Psychedelic art! I like!
Psychedelic art! I like!
Your first surface looks OK, but second one there is definitely something wrong.
Look what happens. First you corner and it gives nice grip...then you start braking (slip ratio increases) and the grip collapses...but as soon as the tyre slips more longitudinally grip comes back magically, almost at pure cornering level!
That's the whole problem with tyre slip curves. Tyre has many variables and gives reaction forces through a friction/stiction process very nice to model with semi-empirical brush models. These models are very intuitive to implement, they deal with real things, not coefficient for magic formulas. And you can "easily" introduce transients.
The lateral and longitudinal forces vs slip curves are two simple pictures showing only a single aspect of the tyre output. They give no information about hysteresis, transients, influence of other vital parameters...and they are not intuitive at all as soon as they are combined...you can easily get something weird changing one parameter. They are far not enough to model a tyre, and they don't help you when you introduce influence of other parameters.
When you use a brush model or something like that, you think about the shape of the contact patch, the pressure distribution, sticking area and sliding area...this is intuitive and you can immediately guesstimate what camber could change for example... For me it looks a lot easier to scale such model.
Funny, I have graphed those coefficients and there is indeed fall off (far more longitudinally than laterally, as you would expect). The example tyre doesn't peak in slip until 14 to 15 degrees so I don't see how you came up with your 8 degrees figure.
Edit: Here's the graphs: http://www.vehicle-analyser.com/p96_tvd_example.PNG
Juls - I would argue, if you're not familiar with either empirical or brush models, than empirical models are at least easier to work with, as each part of the equations directly relates to part of the curve in certain circumstances, and it's easy to see which parts you need to replace if you don't like how part of an empirical model works.
:doh:
Right you are
Juls: You've hit the nail on the head. Also the fact that at some non-zero combination of slip angle/ratio the force capability of the tire increases beyond that of pure slip is a giveaway that something is goofy. Try drawing a friction ellipse type of graph that shows that happening. It'll be some bizarre egg shaped type of thing where the radius is longest at some nonsensical diagonal angles. I've never seen that happen in any tire data.
Indeed, the paper with empirical survey shows somewhat different - the drop is bigger there on lateral force but there could be many issues regarding tyre type.
But nevertheless diagrams you showed (are you Ben or Bob? :tilt
look more alike those empirical than those derived from Pacejka's model and Friction Circle, which I attached (for me Fx vs. Fy diagrams are somewhat non-intuitive and the differences between characteristics are not so clear).AndRand, I still haven't found the time/inclination to get fully into this with all the details of what's wrong. Maybe I will later today.
For now, if you are to plot lateral or longitudinal force by itself rather than the combined force magnitude, what you should get is a shape like one quadrant of this:
http://img215.imageshack.us/img215/6734/lateralforce23.jpg
Here the peak is outrageously high compared to the rest of it (garbage in/garbage out), but in essence this is what you ought to get. Again, you'd only be plotting one quadrant of this, but the point is the worst that ought to happen is at the origin you'd have 0 force which then climbs to a peak roughly some distance away from the origin (which you could trace with an ellipse) which then fans out into a fairly level surface. Unless I'm having a brain fart right now, both lateral and longitudinal ought to look something like this in terms of basic shape with the lateral being rotated 90 degrees to this one.
The combined/resultant force graphs you've been posting are just the vector sums of the other two graphs, which ought to have the same basic shape rather than something where you've got a bump above either of the pure slip force peaks and then a huge dip at some combination out in the combined slip area. Juls was right to point out that when you look at the graph you've got to think about what it's really saying (in his braking example where you suddenly lose a lot of force and then gain it again).
AndRand's last picture http://www.lfsforum.net/attach ... d=103635&d=1270747270
Keep in mind that the bottom graph is mostly, if not entirely, well within the traction capability of the tire. On your other graphs this corresponds to the area inside that initial cone climbing upwards out of the origin. This is why you can find the combined force being greater than either of the pure slip forces (the distance from the origin to any point on any of the curves is plotted as the height coordinate of AndRand's combined force graphs).
EDIT: I wrote "Keep in mind that the bottom graph is mostly, if not entirely, well within the traction capability of the tire." The places that are passed the traction limit are where the curves hook back in on themselves as slip ratio is increased beyond the peak.
For now, if you are to plot lateral or longitudinal force by itself rather than the combined force magnitude, what you should get is a shape like one quadrant of this:
http://img215.imageshack.us/img215/6734/lateralforce23.jpg
Here the peak is outrageously high compared to the rest of it (garbage in/garbage out), but in essence this is what you ought to get. Again, you'd only be plotting one quadrant of this, but the point is the worst that ought to happen is at the origin you'd have 0 force which then climbs to a peak roughly some distance away from the origin (which you could trace with an ellipse) which then fans out into a fairly level surface. Unless I'm having a brain fart right now, both lateral and longitudinal ought to look something like this in terms of basic shape with the lateral being rotated 90 degrees to this one.
The combined/resultant force graphs you've been posting are just the vector sums of the other two graphs, which ought to have the same basic shape rather than something where you've got a bump above either of the pure slip force peaks and then a huge dip at some combination out in the combined slip area. Juls was right to point out that when you look at the graph you've got to think about what it's really saying (in his braking example where you suddenly lose a lot of force and then gain it again).
AndRand's last picture http://www.lfsforum.net/attach ... d=103635&d=1270747270
Keep in mind that the bottom graph is mostly, if not entirely, well within the traction capability of the tire. On your other graphs this corresponds to the area inside that initial cone climbing upwards out of the origin. This is why you can find the combined force being greater than either of the pure slip forces (the distance from the origin to any point on any of the curves is plotted as the height coordinate of AndRand's combined force graphs).
EDIT: I wrote "Keep in mind that the bottom graph is mostly, if not entirely, well within the traction capability of the tire." The places that are passed the traction limit are where the curves hook back in on themselves as slip ratio is increased beyond the peak.
That's some pretty wicked looking software! 
http://www.lfsforum.net/attach ... d=103594&d=1270666115
Look at the valley stemming out from the origin and going off at some diagonal. According to your graph if you increase slip angle and slip ratio together at a certain rate, the tire can not make nearly as much force as it can in some other direction. This is utter nonsense and ignores the fact that out in these areas all you really have is a big blob of rubber with some potentially odd vertical force distribution on top of it sliding across the road. Why would this exhibit behavior anything like in this graph?
Bottom line: That sagging area in the back and the valley leading up to it should not be there at all. I don't understand why you want a saddle shape in the first place. It shouldn't be a saddle...
That's from the x car or whatever sim someone kindly posted earlier in this thread.
The small diagrams I showed beneath those plateaus show the same - just a quadrant and 2d instead of 3d (XMR
). But I noticed how important is not only pure one force view but also the way it changes along with opposite coordinate.I can make charts using Pacejka model using those data:
TABLE 1.2 Average Values of Coefficient of Road Adhesion
Surface Peak Value µp Sliding Value µs
Asphalt and concrete (dry) 0.8–0.9 0.75
Asphalt (wet) 0.5–0.7 0.45–0.6
Concrete (wet) 0.8 0.7
Gravel 0.6 0.55
Earth road (dry) 0.68 0.65
Earth road (wet) 0.55 0.4–0.5
Snow (hard-packed) 0.2 0.15
Ice 0.1 0.07But without data on how separate forces behave in regards to opposite coordinate (if I call it correctly) I would be just speculating. The shape (not onl peak and sliding values) of the forces is also very important.
Like on this next diagram - where in order to avoid "miraculous" traction regaining with tyre of difference and sharp change between peak and sliding value big drop of traction along with opposite coordinate is needed. Also a table if someone likes it colorful.
Forgive the goofy artwork. If those combined force graphs looked like that (saddle shape) you'd wind up with not a friction ellipse theory, but something more like the shape in my attachment. Here, along some combination of slip angle/slip ratio you couldn't make as much force as you could along pure slip or any other combination of slip angle/ratio. Sorry to say, but this is complete nonsense 
Well, I have to disagree - I cant show diagram of Fx vs. Fy right now but I think, looking at Bob's charts (Fx for different SA and Fy for SR) that combined would look alike.
You posted earlier a link to figure 7 here, but I don't want to go find it now so here:
http://hal.archives-ouvertes.f ... 00/05/14/75/PDF/vsd05.pdf
I think you'd made a comment that your graphs are following what's happening in the top diagram. In my own tire models I frequently plot exactly what you have in the top diagram. However, I also plot the resultant force on that same graph. What you see is a line that looks very much like a pure force curve. It goes up very quickly to the point where you have total slippage in the patch and then perhaps decreases slowly.
There is never some weird combination of slip out in this area that results in a valley or saddle shape like all your graphs show.
I just whipped up a quick little proggy to take the data in the top graph of figure 7 and add it all together vectorially. Can't be bothered right now with making a 3D app to display it like you're doing, but perhaps seeing the numerical data laid out in the same manner as yours is might suffice to show that there are no such bumps or valleys along the diagonals as you're getting. Part of your argument was that your graphs reflect this particular diagram. I assure you they most certainly do not
In the top graph of figure 7 you're looking at combined slip very close to and well passed the friction limit. In other words, it's all outside in that "falling down towards a plateau" region. What I want to show here is that there is NOT a valley or a region where the combined forces suddenly drop way off at some weird combination of slip angle and slip ratio. The drop fans out in all directions in a similar manner as you go farther from the origin.
In my attachment the forces are laid out in the same manner as in your graph. The bottom right (2700) is the spike where the combined force is highest. This is slip ratio 0.1 and slip angle 0. This is pure longitudinal force. And it is the highest point on the graph along with the 2703 at slip ratio 0.2 and slip angle 0. Again, I want to point out that the highest point on the graph is right along the pure slip line. It is not off somewhere appearing as a hump in the combined area. If it were, nobody would have bothered coming up with all this friction ellipse theory stuff since it would obviously be wrong. We'd need a friction cross/bubble thing theory instead like I showed earlier.
Moving to the left the slip angles are increasing 5 degrees at a time up to 30 degrees slip angle. Moving upwards the slip ratios are increasing from 0.1 to 0.2, 0.4, and 0.8. (This is what you get when you're drifting with the wheels on fire
)
For others following along, what I'm doing is taking a point on the dotted line at say, slip angle 5 degrees, for Sx = 0.1 and adding it to the point on the solid line at the same slip angle vectorially. (Fx * Fx + Fy * Fy). So this is the total force the tire is producing at all of these combinations of slip angles and slip ratios. They correspond to the height of various spots in AndRand's combined force graphs. This says nothing at all about the actual direction of the force which is another topic entirely that we probably will not get to given how the thread is developing, unfortunately.
You'll see the same trend as in that green graph I posted earlier. Near the origin (bottom right) you have a spike, then as you move to the left and "up" the values quickly drop to a sort of plateau where they slowly continue dropping. However, along the diagonal there is no trend at all toward having any sudden upturn in force again (especially above what you get in pure slip, my goodness...) nor is there a valley along any diagonal where the forces are far lower than what you get in surrounding areas. Note that the "back row" (top row) all have pretty much the same value. It doesn't suddenly collapse to 50% or something at the top left corner like it does in some of your graphs.
Keep in mind that I am loosely eyeballing all this data reading it off the graph, so there is some noise in there. I've been writing tire models for a good 10 years now. I think my first attempt at it was in 1993 or so with nothing but Fred Puhn's "How to Make Your Car Handle" on a 386SX-16Mhz. It doesn't mean I know everything, but I'm not a noob to this stuff and do know what I'm talking about on this one
http://hal.archives-ouvertes.f ... 00/05/14/75/PDF/vsd05.pdf
I think you'd made a comment that your graphs are following what's happening in the top diagram. In my own tire models I frequently plot exactly what you have in the top diagram. However, I also plot the resultant force on that same graph. What you see is a line that looks very much like a pure force curve. It goes up very quickly to the point where you have total slippage in the patch and then perhaps decreases slowly.
There is never some weird combination of slip out in this area that results in a valley or saddle shape like all your graphs show.
I just whipped up a quick little proggy to take the data in the top graph of figure 7 and add it all together vectorially. Can't be bothered right now with making a 3D app to display it like you're doing, but perhaps seeing the numerical data laid out in the same manner as yours is might suffice to show that there are no such bumps or valleys along the diagonals as you're getting. Part of your argument was that your graphs reflect this particular diagram. I assure you they most certainly do not
In the top graph of figure 7 you're looking at combined slip very close to and well passed the friction limit. In other words, it's all outside in that "falling down towards a plateau" region. What I want to show here is that there is NOT a valley or a region where the combined forces suddenly drop way off at some weird combination of slip angle and slip ratio. The drop fans out in all directions in a similar manner as you go farther from the origin.
In my attachment the forces are laid out in the same manner as in your graph. The bottom right (2700) is the spike where the combined force is highest. This is slip ratio 0.1 and slip angle 0. This is pure longitudinal force. And it is the highest point on the graph along with the 2703 at slip ratio 0.2 and slip angle 0. Again, I want to point out that the highest point on the graph is right along the pure slip line. It is not off somewhere appearing as a hump in the combined area. If it were, nobody would have bothered coming up with all this friction ellipse theory stuff since it would obviously be wrong. We'd need a friction cross/bubble thing theory instead like I showed earlier.
Moving to the left the slip angles are increasing 5 degrees at a time up to 30 degrees slip angle. Moving upwards the slip ratios are increasing from 0.1 to 0.2, 0.4, and 0.8. (This is what you get when you're drifting with the wheels on fire
)For others following along, what I'm doing is taking a point on the dotted line at say, slip angle 5 degrees, for Sx = 0.1 and adding it to the point on the solid line at the same slip angle vectorially. (Fx * Fx + Fy * Fy). So this is the total force the tire is producing at all of these combinations of slip angles and slip ratios. They correspond to the height of various spots in AndRand's combined force graphs. This says nothing at all about the actual direction of the force which is another topic entirely that we probably will not get to given how the thread is developing, unfortunately.
You'll see the same trend as in that green graph I posted earlier. Near the origin (bottom right) you have a spike, then as you move to the left and "up" the values quickly drop to a sort of plateau where they slowly continue dropping. However, along the diagonal there is no trend at all toward having any sudden upturn in force again (especially above what you get in pure slip, my goodness...) nor is there a valley along any diagonal where the forces are far lower than what you get in surrounding areas. Note that the "back row" (top row) all have pretty much the same value. It doesn't suddenly collapse to 50% or something at the top left corner like it does in some of your graphs.
Keep in mind that I am loosely eyeballing all this data reading it off the graph, so there is some noise in there. I've been writing tire models for a good 10 years now. I think my first attempt at it was in 1993 or so with nothing but Fred Puhn's "How to Make Your Car Handle" on a 386SX-16Mhz. It doesn't mean I know everything, but I'm not a noob to this stuff and do know what I'm talking about on this one
@AndRand: I'm not sure if you're actually understanding the graphs you're posting here, since if you did you'd immediately notice they're nonsense. 
To give you a rough idea of what it should look like, let's for a moment forget about the longitudinal (slip ratio) grip curve. Just take the lateral one, put a pin at the 0-slip-angle point, grab it by its tail and spin it around 360°, leaving a 3D-trail while doing so. The shape you're left with is one of a rather simplisticly simulated tyre that behaves exactly the same no matter which direction it is being pushed. Now granted, just thinking about the tyre shape and its basic workings a little makes it clear that a real tyre doesn't work like this, but if used in a simulation it would result in a fairly drivable car, already several orders of magnitude better than what your magic fairy dust canyon curve would produce.
Now, that's only one curve which sucks, so lets make that a combination of two curves. But instead of spending ages tinkering with it and somehow ending up with the forces cancelling each other out, just morph the curve from the lateral to the longitudinal one as you do your 360° spin (so I guess you make a linear interpolation between both curves modulated by the current rotation angle or something). That's probably not quite how a real tyre works either, but by doing this really simple procedure you'd have already far surpassed everything you've brought up till now.
Sorry for putting this a bit bluntly, I just can't help myself sometimes :o
To give you a rough idea of what it should look like, let's for a moment forget about the longitudinal (slip ratio) grip curve. Just take the lateral one, put a pin at the 0-slip-angle point, grab it by its tail and spin it around 360°, leaving a 3D-trail while doing so. The shape you're left with is one of a rather simplisticly simulated tyre that behaves exactly the same no matter which direction it is being pushed. Now granted, just thinking about the tyre shape and its basic workings a little makes it clear that a real tyre doesn't work like this, but if used in a simulation it would result in a fairly drivable car, already several orders of magnitude better than what your magic fairy dust canyon curve would produce.
Now, that's only one curve which sucks, so lets make that a combination of two curves. But instead of spending ages tinkering with it and somehow ending up with the forces cancelling each other out, just morph the curve from the lateral to the longitudinal one as you do your 360° spin (so I guess you make a linear interpolation between both curves modulated by the current rotation angle or something). That's probably not quite how a real tyre works either, but by doing this really simple procedure you'd have already far surpassed everything you've brought up till now.
Sorry for putting this a bit bluntly, I just can't help myself sometimes :o
Well, I took data from Figure 7 for lateral force and for Figure 6 for longitudinal and then combined them vectorially (which result is shown on my 3d graphs)
I can see
and appreciate your understanding and answers.Obviously not because your data is showing something quite different from mine. One of us made an error in our math. Quite sure it wasn't me
Right on the money.
Sorry to put it bluntly... but here it IS MEASURED (for both Fx and Fy). And it sure doesnt look like turning that slip ratio 0 curve 360°.
Did you use Figure 7 or Figure 7 and Figure 6?
And your graphs don't reflect this data at all like you thought they did, per my last post. I agree with Android in that it looks like you aren't really understanding what your own graphs are saying and how they relate to the ones in the paper
top 3d chart is result (vector sum) of charts below.
Figure 7. That one is the graph that is showing what is going on at extreme slips where your valleys and bumps are showing up.
Figure 6 is mostly below the limit of traction except in the areas where they hook back to the left as they go down. The rest of it is near the origin where your graphs start at 0 and climb extremely quickly and then go off and do goofy things.
Combination slip below the peaks and combination slip passed them are probably going to be two different things with the Magic Model.
No they aren't. How are you getting values at extreme slip less than 600 given those Fx and Fy graphs? At the highest slips neither of the 2D graphs goes below 800 by itself, let alone what happens if you add the corresponding 900 to 1100 of the other F to it vectorially.
Fx - Slip Ratio from 0 to 90%, Slip Angle for 2, 5, 8 and 12 degrees on Figure 6.
Fy - Slip Angle from 0 to 30 degrees and SR 10, 20, 40 and 80% on Figure 7.
You say they dont match?
Check out my attachment. I challenge you to find any condition plotted to the right of my red slip lines (high slip) where you get a value as low as 600 like you get in the back left area of your graphs. You can not possibly be really plotting the vector sum. Check your math.
Tyre Physics progress spinoff thread for physics geeks
(168 posts, started )
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