I'm working on a tire model. I used the Pacejka magic formula for
different vertical loads. I got the right curves for Lateral Force VS
Slip angle but I don't know how to use the normalizing technique to
fit the curves for different vertical loads in one curve, appreciate
any help
On 12 Aug 2002 12:42:07 -0700, [email hidden] (STEEL) wrote:
>I'm working on a tire model. I used the Pacejka magic formula for
>different vertical loads. I got the right curves for Lateral Force VS
>Slip angle but I don't know how to use the normalizing technique to
>fit the curves for different vertical loads in one curve, appreciate
>any help
You probably need load sensitivity. Not exactly sure what coefficients
they are, but from looking at the formula you can see which ones
affect results with varying Fz.
Ruud van Gaal
Free car sim: http://www.racer.nl/
Pencil art : http://www.marketgraph.nl/gallery/
Not quite sure if I understand your question, but you might find something
in Tire Data Treatment, Chapter 14 of "Race Car Vehicle Dynamics".
-- Doug Milliken
www.millikenresearch.com/rcvd.html
(order from SAE, link at the bottom of our page)
On Tue, 13 Aug 2002, Ruud van Gaal wrote:
Quoted text (18 lines)
> On 12 Aug 2002 12:42:07 -0700, [email hidden] (STEEL) wrote: > > >I'm working on a tire model. I used the Pacejka magic formula for > >different vertical loads. I got the right curves for Lateral Force VS > >Slip angle but I don't know how to use the normalizing technique to > >fit the curves for different vertical loads in one curve, appreciate > >any help > > You probably need load sensitivity. Not exactly sure what coefficients > they are, but from looking at the formula you can see which ones > affect results with varying Fz. > > > Ruud van Gaal > Free car sim: http://www.racer.nl/ > Pencil art : http://www.marketgraph.nl/gallery/ > >I have the book (Tire Data Treatment) my question is about chapter 14,
specifically about how to normalize tire's data, the book suggests
that the lateral force can be normalized by the using the formula
Normalized Lateral Force = Fy/UY * Z
And also the normalized slip angle is
Normalized slip angle = C tan ? / UY * Z
C = Cornering stiffness
UY = Friction coefficient
The book also presents a graph for the Normalized lateral force
against the Normalized slip angle for different vertical loads using
magic formula. My question is how to fit the curves for different
vertical loads in one curve (normalizing)? And if I want to use the
suggested formulae in the book, am I going to get same normalized
curve.
Doug Milliken <[email hidden]> wrote in message news:<[email hidden]>...
Quoted text (28 lines)
> Not quite sure if I understand your question, but you might find something > in Tire Data Treatment, Chapter 14 of "Race Car Vehicle Dynamics". > > -- Doug Milliken > www.millikenresearch.com/rcvd.html > (order from SAE, link at the bottom of our page) > > > On Tue, 13 Aug 2002, Ruud van Gaal wrote: > > > On 12 Aug 2002 12:42:07 -0700, [email hidden] (STEEL) wrote: > > > > >I'm working on a tire model. I used the Pacejka magic formula for > > >different vertical loads. I got the right curves for Lateral Force VS > > >Slip angle but I don't know how to use the normalizing technique to > > >fit the curves for different vertical loads in one curve, appreciate > > >any help > > > > You probably need load sensitivity. Not exactly sure what coefficients > > they are, but from looking at the formula you can see which ones > > affect results with varying Fz. > > > > > > Ruud van Gaal > > Free car sim: http://www.racer.nl/ > > Pencil art : http://www.marketgraph.nl/gallery/ > > > >The vertical load is included in three coefficients or four if camber
is accounted for as mentioned in Pacejka paper presenting the magic
formula, and I think all of them affect results, did I understood your
reply correctly?
[email hidden] (Ruud van Gaal) wrote in message news:<[email hidden]>...
Quoted text (16 lines)
> On 12 Aug 2002 12:42:07 -0700, [email hidden] (STEEL) wrote: > > >I'm working on a tire model. I used the Pacejka magic formula for > >different vertical loads. I got the right curves for Lateral Force VS > >Slip angle but I don't know how to use the normalizing technique to > >fit the curves for different vertical loads in one curve, appreciate > >any help > > You probably need load sensitivity. Not exactly sure what coefficients > they are, but from looking at the formula you can see which ones > affect results with varying Fz. > > > Ruud van Gaal > Free car sim: http://www.racer.nl/ > Pencil art : http://www.marketgraph.nl/gallery/On 20 Aug 2002 19:51:58 -0700, [email hidden] (STEEL) wrote:
Normalizing really is just getting rid of a dimension by a division
somewhere. So for Fz (load) you could take the Pacejka results for Fx
and divide by Fz (and then perhaps even by MaxFx to get values from
0..1). That gives you normalization.
However, because of load sensitivity, the curve's shape can change
depending on Fz (the four coefficients you found). If you normalize
you probably ignore load sensitivity, it would seem to me. You would
then do something like:
pacejka.SetInput(...);
pacejka.Calculate();
nrmFx=pacejka.GetFx();
Fx=nrmFx*Fz;
I'm not sure what exactly the advantage of this all is though. ;-)
One thing though I will implement in my Pacejka Player; that's
normalizing Fx for display, so you can see how the shape and peak (max
friction coefficient) changes when you vary load.
I will divide Pacejka's Fx results by Fz, giving effective friction
coefficients, which are interpreted more clearly by humans (like
mu=1.7) than forces (like Fz=1000 and Fx=1700). Computers don't really
care.
I do think I'm not exactly on to what you want to do though, so you
may want to ignore all this rambling. ;-)
Ruud van Gaal
Free car sim: http://www.racer.nl/
Pencil art : http://www.marketgraph.nl/gallery/
Quoted text (12 lines)
>I have the book (Tire Data Treatment) my question is about chapter 14, >specifically about how to normalize tire's data, the book suggests >that the lateral force can be normalized by the using the formula > Normalized Lateral Force = Fy/UY * Z >And also the normalized slip angle is >Normalized slip angle = C tan ? / UY * Z >C = Cornering stiffness >UY = Friction coefficient >The book also presents a graph for the Normalized lateral force >against the Normalized slip angle for different vertical loads using >magic formula. My question is how to fit the curves for different >vertical loads in one curve (normalizing)?Thank you for your valuable response. I?m trying to use the formula I
found in RACE CAR VEHICLE DYNAMICS page 476 which describes the
normalized slip angle
Normalized slip angle = C tan ? / �y Z
I want to get the same curve for the normalized lateral force Vs. the
normalized slip angle for different vertical loads that I would get by
using the magic formula as the book suggests. I assumed constant
values for both the cornering stiffness C, and the friction
coefficient uy. The result of my simple program was a straight line
instead of the expected S shape curve.
Where did I go wrong here??
[email hidden] (Ruud van Gaal) wrote in message news:<[email hidden]>...
Quoted text (44 lines)
> On 20 Aug 2002 19:51:58 -0700, [email hidden] (STEEL) wrote: > > >I have the book (Tire Data Treatment) my question is about chapter 14, > >specifically about how to normalize tire's data, the book suggests > >that the lateral force can be normalized by the using the formula > > Normalized Lateral Force = Fy/UY * Z > >And also the normalized slip angle is > >Normalized slip angle = C tan ? / UY * Z > >C = Cornering stiffness > >UY = Friction coefficient > >The book also presents a graph for the Normalized lateral force > >against the Normalized slip angle for different vertical loads using > >magic formula. My question is how to fit the curves for different > >vertical loads in one curve (normalizing)? > > Normalizing really is just getting rid of a dimension by a division > somewhere. So for Fz (load) you could take the Pacejka results for Fx > and divide by Fz (and then perhaps even by MaxFx to get values from > 0..1). That gives you normalization. > However, because of load sensitivity, the curve's shape can change > depending on Fz (the four coefficients you found). If you normalize > you probably ignore load sensitivity, it would seem to me. You would > then do something like: > pacejka.SetInput(...); > pacejka.Calculate(); > nrmFx=pacejka.GetFx(); > Fx=nrmFx*Fz; > > I'm not sure what exactly the advantage of this all is though. ;-) > One thing though I will implement in my Pacejka Player; that's > normalizing Fx for display, so you can see how the shape and peak (max > friction coefficient) changes when you vary load. > I will divide Pacejka's Fx results by Fz, giving effective friction > coefficients, which are interpreted more clearly by humans (like > mu=1.7) than forces (like Fz=1000 and Fx=1700). Computers don't really > care. > > I do think I'm not exactly on to what you want to do though, so you > may want to ignore all this rambling. ;-) > > > Ruud van Gaal > Free car sim: http://www.racer.nl/ > Pencil art : http://www.marketgraph.nl/gallery/On 26 Aug 2002 01:06:44 -0700, [email hidden] (STEEL) wrote:
mu isn't really constant; with load sensitivity, mu will decrease with
added load (Fz).
The normalized slip angle as above, with constants, will probabyl be
linear indeed, but feed that slip angle into Pacejka, and the
resulting formula will not.
I'm not sure about RCVD's normalizing; haven't actually dug to deep in
there. But if you normally have:
- calculate SR, SA
- pacejka.SetSR(sr), SetSA(sa)
- pacejka.Calculate()
- Fx=pacejka.GetFx()
you now do:
- calculate normalized SA
- denormalize SA
- pacejka.SetSA(sa)
- etc.
However, I'm not sure what you'd want to divide a slip ANGLE by (or
I'm reading mu*y Z incorrectly; not sure actually what y and Z is
here; Z=Fz?).
Seems like your program only plots 'normalized slip angle' if it's a
line?
Ruud van Gaal
Free car sim: http://www.racer.nl/
Pencil art : http://www.marketgraph.nl/gallery/
Quoted text (11 lines)
>Thank you for your valuable response. I?m trying to use the formula I >found in RACE CAR VEHICLE DYNAMICS page 476 which describes the >normalized slip angle >Normalized slip angle = C tan ? / �y Z >I want to get the same curve for the normalized lateral force Vs. the >normalized slip angle for different vertical loads that I would get by >using the magic formula as the book suggests. I assumed constant >values for both the cornering stiffness C, and the friction >coefficient uy. The result of my simple program was a straight line >instead of the expected S shape curve. >Where did I go wrong here??Thank you for clearifying mu relation to load sensitivity,
Here is what I?m trying to do:
pacejka.SetSA(sa)
pacejka.Calculate()
Fy.pacejka.GetFy()
Then:
Calculate the normalized slip angle using the formula in RCVD?s
Normalized slip angle = CS* tan (sa) / mu * Fz (page 476)
For CS (cornering stiffness) I used CS = BCD (B stiffness factor, C
shape factor, D peak factor)
For mu, I used mu = a1*Fz + a2, where a1, a2 are Pacejka?s
coefficients. (a1 = -22.1 , a2 = 1011 for lateral force calculation)
Then:
Calculate Normalized lateral force using the suggested RCVD?s formula
Normalized lateral force = Fy / mu * Fz (page475)
By doing the above I expected to get the same curve (Normalized
lateral force Vs. Normalized slip angle) for different Fz as in page
477.
I?m using Matlab which accepts angles only in radians, and I?m not
quite certain whether Pacejk?s works for small values of slip angles
(after converting for example 10 degrees to 0.17453 radians)or not.
Where did I go wrong???? I?m desperate for help.
[email hidden] (Ruud van Gaal) wrote in message news:<[email hidden]>...
Quoted text (44 lines)
> On 26 Aug 2002 01:06:44 -0700, [email hidden] (STEEL) wrote: > > >Thank you for your valuable response. I?m trying to use the formula I > >found in RACE CAR VEHICLE DYNAMICS page 476 which describes the > >normalized slip angle > >Normalized slip angle = C tan ? / �y Z > >I want to get the same curve for the normalized lateral force Vs. the > >normalized slip angle for different vertical loads that I would get by > >using the magic formula as the book suggests. I assumed constant > >values for both the cornering stiffness C, and the friction > >coefficient uy. The result of my simple program was a straight line > >instead of the expected S shape curve. > >Where did I go wrong here?? > > mu isn't really constant; with load sensitivity, mu will decrease with > added load (Fz). > The normalized slip angle as above, with constants, will probabyl be > linear indeed, but feed that slip angle into Pacejka, and the > resulting formula will not. > > I'm not sure about RCVD's normalizing; haven't actually dug to deep in > there. But if you normally have: > - calculate SR, SA > - pacejka.SetSR(sr), SetSA(sa) > - pacejka.Calculate() > - Fx=pacejka.GetFx() > > you now do: > - calculate normalized SA > - denormalize SA > - pacejka.SetSA(sa) > - etc. > > However, I'm not sure what you'd want to divide a slip ANGLE by (or > I'm reading mu*y Z incorrectly; not sure actually what y and Z is > here; Z=Fz?). > > Seems like your program only plots 'normalized slip angle' if it's a > line? > > > Ruud van Gaal > Free car sim: http://www.racer.nl/ > Pencil art : http://www.marketgraph.nl/gallery/On 27 Aug 2002 12:43:16 -0700, [email hidden] (STEEL) wrote:
...
>Calculate the normalized slip angle using the formula in RCVD?s
>Normalized slip angle = CS* tan (sa) / mu * Fz (page 476)...
Why would they? The relationship of slip angle and lateral force IS
the Pacejka result; they're certainly not the same!?
Or do you mean as you vary Fz ONLY, you get totally different curves
for one type of curve (for example 'normalized slip angle')? That
would be just a syntax error somewhere. :)
But from above you can see that if CS*tan(SA) == Fy then the curves
would look alike, but slip angle != lateral force.
>I?m using Matlab which accepts angles only in radians, and I?m not
>quite certain whether Pacejk?s works for small values of slip angles
>(after converting for example 10 degrees to 0.17453 radians)or not.
It works BETTER even for small slip angles, and grows worse for large
SA.
I'd suggest to skip normalizing for now; you don't really need them
anyway.
Ruud van Gaal
Free car sim: http://www.racer.nl/
Pencil art : http://www.marketgraph.nl/gallery/
Quoted text (7 lines)
>Calculate Normalized lateral force using the suggested RCVD?s formula > >Normalized lateral force = Fy / mu * Fz (page475) > >By doing the above I expected to get the same curve (Normalized >lateral force Vs. Normalized slip angle) for different Fz as in page >477.Thank you for your valuable information, I think I will just skip
normalizing for now, and as you mentioned I don't really feel like I
want to ignore load sensitivity.
[email hidden] (Ruud van Gaal) wrote in message news:<[email hidden]>...
Quoted text (36 lines)
> On 27 Aug 2002 12:43:16 -0700, [email hidden] (STEEL) wrote: > > ... > >Calculate the normalized slip angle using the formula in RCVD?s > >Normalized slip angle = CS* tan (sa) / mu * Fz (page 476) > ... > >Calculate Normalized lateral force using the suggested RCVD?s formula > > > >Normalized lateral force = Fy / mu * Fz (page475) > > > >By doing the above I expected to get the same curve (Normalized > >lateral force Vs. Normalized slip angle) for different Fz as in page > >477. > > Why would they? The relationship of slip angle and lateral force IS > the Pacejka result; they're certainly not the same!? > Or do you mean as you vary Fz ONLY, you get totally different curves > for one type of curve (for example 'normalized slip angle')? That > would be just a syntax error somewhere. :) > > But from above you can see that if CS*tan(SA) == Fy then the curves > would look alike, but slip angle != lateral force. > > >I?m using Matlab which accepts angles only in radians, and I?m not > >quite certain whether Pacejk?s works for small values of slip angles > >(after converting for example 10 degrees to 0.17453 radians)or not. > > It works BETTER even for small slip angles, and grows worse for large > SA. > > I'd suggest to skip normalizing for now; you don't really need them > anyway. > > Ruud van Gaal > Free car sim: http://www.racer.nl/ > Pencil art : http://www.marketgraph.nl/gallery/On 3 Sep 2002 12:53:44 -0700, [email hidden] (STEEL) wrote:
>Thank you for your valuable information, I think I will just skip
>normalizing for now, and as you mentioned I don't really feel like I
>want to ignore load sensitivity.
I'll read chapter 14 sometime next week, and if it turns out I
understood your question incorrectly I'll repost. :)
Good luck,
Ruud van Gaal
Free car sim: http://www.racer.nl/
Pencil art : http://www.marketgraph.nl/gallery/
