## Slip angle

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Do variables such as vertical load, tyre pressure, etc effect the slip angle of a tyre?

What changes the slip angle? How is a slip angle changed?

Regards,
Birel99

Joined: 14 Nov 2006
Location: Northern USA

Yes and no.

In a pure sense if you had the tire on a flat track and just held the wheel 3 degrees relative to the belt travel, it would be at 3 degrees slip angle regardless of what you did with load, inflation, etc.

When you're driving and following a path.. let's say at point X on your path you need 300 lbf of lateral force. At inflation P, that might take 5 degrees slip angle. If you change the inflation it will change the lateral force curve, so now it might take 6 degrees to get to 300 lbf.. so in the sense of what's required to follow the path your slip angle trace will change as well.
Grip is a four letter word.

2 is the new #1.
Jersey Tom

Joined: 29 May 2006
Location: Huntersville, NC

All right, again it's 11:30 pm and I have some time to make mistakes in my favorite site. I hope Riff_Raff, xpensive, Belatti and the rest of guys that know can (can? will! ) point out any errors I make.

I'll limit myself to speak about maximum slip angle.

Of course, slip angle is proportional to vertical load.

Besides, slip angle varies within the tyre. For example, when you brake, the force exerted by the tyre varies along its longitudinal axis. Something like that:

You can "clearly" see that the normal stress (vertical load) is not uniform (the blue line in the top graph). The shear stress is concentrated on the forward portion of the tyre (black line in the top graph).

Thus, the braking force (and the sliding of the rubber on the asphalt) is also concentrated in the frontal part of the braking tyre.

I guess it's something similar to what you feel when you "brake" with your feet. Most of the load is concentrated on your toes and almost nothing on your heels. I guess torque has something to do with it, but...

Same goes for a tyre that is exerting lateral force: the tyre twists differently along its longitudinal axis. Something like this:

Again, most of the lateral force is concentrated in the front part of the tyre's patch. Notice that the lateral force is more or less proportional to vertical load: the tyre is round (duh!) so the vertical load is not the same in the center of the patch as in the extremes of the patch.

So, the slip angle mentioned in the books is an average of the real tyre deformations. What you see are graphs like these:

The relationship among vertical load and lateral force is not a straigh line. What you see in the literature is something like this, for average slip angles:

The previous graph has three curves for three different slip angles. It shows vertical force (Fz, in the horizontal axis) vs lateral force (Fy, in the vertical axis).

You can see that an increment in vertical load doesn't translate into the same increment in lateral load (NOTE: the Y axis is increasing downwards, because Fy is negative in the frame of reference chosen for this graph).

This change in the Fz/Fy relationship changes the cornering stiffness (NOTE: cornering stiffness is the change in lateral force per unit slip angle change at a specified normal load in the linear range of the tire. In english: how much lateral force you get per degree of slip).

The blue and green lines are for the inner and outer tyres, that have different slip angles (because of Ackerman steering).

Here you have another example (from my pirated copy of Gillespie):

Besides that, tire slip is determined by the load capacity (load carrying) ability of the tyre compared with the load they "see".

Larger tyres or bigger pressure increase slip angle. That is, the larger the weight, the larger the lateral load (or the braking force), and the larger the slip angle. If your car is heavy in one end, you can reduce the slip angle by using larger tyres and higher tyre pressure or by reducing roll stiffness (changing or adjusting roll bars).

By increasing roll stiffness (resistance of the car to lean toward one side) you increase the slip angle on the end of the car that’s resisting the roll.

I read in a truly old "Car and Driver" I rescued from my attic (a 1965 article by Jim Hall... ) the following example I remember reading ages ago:

Fieros and Corvairs have almost the same weight distribution. However, the Fiero has a tyre pressure of 30 psi, front and rear. The Corvair has a tyre pressure of 18/30 front/rear. Why?

Corvair: 18/30

Fiero: 30/30

If you use a stiff spring or sway bar, the outside tyre carries a larger share of the lateral load, something that increases its slip angle. I quote Mr. Hall:

So, they found other ways to equalize the slip angles on the Fiero, namely putting most of the roll stiffness in the front suspension to force it to carry roll loads and generate higher slip angles when the car was pushed in corners to make sure the tail didn’t get away. The early Corvair has tremendous rear roll stiffness and swing axles don’t let you reduce it much, even with softer springs and considerably increased front roll stiffness, so tire pressures were pretty nearly the only tool that would really make a difference on earlies - the lates have very weak rear roll stiffness and this is mostly why they are inherently better handling cars. Most efforts to tame the Corvair are focused on increasing front roll stiffness to transfer cornering loads onto the front wheels to minimize the possibility the rear will generate larger slip angles than the front.

Of course, slip varies with camber, also. Like this:

Why? Because the form of the patch varies with camber. Take in account that tyres incline when you turn them (just turn the steering wheel and look the tyres from the front of the car. Because of Ackerman steering, both tyres incline differently). This lateral patch deformation is larger in bikes because the entire vehicle leans.

Besides, contact patch shape (and thus, slip angle) depends on tire’s geometric characteristics (rolling radius and cross section radius) and carcass’ lateral/radial stiffness, as I imagine is clear by now.

I hope this help a little. Now, I wait for my people to point the dozen wrong parts of my post...
Ciro
Ciro Pabón

Joined: 10 May 2005

I liked my explanation better
Grip is a four letter word.

2 is the new #1.
Jersey Tom

Joined: 29 May 2006
Location: Huntersville, NC

Right now I´m squeezing my brain trying to design a machine to test tyres. It has be cheap because I have no money and there is absolutely no team I have spoken to that is willing to invest on it
In the 99% of the racing series of my country, tyres are homologated and the provider of those tyres gives no info about them. They dont do any test and the quality control its more or less like this: if it is black and round, then its good. Frequently, the variability in weight and dimentions is considerable arround here. I dont know what about lateral stiffness.

Im thinking about a simple portable machine to measure lateral stiffness, also I can measure hardness. Im afraid that with only that information I wont do much but I´ll gather it anyway.

Ciro Pabón wrote:Larger tyres or bigger pressure increase slip angle.

This sounds weird. Could you define larger?

Jersey Tom wrote:Yes and no.
In a pure sense if you had the tire on a flat track and just held the wheel 3 degrees relative to the belt travel, it would be at 3 degrees slip angle regardless of what you did with load, inflation, etc.

Do you think that if the flat track you mention is covered in grease it would be the same?
"You need great passion, because everything you do with great pleasure, you do well." -Juan Manuel Fangio

"I have no idols. I admire work, dedication and competence." -Ayrton Senna
Belatti

Joined: 10 Jul 2007
Location: Argentina

Belatti wrote:
Jersey Tom wrote:Yes and no.
In a pure sense if you had the tire on a flat track and just held the wheel 3 degrees relative to the belt travel, it would be at 3 degrees slip angle regardless of what you did with load, inflation, etc.

Do you think that if the flat track you mention is covered in grease it would be the same?

Yup. No different.
Grip is a four letter word.

2 is the new #1.
Jersey Tom

Joined: 29 May 2006
Location: Huntersville, NC

Evidently there may be a language barrier because I cant understand what you are saying. Is your tire nailed to the ground or something that it cant "slip" over the grease???
"You need great passion, because everything you do with great pleasure, you do well." -Juan Manuel Fangio

"I have no idols. I admire work, dedication and competence." -Ayrton Senna
Belatti

Joined: 10 Jul 2007
Location: Argentina

Jersey Tom is answering the question in the most basic way for the question that was asked.

"slip angle" is just the direction difference between the path the tire is going(the moving belt travel on a tire tester, or the direction the car is moving), and the direction the tire is pointing. And in that sense, it does not change regardless whether you have 1000lb on the tire, or 5lb. Slip angle is just a independent variable that you put of the x-axis of a graph. How that angle is generated on the vehicle will be dependent on other aspect.

Whats different is the load generated by that given tire at the given slip angle. And that obviously varies between road friction, verticle load, tire camber, or other aspects...

When you setup your car, what you are trying to do is to generate max cornering force, and that correspond to let the car present the optimum slip angle(at a given vertical load) to the tire, be that as getting your car to be at a proper amount of load transfer, at the proper steering input and at correct camber/toe setting.
RacingManiac

Joined: 22 Nov 2004

As an addition to RM's post..

Slip angle has nothing necessarily to do with "sliding." It's just an orientation.

That is a flat track. Let's say in that picture it's holding the tire at -5 deg inclination angle, and -4 deg slip angle. If the machine holds the tire in that orientation.. it doesn't matter if its on a plain steel belt, on grit paper, on water, or whatever. The slip angle is the slip angle. Just like changing the belt surface or greasing it up or changing the inflation doesn't change the camber/inclination angle at all.
Grip is a four letter word.

2 is the new #1.
Jersey Tom

Joined: 29 May 2006
Location: Huntersville, NC

When the slip angle appears on the tire, ironically the tire is not slipping. If the surface is greasy and the vertical load is not enough in that Calspan machine, the tire will slip, so the slip angle will be...... 0

I agree RacingManiac and Jersey Tom but what to make an extension (in red) of what has been said:
RacingManiac wrote:Jersey Tom is answering the question in the most basic way for the question that was asked.

"slip angle" is just the direction difference between the path the tire is going(the moving belt travel on a tire tester, or the direction the car is moving), and the direction the tire is pointing as long as there is a determined amount of adherence to make that diference possible the slip angle results in a force that is perpendicular to the wheel direction of travel

Here is another good "wikidefinition"
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:

"You need great passion, because everything you do with great pleasure, you do well." -Juan Manuel Fangio

"I have no idols. I admire work, dedication and competence." -Ayrton Senna
Belatti

Joined: 10 Jul 2007
Location: Argentina

Belatti wrote:When the slip angle appears on the tire, ironically the tire is not slipping. If the surface is greasy and the vertical load is not enough in that Calspan machine, the tire will slip, so the slip angle will be...... 0

Not quite. Slip angle doesn't care if the tire is adhered or sliding or somewhere in between. If there tire is sliding the slip angle doesn't go to 0.
Grip is a four letter word.

2 is the new #1.
Jersey Tom

Joined: 29 May 2006
Location: Huntersville, NC

Jersey Tom wrote:
Belatti wrote:When the slip angle appears on the tire, ironically the tire is not slipping. If the surface is greasy and the vertical load is not enough in that Calspan machine, the tire will slip, so the slip angle will be...... 0

Not quite. Slip angle doesn't care if the tire is adhered or sliding or somewhere in between. If there tire is sliding the slip angle doesn't go to 0.

Ok sorry, you are right, it doesnt follow any relationship I know but it wont be 0 either.
"You need great passion, because everything you do with great pleasure, you do well." -Juan Manuel Fangio

"I have no idols. I admire work, dedication and competence." -Ayrton Senna
Belatti

Joined: 10 Jul 2007
Location: Argentina

Still think you're getting it twisted a bit. Slip angle isn't the angle of deformation of the tread and tire. Just a measure of difference in lateral and longitudinal velocity that the tire is seeing.

On that flat track, if I put a tire down and rotate it 15 degrees, it is at 15 degrees slip angle regardless of if the surface is grit paper or ice or grease or whatever.
Grip is a four letter word.

2 is the new #1.
Jersey Tom

Joined: 29 May 2006
Location: Huntersville, NC