in RBR you moves the gravel under the tyres.
It should be something similar to that, no?
It should be something similar to that, no?
I wonder if the importance of the sidewalls of the tire are given enough study. All the loads on the wheel rim come from the tension and shear loads in the sidewalls. The sidewalls pull up on the contact patch and, therefore, have a lot to do with the pressure distribution across the contact patch, the shape of the contact patch, and which parts are sliding and which aren't. Under lateral load the leaning of the sidewalls steer the tread/belt of the tire and determine the slip angle. With the empirical approach all this is hidden in the curves but, with a physical approach, I would think that this is as important as the lateral bending of the tread belt.
...continuing
If anybody interested I created some diagrams for different characteristics and they look quite interesting. First, I show you how do characteristics look separately - with lines on them you can see section views for both forces. Next are three tyre characteristics with longitudinal constant and lateral changing:
If anybody interested I created some diagrams for different characteristics and they look quite interesting. First, I show you how do characteristics look separately - with lines on them you can see section views for both forces. Next are three tyre characteristics with longitudinal constant and lateral changing:
- first for very forgiving tyre (Fy is almost flat when off the limit) - separate forces diagram is from this one,
- second is for less forgiving tyre - see how the hill of combined force rises
- third is for very unforgiving tyre
I dont hear calls for objection so I think its roughly right 
Although the last diagram is derived by analogy to dynamic change of characteristics of the previous 2 type.
If I can do it in 1 day so I think anybody can
Or I'll charge you with freelance consultant rate of thousand €€ per hour since 2004 or before 
Damn, I feel like being robbed 
Although the last diagram is derived by analogy to dynamic change of characteristics of the previous 2 type.If I can do it in 1 day so I think anybody can
Or I'll charge you with freelance consultant rate of thousand €€ per hour since 2004 or before Damn, I feel like being robbed The separate Fx and Fy look far better than before 
It has been debated over and over, but there has been a change in literacy concerning the FX curve.
In older books like Milliken Milliken, the Fx curve reaches a peak and then decreases significantly (15%-30%).
But more recently, many tyre measures set show something different: Fx reaches a peak and then almost does not decrease...5% maybe...unless you really lock the tyres or reach crazy slip angle.
In most reasonable sliding situation, the decrease in force you feel in the steering wheel comes from the fact that contact patch shape/position changes. As a result, even if Fx decreases only 5%, the point in which it applies moves closer from the tyre pivot point and the aligning moment you feel in steering wheel decreases because of that (pneumatic trail decreases).
Recent sims (including LFS) have IMO adopted this approach, and Fx is almost flat after the peak. This gives ability to drift (real tyres do it, so tyre model should allow it), and avoids the punishing unrecoverable spin you get as soon as you go above grip limit in older sims (GTR2).
It has been debated over and over, but there has been a change in literacy concerning the FX curve.
In older books like Milliken Milliken, the Fx curve reaches a peak and then decreases significantly (15%-30%).
But more recently, many tyre measures set show something different: Fx reaches a peak and then almost does not decrease...5% maybe...unless you really lock the tyres or reach crazy slip angle.
In most reasonable sliding situation, the decrease in force you feel in the steering wheel comes from the fact that contact patch shape/position changes. As a result, even if Fx decreases only 5%, the point in which it applies moves closer from the tyre pivot point and the aligning moment you feel in steering wheel decreases because of that (pneumatic trail decreases).
Recent sims (including LFS) have IMO adopted this approach, and Fx is almost flat after the peak. This gives ability to drift (real tyres do it, so tyre model should allow it), and avoids the punishing unrecoverable spin you get as soon as you go above grip limit in older sims (GTR2).
You are both discussing NON-COMBINED characteristics (these are the differences between slicks, flatrounds and so on): Fx measured with slip angle equalings 0 and Fy measured with slip ratio equaling 0. I used characteristics EMPIRICALLY measured (Dynamic Tire Friction Models f ... nd Lateral Vehicle Motion) for combined situation (the first diagram). The 2 following diagrams are derived per analogy (flattening and lowering the characteristic) for 2 different types of tires.
And there you have significant drop when adding second component and then because of flattened characteristics rise of combined force.
And there you have significant drop when adding second component and then because of flattened characteristics rise of combined force.
very interesting thread. There's a lot of good literature out there on tyre modeling. Here's two I found:
Understanding Parameters Influencing Tyre Modeling:
http://www.engr.colostate.edu/ ... ing%20Tire%20Modeling.pdf
Mechanics of Pneumatic Tyres:
http://media.wiley.com/product ... 9/04713546/0471354619.pdf
Even if the equations become too confusing, most of the papers out there still contain a lot of partial experiment data that would help a lot when making your own model.
Please share any other links you guys find
Understanding Parameters Influencing Tyre Modeling:
http://www.engr.colostate.edu/ ... ing%20Tire%20Modeling.pdf
Mechanics of Pneumatic Tyres:
http://media.wiley.com/product ... 9/04713546/0471354619.pdf
Even if the equations become too confusing, most of the papers out there still contain a lot of partial experiment data that would help a lot when making your own model.
Please share any other links you guys find
I don't play RBR so I don't know, but that would sound more like deformable terrain to me?
In nKp, iRacing and LFS there's no feedback from the wheel if you turn it when the car's stopped. I do know that nKp however handles tyres differently if the speed is under a threshold, that might be something to keep in mind.
As far as I know, there are some forces when stopped in iRacing.
Yes I look at the end of slip curves and see at least 20%-30% drop. I know it is for wide slip angle but for me such drop should happen only when tyres are locked and what remains is only rubber dynamic friction...but these friction curves are used all the time by the game even when tyres are rolling and progressively sliding.
For me the key in tyres are transients. For example, when a tyre deforms during very quick actions it can give 1.5 times peak forces for 1/10th of a second....seen something in a study about that somewhere. This is massive stability help during transients! Which sim models that?
Yes in Shift when stopped if you turn the wheel it resists, and when you release it the tyres relax that's pretty well done...there is no such thing in iRacing or it is hidden by the strong dampening they add.
Cars with power steering have it modelled in iR
I disagree with the interpretations you've put forth concerning the force resultant, or I'm misunderstanding what you're plotting. This is something along the lines of the magnitude of the total force ((Fx * Fx + Fy * Fy)^0.5), right?
If so these are not right:
http://www.lfsforum.net/attach ... d=103471&d=1270423573
If we start at the front corner at 0,0 slip and trace along the left axis, the force rises and somewhat levels off. I assume this is combined force in slip angle, which in this case is simply the lateral force. If we go back to 0,0 slip and trace up and to the right, the force climbs and then dips a bit. This I assume is slip ratio, with the corresponding pure longitudinal force. So far so good.
But what happens when both slip angle and slip ratio are very large at the same time? This is the far corner of the graph where F combined has plummeted from as high as 950 or 1100 in some places (pure slip along the axes as described above) clear down to about 400.
The statement: "(Fy is almost flat when off the limit)" is not correct. It takes a huge plunge into nothingness when you have lots of combined slip. If anything, it should somewhat level off somewhere if the forces were being trimmed to a friction ellipse rather than whatever you did there
There's nothing forgiving at all about any of those tires. They would feel truly bizarre and rather impossible to drive, I suspect.
If I'm misunderstanding what was plotted, please explain.
Another issue are some of the earlier plots in addition to these. Slip ratio of 12 or 15 or something with large slip angles is not going to result in such large lateral forces. It'll be almost completely longitudinal even out to 90 degrees slip probably. The directions of the final force vectors are very far off everywhere in the combined areas. Take a look at the top graph you posted here:
http://www.lfsforum.net/attach ... d=103383&d=1270299686
See what happens to Fy (lateral force) at only 12 degrees slip angle and slip ratio of 1. It drops substantially. This isn't reflected remotely accurately in your curves yet, although some of the shapes in some places are starting to look a bit better in general. It's not so simple to think purely mathematically about this and come up with the right answer. Not for me at least. Most people must think about the underlying physics and come up with the math afterward, but perhaps you'll turn out to be an exception.
You haven't quite reached the point to charge consultant fees, but keep at it and maybe you will
EDIT: One more thing for you to look at and think about. Check out the force resultant hump that pops up towards the middle of the combined slip area, especially prominent on the "least forgiving tire." Can you think of any physical reason why at this point where the tire is completely sliding there would be an area where if you altered slip ratio and slip angle just a bit this way, then just a bit that way, the force would suddenly rise way up and then fall off again? It's wise to think about what the math model is producing in physics terms. Really think about what the tire and rubber is doing at each spot on the curve and why the forces might be changing as shown.
Indeed there is a slight force which seems to be changing position after the wheels are turned. It's so weak it almost seems it has power steering... but you are right.
Nope... I perceive it is combined force in function of both slip angle and slip ratio.
This is http://www.lfsforum.net/attach ... d=103383&d=1270299686 those characteristics (Fy and Fx for slip angle, there is second one for slip ratio) plotted here separatedly and on my diagram combined and plotted on one 3 dimensional plateau. Imagine those diagrams from "Dynamic Tire Friction..." as segment views on that 3d diagrams.
Now I am fiddling this mathematical model and in fact, first I make theoretical changes to see what would be the result and if it is correct with empirical data. I hope you understand that at this stage I dont really care for detailed precisio of the numbers because for me everything is scalable and I am rather experimenting with limits of that Pacejka model.
Pacejka model in fact has 3 tyre physics coefficients: load, load sensitivity, maximum tyre force it can generate. All of other are purely geometrical. And they are of 2 types: base coefficients for polynomial equations (like A = b1*x^3 + b2*x^2 + b3*x) which are then used in trigonometral equations, like Ax*sin(Bx)*atan(Cx). I just put simple "coefficients" there, like (m*x+1)^n, to obtain something similar to "Dynamic Tire Friction.." results because I don't mind (and probably don't have experience with such models) to implement their model which, they say, is completely correct with empirical data. But my purpose was to imagine how do combined force look like with empirical data deployed.
I am quite happy with this modelling and I attached two more examples. I got this first one with characteristics of slick type tyres. Second one is on the other hand very surprising - I called this type of characterisics as "unforgiving" because of steep and high threshold and significant drop afterwards (rain type conditions?). So here you go with those 2 types and segment views of Fx and Fy characteristics in function of opposite input value (SR, SA).
About "Grip Circle": using these kind of characteristics there is no use for Friction Circle term. Why? Combined force is combined force - if you have both forces measured in function of oppsit value you combine two components to get combined force, right? So there is no such thing as Friction Circle - it is just combining data for given Slip Ratio AND Slip Angle.
Only have a minute now so I'll just address this:
Imagine slip ratio 0 and slip angle 10. Lateral force is 1000. What are Fx and Fy?
We have in this case:
Fy = 1000
Fx = 0
The resultant of a 2D vector is its length. In this case, it's 1000.
The pure slip force is the combined force when you're moving directly along one axis with the other axis at 0.
My assertion that
is therefore correct.
Once you move off of both axes into the middle area you are in a combined slip state and your statement is correct.
Perhaps you could try doing this with 2 flat curves that do not have any drop off after the peaks and see what the combined slip area looks like. I'm curious if the hump in the middle goes away and the nose-dive at high slip angle and ratio disappear.
Imagine slip ratio 0 and slip angle 10. Lateral force is 1000. What are Fx and Fy?
We have in this case:
Fy = 1000
Fx = 0
The resultant of a 2D vector is its length. In this case, it's 1000.
The pure slip force is the combined force when you're moving directly along one axis with the other axis at 0.
My assertion that
is therefore correct.
Once you move off of both axes into the middle area you are in a combined slip state and your statement is correct.
Perhaps you could try doing this with 2 flat curves that do not have any drop off after the peaks and see what the combined slip area looks like. I'm curious if the hump in the middle goes away and the nose-dive at high slip angle and ratio disappear.
yup, you can see it on the front walls of the diagram.
You can see on those empirical diagrams that mainly 2 things happen - the curve gest flatter and the available force lowers a bit, but longitudinal stays almost at the steady level for off-grip values.
As far as I experimented with inputs - the more flat characteristics is the more hump gets flattened also. And nose-dive at the edge disappears when the curve doesnt go lower along with increasing the opposite coordinate. I'll post some in the afternoon (GMT+1
). I also obtained perfect saddle with flat characteristics that lowers along the opposite coordinate.So far it is all sensible for me - it is perfectly clear why rally drivers on tarmac with very grippy tyres (they have stints around 10 minutes so they dont bother) drift all along at peak values of grip (SA at 3-5deg offset and SR 5-10%).
The more confusing are the characteristics for rain conditions (big threshold and drop off) - combined force shows big valleys of combined drop off and then regain when peak values for one coordinate sums up with off-grip value for another.
Looking forward to seeing your new graphs. I have a question concerning my attachment. The red circles correspond to the highest force possible in pure slip (unless the friction ellipse turns into some kind of off-axis egg shape). It's difficult to tell from the graph, but is any force in the region with the blue circle higher than the red circles? To me it appears to be, but I'm not sure.
It must have been a long day for you, Todd.
If it isn't higher, coloring of the graph makes no sense at all.
Love the thread, btw.
If it isn't higher, coloring of the graph makes no sense at all
.Love the thread, btw
.I have problems with showing slip angle units because Excel treats them as Series and doesnt want to take the units
The place you showed with blue circle would be for around 6%-8% (I dont have access to this file now
hard at work 
:tilt of Slip Angle. So combined force sums with Fx for 6-8% of SA and Fy for 8-10% SR (where the peak for non-combined Fx is) - as on the lower diagrams. And combined force in fact is higher on the diagram - hence the hump.Maybe what you could do when you get access to the file is check the max combined force in pure slip in either direction, then see if there are any values off either axis that are higher than this maximum value. In the exaggerated diagram this is clearly not the case, but perhaps for the other it is. If so, there is a point to be made about something that I'll get to.
According to those diagrams for separate force component for opposite coordinate... it always is when the off-grip part of curve doesn't drop much if at all (with change of opposite coordinate).
I will post today a graph with Lateral Force characteristic more like this one (dotted line on the higher diagram): http://www.lfsforum.net/attach ... d=103386&d=1270299972 - these measures were taken for, as I remember, normal threadded tyre with high sidewalls, so for low slicks it would look different.
Nevertheless, before I step into fiddling data to represent reality I think this approach is viable, more viable than Friction Circle approach which is in fact only one of the states for given coefficients. While using Friction Circle leads to sheer guess what happens beyond that and in fact as you stated Todd, it is based on fake assumption that forces for opposite coordinate equaling zero can be summed as vectors to get combined force (so in fact that is also sheer guess).
OK, so here you go with the perfect saddle I have mentioned earlier. You can see how do segment views look in this situation. In fact this is the graphical representation of Grip Circle (although there should be some kind of one level area). Furthermore, you can see the nose-dive when going off the circle, which without empirical data was in fact guessing.
In extreme situation it looks like on the second diagram I named "rain".
In extreme situation it looks like on the second diagram I named "rain".
that seems odd.
here is a picture of what a pacejka combined force plot looks like. (some of the params might be a tiny bit off) for some random 195/65/15 tyre
the quality is a bit bad.
Red = greater magnitude, Green = less magnitude, used blue to show band lines. an interesting note is that it's not symmetrical over braking and acceleration.
here is a picture of what a pacejka combined force plot looks like. (some of the params might be a tiny bit off) for some random 195/65/15 tyre
the quality is a bit bad.
Red = greater magnitude, Green = less magnitude, used blue to show band lines. an interesting note is that it's not symmetrical over braking and acceleration.
where are the axis? what are the segment views for Fx (fn to SA) and Fy (fn to SR)? What empirical data was that based on? I just wanted to know so I could tell - should you just tweak some inputs or you have plainly wrong model?
And did you measured it? guestimated? or just guessed? if first - great! if second - not bad! if the last - wish you luck!
The coefficient's are from pacejka's book (http://www.flipkart.com/book/t ... namics-pacejka/0750669187) but four of the coefficients were missing so I guesstimated those. The data they are based off of is empirical but judging from the curves they only measured slip angles up to about 8 degrees (doesn't capture falling off of force at higher slip)
I went to the local engineering library and looked at some more recent literature (2004,2007) on tyre modelling.
Two new articles of interest... apparently speed has a huge effect on slip angle vs Fy curves!!! At low speed the tyre is much more forgiving than at higher speeds... kind of intuitive actually.
I also noticed you mentioned transient response early - this is actually very easy to add from a programming perspective. You simply create a 2DOF spring connecting the tyre to the suspension point where it is supposed to be mounted. The tyre forces move only the tyre and the suspension will be affected by the forces in the connecting spring (instead of the tyre forces directly affecting the suspension).
I went to the local engineering library and looked at some more recent literature (2004,2007) on tyre modelling.
Two new articles of interest... apparently speed has a huge effect on slip angle vs Fy curves!!! At low speed the tyre is much more forgiving than at higher speeds... kind of intuitive actually.
I also noticed you mentioned transient response early - this is actually very easy to add from a programming perspective. You simply create a 2DOF spring connecting the tyre to the suspension point where it is supposed to be mounted. The tyre forces move only the tyre and the suspension will be affected by the forces in the connecting spring (instead of the tyre forces directly affecting the suspension).
Tyre Physics progress spinoff thread for physics geeks
(168 posts, started )
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