Tire Sideslip Angle vs. Side Force

A long time ago, in a university far, far away (23 years and 2500 miles counts, right?) I learned that when you exert a side force on a
pneumatic tire as it's rolling along, it slips sideways a bit, without actually skidding (it has something to do with flexible sidewalls and where the tread goes with relation to the rim and other stuff that I can't visualize without moving my hands and staring into space and mumbling and generally alarming bystanders).
I learned this from a really neat book for automotive/mechanical engineer types, published in the 1950s -- one of those where the pages with pictures were really thin and shiny and the contrast of the black and white photos was almost surreal. It was old enough that it was mostly about bias-ply tires, but it did mention those newfangled "radial" things as an aside. Great book, but it's a long drive to Worcester MA from Oregon City.
Now I'm working for a customer who wants me to assume that the direction that a car is pointing is the direction that it's actually moving, even when it's going around a corner at a safe but still pretty good clip. I just know that the assumption isn't true, and I'm pretty sure that with normal passenger tires you're not going to make yourself into a cop attractant until the sideslip angle is a good portion of ten degrees -- but I don't know.
Anyone with direct experience? Numbers?
Anyone know any web references? Any titles that I might look under? Library of congress numbers, as a starting place for my search? I'm thinking of traipsing off to Portland State University to dig through their library, but cruddy old automobile tires aren't Green or Digital or Silicon or .com or any of the other technology fads that have swept through Oregon without leaving many jobs behind*. So I'm not sure if there'll be much there.
Thanks in advance.
* The jury is still out on Green, but color me dubious.
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Tim Wescott
Control system and signal processing consulting
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Try this: http://f1elites.com/4d/?p=54
Another guru: http://www.tonyfoale.com / He explained rake, trail and steering geometry to me very clearly.
jsw, once an ABS test engineer.
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Tim, You are correct, but because of all the variables involved, I know of no way to compute it. In a curve at any speed all tires are in a state of slip. Lateral acceleration is only one of the variables. Please keep in mind that the contact patch is not a single point and tire slip is in forward, backward and to the side depending on where your point of reference is within the tire patch. Some of this slew is absorbed by tread and sidewall flex as well. (Squirm) As Jim has responded, this fellow Tony Foale is really knowledgeable, but his books are only available from SAE. ( I just bought one) Steve

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On 06/15/2010 09:03 PM, Steve Lusardi wrote: (top posting fixed)

(drivel snipped)

(more drivel snipped)
> Tim, > You are correct, but because of all the variables involved, I know of no > way to compute it. In a curve at any speed all tires are in a state of > slip. Lateral acceleration is only one of the variables. Please keep in > mind that the contact patch is not a single point and tire slip is in > forward, backward and to the side depending on where your point of > reference is within the tire patch. Some of this slew is absorbed by > tread and sidewall flex as well. (Squirm) As Jim has responded, this > fellow Tony Foale is really knowledgeable, but his books are only > available from SAE. ( I just bought one)
One of Jim's links was to a site that showed that a rubber-band tire that had been shaved for racing (which reduces the sideslip angle before the onset of a real skid) gets up to around six degrees sideslip. Since I wrote the query I found some web references that bear out my recollection, that sideslip will get up to ten degrees or more before the car skids.
I don't want to compute it, I just want a factoid to use in a discussion -- the fact that in moderately normal driving one can have a multiple-degree difference between the car's path and pointing direction is enough for me.
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wrote:

Understeer: http://en.wikipedia.org/wiki/Understeer has a table of linear understeer values (i.e. 'normal' driving, not limit understeer) for a range of cars, which may provide the required factoids. The supporting text says "Most road cars have fairly similar ratios, typically around 1415:1" (degrees understeer per G of lateral acceleration), although this assertion is not supported by a cited source.
Understeer is not from sideslip only: there are other suspension effects such as roll understeer, lateral force compliance understeer, aligning torque compliance understeer, etc. Table C.1 of "Tires, Suspension and Handling" (Second Edition) by John C. Dixon (SAE 1996, ISBN 1-56091-831-4) gives some order-of-magnitude estimates for generic vehicle types.
The numbers in the wikipedia table are likely to come from a single overall measurement rather than an analysis or measurement of the various contributing factors.
Regards
James Cunnane
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On 6/15/2010 8:42 PM, Tim Wescott wrote:

Tread crawl is more pronounced in bias ply tires than with radials, but the effect with radials is obvious enough. I presume your car goes straight ahead on a flat road. On a crowned road, the car will try to head for the near shoulder. To make the car go straight, the wheel will have to be turned toward the center line. The car travels straight down the road, but the front wheels are steering slightly left. I'm sure you don't actually need to perform the experiment. You've experienced this already. Consult Eric Jacobson at comp.dsp. He's up on this stuff. http://www.ericjacobsen.org /
Jerry
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On 6/16/2010 12:04 AM, Jerry Avins wrote:

Correction: the rear tires will crawl sideways as well, so the car actually crabs down the road.
Jerry
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Tim Wescott wrote:

Tim, I'd bet one of the Carroll Smith "_______to Win" books would be a great starting point. Tune To Win would most likely do it. If you happen to come up with a title for the book you are remembering, I may have it on the bookshelf.
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<snip>
_From Slipping to Sliding_, by Paul Frere (Pete Albrecht's race-driving instructor). I think a new edition is in print.
You have it right. It gets complicated when you look at the relative loads on *outside* front and rear tires; it's the primary cause of oversteer and understeer, as the terms are correctly defined. There is no sliding involved in oversteer.
Front/rear weight bias is a major cause of different slip angles front and rear, but roll stiffness can completely overcome weight bias and make a car to the opposite of what you think it will do, in terms of weight bias. For example, an older Porsche 911 will understeer until it reaches the limit of adhesion, at which time it transitions to oversteer just before sliding begins.
Most ordinary cars understeer severely. In other words, they're pointed in a tighter turn than they actually achieve. There are few that oversteer before they start to slide.
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On 06/16/2010 07:43 AM, Ed Huntress wrote:

I was taught that understeer is when you go off into the pucker brush front bumper first, and oversteer is when you go off into the pucker brush rear bumper first.

I was getting impatient with all this discussion about over/understeer -- then I realized that to some extent it's what I care about more than tire slip itself. So thank you and anyone else who mentioned it.
Most ordinary cars understeer severely because most ordinary car drivers don't really know how to drive (not that I'm opinionated or anything). A disinterested and disengaged driver is less likely to get into an accident with a car with understeer than one with over- or neutral steering, so that's what you find for anything that's not seriously designed for performance.
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Tim Wescott
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a racing engineer. That's sliding.

Well, cars understeer because there is greater weight transferred to the outside front wheel than to the outside rear wheel. Whether one gets into trouble as a result of this may be a measure of how well they drive.
Mild understeer was considered desirable in the old days of low-grip tires because it could allow you to "drift" (old definition) a car at very high speed in fast turns. It also kept the racing tyros, like me, from killing themselves. My Alfa Romeo Guilietta was well-known for its mild understeer at all speeds, which is why I felt so good driving it on the track.

Uh...Ok, I guess. I would say that it's mostly because American cars have traditionally had cast-iron lumps in the front and shitty front suspension that produced too little camber change with roll. Today, it's because they're front-wheel drive and everything is up front.
Interestingly, when GM and Ralph Nader were suing each other over _Unsafe at Any Speed_, GM had Stirling Moss testify as an expert witness.
"Mr Moss, can you name any other American car that oversteers, besides the Corvair?"
"Yes," said Moss. "The AC Cobra." <g>
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On Wed, 16 Jun 2010 07:53:34 -0700, Tim Wescott wrote:

The slip angle of a tire is a function of both down force and side force on the tire; increasing with increasing side force and decreasing with increasing down force. Since the center of gravity of all cars is above the road surface, acceleration produces a moment which increases down force on the rear wheels and decreases down force on the front wheels, generally if imprecisely thought of in the racing community as "transferring weight to the rear wheels" - as braking "transfers weight to the front wheels". Acceleration thus reduces slip angle of the rear wheels and increases slip angle of the front wheels, thus pushing the car towards understeer, while braking does the opposite, changing slip behavior towards oversteer.
Most passenger cars understeer even with moderate braking (and understeer even worse with acceleration), and will tend to fail to negotiate a turn by going wide without spinning out even with the brakes applied. Formula racing cars on the other hand have nearly neutral steering at neutral throttle (constant speed), oversteer on braking (cornering fails with a spin-out while braking, as the rear tire reaches it's slip angle limit first) and understeer on acceleration (no spin while accelerating). This provides maximum speed through a corner (all else being equal) at the cost of increased probability of a spin-out.
Note also the stability issue: oversteer tightens the corner increasing cornering force while understeer does the opposite; consider the case of being at the cornering limit and letting up on the throttle while holding steering steady.
IMO the passenger car designers have made the right trade-off here, as going wide is usually less risky than spinning out. And an under- steering sports car like my ex 1960 Alfa Rojunko Guilietta Duetto was more fun to drive (toss it around hard and skid a lot without spinning) than a formula race car, which requires a very precise touch. (More precise than I managed anyhow :-).
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That's a good and very clear explanation, Glen.
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Nice description.
For us older civilians the VW Beetle oversteered enough to spin out under some conditions. They were good but a "learning experience" on ice.
jsw
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Jim Wilkins wrote:

You should have taken the National Safety Council's safe winter driving course. At Ft. Greely, AK. they did it on a sheet of ice, with water standing on top of the ice. Talk about oversteer! :(
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This is fairly easy to calculate if you have access to simulation software and some basic vehicle parameter data.
Full vehicle models like CarSim by MSC can simulate vehicle dynamics accurately, but you can get the basic effects of vehicle dynamics with a simple two-wheel model of the car known as a "bicycle model". At it's simplest this amounts to a 4th order linear matrix equation you can solve with Simulink or other such software.
Anyway you're asking, is the vehicle slip angle always zero and the answer is of course no. For example, at low speed you're in Ackerman steering where the vehicle is pointing away from the turn circle, just based on geometry. As you increase speed, the tires starting slipping and the rear end will swing out, decreasing the vehicle slip angle, but where it ends up depends on the weight distribution of the vehicle, vehicle geometry, tire chacteristics and steer angle.
But that's steady state. Dynamically, say during an evasive maneuver, the vehicle slip angle can be an oscillatory response or even go unstable, since in reality the tire cornering coefficient is not linear.
dave y.
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On 06/15/2010 07:42 PM, Tim Wescott wrote:

Before you start worrying about side slip, what about the little matter that not all parts of the car are moving in the same direction? As a crude approximation at zero slip, the front of the car is moving in the direction the front wheels are pointing, and the rear of the car is moving in the direction the rear wheels are pointing. Depending on how your customer's assumption is being used, that might or might not be significant.
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Bob Nichols AT comcast.net I am "RNichols42"

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On 6/16/2010 3:19 PM, Robert Nichols wrote:

The car is pretty much a rigid body, so its motion is fairly well described as a combination of translation and rotation. Consider the wheel: the part on the road is (with luck) stationary, another part is moving forward with twice the vehicle speed, and so on. Combining rotation and translation greatly simplifies the description.
Most of the discussion so far has been about turns. Don't transverse grades matter on real roads?
Jerry
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On 06/16/2010 01:14 PM, Jerry Avins wrote:

That would matter too, yes. I'm also not entirely sure that driving transversely to a road that is heavily dished or crowned wouldn't cause some rotation just from geometric effects.
But at the moment I don't care. I'm enough of a mathematician that if you tell me "thus and thus is so" I won't (initially) feel like I have to find 100 examples of it not being so to disprove it -- I only need one counter example to disprove a theorem. Politically I may need more, but mathematically only one is necessary. I'm worried about the math right now -- the politics will come later.
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Tim Wescott
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On 06/16/2010 12:19 PM, Robert Nichols wrote:

I've got that one covered, already. I can project all measurements back to a point directly between the rear wheels. What I can't do is assume that the tires are rigidly attached to the road in two directions, or in a car with independent rear suspension that the rear wheels maintain orientation with the car when it is heeled over.
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Tim Wescott
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