Slip Angle - an accurate definition please.

[S. Gonzales Esq.]

I think I know what the term 'Slip Angle' means, but I often see it used in contexts where others appear to think it means something different. I'd like to clear this up once and for all.

There's information on it on Wikipedia and Don Palmer's site, but most of that technical stuff just makes my head hurt.

Here are two options to get you started:

I think that the slip angle is measured between the centre of a wheel and the direction that the contact patch of the tyre is pointing - i.e. the 'twist' in the tyre sidewalls. This means the slip angle can be affected by the stiffness of the sidewalls and the torque applied to the wheel (if driven) by the engine.

Alternatively, I've read things that suggest that 'slip angle' refers to the angle measured between the direction of travel of the contact patch, and the actual direction of travel on the road. (Which would seem to fit better with the term 'slip'.) If this is the case, then it will be affected by the nature of the surface and the grippiness of the tyre.

Over to you, PH:


Edit - following Dave's post below, I've added a third option that fits what he's described.

Edited by S. Gonzales Esq. on Thursday 3rd March 14:33

[StressedDave]

Wikipedia's definition matches the SAE definition - it's the angle between the heading of the tyre (and probably best described as measured parallel to the edge of the tyre rim rather than twisting yourself up trying to work it out in terms of the contact patch) and it's direction of travel.

[reggie82]

Don Palmer's YouTube video is a great example.

http://www.youtube.com/watch?v=H_PaB0J9AXc

[waremark]

It seems to me that what Dave is saying is different to what Don says on the video. Am I right in thinking that they disagree?

[S. Gonzales Esq.]

Mark- that's exactly what I was thinking.

I might well have got my ideas from that video of Don's (I remember looking at the really low profile tyres on that 911 and wondering just how easy it is to feel what they're doing), so it would be helpful to know if he's not using the term in the way others do.

[Munter]

I also find the two options confusing.

What I don't understand is why anybody would care about Don Palmers version. If it's the difference between where the wheel is pointed and where the tyre is pointed, just turn the wheel a bit more until the tyre points where you want to go. Only becomes an issue if you're on full lock and want to use those few degrees.

The version where it's the difference between where the tyre is pointed and the direction of travel, then that makes more sense to me as something to be interested in.

[reggie82]

Munter said:

What I don't understand is why anybody would care about Don Palmers version. If it's the difference between where the wheel is pointed and where the tyre is pointed, just turn the wheel a bit more until the tyre points where you want to go. Only becomes an issue if you're on full lock and want to use those few degrees.

My (very) basic (and quite possibly wrong) understanding is that you can only generate so much slip angle. It's not as simple as saying turn the wheel until the tyre points where you want it to go, because if you turn it past the max slip angle that can be generated you will skid.

[StressedDave]

It's wrong I'm afraid... because slip angle is purely a geometric thing you can generate any slip angle you like (up to the limits of steering lock and current attitude of car). There is a slip angle (which is a function of vertical load on the tyre, inflation pressure, tyre construction and camber) beyond which the tyre will not generate any extra cornering force, and because of the mechanisms of force generation, you get less cornering grip and more longitudinal drag.

[Munter]

reggie82 said:

Munter said:

What I don't understand is why anybody would care about Don Palmers version. If it's the difference between where the wheel is pointed and where the tyre is pointed, just turn the wheel a bit more until the tyre points where you want to go. Only becomes an issue if you're on full lock and want to use those few degrees.

My (very) basic (and quite possibly wrong) understanding is that you can only generate so much slip angle. It's not as simple as saying turn the wheel until the tyre points where you want it to go, because if you turn it past the max slip angle that can be generated you will skid.

Well yes if you turn the wheel too far it will "skid" and then will have a (big) angle between where the tyre is pointing and the direction of travel. While if you turn gently enough that the "skid" is not perceptible, you are still experiencing some slip between the direction the tyre is pointing and the direction of travel. There is obviously a point at which it becomes noticeable, but I've no idea what to call that. You could measure it using the slip angle though if my understanding was correct.

The same as when you are powering the wheel, there is a very slight difference between the speed of the road and the speed of the tyre surface. At some point this becomes noticeable as "wheelspin" but it's there the whole time you are powering the wheels in a very small way. If you brake you get the same effect but in the opposite direction.

[S. Gonzales Esq.]

Munter said:

What I don't understand is why anybody would care about Don Palmers version. If it's the difference between where the wheel is pointed and where the tyre is pointed, just turn the wheel a bit more until the tyre points where you want to go. Only becomes an issue if you're on full lock and want to use those few degrees.

I'm very interested in Don's version (first option in the poll) because it helps me to explain to my IAM Associates how adding power in a corner can tighten the line of the car and actually reduce understeer.

My experience is primarily FWD so this may not apply to all cars, but in the example you give where the car is understeering mildly, you have three options to bring the car back onto the line you want. First is to reduce speed, second is to add more steering, and the third (and my favourite) is to add more power. This sounds counter-intuitive, but it works, and my impression is that the extra torque applied to the tyre reduces the 'slip angle' and turns the car more effectively.

It would be nice to get a definitive answer on whether or not I'm talking bks, but we don't seem much closer to that yet.

[StressedDave]

The standard definition deals with the velocity of the wheel rather than the speed of the tyre (as you've pointed out, there is the potential for a difference between ground speed and tyre speed). Depending on which modelling method you use for tyre data, the combined slip from torque application (be it power or braking) gets turned into an effective speed of contact patch and used to vary the cornering force generated. It's a horribly complex area with inumerable kludges and bodges used to fit measured data to slip angles.

Two of the approaches: http://www.racer.nl/reference/pacejka.htm (which has been developed for road car, not at the limit, type use) and Dufornier's (which has been optimised for racecars): http://www.ipg.de/uploads/media/V142_DUFOURNIER_IP...

All work on the basis of slip angle and slip being the standard definitions according to SAE, which are the ones mentioned in Wikipedia.

[StressedDave]

I've had a good look at Don's video (I haven't seen it for a while and couldn't remember what he'd said). Don's definition of slip angle is wrong, as his description of what causes the feedback (for those who really care it's the self-aligning torque that he's describing which is caused by the centroid of the cornering force not coinciding with the middle of the contact patch rather than some mythical twisting of the contact patch).

That's not to take anything away from Don's talents (and they are truly copious and I'd recommend anyone who is serious about their driving to chuck some money his way), and there's a lot of sound stuff in the video.

[pikeyboy]

http://www.mrfizzix.com/autoracing/tiresgrip.htm

this might help explain things, trction circle theory is quite easy to understand and slip anlge is part of this.

Edited by pikeyboy on Saturday 5th March 16:23

[waremark]

Dave, do you agree with what Don implies about steering sensation? That if the self centring action starts to reduce when you have not reduced steering or speed, either you have passed the max turning effect the front tyres can achieve, or the rear tyres have started to let go? (ps I have probably just demonstrated that I have wasted any money which I may have sent Don's way!)

[reggie82]

Munter said:

reggie82 said:

Munter said:

What I don't understand is why anybody would care about Don Palmers version. If it's the difference between where the wheel is pointed and where the tyre is pointed, just turn the wheel a bit more until the tyre points where you want to go. Only becomes an issue if you're on full lock and want to use those few degrees.

My (very) basic (and quite possibly wrong) understanding is that you can only generate so much slip angle. It's not as simple as saying turn the wheel until the tyre points where you want it to go, because if you turn it past the max slip angle that can be generated you will skid.

Well yes if you turn the wheel too far it will "skid" and then will have a (big) angle between where the tyre is pointing and the direction of travel. While if you turn gently enough that the "skid" is not perceptible, you are still experiencing some slip between the direction the tyre is pointing and the direction of travel. There is obviously a point at which it becomes noticeable, but I've no idea what to call that. You could measure it using the slip angle though if my understanding was correct.

The same as when you are powering the wheel, there is a very slight difference between the speed of the road and the speed of the tyre surface. At some point this becomes noticeable as "wheelspin" but it's there the whole time you are powering the wheels in a very small way. If you brake you get the same effect but in the opposite direction.

I'm confused. You asked what the point of Don's version is, and I've responded with why I think it is. But your response is based on your version?

I have no idea which is the correct one. Seems odd that there are differing versions!

[Munter]

reggie82 said:

I'm confused. You asked what the point of Don's version is, and I've responded with why I think it is. But your response is based on your version?

Sorry but I didn't realise you were trying to explain Don's version. You appeared to say that you can only generate slip angle until a tyre "skids". I guess that's true of Dons version (because you can only "twist" the tyre so much before it has no more "give"), but I hadn't thought of it like that.

I didn't think you'd grasped my version and were questioning what it was.

[bigdog3]

Slip angle is the angle between a rolling wheel's actual direction of travel and the direction in which it is pointing. Front slip angle results from steering input whereas rear slip angle is a consequence of cornering. Rear slip is the angle between the vehicle body's longitudinal axis and its direction of travel, ignoring any small steered effects of the rear suspension.

Tyres generate cornering force by two mechanisms: slip angle and camber thrust. Cars utilise slip angle dominantly whereas motorcycles utilise camber thrust dominantly. Tyres rolling at significant camber (negative or positive) generate cornering force even when travelling in a straight line. Fortunately this is counteracted by the opposing tyre across the axle, except when one wheel experiences significantly less vertical load (eg one wheel bump). Also longitudinal force capability declines with camber (although most tyres are tolerant to a few degrees) which degrades braking performance and acceleration adhesion.

Edited by bigdog3 on Saturday 5th March 23:44

Edited by bigdog3 on Sunday 6th March 00:44

[StressedDave]

waremark said:

Dave, do you agree with what Don implies about steering sensation? That if the self centring action starts to reduce when you have not reduced steering or speed, either you have passed the max turning effect the front tyres can achieve, or the rear tyres have started to let go? (ps I have probably just demonstrated that I have wasted any money which I may have sent Don's way!)

More or less, yes. Although the self aligning torque leads cornering force, i.e. it drops away before you've reached max force rather than at max force.

[StressedDave]

bigdog3 said:

Slip angle is the angle between a rolling wheel's actual direction of travel and the direction in which it is pointing. Front slip angle results from steering input whereas rear slip angle is a consequence of cornering. Rear slip is the angle between the vehicle body's longitudinal axis and its direction of travel, ignoring any small steered effects of the rear suspension.

Front slip angle doesn't just result from steering input, and rear slip angle is not the angle between the car's direction of travel and its heading angle. Both are partially a function of body slip angle (the one you quoted) and rate of turn.

bigdog3 said:

Tyres generate cornering force by two mechanisms: slip angle and camber thrust. Cars utilise slip angle dominantly whereas motorcycles utilise camber thrust dominantly. Tyres rolling at significant camber (negative or positive) generate cornering force even when travelling in a straight line. Fortunately this is counteracted by the opposing tyre across the axle, except when one wheel experiences significantly less vertical load (eg one wheel bump). Also longitudinal force capability declines with camber (although most tyres are tolerant to a few degrees) which degrades braking performance and acceleration adhesion.

With modern tyres the ratio of force generation per degree of slip angle and per degree of camber angle is around 20:1 so it's still slip angle that dominates in both motorcycle and car. It's the fact that you can move the c of g around on a motorcycle that means you can use the reaction at the tyres (which is a different force generation than camber thrust) to generate cornering force .

Edited by StressedDave on Sunday 6th March 17:10

[reggie82]

Munter said:

reggie82 said:

I'm confused. You asked what the point of Don's version is, and I've responded with why I think it is. But your response is based on your version?

Sorry but I didn't realise you were trying to explain Don's version. You appeared to say that you can only generate slip angle until a tyre "skids". I guess that's true of Dons version (because you can only "twist" the tyre so much before it has no more "give"), but I hadn't thought of it like that.

I didn't think you'd grasped my version and were questioning what it was.

I 'think' I understand both versions - no idea which one is correct though!