn the Hooke's law empirical spring model of F = -kx.
...

This is the first time I have heard Hooke's Law mentioned in connection with a viscoelastic material, neither would I refer to it as "empirical", you sure you don't have it mixed up with Maxwell's model, not that I would call that "empirical" either?

Was not mentioned at all with regard to a viscoelastic material. The specific example mentioned was a coil spring made of steel, and the examples given as things easier for your average engineer to grasp for the difference in empirical vs physical, or "external" vs "internal" models of system behavior if you'd prefer to think of it that way.

Now, if you'd ditch the elitist/smartass routine and read a bit you might actually learn something. Just a suggestion.

[elf341]

This is the first time I have heard Hooke's Law mentioned in connection with a viscoelastic material

Isn't it one of the first simple things you come to when exploring deformation properties of viscoelastic materials?

That is, a simple model could be a bipartite system with a hookean spring coupled parallel with viscosity from a newtonian fluid. I have modelled that up and fitted empirically as a simple model for a material in the past.

[xpensive]

Very true elf341,

- If you arrange an elastic element in series with a viscous damper; That's Maxwell's model.
- If you arrange those in parallell; You'se got the Kelvin-Voigt model.

You can of course build more complex models than those two, but we shouldn't get too elitistic here.

@JT: I still believe you've got your terminology confused, "physical" is by no means a synonym to "analytical".

[gato azul]

@silente

maybe you can explain a bit better, in which context you have read the statement you quoted, because the way I see it (which could be wrong off course), it comes down to the definition of the term "speed".

What do you (or the author of the article/book/statement you read) mean by this term, and are we're talking about a free rolling tyre, or a tyre under longitudinal (braking/driving) loads?
Are we talking about the rotational (angular) speed/velocity of the tyre or about the forward speed/velocity of the vehicle?

If it is the later, then it (the forward velocity of the vehicle) in all likelihood will have/can have an rather strong effect on the sliding velocity of the tyre in relation to the ground/pavement, this in turn has an influence on the friction forces between the tyre and the ground.
Or does the term "speed", refer to "sliding speed/velocity of the tyre, in relation to the ground,in the first place?

So without knowing the proper context of the claim/statement, it's a bit difficult to say, if it´s BS or not?
And then it depends on what you are intending to do, with your tyre model, just that one model, does not include all parameters (such as temperature for example) does not mean, that they don't have an effect.

It may just mean, that if you try to access/predict road car tyre behavior in the linear range, you can "ignore them" and still have a sensible result from your model.

Now on the other hand if you try to predict limit behavior in a race car, you may find that temperature and sliding velocity have a rather large effect, and that one tyre model which worked reasonable well in predicting linear range (sub limit) behavior becomes insufficient for the later case.

The fact, that some parameters have no or minor effects in some analysis or for some users, does not mean, that they don't exist or are "BS", and that they can be ignored for all types of analysis.

It's all a matter of context, and what you try to do with your model, and what your "end goal" is.
Depending on the goal, you chose your model, and with this the parameters which will effect your analysis/outcome most.

It is reasonable to use the constant friction model when predicting the tire-pavement contact stresses at the free rolling condition or at the cornering condition with small slip angles.
However, it is important to use the sliding velocity-dependent friction model when predicting the friction force at tire braking.
The constant friction model cannot simulate the decay of friction coefficient as the slip speed increases and thus will overestimate the values of friction force.

So unless, we define the term "speed" a bit more precisely in the OT quoted statement, I would be careful, to dismiss the statement out of hand or call it BS.