Engineers: I've got a 'slip angle' question

[Jack Olsen]

And it's very simple -- for you.

I understand that a tire carcass twists when it gets hit by all the forces that a tire is subject to in the course of a high speed corner. And I understand that the orientation of the contact patch ends up being slightly different from the orientation of the wheel -- that the tread lines in the contact patch are no longer actually parallel to the centerline of the rim, and that the angle between those two is the slip angle.

I know that there is an optimal slip angle for a given tire and a given piece of pavement under a given set of circumstances where that tire's traction is going to be at its best. And I know that when the tire exceeds that optimal slip angle, traction decreases.

I understand all of that, pretty much.

Except this part: why?

Is it simply that there's an ideal angle between direction of travel and the direction the tire contact patch is headed in (for a given set of circumstances, force-wise), and the twist of the tire and the angle of the wheel itself are both incidental aspects of getting the contact patch to that point? And what exactly it is about the tire (I imagine the rubber's coefficient of friction and the track's coefficient of friction and the forces exerted on the tire are all part of this) that its capacity to grip somehow increases under some sets of circumstances in a way that is more complicated than simply a lot of coefficients of friction and complicated rotating, lateral and thrusting forces?

Can somebody explain it to me like they might to a third grader?

It's been decades since I saw a physics textbook, and I majored in Philosophy. (I swear, it seemed like a good idea at the time.)

[rusnak]

From Wikipedia: (consider the source: i.e. may not be accurate)

"In car handling, slip angle is the angle between a rolling wheel's actual direction of travel and the direction towards which it is pointing (i.e., the angle of the vector sum of wheel translational velocity v and sideslip velocity u). This slip angle results in a force perpendicular to the wheel's direction of travel -- the cornering force. This cornering force increases approximately linearly for the first few degrees of slip angle, then increases non-linearly to a maximum before beginning to decrease. (This is directly analogous to the Coefficient of lift in Aerodynamics.)

A non-zero slip angle arises because of deformation in the tire carcass and tread. As the tire rotates, the friction between the contact patch and the road result in individual tread 'elements' (infinitely small sections of tread) remaining stationary with respect to the road. If a side-slip velocity u is introduced, the contact patch will be deformed. As a tread element enters the contact patch the friction between road and tire means that the tread element remains stationary, yet the tire continues to move laterally. This means that the tread element will be ‘deflected’ sideways. In reality it is the tire/wheel that is being deflected away from the stationary tread element, but convention is for the co-ordinate system to be fixed around the wheel mid-plane.

As the tread element moves through the contact patch it will be deflected further from the wheel mid-plane:



This deflection gives rise to the slip angle, and to the cornering force.

Because the forces exerted on the wheels by the weight of the vehicle are not distributed equally, the slip angles of each tire will be different. The ratios between the slip angles will determine the vehicle's behavior in a given turn. If the ratio of front to rear slip angles is greater than 1:1, the vehicle will tend to understeer, while a ratio of less than 1:1 will produce oversteer. Actual instantaneous slip angles depend on many factors, including the condition of the road surface, but a vehicle's suspension can be designed to promote specific dynamic characteristics. A principal means of adjusting developed slip angles is to alter the relative roll couple (the rate at which weight transfers from the inside to the outside wheel in a turn) front to rear by varying the relative amount of front and rear lateral load transfer. This can be achieved by modifying the height of the Roll centers, or by adjusting roll stiffness, either through suspension changes or the addition of an anti-roll bar.

Retrieved from "http://en.wikipedia.org/wiki/Slip_angle"

Jack:
There is a really great primer titled "How to make your car handle" by Fred Puhn. I'll look this up and post the pics if this question remains unanswered.

[don911]

My speed secrets book defines slip angle as the angle between steering angle and direction of travel. Your description sounds like angle of the tire tread in relationship to the wheel?

Speeds secrets also states that "primarily due to elasticity of rubber, tires have to slip a certain amount to achieve maximum traction".

I'm not sure this was your question but best I can do.

[Jeff Hail]

At any moment in time a car turning a corner is accelerating toward the center of an instantaneous circular arc. The radius of that arc might be changing, but at any instant the path is a specific arc. The car's tires supply the force to turn the car. That force is called lateral force or side force or just grip.

Slip Angle
A tire produces lateral force with a slip angle. Slip angle happens when the steering wheel is turned from straight ahead and it's the angle, "a" in the schematic, between where the tire is pointed and where the car is actually going.

The elastic nature of a tire makes a slip angle possible. The tire grips the road but also yields to external force, resists movement with an opposing force, and recovers when the external force is removed. This elastic characteristic of a tire allows the tire to be pointed in a direction different from the direction the car is headed.

It's important that we understand what's going on in the contact patch between road and tire that creates a slip angle. The tire is rolling, so any one point on the tread rotates into and out of the contact patch with every revolution. When the tire is rolling in a straight line that point on the tread sees a regularly repeating thump of vertical force as it rotates into the contact patch and momentarily bears this tire's share of the vehicle weight.

As soon as the driver turns the steering wheel, conditions change at the contact patch. Steering input causes the tire to turn, and now the leading edge of the tread rotates on to the road slightly to one side of the rest of the contact patch. As the tire rolls, each small increment of tread rubber coming onto the road sits down another small distance toward the direction the tire is pointed.

As the car's weight comes onto these small increments, they stick to the road. The tread is now pulling the rest of the tire and generating forces that go through the wheel and the suspension to turn the car. The force needed to change the car's path is generated by the tire. This is called lateral force or side force.

We can use the analogy of a person walking to further explain slip angle. A person walking on a circular path changes direction in small increments. At each step a foot is turned in a small angle toward the path of the arc. The heel contacts the ground and the rest of the shoe comes down in this new direction. As weight comes onto the shoe sole, the shoe is pointed in the new direction. The next step also changes the walker's path a small amount. These small changes continue to build up and the direction the walker is headed changes also.

That's exactly what happens when a tire is given some steering input. Each small increment of tread rubber rotating into contact with the road surface latches onto the road surface a small increment toward a new heading. As long as the steering input remains the same, each increment of the tread contacts the road the same amount toward the new direction. The rest of the contact patch thinks it's headed in the old direction, but the old contact patch continually rotates out of road contact. The next time that part of the tire touches down, the heading of the tire and car will have changed.

The tire tread actually deforms as it rotates through the contact patch area and then recovers as the car's weight comes off the contact patch. The force needed to deform the tire is what produces the lateral force needed to change the path of the car.

When the front tires respond to steering input with a slip angle and begin to develop lateral forces, the front of the car turns to a new heading and the entire car rotates in yaw. If the rear wheels were mounted like casters they would swivel and the rear of the car would spin outward, away from the turn. But the rear tires are fixed in direction and they resist yawing with their own slip angles and lateral forces.

Lateral Force vs. Slip Angle
The general relationship between the lateral force a tire generates and the slip angle of the tire. A tire does not generate side force until it is steered away from its current course and it assumes a slip angle. The shape of this curve is not the same for all tires. A graph like this is a specific characteristic of a tire design-the result of the cord angles and rubbers used in the tire structure and the rubber compounds in the tire tread.

Notice that this curve has three distinct shapes. First there's an almost straight section at small slip angles where an increase in slip angle gives a proportional increase in lateral force. The slope of this section of the curve is the "stiffness" of the tire. In this region of the curve the tread is not sliding on the road at any point in its contact patch. A tire designed to have more stiffness in the tread and sidewalls will have a steeper slope in this area of the curve.

At higher slip angles portions of the tire patch are sliding, and you get less increase in lateral force with an increase of slip angle. This is called the transition region. As the curve tops out, more of the contact patch is sliding and the tire produces less lateral force. After the peak of the curve, lateral force can fall off 30% within a few degrees of extra slip angle. At these high slip angles most of the contact patch is sliding, producing a lot of heat and wear.


Longitudinal Forces
The forces on a tire during acceleration and braking deform the sidewall enough that the contact patch moves a noticeable amount.

During braking and acceleration tires generate longitudinal force, and there is some longitudinal slip between the tread and the road. This shows up as a difference between the actual rotation of the tire and the rotation needed if there were no slip. Under hard acceleration the tire turns a little faster, and during hard braking the tire rotates less than it would if there were no slip.

As soon as driving slip approaches 50%, driving force falls off rapidly. Braking slip falls off at only 25% slip, but the force reduction is more gradual. I don't know the source of the data for these graphs but they might look more alike if the percent-slip scale were the same.

Another possibility is that the driving-force curve drops off and flattens out because the tire is still spinning and the tread surface has a chance to cool, where the braking tire is locked at 100% slip and slides on the same contact patch. This heats up the rubber, lowering its friction capability. I'll bet the braking curve continues to fall off after 100% slip, off the scale of this graph.


Combined Forces
Data showing tire behavior under a combination of both lateral and longitudinal slip is almost nonexistent outside of the tire companies' test facilities. The main point made is that lateral force falls off rapidly with any additional slip due to acceleration or braking.

Friction Circle
When the tire sees a combination of forces, driving force and lateral force are shown here, maximum lateral force is not available. In this example, adding driving power to the tire reduces the available lateral force. Of course this is what we feel powering out of a slow corner-power oversteer-one of the most fun things you can do with a car.

Lateral Deformation of the Tread
It bears repeating that it is the elastic characteristic of the pneumatic tire that allows the generation of a slip angle, and it is the forces resisting the deformation of the tire structure combined with the tread's grip on the road that allows a car to turn a corner at speed.

The curved solid red line represents tire lateral deformation from its unstressed position. Once again, it is the tire's resistance to this deflection that creates the lateral force that turns the car. The curved line tracks the lateral deformation of a single point on the surface of the tread rubber as it travels through the contact patch and is deformed by the road acting on the tire. The solid line with a left-pointing arrow is the zero-deflection line. The difference between those two lines is the distance the tire deflects.

The tread rotates into the contact patch at point A, and the lateral deflection at point A is called the initial deflection. Point A marks the leading edge of the contact patch, but deflection starts prior to that. The tire carcass has some stiffness and the tread is even more stiff, so there has to be some deflection starting well before the tire rotates into the contact patch.

From point A to point B, somewhere near the midline of the contact patch, the tread stays stuck to the road (at this slip angle anyway) and lateral deflection in the carcass and in the tread rubber increases linearly. But at some point the force required to deflect the tread exceeds the local friction coefficient times the local load, and the tread begins to slide on the road. At higher slip angles sliding starts farther forward.

At point B the tread begins to recover from maximum lateral deflection and at point C the tread rotates out of the contact patch. Notice that there is still some lateral deflection at C. The tire has to rotate farther before the lateral deflection fully recovers. Once again it is the remarkably strong but elastic nature of a tire that enables it to deform, assume a slip angle, and generate turning forces.

Film at 11:00

[Bill Verburg]

All "things" deform when subject to a force.

In this case there is a couple, the force between the rolling friction of the tire and the road going one way and the force between the tire and the inertial force of the car going in the opposite direction. This twists or deforms all of the suspension pieces and the chassis and the wheel and the tire. The force of the road on the tire is greatest before the point at which the tires ultimate "twist" is reached at which point it transforms to sliding friction which is less than rolling friction. It doesn't happen all at once for every point of the contact patch so there is a window right on the edge where there is a combination of normal rolling and less effective sliding friction. A street tire will generally have a wider window where this happens than a race tire. But there are other variables involved such as the summation of the deflections in the other parts of the suspension and chassis. It all has to work together to most effectively translate inertial energy into heat energy.

The lower the slip angle a given tire runs at, the more efficient it is at resisting lateral forces

Lower pofile tires run at lower slip angles than higher and so more efficiently trasform inertial energy to rotate the car. 235/40 will be more efficient and have less twist or slip angle than a 235/50.

[Early_S_Man]

Jack,

The pic [the Wing] you posted served to remind me that the maximum cornering force that a tire can generate for a given slip angle is also a variable ... dependent on the vertical downforce or loading of the tire.

That very topic was much on the minds of F1 and Can-Am car designers Colin Chapman and Bruce McLaren in 1968 - 69 with hub-mounted wing struts ... the era of aero-wing wars vs the sanctioning bodies!

[porsche735]

I describe it to my students very simply. Like the 3rd grader description you are looking for.
Take your hands and rub them back and forth together like you are trying to make them warm. This is the same as the friction of the tire over the surface with no slip angle.
Now put your hands together and while keeping pressure twist them at about 20 degrees. Now try to move them back and forth while pressing the same as you did before with the 20 degree angle.
That is what slip angle does....

Chris

[Grady Clay]

There is a lot to this.

I like to describe driving in this range in serendipity terms. It is a “feel”. Good ‘ol ‘60s.

Driving in this realm is transitional – you are watching yourself as above in a spiritual sense. Yes, part of you is operating the car. Another part is watching what you are doing. The combination is how you actually operate the car.

Driving at the limit of traction is an art and skill. It is like dancing, flying and many other. A great deal is your ability to recognize where you are, relative to some limit. Every racer exceeds the limit. The issue is to recognize when (future tense) you are going to exceed the limit before it happens. The “art” is to recover before anyone realizes you are over the limit. That may slow you somewhat. The “skill” is where no one notices.

Fast laps are when all above are achieved simultaneously.

My fastest laps were surreal experiences in addition to deliberate racing. I remember watching from above.

Best,
Grady

[911pcars]

Third grade answer:

"The tire sticks better"

Sherwood
(from a third grade mind)

[randywebb]

Jack - does the above make sense?
You were right with your very first sentence - it is the forces.

I can add one thing - you can break any force down into components. Imagine an arrow drawn for the force on the car -- it points in the direction the force pushes, and the length is the amount of force. To analyze it, we break it down into 2 arrows: one points in X direction and one points in the Y direction -- when we add them together, the result is the original force 'arrow.'

If you draw the arrows for the force on your car that might help. Then add the twist/distortion that Bill noted. It will be nil for the steel car, but fairly large for the tire; and moderate for the rubber bushings in the suspension.

[rick-l]

I wish I could find (Dr.?) Steve Timmons course notes (Power Point slides, XL spreadsheets) for the ME class he taught at some college in the east. It answers all these questions.

I read through them once and saved the links thinking I could go back later.

The links but they are dead. I think the course was called automotive suspension and handling or something like that.

Does anyone know where to get hold of them.

[JohnKo]

Originally posted by Grady Clay
Driving at the limit of traction is an art and skill. It is like dancing, flying and many other. A great deal is your ability to recognize where you are, relative to some limit.

Just couldn't resist chiming in... This reminded me of a very illuminating lap w/Hurley Haywood around a racetrack in a dead-stock C4. He was probably at about 7/10ths, but constantly correcting his line in some faster corners, and I was saying to myself (after years of wheel-to-wheel 'racing'), "ah, so that's what it's all about!"

[island911]

Originally posted by Jack Olsen
. .. .
I understand all of that, pretty much.

Except this part: why?
. . .

Why, What!?

I can't figure out what part of the scenario you don't understand.

Perhaps somebody explain the question to me like they might to a third grader.


. . .if the question is actually; "is this a cool pic of my BBII, or what?" --then I need no further explaination.

[Eagledriver]

Jack,

I think you are looking at the question backwards. If you asked: Why does the slip angle increase as the cornering force increases you'd see the obvious answer.

Eventually the slip angle of the tread stops increasing and further increase in cornering becomes impossible. This limit is primarily based on the coefficient of friction between the track and the tread. The slip angle can continue to grow but only by the amount the tire slides not by the angle of the tread.

Make sence?

-Andy

[oldE]

Jack,

Aside from the misunderstanding in your first paragraph, which was corrected by Rusnak, the only thing I can add is the nature of rubber changes as force is applied/transferred through it. You see this under acceleration and braking. There is a level at which the energy transferrence is optimal, then the level is exceeded, (wheelspin under acceleration, lock-up under braking).
As you turn the wheel to change the orientation of the front wheels relative to the direction of travel, the side loads imparted deflect the vehicle from its course. There is always some slip angle, even when it feels like the car is "on rails". You just don't detect it until it reaches a certain level. Where you detect it is , I suspect, in the range where the energy the tire is able to handle is exceeded and the slip angle suddenly increases.

Les

[Jack Olsen]

Thanks, everybody. I can't claim to understand everything written here, but I'm still learning something. It seems like there isn't anything magical happening when the tire carcass is twisting. The rubber compound still has a certain coefficient of friction, and the car/suspension/wheel/sidewalls are all working to push it one way while the track surface is resisting that.

What I'm learning new here is that the amount of grip at the contact patch isn't a constant for all parts of the contact patch -- that some parts will be maximizing their grip as other parts are losing it -- and that there's an optimal point where the benefits from the good gripping parts exceeds the trade-off of the parts that are now doing more sliding than gripping.

I guess another way to look at my question would be this: Let's say it was possible to find a hypothetical substance that had the same coefficient of friction as a tire's rubber compound, but which had none of the elasticity of a tire's rubber compound. If you filled a tire made with that compound with some light-as-air concrete (in other words, eliminating flex from the air pressure inside the tire) and somehow managed to get that tire to form a contact patch that mated to the flat surface of the track (but then instantly lost its elasticity), would the capability of that tire be the same as the kind of real-world tire we're talking about? I know it's not possible, since a tire has to deform in order to flatten out where it meets the road, and that means it has to have some ability to deform. But if you could create a hypotethical non-elastic rubber that still was able to do that one trick, would there be any benefit to the standard model where the tire deforms as much as it does?

[island911]

for a third-grade level, it's enough to not commingle (in your mind) the "slip"(of slip angle) with "slide"(of static vs dynamic friction.)

Beyond that you're talking about a lot of visco-elastic dynamics . . as a whole lot of non-linear transitions happen. --that is not going to be explained at a 3rd grade level.

[randywebb]

"taught at some college in the east."

try U. Del. -- a search might find a web site for him with the presentation on it...

[randywebb]

Jack - I'd have to say no, as the 'twist' in the carcass usually will allow the tire to stay planted a little longer.

But that would be an equilibrium or steady-state guess... my bet is that such a 'rigid' tire might also breakaway very abruptly so that it would be less controllable, and hence not as capable in that sense.

[Grady Clay]

Guys,

As much as the engineer in me wants to respond in engineering terms, I’m going to stay in the ethereal quadrant. Very non-linear.

I am surprised no one discusses their experience racing and driving at the limit as I have.

Most of the time I am the quintessential analytical engineer. I use diagrams and formulas regularly. I can read my son’s data download just fine. I measure tire temperature patterns and tweek the tire alignment at every opportunity.

There is more to the driving experience than engineering. Sure, part of me is constantly re-engineering the car while driving. Mostly that is analyzing the tire grip (or lack) and how to get the most from what you have. There is another part I tried to describe above. It is a mental state. I find it very similar to skiing at the limit – not contacting the snow much. When you have grip, use it. Stand back and watch yourself do it.

As founder of the RMR “Grady Clay School of Sideways Driving” I have worked backwards to push. Forty years ago I liked a loose car and a SWB 911 fit the bill. Today I prefer a 993 and later with push. I fight to make it loose at the limit. Great fun there.


Race cars are a different beast. You can tune the balance to maximize grip. Even when there, the “art” is to drive around some ideal point. At my lame old age, working from push to aggressive driving loose is safer (faster) than dancing a loose car.

In the next 18 months I’ll get my son’s 914-6 GT2 race car up to speed. That car dances around the ultimate grip (or lack) the tires will allow. My goal is to lower the CG and build in some high speed push (well … at least lack of oversteer). This is not so much as it is faster, I can drive a loose car just fine. Chris’ experience is shifter karts, Spec Miata and Formula Mazda – all pushers at heart.


I totally agree with the non-linear aspect of “grip.” If Goodyear or Michelin could perfect this they would rule. In fact this is an issue not well defined. Yes, we can write equations, define slip angles and traction vs. temperature. In the end it is very personal “grip” just like a ski. Some are better than others and a knowledgeable user wins.


Jack, to answer your specific question, I think it is adding temperature to the equation. Slip = gain in temperature of the tire surface. Some rubber compounds gain grip with increasing temperature. Almost all loose grip when over temperature. The tread temperature is a dynamic thing. It can vary with almost every revolution of a tire – and there are four. We all measure the (average) temperature across the tire when looking at camber, roll and caster in front.

As you have experienced, tire size, rim width, pressure, suspension geometry, alignment and specific track all effect this. So does driving style.

My point is the operator searches for the best grip point. That technique is the key to going fast.

Best,
Grady