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Yaw damping

Yaw damping

Yaw damping

Is this only useful in the linear range of the tire?  It is a function of cornering stiffness which is the derivative of the lat force vs slip angle curve.. which is zero at the lat force peak.  I have heard of Milliken suggesting that in some cases oversteer at high speed and not at low speed could be due to yaw damping making the car easier to control at low speeds and covering up a naturaly oversteering car.  Seems like this only applies to the linear range though and would have little effect on limit or near limit behaviour no matter what the speed is.  It also seems the variables that influence yaw damping also influence under-oversteer in most cases.  I am trying to determine if yaw damping is useful in racing especially autocrossing since it has more influence at low speed?

RE: Yaw damping

Am I way off base here? I figured someone would have something to say by now. Anyone ever look at yaw damping as a parameter to work with or tune when developing a race or road car and how so?

RE: Yaw damping

The quick answer is that if you set up a bicycle model (in say Excel) you can investigate this yourself. I have investigated yaw overshoot using a bicycle model and the results agreed with both vehcile tests and a full non linear ADAMS model.

Not being from a control background I don't know what to say about the derivative stuff. An oversteering car has less overshoot, which is what we were concerned with at the time.

However if the derivative is the source of yaw damping then you could get negative damping on the far side of the lat force curve, which sounds like a bad thing.



Greg Locock

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RE: Yaw damping

Did a quick search for yaw overshoot as I am unfamiliar with the term and came up with nothing.  Can you describe it a little further?

RE: Yaw damping

If you're referring to Milliken I'd look at the moment method chapter. We've used that approach fairly successfully to develop racing tyres and the way they separate linear range stability and control from limit plow, spin or drift (flat slide front or rear in racing speak) certainly makes sense.

I believe they did an SAE paper using the moment method with Lotus in F1 at one of the MSEC conferences.


RE: Yaw damping

From a controls standpoint, yaw damping can be easily calculated using the axle cornering stiffness derivatives. In a nutshell, the effective damping coefficient is the sum of the load normalized cornering stiffness reciprocals over their product.  Keep in mind that vehicle dynamics is NOT a 2nd order pendulum or a spring mass damper.  There is a lead term in the numerator that is proportional to input velocity. Sideslip (and of course lateral acceleration, has both a lead term and a 3rd order term in the numerator.  These terms dominate the responses of race cars.  That's why 'smooth' drivers (i.e one's who control with low steer velocity) do better than jerky ones. Jerks have high steer velocity, get it?

Back to your original question, though, if the derivatives are continuous, the damping can be calculated.  In a practical sense, the camber effects on lateral stiffness are more important that the slip effects because weight transfer still works with camber and not very much with slip changes.

Keeping the vehicle stable will also depebd on where the net rigid body aligning moment ends up.  This is a 'built in' stabilizing moment that can go away suddenly if a tire breaks loose.  Driving beyond the NET peak Mz is a lofty goal of most race chiefs but few are able to practice it.

Note also that the same yaw damping ratio can be achieved with an infinite set of cornering stiffnesses.  The best car though, is the one with the lowest denominator. As you might have figured out already, the rear axle cornering stiffness is thus the absolute most important one to manage.  

In other cases, (as in driving straight ahead), you can find vehicles with high rear stiffness and low front stiffness such that the vehicle is technically unstable at very low frequency. This causes the vehicle to hunt around zero steer at the straight ahead position.  If you put a very low steer frequency in (say 0.2 Hz), you can watch the phase lead of the car relative to the drivers' steer position input.  All it takes is a sloppy steering gear and I-shaft, and a low flow steering pump to get you into this position.  As with all things, enough money will cure all ills.  Nothing beats a good set of tires, though.  Good, fast, cheap, you can only achieve two at a time.    

RE: Yaw damping

Cibachrome- My only glean upon these equations is Milliken, so Im trying to absorb your post, but have a few questions.  I would have thought load transfer would have more effect on cornering stiffness than camber.  Is this what you were getting at?  I dont understand why the rear is more important to get right than the front either.  The equation you mentioned at the top seems to show equal importance for both.  Can you describe what driving beyond the net Mz means?  

I didn't realize I was asking a question that I was so ignorant of.

RE: Yaw damping

I guessed it meant a tendency to fishtail, but despite my interest, I am also well out of my depth in this discussion.

I was surprised by camber a real factor. I know it corrects for compliance, but did not think it impacted on it at source. Maybe I am very wrong in my reading this.

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RE: Yaw damping

Sorry for the late post. I'm a farmer now...

You stated 'racing' so my comments were mainly aimed at a max vehicle cornering scenario instead of a 'Touring' campaign such as a weekend warrior would enjoy.

At this level of handling, the vehicle domain is mainly defined by the tire's characterizing functions, not much or none left from slip/steer changes but quite a bit left from FZ and Camber (and air pressure).  Thus the load transfer generation and the camber changes in each tire both from geometry and structural reactions are still manageable.  Recall that the tire is a velocity device, so damping and other transient variables are strong players.  This includes tire transient properties.  Although the FY transient is mentioned a lot and incorrectly: its NOT a first order function) The MX and especially the MZ transient response is quite facinating.  This is because of the large change in the magnitude of the time 'delay' (keep in mind its 3rd order, not 1st order) and also because its affected by the level of FY stiffness (ie. derivative), AND because of the initial spike in the MZ function at zero distance traveled. [This is a big part of the 'feel' in 'road feel'.  Thus a vehicle can be decribed as 'tight' (understeering) because of the long settling time but is actually quote oversteering ('loose') if you wait it out.  As Terry Satchell used to (and still does) call it 'tighty-loose'.  BTW: Terry and I go WAY back to the late '70s and 80's.  These properties also produce turn out (return to straight ahead) reactions that can be quite awkward because a car set up to accept the low rigid body MZ (the sum of all 4 tires Mz's) can go berserk in closed loop control (driver in the loop) when it all kicks back in late in the maneuver.

The tire's MX reaction control point is also strongly influenced by camber, thus camber is used to optimize the MX level (low) because that's where the FY is highest. We call this a 'happy tire'.  Ever heard a driver call out that the car was rolling over on its tires?   Well, its IS ! Think of a race tire as a jelly doughnut with a rubber band around it.  When the tire is loaded and slipped and cambered, the tread moves to a balanced position.  By tread I mean the actual film surface of the tire, not necessarily the tire tread belt package. With too much camber, the tread moves away from the wheel in one direction (and off the tire).  With too little camber, the tread moves off the tire in the other direction.  A good oval racing strategy is to use this 'feature' of the tire tread to put the tread back in place during straightaway action.  Then the tread can come outward during cornering.  BTW, where do you think the marbles come from?  That's also why you see them turning to the right when going straight.

Now, back to the original question on damping.  The front and rear axle sideslip derivatives, (Bundorf and Leffert's Cornering Compliances) affect the steady state as well as dynamic portions of race car control as well as a limosine's control. (Did I mention that I used to work for both Tom Bundorf and Ron Leffert?) The difference in the front and rear cornering compliances (viewed as positive scalar quantities) is the vehicle control gain. You could call it understeer or oversteer) and the sum divided by the product is the 'damping ratio' of system (remember its not a second order system though).

So, you can study analytically the nonlinear system responses of various vehicles at all levels of maneuvering severity, including racing where some of these derivatives are very small or maybe even negative.  For cars with the same understeer yet different cornering compliances, the control gain is the same, but the response time and overshoot are very different.  Also, for cars with a cornering compliance recipe with the same damping level, the gains and natural frequencies are very different. It doesn't take very long to establish the need to set the rear cornering compliance at a low level in order to have moderate and positve control gain (goes to the right when you turn to the right) and fast response (high natural frequency) with low overshoot in the yaw and sideslip variables. 'Understeer' raises the natural frequency of the car, which is good.  Too much is bad, though. With a bad rear, you can fix the gain by adding more to the front and screw up the dynamic response as well as reducing the max lateral capability.  Also with a bad rear, you can produce a nice steering feel presense but have a vehicle that is unstable to drive without excessive driver involvment (they eventually wear out).  You say that this seems simple?  The problem is then getting a set of tires that have these high cornering stiffnesses, great transient responses (vs. distance remember?) and live for more than a few laps.

SO starting with the rear and adding front axle factors (including nonlinear steering system compliance), some traction influences and some appropriate tie rod loads with a great set of tires set to the best pressures gives you the best car on any given day in my book.  A good driver can make any good car perform at the expense of exhaustion.  A Great driver knows how to differentiate which end of the car needs to be fixed and when the best car needs to arrive from this fix at the desired lap.


RE: Yaw damping

Can you describe what you mean by "initial spike in the Mz function at zero distance traveled"?

RE: Yaw damping

Just about all math models of the MZ function are based on some proportional constant times the FY function (pneumatic trail theory). This assumption is a very poor one and easily shown to be just plain wrong.

A 'perfectly ideal' tire responding to a step steer input has zero lateral force initially.  However the aligning moment (MZ) has a very much finite value because of the F/A carcass stiffness. As the tire rolls out further distance, this initial MZ value rolls out to a minimum and then settles to a finite value that is usually some fraction of the initial value (like 1/2 to 1/4).  You may have heard about 'relaxation length'.  That's a small part of this expression, too.  It is relatively easy to measure this phenomenon using a tire test machine, especially a low speed machine.  Clever readers may figure out how exactly this is accomplished, but it is NOT a time based procedure, so punching in an approximate step input to a moving tire on a belt just ain't gonna make it happen.

Those of you involved with the never ending search for 'road feel' will find a great amount of satisfaction in discovering the magnitude, phase and response shape of this function especially relative to the FY function.  In fact, the normalized difference between these functions is the key to having a car with GREAT road feel and one without.  Now can you guess why they say it feels like its 'riding on rails'?  That's because this analogy fits into a tire's characterizing functions just like those of a flanged wheel on a railroad car or trolley.

I doubt if any tire manufacturers are able at the present time to design for these two functions for optimum performance (using FEA), but clearly there are tires being made for cars such as one with 3 letters and starts with a B that have been screened by professional company evaluators to produce great results.  And, it's not size, aspect or pressure conditions that produce it.  It is affected by them, but a bigger, wider, stiffer tire is probably not going to produce much better road feel by this recipe.  Clearly some brands are better than others and the same size and construction made on different continents (proprietary plant machinery differences) of the same brand are usually found to be very different. Keep those OEM tires on your Bxx and you know how to tell an OEM tire form an aftermarket one, right??  Even the dealers aren't much aware of this issue.

So, that's the MZ spike deal. But its more complicated because you simultaneously have to demand a corresponding response from FY.

You may now get the BIG picture on how to design a road or simulation test for road feel in which you are trying to excite this response and measure it with enough confidence to compare steering systems, ball joints, tires, and rear suspension involvement.

See you at the EXPO in Novi !

RE: Yaw damping

Cobb I presume?

RE: Yaw damping

Your comments about road feel are interesting.  Please correct any misunderstanding if you see any.  In the past I have looked at steering geometry of some cars with great road feel like the nsx and the old elan's, and no obvious scrub offset or trail or castor/kingpin inc. etc was ever tied to it.  Neither were the tire sizes, the elan had ancient 80 profile skinnies (Three were offered I believe and they likely never had much data on them or any sort of tire model, probably just empirical testing), the nsx had 50 profile a good bit wider and the ferrari f40 had low profile and wide tires.  People seem to try different tire sizes and offsets with out destroying road feel through the wheel (not that it didnt change some maybe) so its not like thats the end all.  Seems like relaxation length comes into play I thought, but when you said that was only a piece and it has to do with how the Mz function aligns with the Fy, and its relative significance to steering torque in relation to each other at what point (thats what I took normalized difference between Mz and Fy functions to mean, was that right?) it made me think that steering feel is something that cannot be readily seen in obvious specifications like I was hoping.  No magical recipe so to speak.

 I mean the elan has some of the greatest steering feel of all time, but its steering components were dug out of the triumph parts bin.  Im wondering if that feel was happened upon rather than intentionally designed in, and Im not saying Colin didn't know what he was doing but the car was penned in about 1960 when vehicle dynamics were less understood so I have my doubts.  

  I've learned a great deal in trying to understand your responses, but Im still having trouble understanding how it all relates.  Still seems like geometric offsets should be the greatest factor especially at mid corner to road feel.  

RE: Yaw damping

No magical recipe so to speak

- yes that,s about it. First of all you have to quantify what you mean by great steering feel, then you can attempt to establish good and bad values for each parämeter, and how they interlink. Then you need to accept that a bad set of tires can modify the steering out of all recognition, subjectively and objectively.



Greg Locock

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