GPL handling question--Physics model

Hello, everyone I don't own a copy of GPL because my computer's too slow :-( I'm writing a vehicle physics model and have a question regarding the handling of GPL cars. When you are turning somewhat gently through a corner (not close to the traction limit), and give the car some gas without changing the steering angle, does the car tend to turn in a little more? I'm talking about neglecting fore-aft weight transfer here, so perhaps someone who has run very soft shocks and dampers could tell me what happens initially (before the car "sets" into the corner, aka transient behavior). when the gas is pushed in a little. I'm waiting for my book to arrive, Racing Vehicle Dynamics, which will hopefully have more complete info on limiting side forces in tire models. I've got two options right now and am curious which one GPL is using, if either. Thanks! Todd Wasson --- Performance Simulations Drag Racing Prediction Software http://PerformanceSimulations.Com

I would suggest reading this: http://bovineracing.com/eoa/pt5/pt5.htm Ken

Whoops, I must have missed this post you just replied to, Doug. Gavitt said (I didn't get the whole post, just what Mr. Milliken quoted): >>" As for the car in your model not wanting to return to a straight line, haveyou modeled all the self-centering torques? A tire is a spring. When it moves at a slip angle it loads in torsion, and thus generates an equal and opposite torque."<< The answer is yes. This didn't occur to me until after I downloaded a study conducted on motorcycle tires. I thought this would surely solve my problem, but it had very little effect. All four tires' self centering torques seemed to more or less cancel each other out and have little effect. I have left it in anyway, although may remove it since I fudged the data for this. Doug, I assume you are correct, since you wrote the book, but I have also read in other sources that the grip level will decrease slightly (in some, such as Nascar tires) after a certain slip angle range has been exceeded. I'm looking right now at a chart in "Circle Track" Annual 1995 that shows a Nascar tire's lateral acceleration increasing with slip angle until about the 5 degree point (1.2g), then dipping slightly and rising again around the 9 degree point, then falling sharply after that. Perhaps this is because the direction of the force as measured in this magazine was perpendicular to the car's chassis, and not perpendicular to the direction the tire was facing. That would be a huge difference! So could we conclude that:

Whoops! I hate it when I get in the middle of writing a post and send it by accident. Kevin, you posted: >> As for the car in your model not wanting to return to a straight line, have >> you modeled all the self-centering torques? A tire is a spring. When it >> moves at a slip angle it loads in torsion, and thus generates an equal and >> opposite torque. Yes, I included self-aligning torque (a greatly simplified, fudged pneumatic trail type set of equations that approximated the effect), suspecting it would cure the problem, but the forces that the torques generated on the center of gravity of the car more or less cancelled each other out. It had very little, if any, effect on straightening the car. ** I missed your other post with quote I showed above, Kevin, could you please repost it?**

Kevin and Doug, Sorry about posting all over the place and repeating myself here, this is my third attempt now. :-) Hate it when I accidentally hit enter! What I was saying was: "So could we conclude that:" Ah... Nevermind. My head is spinning and it's bedtime now! One more thing though. I am curious about these other test results being wrong, though, Doug. I've seen data that goes both ways with this. The Nascar tire example where the grip coefficient dropped off rapidly after a double spike from 5 to 9 degrees of slip, as well as the motorcycle tire test, where the grip rose and just stayed high, even if the thing was sliding at 40 or 50 degrees. Doesn't this go against the concept of dynamic vs. static friction? Or is the tire always sliding a little somewhere in the contact patch (if you drag out the magnifying glass) so the abrupt change between dynamic/static is lost gradually, resulting in a smooth curve? Of course, as you said, this would depend on the tire. But don't high performance racing tires operate this way? Peak at a high grip, then drop off afterward? Street tires probably don't do this, but racing tires? Todd Wasson

A couple of random comments.... On Mon, 22 May 2000, Kevin Gavitt wrote: .....

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> A simplfied tire does the same thing. If you only load it to .25 of it's > force generating capacity it has a reserve capacity. Load it to .2 g at a > real force of 200 lbs. and it is still capable of generating 600 lbs. > additional force. Accelerate the car to .4 g and the tire responds by simply > generating the additional force neccessary to balance the load and the car > remains on the same arc. You can continue this right up to the limit, which > is *defined* as the point where the arc of the car must widen to balance the

Fine for a simple tire, but not quite true for real ones! In a tire the "block of rubber" in the print is constantly changing, the tread rubber and the carcass structure all deform, etc. As I said before, nothing is simple about tires! > Can you pick up a copy of Skip Barber's Going Faster? It's available off the Nice book, except that the plots of tire data are wrong -- after the peak, they show a drop off in force...and this doesn't happen. After the peak, the sideforce stays pretty constant, out to 90 deg slip angle. The fact that the force "stops increasing" with additional slip angle is enough to cause the driver to "lose it". > As for the car in your model not wanting to return to a straight line, have > you modeled all the self-centering torques? A tire is a spring. When it > moves at a slip angle it loads in torsion, and thus generates an equal and > opposite torque. ??? Are you talking about tire self-aligning torque (or pneumatic trail)? -- Doug Douglas Milliken <[email hidden]> Milliken Research Associates Inc.

On Sun, 21 May 2000 20:35:21 GMT, Doug Milliken <[email hidden]> wrote in message <[email hidden]> : >Amazon.con is not the quick way to get our book -- I've checked with them >and also with our publisher, SAE. Amazon doesn't stock it (probably true >for most "low volume" titles) so they have to order it from SAE anyway. > --> Direct orders from SAE usually ship the next day. FWIW I use the UK branch of Amazon & have never had a problem with them. I ordered your book from them on 30th Dec & it was shipped on 4th Jan - not bad considering that due to the millennium celebrations this was the next working day. Maybe amazon.co.uk has a different approach to their parent company? I had previously tried to order it via Barnes & Noble and it took them about 2 months before finally admitting that they weren't going to supply it.... Cheers, Richard PS: Thanks for writing such a fascinating book!

Youch. $20,000-$30,000 for a full project? Think I'll pass on that one! I wish now that I'd have ordered your book directly from your publisher. Oh well, that gives me 2-4 more weeks or so to make a suspension model. The tire model as it is now works well, I think it's basically correct, just needs realistic data. I have some excellent material from a study that was conducted, but unfortunately, it's for motorcycle tires. Look forward to receiving your book! Todd Wasson Drag Racing Prediction Software: http://PerformanceSimulations.com

Thanks for the link, Mike. I have seen that before, it's an excellent tutorial. Todd Wasson

Shucks, now I'll have to wait 2-4 more weeks for your book... :-( Todd Wasson

Ok, I'm sorry if I've underestimated your physics knowledge. I've only your questions here to go on, and I guess I'm not understanding you properly. I'm afraid I still don't get the feeling from your questions what you're driving at. Let's take a super simplified lab example. A large block of rubber sitting on the concrete lab floor. Let's say it will take 200 lbs. of force to overcome it's cf and start it sliding across the floor. What happens when you push it with 50 lbs. of force? ( I'm using 50 lbs. because it is .25 of 200, and the .2 g you use as an example is .25 of the cornering force a decent road car can generate.) Well, it pushes back with 50 lbs. of force and other than that just sits there. Push it with 100 lbs. of force and it pushes back with 100 lbs. of force and continues to just sit there. Push it with 201 lbs. of force and it will accelerate under 1 lb. of force by sliding across the lab floor. A simplfied tire does the same thing. If you only load it to .25 of it's force generating capacity it has a reserve capacity. Load it to .2 g at a real force of 200 lbs. and it is still capable of generating 600 lbs. additional force. Accelerate the car to .4 g and the tire responds by simply generating the additional force neccessary to balance the load and the car remains on the same arc. You can continue this right up to the limit, which is *defined* as the point where the arc of the car must widen to balance the force in accordance with the rules of circular motion. By definition if you are below the limit the car will follow the same arc whether you increase or decrease speed as long as the car stays below the limit. This is essentially the same way banked turns work, and why at a particular speed a car can hold it's wheels straight and follow a curved path with 0 side loading, using gravity to supply a centripital force rather than the tires. Correct? What about this don't you understand? You can go out test this on your own street car, can't you? .2 g is well below a speed likely to gain the interest of the authorities on turns you can find around any city. You understand all this? So perhaps you can see my quandry at your question. I'm using a very simplified model here that dosn't take the fact that the capacity of a tire to generate force is variable with the slip angle. At .2 g this is irrelevant to the driver because of the huge reserve capacity of the tire. It's only the small window around the limit that things get interesting, where the reserve capacity of the tire is small and may actually disappear. Are you being confused about the idea of slip angle and what it does and what it is? Am I being confused about what you are and are not confused about? The next issue is your specific question about the reaction of GPL. GPL does not use a simple single tire in the lab model. It uses a model of 4 tires attached to a semi-rigid body. It resolves the vector sum of those forces. How can the behaviour of such a model be used to deduce a hypothetical simplified single tire model? Isn't that rather like trying to deduce an Elephant's DNA sequence by looking at the elephant, rather than the other way around? I can set up a GPL car to exhibit just about any behaviour you want. The static loadings are user variable. Roll resistence is user variable. Tire pressures are user variable. Damping rates are user variable. All on each corner of the car seperately. Different chassis have different inate properties such as roll center, weight bias, suspension geometry, etc. Even aerodynamic properties are taken into account. And the arc taken by a car with 4 tires attached to it will be the vector sum of the forces on all four tires right? Each with a different load and perhaps even a different cf. Slip angle may even be different on all four tires depending on suspension geometry. The degree to which the arc changes will be the dependant on the ratio of the total slip angles of the front tires to the total slip angles on the rear, right? A car with larger slip angles at the rear will oversteer and one with larger slip angles at the front will understeer, correct? And the slip angles are user settable to a large degree, yes? I fail to see what you are attempting to deduce from the behaviour of GPL, or how you feel you can deduce anything at all by it. I can leave you with the same answer I gave before. In GPL if you are cornering at .2 g and increase your speed to .4 g the arc will change by not changing at all, which is exactly what it should do, and exactly what your street car will do. Can you pick up a copy of Skip Barber's Going Faster? It's available off the shelf at at any Borders or Barnes and Nobles, as is Van Valkenburgh's Race Car Engineering and Mechanics. I highly reccomend you suppliment the Milliken's work with these to give you a drivers perspective on the hard science. As for the car in your model not wanting to return to a straight line, have you modeled all the self-centering torques? A tire is a spring. When it moves at a slip angle it loads in torsion, and thus generates an equal and opposite torque. Caster and camber also need to be modeled correctly for their self-centering torques. I really have no idea whether I'm being helpful here, or just condescending. I MEAN to be helpful. Honest. Yours, Kevin F. Gavitt

"> > Fine for a simple tire, but not quite true for real ones! In a tire the > "block of rubber" in the print is constantly changing, the tread rubberand > the carcass structure all deform, etc. As I said before, nothing issimple > about tires! > > > Can you pick up a copy of Skip Barber's Going Faster? It's available offthe

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> > Nice book, except that the plots of tire data are wrong -- after the > peak, they show a drop off in force...and this doesn't happen. After > the peak, the sideforce stays pretty constant, out to 90 deg slip angle. > The fact that the force "stops increasing" with additional slip angle is > enough to cause the driver to "lose it". > > -- Doug > Douglas Milliken <[email hidden]> > Milliken Research Associates Inc. >

Doug, I know, I know. I'm getting extremely simple here. In my defense I can only say that I was trying to get down to as low a level as possible for the clarity of analogy. I was also concerned that this would devolve into a hard core thread, which I'm not sure is appropriate here, and last, but definately not least, I knew YOU were reading this thread. I'm a chassis man. I bless the Lord everyday for people such as yourself. Tire men are the wizards of archane knowledge as far as I'm concerned. To me trying to understand, let alone describe, the actual dynamic properties of a tire are like trying to work a three body problem on an old crank arm adding machine.

Doug Milliken wrote ... > > A couple of random comments.... > > On Mon, 22 May 2000, Kevin Gavitt wrote: > .....<snip> > > > Can you pick up a copy of Skip Barber's Going Faster? It's available offthe > > Nice book, except that the plots of tire data are wrong -- after the > peak, they show a drop off in force...and this doesn't happen. After > the peak, the sideforce stays pretty constant, out to 90 deg slip angle. > The fact that the force "stops increasing" with additional slip angle is > enough to cause the driver to "lose it". But is it true that the friction coefficient (cf) reduces/increases with changing load (weight transfer). I've read that cf reaches a peak at optimum load and is lower at higher/lower loads. For something as dynamic as a vehicle; can load and slip angle be separated? > > As for the car in your model not wanting to return to a straight line,have > > you modeled all the self-centering torques? A tire is a spring. When it > > moves at a slip angle it loads in torsion, and thus generates an equaland > > opposite torque. > > ??? Are you talking about tire self-aligning torque (or pneumatic trail)? I'm biting. What are you talking about here? Tony

Sorry for all this off-topic chatter. Thanks for the update on Amazon UK -- seems like they must have put in a stock to ship it so quickly. -- Doug On Mon, 22 May 2000, Richard Walker wrote:

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> FWIW I use the UK branch of Amazon & have never had a problem with them. I > ordered your book from them on 30th Dec & it was shipped on 4th Jan - not > bad considering that due to the millennium celebrations this was the next > working day. Maybe amazon.co.uk has a different approach to their parent > company? > PS: Thanks for writing such a fascinating book!

pps. Always nice to hear this!

On Mon, 22 May 2000, Kevin Gavitt wrote: > Tire men are the wizards of archane knowledge as far as I'm concerned. Agreed. Just went to an SAE technical conference and one evening we had dinner with several tire engineers and modelers. It was a good dinner but I barely noticed the food... When I get an opportunity like this, I always listen hard, because there are so many details involved in understanding tires. -- Doug

On Tue, 23 May 2000, Tony Lake wrote: > But is it true that the friction coefficient (cf) reduces/increases with > changing load (weight transfer). I've read that cf reaches a peak at optimum > load and is lower at higher/lower loads. For something as dynamic as a > vehicle; can load and slip angle be separated? If one could test at "constant conditions", then I think there is a good chance that the friction _coefficient_ will decrease with increase in load. Of course, in reality, things are always changing when a tire is tested, I leave it to your imagination to figure out some of the other variables that change..... Tire performance is certainly a function of all the operating variables, including load and slip angle (and many other things too). Easy to say, very hard to actually measure and characterize. > > ??? Are you talking about tire self-aligning torque (or pneumatic trail)? > > I'm biting. What are you talking about here? Basic property of a rolling tire -- it tries to align with its direction of travel. The effect is nonlinear and of course it goes away at/above the limit, when the tire print is fully sliding across the road. Pics and diagrams are in chapter 2 of our book<shameless plug!>. -- Doug Douglas Milliken <[email hidden]> Milliken Research Associates Inc.

And the absolute best of drivers can hold the car right on the point of not quite losing it by sensing the the reduction in pnuematic trail. Frequently refered to as the point where the steering "goes all funny." Now if only the FF in GPL would realisticly model this.....

"Kevin Gavitt" <[email hidden]> wrote in message news:nKAW4.895$[email hidden]... > And the absolute best of drivers can hold the car right on the point ofnot > quite losing it by sensing the the reduction in pnuematic trail. > > Frequently refered to as the point where the steering "goes all funny." > > Now if only the FF in GPL would realisticly model this..... >Oops, I've been infected by JTW's wrong posting virus. This was, of course, intended to go to Tony Lake's thread.

"JTW62074" <[email hidden]> wrote in message news:[email hidden]... > Cris, > Drum roll please..... Ta da!! Perfect answer! Thanks. That's exactlywhat > I'm looking for: Behavior when the tire is NOT anywhere near the traction > limit. Seems I read in "How to Make Your Car Handle" (think that was thename) > that even at a small slip angle (nowhere near the traction limit), thatadding > a longitudinal force would lessen the lateral force, but I don't recallfor > sure. I tried the car model this way and it drove pretty neat, until youtried > to straighten out.... You just couldn't do it, even with only a tinyamount of > throttle/brake. Doing it the other way (only limiting the sideforce whenthe > combined vector sum blah blah reached the traction limit) worked muchbetter. > Hopefully that's correct. > Thanks, > Todd Wasson Ah! No, no. I believe that if you could find your copy of How to Make Your Car Handle you would find that it would say that if you add longitudinal load it will reduce the force AVAILABLE to generate lateral load. Therefore, again, if we are well below the limit mild braking or acceleration won't have any effect on the arc taken by the car. I still get the feeling, and perhaps I'm wrong, that you've got some fuzzy ideas about slip angle and forces generated. Slip angle is part of the mechanical means by which a tire can generate a force. This isn't at all the same thing as saying that a particular slip angle generates a particular force. Since the cf is dependant on slip angle, slip angle imposes a MAXIMUM force that the tire can generate. It can split up that force in any combination of vectors it "likes," but as long as the tire stays within the confines of its limit it will basically keep on doing whatever it was doing. Again, this is very simplified but well within the parameters of our discussion. If you are modeling a car in a turn it's very important to remember that what you are dealing with here is a problem in ballistics. The car is a freely moving body moving along an arc in a plane. At any given arc and speed the loads are given. Period. So, we have two drivers going around a skidpad at the limit. One is Gilles Villineuve, all crossed up, the other is Alain Prost tracking like he's on rails. Very different slip angles on these two cars, but they're both following the same arc and the cars both experience the same load, slip angles be damned. Slip angles are engineer and driver adjustable. Now, if they both track around this circle at .2 g the tires have unused capacity, regardless of the slip angles. This unused capacity can be used to accelerate or brake. The tire generates ADDITIONAL forces, up to the limit, to deal with the added loads. I know I'm repeating myself ad naseum, but I don't know which idea or combination of ideas is going to "click" for you, so I'm just throwing all the speghetti against the wall here.

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>Subject: Re: GPL handling question--Physics model >From: "Kevin Gavitt" [email hidden] >Date: 5/22/00 7:17 AM US Mountain Standard Time >Message-id: <5kbW4.12333$%[email hidden]> > >Ok, I'm sorry if I've underestimated your physics knowledge. I've only your >questions here to go on, and I guess I'm not understanding you properly. I'm >afraid I still don't get the feeling from your questions what you're driving >at. > >Let's take a super simplified lab example. A large block of rubber sitting >on the concrete lab floor. Let's say it will take 200 lbs. of force to >overcome it's cf and start it sliding across the floor. > >What happens when you push it with 50 lbs. of force? >( I'm using 50 lbs. because it is .25 of 200, and the .2 g you use as an >example is .25 of the cornering force a decent road car can generate.) > >Well, it pushes back with 50 lbs. of force and other than that just sits >there. >Push it with 100 lbs. of force and it pushes back with 100 lbs. of force and >continues to just sit there. > >Push it with 201 lbs. of force and it will accelerate under 1 lb. of force >by sliding across the lab floor. > >A simplfied tire does the same thing. If you only load it to .25 of it's >force generating capacity it has a reserve capacity. Load it to .2 g at a >real force of 200 lbs. and it is still capable of generating 600 lbs. >additional force. Accelerate the car to .4 g and the tire responds by simply >generating the additional force neccessary to balance the load and the car >remains on the same arc. You can continue this right up to the limit, which >is *defined* as the point where the arc of the car must widen to balance the >force in accordance with the rules of circular motion. By definition if you >are below the limit the car will follow the same arc whether you increase or >decrease speed as long as the car stays below the limit. This is essentially >the same way banked turns work, and why at a particular speed a car can hold >it's wheels straight and follow a curved path with 0 side loading, using >gravity to supply a centripital force rather than the tires. Correct? What >about this don't you understand? > >You can go out test this on your own street car, can't you? .2 g is well >below a speed likely to gain the interest of the authorities on turns you >can find around any city. > >You understand all this? So perhaps you can see my quandry at your question. >I'm using a very simplified model here that dosn't take the fact that the >capacity of a tire to generate force is variable with the slip angle. At .2 >g this is irrelevant to the driver because of the huge reserve capacity of >the tire. It's only the small window around the limit that things get >interesting, where the reserve capacity of the tire is small and may >actually disappear. Are you being confused about the idea of slip angle and >what it does and what it is? Am I being confused about what you are and are >not confused about? > >The next issue is your specific question about the reaction of GPL. > >GPL does not use a simple single tire in the lab model. It uses a model of 4 >tires attached to a semi-rigid body. It resolves the vector sum of those >forces. How can the behaviour of such a model be used to deduce a >hypothetical simplified single tire model? Isn't that rather like trying to >deduce an Elephant's DNA sequence by looking at the elephant, rather than >the other way around? I can set up a GPL car to exhibit just about any >behaviour you want. The static loadings are user variable. Roll resistence >is user variable. Tire pressures are user variable. Damping rates are user >variable. All on each corner of the car seperately. Different chassis have >different inate properties such as roll center, weight bias, suspension >geometry, etc. Even aerodynamic properties are taken into account. > >And the arc taken by a car with 4 tires attached to it will be the vector >sum of the forces on all four tires right? Each with a different load and >perhaps even a different cf. Slip angle may even be different on all four >tires depending on suspension geometry. The degree to which the arc changes >will be the dependant on the ratio of the total slip angles of the front >tires to the total slip angles on the rear, right? A car with larger slip >angles at the rear will oversteer and one with larger slip angles at the >front will understeer, correct? And the slip angles are user settable to a >large degree, yes? > >I fail to see what you are attempting to deduce from the behaviour of GPL, >or how you feel you can deduce anything at all by it. > >I can leave you with the same answer I gave before. In GPL if you are >cornering at .2 g and increase your speed to .4 g the arc will change by not >changing at all, which is exactly what it should do, and exactly what your >street car will do. > >Can you pick up a copy of Skip Barber's Going Faster? It's available off the >shelf at at any Borders or Barnes and Nobles, as is Van Valkenburgh's Race >Car Engineering and Mechanics. I highly reccomend you suppliment the >Milliken's work with these to give you a drivers perspective on the hard >science. > >As for the car in your model not wanting to return to a straight line, have >you modeled all the self-centering torques? A tire is a spring. When it >moves at a slip angle it loads in torsion, and thus generates an equal and >opposite torque. Caster and camber also need to be modeled correctly for >their self-centering torques. > >I really have no idea whether I'm being helpful here, or just condescending. >I MEAN to be helpful. Honest. > >Yours, > > Kevin F. Gavitt > > > > > > > >

The reply to this is long. Disable "Don't show me messages longer than xxx characters" in Preferences to view. Look for "GPL handling question--Physics model Warning..Long post" Todd Wasson

Subj: Re: Missing r.a.s. post Date: 5/24/00 8:14:46 AM US Mountain Standard Time From: JTW62074 To: [email hidden] Kevin, I apologize for over reacting to your initial response to my post. I do appreciate your input. So you understand where I'm at, here's how my model basically works at this point: ---- * The car is one solid mass, completely unsprung. 1. The slip angles (all four tires are done seperately) are calculated based on the positions of the wheels in relation to the center of gravity, the vehicle's x and y velocity, rotational velocity, and steering angles. 2. When these slip angles are found, the cf is computed from a simple equation as an approximation. The equation gives a peak cf of 1.2 in the 5-9 degree slip angle area, similar to what a Nascar tire test showed. I realize that the cf changes with vertical load, camber, tire pressure, temperature, etc., at all of these slip angles, but I was keeping it simple to get the basics down and see if my approach would work as anticipated. Either way, this variable is the only part of the model that needs to be updated to allow these other factors to be taken into account. 3. There is no suspension model yet, so the static weight on each tire, plus any fore/aft weight transfer and front/rear wing downforce respectively, is multiplied by this cf to get the lateral force. Lateral weight transfer is not included, as there is no cf variance with vertical load in this model yet. Since the weight transfer happens almost instantly in this model, it drives like a car with the chassis bolted directly to the wheels and with super hard tires (wheel rate is infinite here). 4. These lateral forces are then broken into x/y and rotational components and added to wind resistance to change the x/y and rotational velocities and postions of the car. 5. Loop back to 1, calculate again for the next .005 second or whatever ---- That's basically it. As you may see here, slip angles are determined by the model from the motion of the car, rather than the other way around (your explanation of the arcs a vehicle will follow is the kind of info I needed BTW, thank you, Kevin). In step 2, throttle and brakes are used to produce a longitudinal force for each tire seperately. Your approach was one of two I had tested and it works perfectly, as far as I can tell. It follows the paths you described when changing longitudinal forces, and all other things happen as you and Doug Milliken have described so far. Step 2 also had to limit the lateral force produced by each tire. My "tire model problem" was in how to do this correctly. I thought of two methods, yours was one of them. **Method 1-Your way**- Using your method, the total available force (in any direction) at each tire is calculated, based on their maximum cf and total vertical force on each tire. Then, based on step 2 above, the lateral force at the tire is calculated (slip angle's cf times vertical force). The lateral and longitudinal forces are run through the Pythagorean Theorem to limit the lateral force if necessary, so the vector sum of the two forces will not exceed the total traction force available (as you also described). So, in essence, with this lateral force limiting method, a very small slip angle of 2 degrees producing 200 lbs of lateral force will keep producing 200 lbs of lateral force after the longitudinal force changes (unless it's enough to exceed the total traction available at that instant, in which case the lateral force gets limited, and the fun power slides begin). As you said, the car continues to follow the same arc when the longitudinal force is increased (as long as we stay inside the total traction available). Slip angle and everything else will change along with it as the vehicle's speed, weight transfer, etc., changes. This happens automatically through the other steps and is why I wanted to isolate the basic tire behavior from these factors to see if the approach was basically correct. The method just described produces the results you spoke of. There are no problems with the car refusing to straighten out with throttle or brakes on, regardless of whether the self-aligning torque model is implemented or not. **Method 2**- The other lateral force limiting method, the one that would not let the car straighten out with the throttle or brakes on even the minutest amount, was similar. Slip angle of a tire was calculated the same way, the cf was calculated, and the initial lateral force was calculated for the tire the same way. Now, I read that hitting the gas in some cars while cornering causes the car to yaw a bit more quickly (of course, my '79 Firebird didn't do this, come to think of it), and couldn't recall from How to Make Your Car Handle exactly whether or not this happened when the tires were nowhere near their traction limit. You pointed out that *** "...if you could find your copy of How to Make Your Car Handle you would find that it would say that if you add longitudinal load it will reduce the force AVAILABLE to generate lateral load." *** Then the effects on yaw rate due to throttle changes (getting on the gas to get the back end out a little more) are due to exceeding the AVAILABLE traction, and Method 2 is incorrect. I thought I had read in this book that the rear slip angles changed whenever the rear wheels were fed more torque (i.e., the lateral force was reduced by ANY amount of longitudinal force, even though the tire wasn't near the traction limit, therefore, the car yaws slightly more quickly for a moment, the slip angle increases until the old lateral force returns, it stabalizes at this new slip angle, the yaw rate slows back down a little, but the car is now following a different arc after a brief wobble.) As you described, this is against the very definition of traction limit force and must be incorrect. This also made it impossible to straighten out the car if any throttle or brakes were applied to the rear wheels. I too, thought that using self-aligning torques would solve the problem, but it did not. When all the tires produced a counter-clockwise torque in a right hand corner, the forces they produced on the center of gravity of the car more or less cancelled each other out (depending on the geometric details of the chassis and cg location). The left front tire pushed the cg forward and to the right, the front right tire pushed the cg backwards and to the right, the rear right pushed it backwards and to the left, and the rear left pushed it forwards and to the left. It does change the handling of the car slightly (not enough for me to tell from the in-car view), but had roughly zero effect on straightening the vehicle, even with nearly zero grip tires on the front end, so this wasn't the problem. So I asked the initial GPL question, "What happens in the first instant when you hit the gas in GPL when using the softest suspension settings?" By using the softest suspension settings, the weight transfer would have very little effect in the first couple of instants, as the springs would need to compress and/or the dampers would need to rise in velocity in order to plant more force on the tires (how the sprung weight's weight transfer really happens, right?). Of course, the unsprung weight would transfer more quickly, but believe I could still get an idea which lateral force limiting method GPL was using, if either, from someone's answer. If someone said the car "kind of yawed in a little, wobbled, then moved outside the turn more", or "it turned in a little tighter at first, so I had to back off the wheel for a split second until it set into the turn, then give it more steering than before to keep my line", I would suspect GPL was using something like the second method (the one that didn't let my car straighten out). If they said the car immediately started pushing towards the outside of the corner, I would suspect that weight transfer caused this, and since there was no sudden increase in yaw rate, the first method (your method) was more correct. I received one email that said " ....[In GPL] it seems that adding gas before nearing the traction limit simply pushes the car away from the corner without changing it's attitude. Letting off on the gas, however, turns it in a little. Of course, things change when you hit the traction limit." This, in combination with my assumption that GPL cars can drive straight ahead with some throttle or braking applied, unlike my model when using method 2, tells me that your method (method 1), is more correct, just from reading this description of GPL handling. What this email indicates to me is that weight transfer off the front tires and onto the rear caused it to push away from the corner. The attitude didn't change, so the rear slip angles probably didn't get a sudden boost when a small amount of throttle was applied. If the emailer had indicated a sudden wobble and subsequent push, I'd have second thoughts. This answers my question, and method 1 (that follows yours and Doug Milliken's descriptions of vehicle behavior) is now being used. Cheers, J. Todd Wasson http://PerformanceSimulations.Com

lol My wrong posting virus is contagious! Todd Wasson