torcs-users Mailing List for TORCS - The Open Racing Car Simulator

----- Bernhard Wymann wrote:
> Hi David
> 
> This patch is wrong, the original is correct. The differential equations 
> are calculated with an euler step, so:
> 1. Calculate Forces F(t)
> 2. Calculate accelerations : a(t) = f(F(t))
> 3. Calculate speed, v(t) = v(t-1) + a(t)*dt
> 4. Calculate positions, s(t) = s(t-1) + v(t)*dt
> 
> 10 years ago or so we tried an alternative integration scheme for some 
> forces (e.g. tires), but the calculation/complexity overhead was not 
> worth the effect.
> 
> Kind regards
> 
> Bernhard
>

Thanks for the feedback.
I reverted the last patch and made a new one that works better.
It is noteworthy that F(t) is also a function of speed (slip velocity),
and is subsequently used to calculate a new speed. One misordered
line of code could give SimWheelUpdateForce() some data from a
wrong iteration.
--- torcs-1.3.7/src/modules/simu/simuv2/simu.cpp	2016-10-14 21:50:11.000000000 -0700
+++ torcs-1.3.7/src/modules/simu/simuv2/simu.cpp	2016-10-14 21:51:33.000000000 -0700
@@ -380,14 +380,14 @@
 				SimAxleUpdate(car, i);
 			}
 			CHECK(car);
+			SimWheelUpdateRotation(car);
+			CHECK(car);
 			for (i = 0; i < 4; i++){
 				SimWheelUpdateForce(car, i);
 			}
 			CHECK(car);
 			SimTransmissionUpdate(car);
 			CHECK(car);
-			SimWheelUpdateRotation(car);
-			CHECK(car);
 			SimCarUpdate(car, s);
 			CHECK(car);
 		} else {
> On 14.10.2016 01:45, David Savinkoff wrote:
> > Tire forces are calculated in:
> > torcs-1.3.7/src/modules/simu/simuv2/wheel.cpp :: SimWheelUpdateForce()
> >
> > Torcs now drives and slides with less swaying and spinning instabilities.
> >
> > See following in patch (torcs-1.3.7/src/modules/simu/simuv2/car.cpp):
> >
> > @@ -400,10 +384,10 @@
> >  void
> >  SimCarUpdate(tCar *car, tSituation * /* s */)
> >  {
> > -	SimCarUpdateForces(car);
> > -	CHECK(car);
> >  	SimCarUpdateSpeed(car);
> >  	CHECK(car);
> > +	SimCarUpdateForces(car);
> > +	CHECK(car);
> >  	SimCarUpdateCornerPos(car);
> >  	CHECK(car);
> >

Hi David

This patch is wrong, the original is correct. The differential equations 
are calculated with an euler step, so:
1. Calculate Forces F(t)
2. Calculate accelerations : a(t) = f(F(t))
3. Calculate speed, v(t) = v(t-1) + a(t)*dt
4. Calculate positions, s(t) = s(t-1) + v(t)*dt

10 years ago or so we tried an alternative integration scheme for some 
forces (e.g. tires), but the calculation/complexity overhead was not 
worth the effect.

Kind regards

Bernhard

On 14.10.2016 01:45, David Savinkoff wrote:
> Tire forces are calculated in:
> torcs-1.3.7/src/modules/simu/simuv2/wheel.cpp :: SimWheelUpdateForce()
>
> Torcs now drives and slides with less swaying and spinning instabilities.
>
> See following in patch (torcs-1.3.7/src/modules/simu/simuv2/car.cpp):
>
> @@ -400,10 +384,10 @@
>  void
>  SimCarUpdate(tCar *car, tSituation * /* s */)
>  {
> -	SimCarUpdateForces(car);
> -	CHECK(car);
>  	SimCarUpdateSpeed(car);
>  	CHECK(car);
> +	SimCarUpdateForces(car);
> +	CHECK(car);
>  	SimCarUpdateCornerPos(car);
>  	CHECK(car);
>
>
>
> ------------------------------------------------------------------------------
> Check out the vibrant tech community on one of the world's most
> engaging tech sites, SlashDot.org! http://sdm.link/slashdot
>
>
>
> _______________________________________________
> Torcs-users mailing list
> Tor...@li...
> https://lists.sourceforge.net/lists/listinfo/torcs-users
>

Tire forces are calculated in:
torcs-1.3.7/src/modules/simu/simuv2/wheel.cpp :: SimWheelUpdateForce()

Torcs now drives and slides with less swaying and spinning instabilities.

See following in patch (torcs-1.3.7/src/modules/simu/simuv2/car.cpp):

@@ -400,10 +384,10 @@
 void
 SimCarUpdate(tCar *car, tSituation * /* s */)
 {
-	SimCarUpdateForces(car);
-	CHECK(car);
 	SimCarUpdateSpeed(car);
 	CHECK(car);
+	SimCarUpdateForces(car);
+	CHECK(car);
 	SimCarUpdateCornerPos(car);
 	CHECK(car);

The last two patches accidentally had the proper slip angle reverted.
This patch corrects this. Drive this one.

Thanks,
David

----- David Savinkoff wrote:
> ----- David Savinkoff wrote:
> > Speed Dreams noted:
> > // elevate car when it has slightly impacted into ground. (SD r6312),
> > and made a workaround without addressing the real problem.
> > 
> > torcs-1.3.7/src/modules/simu/simuv2/collide.cpp line 40
> > erroneously changes car->DynGCg.pos.z by the amount the wheel
> > is displaced... but the wheel is Not directly beneath the
> > center of gravity (COG). The wheel actually acts as a lever
> > with the other wheels to displace the COG approximately half
> > as much.
> > 
> > There are possibly two solutions:
> > 1) multiply by 0.5
> 
> This should be 0.25 to divide the leverage between 4 wheels.
> New patch included. works better than 0.5 also.
> 
> > 2) assign the value to a variable other than car->DynGCg.pos.z
> > 
> > torcs-1.3.7.2016oct08.diff attached (yes, TORCS drives a little better)
> > 
> > Sincerely,
> > David Savinkoff
> 

----- David Savinkoff wrote:
> Speed Dreams noted:
> // elevate car when it has slightly impacted into ground. (SD r6312),
> and made a workaround without addressing the real problem.
> 
> torcs-1.3.7/src/modules/simu/simuv2/collide.cpp line 40
> erroneously changes car->DynGCg.pos.z by the amount the wheel
> is displaced... but the wheel is Not directly beneath the
> center of gravity (COG). The wheel actually acts as a lever
> with the other wheels to displace the COG approximately half
> as much.
> 
> There are possibly two solutions:
> 1) multiply by 0.5

This should be 0.25 to divide the leverage between 4 wheels.
New patch included. works better than 0.5 also.

> 2) assign the value to a variable other than car->DynGCg.pos.z
> 
> torcs-1.3.7.2016oct08.diff attached (yes, TORCS drives a little better)
> 
> Sincerely,
> David Savinkoff

Speed Dreams noted:
// elevate car when it has slightly impacted into ground. (SD r6312),
and made a workaround without addressing the real problem.

torcs-1.3.7/src/modules/simu/simuv2/collide.cpp line 40
erroneously changes car->DynGCg.pos.z by the amount the wheel
is displaced... but the wheel is Not directly beneath the
center of gravity (COG). The wheel actually acts as a lever
with the other wheels to displace the COG approximately half
as much.

There are possibly two solutions:
1) multiply by 0.5
2) assign the value to a variable other than car->DynGCg.pos.z

torcs-1.3.7.2016oct08.diff attached (yes, TORCS drives a little better)

Sincerely,
David Savinkoff

Hi,
This patch changes the default values (wrt torcs-1.3.7.2016oct01.diff)
[patch line 198]
-	wheel->lfMax          = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMAX, (char*)NULL, 1.6f);
-	wheel->lfMin          = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMIN, (char*)NULL, 0.8f);
+	wheel->lfMax          = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMAX, (char*)NULL, 1.4f);
+	wheel->lfMin          = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMIN, (char*)NULL, 1.0f);
and reverts previous code that used scaled defaults.

This patch also changes this line so that it has
the same value as torcs-1.3.7 ('sa' is not utilized in patch)
[patch line 327]
-	wheel->sa = sa;
+	wheel->sa = atan2(wheel->bodyVel.y, wheel->bodyVel.x) - waz;


----- David Savinkoff wrote:
> ----- Bernhard Wymann wrote:
> > Hi David
> > 
> > You can set these parameters directly in the xml configuration of the 
> > car, no reason to fudge with the code, see wheel.cpp:
> > wheel->lfMax = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMAX, 
> > (char*)NULL, 1.6f);
> > wheel->lfMin = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMIN, 
> > (char*)NULL, 0.8f);
> > 
> > Look up the definition in car.h for the effective xml parameter name:
> > #define PRM_LOADFMIN            "load factor min"
> > #define PRM_OPLOAD              "operating load"
> > 
> > Kind regards
> > 
> > Bernhard
> >
> Hi Bernhard,
> 
> Thanks for the info. I just used grep on TORCS to scan everything
> and found that ./data/cars/models/kc-bigh/kc-bigh.xml is the only
> car in torcs-1.3.7 that sets "load factor max" or min.
> All of the other cars use the default that you showed here:
> > wheel.cpp:
> > wheel->lfMax = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMAX, 
> > (char*)NULL, 1.6f);
> > wheel->lfMin = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMIN, 
> > (char*)NULL, 0.8f);
> 
> I believe the default should be changed to
> 
> wheel->lfMax = GfParmGetNum(... , ...PRM_LOADFMAX, ... 1.4f);
> wheel->lfMin = GfParmGetNum(... , ...PRM_LOADFMIN, ... 1.0f);
> 
> because this improves all of the cars that I tested on different tracks.
> 
> Sincerely,
> David Savinkoff
> 
> > On 02.10.2016 00:02, David Savinkoff wrote:
> > > Hi,
> > >
> > > I found that halving the range of wheel->lfMax and wheel->lfMin
> > > greatly improves realistic tire performance in TORCS
> > >
> > > see line 283 in the patch:
> > >
> > >  	// load sensitivity
> > > -	mu = wheel->mu * (wheel->lfMin + (wheel->lfMax - wheel->lfMin) * exp(wheel->lfK * zforce / wheel->opLoad));
> > > +	mu = wheel->mu * ((0.75f*wheel->lfMin + 0.25f*wheel->lfMax) + 0.5f*(wheel->lfMax - wheel->lfMin) * exp(wheel->lfK * zforce / wheel->opLoad));
> > >
> > > Test the true limits with TORCS.
> > 
> 

Does that mean that there is an updated robotgen script I should use
instead? or just copy the example files?  Sorry for my ignorance.

On Sun, Oct 2, 2016 at 6:09 PM, Bernhard Wymann <be...@bl...> wrote:

> Hi Joseph
>
> Yes, there was an API-Change, use strdup, example from bt.cpp in TORCS:
> extern "C" int bt(tModInfo *modInfo)
> {
>     ...
>     modInfo[i].name = strdup(botname[i]);
>     modInfo[i].desc    = strdup(botdesc[i]);
>
> Btw. if somebody wants to bring the tutorial to the current date, let me
> know (I plan to update it and integrate it into the TORCS documentation
> when the 1.3.x series will get to pure mantainance mode, so this can take
> another year or so).
>
> Kind regards
>
> Bernhard
>
> On 02.10.2016 03:12, Joseph Giancarlo wrote:
>
>> I (semi) successfully compiled 1.3.7! and am now trying to make a
>> driver. I followed the steps in the tutorial and everything seemed ok
>> until I run make on the new bot and I get this warning:
>> _________________________________________________________
>> jbt.cpp: In function ‘int jbt(tModInfo*)’:
>> jbt.cpp:52:22: warning: deprecated conversion from string constant to
>> ‘char*’ [-Wwrite-strings]
>>      modInfo->name    = "jbt";  /* name of the module (short) */
>>                       ^
>> jbt.cpp:53:22: warning: deprecated conversion from string constant to
>> ‘char*’ [-Wwrite-strings]
>>      modInfo->desc    = "test"; /* description of the module (can be
>> long) */
>>                       ^
>> g++ -shared -o jbt.so jbt.o -L/usr/src/torcs/torcs-1.3.7/export/lib
>> -lopenal -lalut -lvorbisfile -L/usr/lib
>>  Exporting jbt.so to /usr/src/torcs/torcs-1.3.7/export/drivers/jbt/jbt.so
>>
>> ____________________________________________________________
>>
>>
>> Then if i run torcs and start a race with the bot it closes
>>
>> Any advice would be appreciated.  Thanks!
>>
>> On Sun, Sep 25, 2016 at 6:48 PM, David Savinkoff <dsa...@te...
>> <mailto:dsa...@te...>> wrote:
>>
>>     ----- Joseph Giancarlo wrote:
>>     > Hello all,
>>     >
>>     > I finally got around to reinstalling ubuntu and am now trying to
>>     get torcs
>>     > going and hopefully race next season. I ran into some errors
>>     configuring
>>     > torcs and would appreciate someone helping me through the error
>> log. I
>>     > could not figure out where it breaks.
>>     >
>>     > thanks,
>>     > --
>>     > Joe
>>
>>     You are compiling torcs-1.2.4 and 'configure' cannot find libm because
>>     much has changed since torcs-1.2.4
>>
>>     torcs-1.3.7 is the current version, it should compile.
>>
>>
>>
>>
>> --
>> Joseph Giancarlo
>> Michigan Technological University
>> Civil Engineering 2016
>> 248-763-9592
>>
>>
>> ------------------------------------------------------------
>> ------------------
>> Check out the vibrant tech community on one of the world's most
>> engaging tech sites, SlashDot.org! http://sdm.link/slashdot
>>
>>
>>
>> _______________________________________________
>> Torcs-users mailing list
>> Tor...@li...
>> https://lists.sourceforge.net/lists/listinfo/torcs-users
>>
>>
>


-- 
Joseph Giancarlo
Michigan Technological University
Civil Engineering 2016
248-763-9592

Hi

 From your variables I would guess that TORCS_BASE points to the wrong 
directory:
TORCS_BASE is supposed to point to the TORCS sources (e.g. just check if 
"ls $MAKE_DEFAULT" is able to list the file), from your variable I guess 
it is pointing to the binaries.

http://www.berniw.org/tutorials/robot/torcs/install/torcs-setup.html

The variables/make etc. just work if you have configured/installed TORCS 
from your source directory. Additionally it could be that "sudo" does 
not propagete the environment and that the variables are not set for root.

Kind regards

Bernhard

On 03.10.2016 10:00, Juan Luis Hortelano wrote:
> Hi,
>
> I have been trying to make the driver bt following berniw tutorial with
> no luck. I keep finding the message after executing "sudo make" in the
> bt folder:
>
> "make: *** No targets.  Stop."
>
> I think I've set up the environment variables right, this is in my .bashrc:
>
> export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib
> export TORCS_BASE=/usr/local/share/games/torcs
> export MAKE_DEFAULT=$TORCS_BASE/Make-default.mk <http://default.mk>
>
> I'm using torcs 1.3.7 and I followed the installation manual step by
> step. I've been trying to fix this for several days now.
>
> Could somebody help me out please?
>
>
> ------------------------------------------------------------------------------
> Check out the vibrant tech community on one of the world's most
> engaging tech sites, SlashDot.org! http://sdm.link/slashdot
>
>
>
> _______________________________________________
> Torcs-users mailing list
> Tor...@li...
> https://lists.sourceforge.net/lists/listinfo/torcs-users
>

Hi,

I have been trying to make the driver bt following berniw tutorial with no
luck. I keep finding the message after executing "sudo make" in the bt
folder:

"make: *** No targets.  Stop."

I think I've set up the environment variables right, this is in my .bashrc:

export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib
export TORCS_BASE=/usr/local/share/games/torcs
export MAKE_DEFAULT=$TORCS_BASE/Make-default.mk

I'm using torcs 1.3.7 and I followed the installation manual step by step.
I've been trying to fix this for several days now.

Could somebody help me out please?

----- Bernhard Wymann wrote:
> Hi David
> 
> You can set these parameters directly in the xml configuration of the 
> car, no reason to fudge with the code, see wheel.cpp:
> wheel->lfMax = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMAX, 
> (char*)NULL, 1.6f);
> wheel->lfMin = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMIN, 
> (char*)NULL, 0.8f);
> 
> Look up the definition in car.h for the effective xml parameter name:
> #define PRM_LOADFMIN            "load factor min"
> #define PRM_OPLOAD              "operating load"
> 
> Kind regards
> 
> Bernhard
>
Hi Bernhard,

Thanks for the info. I just used grep on TORCS to scan everything
and found that ./data/cars/models/kc-bigh/kc-bigh.xml is the only
car in torcs-1.3.7 that sets "load factor max" or min.
All of the other cars use the default that you showed here:
> wheel.cpp:
> wheel->lfMax = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMAX, 
> (char*)NULL, 1.6f);
> wheel->lfMin = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMIN, 
> (char*)NULL, 0.8f);

I believe the default should be changed to

wheel->lfMax = GfParmGetNum(... , ...PRM_LOADFMAX, ... 1.4f);
wheel->lfMin = GfParmGetNum(... , ...PRM_LOADFMIN, ... 1.0f);

because this improves all of the cars that I tested on different tracks.

Sincerely,
David Savinkoff

> On 02.10.2016 00:02, David Savinkoff wrote:
> > Hi,
> >
> > I found that halving the range of wheel->lfMax and wheel->lfMin
> > greatly improves realistic tire performance in TORCS
> >
> > see line 283 in the patch:
> >
> >  	// load sensitivity
> > -	mu = wheel->mu * (wheel->lfMin + (wheel->lfMax - wheel->lfMin) * exp(wheel->lfK * zforce / wheel->opLoad));
> > +	mu = wheel->mu * ((0.75f*wheel->lfMin + 0.25f*wheel->lfMax) + 0.5f*(wheel->lfMax - wheel->lfMin) * exp(wheel->lfK * zforce / wheel->opLoad));
> >
> > Test the true limits with TORCS.
> 

Hi Joseph

Yes, there was an API-Change, use strdup, example from bt.cpp in TORCS:
extern "C" int bt(tModInfo *modInfo)
{
     ...
     modInfo[i].name = strdup(botname[i]);
     modInfo[i].desc    = strdup(botdesc[i]);

Btw. if somebody wants to bring the tutorial to the current date, let me 
know (I plan to update it and integrate it into the TORCS documentation 
when the 1.3.x series will get to pure mantainance mode, so this can 
take another year or so).

Kind regards

Bernhard

On 02.10.2016 03:12, Joseph Giancarlo wrote:
> I (semi) successfully compiled 1.3.7! and am now trying to make a
> driver. I followed the steps in the tutorial and everything seemed ok
> until I run make on the new bot and I get this warning:
> _________________________________________________________
> jbt.cpp: In function ‘int jbt(tModInfo*)’:
> jbt.cpp:52:22: warning: deprecated conversion from string constant to
> ‘char*’ [-Wwrite-strings]
>      modInfo->name    = "jbt";  /* name of the module (short) */
>                       ^
> jbt.cpp:53:22: warning: deprecated conversion from string constant to
> ‘char*’ [-Wwrite-strings]
>      modInfo->desc    = "test"; /* description of the module (can be
> long) */
>                       ^
> g++ -shared -o jbt.so jbt.o -L/usr/src/torcs/torcs-1.3.7/export/lib
> -lopenal -lalut -lvorbisfile -L/usr/lib
>  Exporting jbt.so to /usr/src/torcs/torcs-1.3.7/export/drivers/jbt/jbt.so
>
> ____________________________________________________________
>
>
> Then if i run torcs and start a race with the bot it closes
>
> Any advice would be appreciated.  Thanks!
>
> On Sun, Sep 25, 2016 at 6:48 PM, David Savinkoff <dsa...@te...
> <mailto:dsa...@te...>> wrote:
>
>     ----- Joseph Giancarlo wrote:
>     > Hello all,
>     >
>     > I finally got around to reinstalling ubuntu and am now trying to
>     get torcs
>     > going and hopefully race next season. I ran into some errors
>     configuring
>     > torcs and would appreciate someone helping me through the error log. I
>     > could not figure out where it breaks.
>     >
>     > thanks,
>     > --
>     > Joe
>
>     You are compiling torcs-1.2.4 and 'configure' cannot find libm because
>     much has changed since torcs-1.2.4
>
>     torcs-1.3.7 is the current version, it should compile.
>
>
>
>
> --
> Joseph Giancarlo
> Michigan Technological University
> Civil Engineering 2016
> 248-763-9592
>
>
> ------------------------------------------------------------------------------
> Check out the vibrant tech community on one of the world's most
> engaging tech sites, SlashDot.org! http://sdm.link/slashdot
>
>
>
> _______________________________________________
> Torcs-users mailing list
> Tor...@li...
> https://lists.sourceforge.net/lists/listinfo/torcs-users
>

Hi David

You can set these parameters directly in the xml configuration of the 
car, no reason to fudge with the code, see wheel.cpp:
wheel->lfMax = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMAX, 
(char*)NULL, 1.6f);
wheel->lfMin = GfParmGetNum(hdle, WheelSect[index], PRM_LOADFMIN, 
(char*)NULL, 0.8f);

Look up the definition in car.h for the effective xml parameter name:
#define PRM_LOADFMIN            "load factor min"
#define PRM_OPLOAD              "operating load"

Kind regards

Bernhard


On 02.10.2016 00:02, David Savinkoff wrote:
> Hi,
>
> I found that halving the range of wheel->lfMax and wheel->lfMin
> greatly improves realistic tire performance in TORCS
>
> see line 283 in the patch:
>
>  	// load sensitivity
> -	mu = wheel->mu * (wheel->lfMin + (wheel->lfMax - wheel->lfMin) * exp(wheel->lfK * zforce / wheel->opLoad));
> +	mu = wheel->mu * ((0.75f*wheel->lfMin + 0.25f*wheel->lfMax) + 0.5f*(wheel->lfMax - wheel->lfMin) * exp(wheel->lfK * zforce / wheel->opLoad));
>
> Test the true limits with TORCS.

I (semi) successfully compiled 1.3.7! and am now trying to make a driver. I
followed the steps in the tutorial and everything seemed ok until I run
make on the new bot and I get this warning:
_________________________________________________________
jbt.cpp: In function ‘int jbt(tModInfo*)’:
jbt.cpp:52:22: warning: deprecated conversion from string constant to
‘char*’ [-Wwrite-strings]
     modInfo->name    = "jbt";  /* name of the module (short) */
                      ^
jbt.cpp:53:22: warning: deprecated conversion from string constant to
‘char*’ [-Wwrite-strings]
     modInfo->desc    = "test"; /* description of the module (can be long)
*/
                      ^
g++ -shared -o jbt.so jbt.o -L/usr/src/torcs/torcs-1.3.7/export/lib
-lopenal -lalut -lvorbisfile -L/usr/lib
 Exporting jbt.so to /usr/src/torcs/torcs-1.3.7/export/drivers/jbt/jbt.so

____________________________________________________________


Then if i run torcs and start a race with the bot it closes

Any advice would be appreciated.  Thanks!

On Sun, Sep 25, 2016 at 6:48 PM, David Savinkoff <dsa...@te...> wrote:

> ----- Joseph Giancarlo wrote:
> > Hello all,
> >
> > I finally got around to reinstalling ubuntu and am now trying to get
> torcs
> > going and hopefully race next season. I ran into some errors configuring
> > torcs and would appreciate someone helping me through the error log. I
> > could not figure out where it breaks.
> >
> > thanks,
> > --
> > Joe
>
> You are compiling torcs-1.2.4 and 'configure' cannot find libm because
> much has changed since torcs-1.2.4
>
> torcs-1.3.7 is the current version, it should compile.
>



-- 
Joseph Giancarlo
Michigan Technological University
Civil Engineering 2016
248-763-9592

Hi,

I found that halving the range of wheel->lfMax and wheel->lfMin
greatly improves realistic tire performance in TORCS

see line 283 in the patch:

 	// load sensitivity
-	mu = wheel->mu * (wheel->lfMin + (wheel->lfMax - wheel->lfMin) * exp(wheel->lfK * zforce / wheel->opLoad));
+	mu = wheel->mu * ((0.75f*wheel->lfMin + 0.25f*wheel->lfMax) + 0.5f*(wheel->lfMax - wheel->lfMin) * exp(wheel->lfK * zforce / wheel->opLoad));

Test the true limits with TORCS.