Roll Centres
Author
Discussion

martin a

Original Poster:

344 posts

259 months

Wednesday 30th August 2006
quotequote all
I read somewhere that the rear roll centre should be higher than the one at the front. Does this just apply to rear engined cars which will tend to have a higher centre of mass at the rear? Surely a front engined car a la Lotus 7 should have a higher roll mcentre at the front so that the roll couple is similar to that at the rear or have I got the wrong end of the stick?

Sam_68

9,939 posts

261 months

Wednesday 30th August 2006
quotequote all
All a bit more complicated than that, I'm afraid.

Forget front and rear roll couples and the 'mass centroid axis'. Unless your chassis is made out of boiled spaghetti, they are irrelevant - the front and rear of the car can't roll independently of each other!

Also, be aware that contrary to what many textbooks either state or imply, a car does not roll around its roll centres or roll axis.

Effectively, the only thing you are interested in is the centre of gravity of the sprung mass. Imagine attaching a string to this point and pulling - sideways to simulate a cornering load, fore or aft to simulate acceleration or braking, diagonally to simulate a combination. The attitude a car adopts when subject to these forces is dependent upon how stiff the springs and anti roll bars are, and of course these will be different front and rear. Due to differing roll resistances front and rear, and the fact that weight is transferred diagonally, the car will almost always be operating in what Allan Staniforth refers to as 'skewed roll' - ie. a combination of roll and dive/squat.

The main implication of the roll centre locations are that they are used to calculate diagonal weight transfer, which in turn can be used to derive suspension deflection and individual tyre loads (which in turn influence understeer/oversteer balance).

The traditional rule of thumb was that that the roll centre is lower at lighter end of the car, but many other factors have to be taken into account - spring/roll bar stiffness, tyre sizes, front and rear track, CG location etc., so this rule is by no means hard-and-fast.

Probably more important to make sure that your roll centres don't move about much in relation to the sprung mass, as movement changes the diagonal weight transfer and can lead to very uncertain handling characteristics.

Sorry, that's a very simplistic overview - a proper explanation would take a book, and a proper analysis of a given design would require a huge abount of data and a complex computer program!

bales

1,905 posts

234 months

Monday 4th September 2006
quotequote all
Sam_68 said:
All a bit more complicated than that, I'm afraid.

Forget front and rear roll couples and the 'mass centroid axis'. Unless your chassis is made out of boiled spaghetti, they are irrelevant - the front and rear of the car can't roll independently of each other!

Also, be aware that contrary to what many textbooks either state or imply, a car does not roll around its roll centres or roll axis.

Effectively, the only thing you are interested in is the centre of gravity of the sprung mass. Imagine attaching a string to this point and pulling - sideways to simulate a cornering load, fore or aft to simulate acceleration or braking, diagonally to simulate a combination. The attitude a car adopts when subject to these forces is dependent upon how stiff the springs and anti roll bars are, and of course these will be different front and rear. Due to differing roll resistances front and rear, and the fact that weight is transferred diagonally, the car will almost always be operating in what Allan Staniforth refers to as 'skewed roll' - ie. a combination of roll and dive/squat.

The main implication of the roll centre locations are that they are used to calculate diagonal weight transfer, which in turn can be used to derive suspension deflection and individual tyre loads (which in turn influence understeer/oversteer balance).

The traditional rule of thumb was that that the roll centre is lower at lighter end of the car, but many other factors have to be taken into account - spring/roll bar stiffness, tyre sizes, front and rear track, CG location etc., so this rule is by no means hard-and-fast.

Probably more important to make sure that your roll centres don't move about much in relation to the sprung mass, as movement changes the diagonal weight transfer and can lead to very uncertain handling characteristics.

Sorry, that's a very simplistic overview - a proper explanation would take a book, and a proper analysis of a given design would require a huge abount of data and a complex computer program!


All the above is true, but what is not mentioned is the fact that the roll centres are a direct consequence of the suspension geometry. So in reality the weight distribution is not the defining factor of the roll centres or roll axis, but the roll centres define the weight transfer (as do the front and rear roll stifness rates i.e spring rates and arb's). The roll centres can be changed very easily by the suspension geometry but the hard part is maintaining good roll centre charecteristics when in a dynamic sense. This is very very hard and we have fancy computer programs now to calculate the geometry.

The subject of whether the rear roll centre should be higher than the front is a question that even now people argue over. A big factor is the type of suspension you have, my 205 has a beam axle at the rear which means the rear roll centre is always at ground level and doesnt vary when in a dynamic sense, this is good and bad depending on what you want out of the car. Hence the front roll centre is actually higher than the rear, this is why they feel very responsive when entering a corner and they "seem" to rotate around an area ahead of the driver, this is due to the polar moment of inertia (dont ask me any questions about this as I dont really know a huge amount) the height and positioning of the PM of inertia define how the car turns or "what it rotates about" which is why some cars feel very responsive and others dont.

Chassis dynamics is a "very" complicated area and I only undertsnd the absolute basics of how everything works so I could well be wrong, so feel free to correct me i always like to learn.

Alex

Edited by bales on Monday 4th September 17:42

bales

1,905 posts

234 months

Monday 4th September 2006
quotequote all
sam 68 said:
Effectively, the only thing you are interested in is the centre of gravity of the sprung mass


I dont necessarily agree with this though, in the most basic sense yes but there are many other factors other than just the C of G that effect how the car handles dynamically.

Sam_68

9,939 posts

261 months

Monday 4th September 2006
quotequote all
bales said:
All the above is true, but what is not mentioned is the fact that the roll centres are a direct consequence of the suspension geometry.


Quite correct, but I don't think you can say that roll centres define weight transfer or vice versa, since they are inter-related. Roll centres (usually) move as the suspension moves; as you say, some beam axle linkages* being the exception. How much the suspension moves depends on the weight transfer, which in turn depends on the roll centre position...it's a horribly complicated circular argument.

And that's without taking into account the 'skewed roll' - differing roll resistances due to differing spring and ARB rates front and rear mean that the roll centre position doesn't just depend on the weight transfer. It depends on how much the springs resist that weight transfer at one end of the car compared to the other, thus channelling the weight transfer diagonally across the chassis.

If you think about it too much, your brain starts to turn to marmalade, so the best advice is not to think about it - either get a computer to do it for you (unfortunately the computer programs that do it right are very, very expensive) or just try to make sure that your roll centres don't move about too much in relation to the sprung mass, no matter what the suspension movement.

edited to add:

*and swing axles, and parallel, equal length wishbones etc., but I was thinking mainly of linkages that sane people would actually consider using. boxedin


Edited by Sam_68 on Monday 4th September 20:02

Sam_68

9,939 posts

261 months

Monday 4th September 2006
quotequote all
bales said:
sam 68 said:
Effectively, the only thing you are interested in is the centre of gravity of the sprung mass


I dont necessarily agree with this though, in the most basic sense yes but there are many other factors other than just the C of G that effect how the car handles dynamically.

yes Oh yes, for sure...sorry, I probably worded that badly. I meant as opposed to the mythical 'mass centroid axis' or the equally mythical 'roll axis', and certainly as opposed to the entirely separate front and rear roll couples (ie. each end of the car having its own, individual centre of gravity) that some people believe in!

Even if you know the position of the sprung mass CG, you need to feed in a lot more data on suspension geometry and spring rates to use it for anything useful, and certainly there are a huge number of other factors which influence handling.

The point I was trying to get across is that the 'geometric roll centre' is really only useful as part of the calculations for determining dynamic weight transfer.

There are an enormous number of people out there (some of them writing books on the subject!) who seem to think that a car neatly rolls around an axis linking front and rear roll centres as it negotiates a corner, as if it were rotating on some imaginary spit that skewered the two points!

bales

1,905 posts

234 months

Monday 4th September 2006
quotequote all
sam 68 said:
Quite correct, but I don't think you can say that roll centres define weight transfer or vice versa, since they are inter-related.


Yeah definately, its a pretty hard thing to describe because as you say everything is related and its is very confusing when you try and think about in depth.

I kind of meant that the suspension geometry dicatates the roll centres (as is obvious when you draw a neat little diagram with intercrossing lines) but obviously it doesnt dictate the weight transfer. One thing that gets me which you maybe could help me understand is about the weight transfer.

As you said there isnt a neat little axis that the car conveniently rotates about, but the actual roll axis must dictate the overall weight transfer, whilst the roll rate or spring rates dicatate the proportion front to rear of the weight transfer. As you can never change the weight transfer just proportion between the front and rear differently.

However if i think about that in more depth it doesnt actually make sense as you would think the c of g is what dictates the overall weight transfer, and then there is the whole polar moment of inertia malarky which makes things even more confusing confused

Edited by bales on Monday 4th September 20:09


Edited by bales on Monday 4th September 20:10

Sam_68

9,939 posts

261 months

Monday 4th September 2006
quotequote all
bales said:
...but the actual roll axis must dictate the overall weight transfer, whilst the roll rate or spring rates dicatate the proportion front to rear of the weight transfer. As you can never change the weight transfer just proportion between the front and rear differently.


Ah, good! An Easy One! I like easy questions!

bales said:
However if I think about that in more depth it doesnt actually make sense as you would think the c of g is what dictates the overall weight transfer


...which you've just answered yourself!

Overall (total) weight transfer is dependent upon the height of the centre of gravity and the average track of the car (or wheelbase, if you are talking about longitudinal weight transfer under braking or acceleration). It is nothing whatsoever to do with the roll centres.

There is a chapter in Staniforth's book 'Competition Car Suspension', which takes you through the basic calculations to show where roll centres influence diagonal weight transfer.

bales

1,905 posts

234 months

Monday 4th September 2006
quotequote all
So the logical question from that would be what do the roll centres dicatate, and also in staniforths book he talks alot about swing arm lengths, and that f1 cars have exceptionally long ones i.e the wishbones are near enough parallel.

So I understand the need for the roll centres to stay consistent when in a dynamic sense, we had a program at uni called Susprog that calculates all the displacements of the roll centres under maxiumum bump and droop etc....but what does the swing arm length dicatate is it just purely less vertical movement in the roll centre?

So is the roll axis unrelated to the weight transfer and only effects suspension geometry? - which I supppose in turn then does effect the weight transfer due to the roll rate of the car arrrgghhh!!!!! its too confusing?!?

On a completely different note I actually saw Allan Staniforth at the last hillclimb I went to at Harewood, I didnt realise how old he was and still driving that suprisingly quick megapin that he designed and built at a suprisingly quick rate

Edited by bales on Monday 4th September 20:34

Sam_68

9,939 posts

261 months

Monday 4th September 2006
quotequote all
bales said:
So the logical question from that would be what do the roll centres dicatate


Read the chapter on weight transfer, and all will become clear! For the record, that particular chapter was written by David Gould, not Staniforth himself. Staniforth has a pretty wooly comprehension of the whole roll centre issue, too, from my limited conversations with him on the subject.

bales said:

So I understand the need for the roll centres to stay consistent when in a dynamic sense, we had a program at uni called Susprog that calculates all the displacements of the roll centres under maxiumum bump and droop etc....but what does the swing arm length dicatate is it just purely less vertical movement in the roll centre?


Swing arm length on its own doesn't dictate roll centre movement. You can have two suspension layouts with identical static swing arm lengths that behave completely differently in terms of geometric roll centre movement, once you get into dynamic behaviour.

bales said:

So is the roll axis unrelated to the weight transfer and only effects suspension geometry?


Repeat after me...there IS no roll axis. The roll axis is a MYTH.

bales said:

On a completely different note I actually saw Allan Staniforth at the last hillclimb I went to at Harewood, I didnt realise how old he was and still driving that suprisingly quick megapin that he designed and built at a suprisingly quick rate


Yep, he's an old gimmer!

For the record, he didn't design and build the Megapin, though. He built a Mini-engined single seat hillclimb called the Terrapin back in the 1960's and wrote a book called 'High Speed, Low Cost' telling you how build your own version (a sort of distant anscestor of Ron Champion's Locost book). The Terrapin is regarded as the spiritual ancestor of the current generation of hillclimb specials and the Megapin was named in its honour, but it was designed and built by a guy called Ian Scott; he's built a series of them, some with carbon fibre monocoques, some (including Staniforth's) with a cheaper, simpler spaceframe chassis.

Staniforth's Race and Rally Car Source book has a chapter about the Megapin 5.

I actually have the spaceframe chassis from the first Megapin propped up at the back of my mother's garage, gradually rusting away to nothing. A friend of mine owned the car and when we stripped it down for a rebuild we found that the chassis was such a mess (both in terms of design and condition) that the car wasn't worth rebuilding. The Megapin 1 chassis was an abortion; very badly designed, angled doglegs in tubes, inadequate diagonal bracing, that sort of thing.
Which just goes to show how far and how fast some people can climb the learning curve; Ian Scott's latest Megapins are works of art!

Mr Whippy

31,169 posts

257 months

Tuesday 5th September 2006
quotequote all
Sam_68 said:
It depends on how much the springs resist that weight transfer at one end of the car compared to the other, thus channelling the weight transfer diagonally across the chassis.


Does a spring resist weight transfer? I thought they just altered the speed of weight transfer before a steady state condition.

Channelling weight transfer? I thought that was simply a function of roll couples, not the spring rates?

Are we talking about dynamic or static? I can see how you would channel weight transfer for a brief period, say bias front weight transfer to reduce front end grip on turn-in, but once in steady state the weight transfer isn't a function of springs/arbs is it???!!

Dave

GreenV8S

30,902 posts

300 months

Tuesday 5th September 2006
quotequote all
Mr Whippy said:
Sam_68 said:
It depends on how much the springs resist that weight transfer at one end of the car compared to the other, thus channelling the weight transfer diagonally across the chassis.


Does a spring resist weight transfer? I thought they just altered the speed of weight transfer before a steady state condition.

Channelling weight transfer? I thought that was simply a function of roll couples, not the spring rates?


I think it would be more accurate to say that the springs (and dampers) resist the body roll.

The way I see it, the position of roll center at each axle detemines how much weight transfer occurs through the mechanical components of the suspension at that axle. The position of the CoG relative to the roll axis determines how much roll moment is applied to the sprung mass. This moment causes the sprung mass to roll under lateral acceleration. The roll will normally be resisted by the springs and dampers at each axle, and this will cause an additional weight transfer (i.e. additional to the mechanical weight transfer through the suspension links). The total weight transfer over the whole car is determined by the CoG height and is non-negotiable, but these other details tell us where this weight transfer will occur, transiently and steady state and how much body roll will occur. The body roll then determines what other geometry changes will occur.

Varying the amount of weight transfer front versus rear obviously has a huge affect on the understeer/oversteer characteristics of the car, but the more subtle effect of the roll axis is that it determines the transient characteristics which have a big effect on high speed stability.

Edited by GreenV8S on Tuesday 5th September 14:17

Mr Whippy

31,169 posts

257 months

Tuesday 5th September 2006
quotequote all
GreenV8S said:
Varying the amount of weight transfer front versus rear obviously has a huge affect on the understeer/oversteer characteristics of the car, but the more subtle effect of the roll axis is that it determines the transient characteristics which have a big effect on high speed stability.


Yeah, I agree with that concept, but the second or third post said that the roll-axis was simply a concept worth ignoring. Later described as a myth.

Surely because it relates to the amount of load that is transferred through suspension deflection vs mechanical transfer through the suspension linkages, then it is important, especially when considered next to the cofg > rc vs cofg > cp height... weight transfer vs roll front and rear, and like you say that effects small subtle transfers of weight and where they go at high speeds and small suspension deflections. Go quickly to the CP or more slowly through the suspension which momentarily absorbs and controls the force transfer.

Anyway, I guess it's just whichever way you like to look at it all. I've always seen the roll-axis vs CofG height vs roll stiffness f/r as quite a telling component of a cars setup, whether it exists in reality or not, it's measurable and calcuable

Dave

GreenV8S

30,902 posts

300 months

Tuesday 5th September 2006
quotequote all
I think I agree. The concept of a roll axis is one way of visualising how and where the weight transfer occurs. It may be that some people think of this too literally and visualise the car doing a compound roll/yaw around the roll axis as if the axis was a physical anchor, and that imo is misleading and perhaps why the roll axis is referred to as a myth.

Sam_68

9,939 posts

261 months

Tuesday 5th September 2006
quotequote all
Apologies - not much time, so this post will be rushed...apologies for typos, etc.

GreenV8S said:
I think it would be more accurate to say that the springs (and dampers) resist the body roll.


If you prefer.

Most people would happily accept that if they push against a coil spring, the spring resists them, yes? The weight transferred during roll pushes against the spring; the spring resists.

If we are getting into advanced level semantics, however, it is the tarmac which ultimately resists both body roll and weight transfer via the springs.

I prefer to stick with my semantically flawed wording, however, simply because the description becomes very clumsy, otherwise. However, for those who demand perfect semantics, please feel free to substitute the phrase 'tarmac, via the springs' in place of 'spring'/'springs' in the following.
--------------------------------------------------------------------------

Springs of different stiffness resist the weight transfer by different amounts. If the springs are stiffer at the front of the car, the front end will resist the weight transfer more, causing that diagonal weight transfer. This is why front anti-roll bars tend to promote understeer:

An anti-roll bar (which is, after all, simply a torsion spring with freedom in pure bump/droop) makes the front end stiffer in roll...the front springs resist weight transfer more, therefore the load at the front contact patch increases more at the front than it does at the rear. Increased load makes the tyre operate at higher slip angles and, voila, we have understeer!

I say that the roll axis is a myth for 2 reasons:
1) At no point in the necessary calculations is the 'roll axis' relevant. You need to calculate the mean roll couple. If you are doing this graphically, the 'roll axis' is one of the lines you would draw, but in itself it has no mathematical or geometric importance.

2) In practical terms, all of the affordable computer software I have come across works by using a given degree of body roll (lets say 3 degrees) and then generates the suspension geometry (including instantaeous roll cente) by rotating the sprung mass by 3 degrees around the static single roll centre. If you are lucky, the software will do iterative calculations to take account of the fact that the roll centres are moving as the srung mass rotates. If you are unlucky (eg. if you bought the industry-leading Mitchell software) it won't even try to rotate the sprung mass around the roll centres - it will use the pont where the car centreline intersects the ground, which is even more meaningless.

Whatever, the 'skewed roll' generated by differing roll resistances means that the roll centres are not where the software is predicting that they are, therefore all the rest of the geometry generated - including your precious 'roll axis', is not what the computer calculates it to be. The data is, quite simply, worthless.

The only valid model would be one in which the computer is supplied with a full set of data, including spring rates, then mathematically pulls that imaginary string of mine, connected to the CG, and calculates the results. Iterative calculation for the geometric roll centre position would be part of this, but would actually have no real value in itself...what you would be interested in as an end result would be the graph of tyre loads and wheel camber angles versus cornering load.

Since I'm short of time, I'll quote from Staniforth's book:

David Gould in Chapter 8 said:

When visualising the sprung mass, we must never think in terms of front or rear axles, front or rear weights, front or rear heights or front and rear roll centres if we are to grasp a full understanding. Sitting somewhere near the middle of the car is a mass whose centre is the Centre of Gravity of the entire sprung weight of the car. It knows nothing about front and rear tracks, front and rear roll centres or front and rear CoGs. What it does know is about its own track, its own roll centre and its own CoG. We will call these the mean track, the mean roll centre and the mean CoG.


In other words, front and rear roll centres (and therefore roll axis) are meaningless apart from as part of the calculations to arrive at mean roll centre and mean roll couples. And even when utilizing them as part of those calculations, you must never forget that they won't be where you think they are unless you take into account the effects of skewed roll, cause by differing roll resistances front and rear.

Edited by Sam_68 on Tuesday 5th September 19:01

Mr Whippy

31,169 posts

257 months

Tuesday 5th September 2006
quotequote all
Sam_68 said:
2) In practical terms, all of the affordable computer software I have come across works by using a given degree of body roll (lets say 3 degrees) and then generates the suspension geometry (including instantaeous roll cente) by rotating the sprung mass by 3 degrees around the static single roll centre. If you are lucky, the software will do iterative calculations to take account of the fact that the roll centres are moving as the srung mass rotates. If you are unlucky (eg. if you bought the industry-leading Mitchell software) it won't even try to rotate the sprung mass around the roll centres - it will use the pont where the car centreline intersects the ground, which is even more meaningless.


I understand the varying semantics used, and this above post illustrates why you could happily say that the roll axis is a myth when visualising something in your mind.

I simply use it as a guide along with other simplified terms like roll stiffness and torsional rigidity and geometry changes which ignore the fact we are not using ball joints.

I've seen alot of these software packages and then you head on over to eng-tips and see alot of chassis engineers simply ignoring them because they just overlook lots of real world fundamentals that "theory" totally misses out on.


Anyway, far too complex for me, it's just a passing interest but I raised my questions because for a moment I thought I had totally misunderstood a concept, but now you have explained it I agree with you

Dave

bales

1,905 posts

234 months

Tuesday 5th September 2006
quotequote all
Does anyone care to explain the polar moment of inertia, I understand it is very important for it to be as low as possible, and in race cars especially it seems to be pursued as hard as maintaining a low C of G. I understand the concept in terms of simple beams i.e resisting torsion due to a torque (as this is taught quite early on at uni) but in terms of a vehicle it is harder to define.

As far as I can understand it is what defines the cars rotational responsiveness and defines how the car accelertaes around the invisible vertical axis that the car roatates about, this would explain why my 205 is very responsive as supposedly has a very far forward polar moment.

In that sense it also must be linked to the C of G, but how it fits in in terms of weight transfer I do not know.

I read a very interestign article recently about this seasons F1 cars, if anyone has noticed when they are doing there warm up lap or are behind a pace car they seem to throw them about exceptionally violently to warm the tyres. They dont just weave they physically almost spin them (well montoya actually did) but if you actually watch Alonso doing this it is amazing really as it looks like the car is actually out of control it changes direction so quickly.

The article was discussing that the cars have become increasingly snappy handling, and this "could" be a knock on effect of the C of G being brought forward due to the lack of two cylinders that the V10 loses. This in turn allows other masses to be moved about and "could" be allowing for a much lower polar moment of inertia.

Which is basically saying that have F1 cars become too responsive and that there is an optimum minimum polar moment not just "as low as possible". So in reality if the car is responsive enough for the tightest chicane in a race, then is a lower polar moment than this actually a disadvantage in terms handling and controllability of the car.

This also raises the question to sad people like me that would this actually be calculated by the teams and masses actually re-arranged in the car for specific tracks depending on the tightest corners. So that the polar moment is moved about to suit each track and get the best combination of responisiveness and stabilty.

Ahh well I found it intersting to think about for a while anyway, I just need to get a bloomin job know in the industry which is definately not easy.

GreenV8S

30,902 posts

300 months

Tuesday 5th September 2006
quotequote all
Sam_68 said:
Springs of different stiffness resist the weight transfer by different amounts. If the springs are stiffer at the front of the car, the front end will resist the weight transfer more, causing that diagonal weight transfer. This is why front anti-roll bars tend to promote understeer


I agree that we're quibling over semantics, and it's perfectly obvious by now that you know what you're talking about, but I still feel that the terminology you have adopted is at best wooly and at worst wrong. I can't see any sensible meaning of the term 'weight transfer' which corresponds to the thing that springs resist. I think it is worth using the correct physical terms if you're going to talk about this in any detail, even if it means you don't use colloquial terms, because otherwise everyone ends up talking at cross purposes again. For the record, in this context what the springs are resisting is body roll.

Sam_68

9,939 posts

261 months

Wednesday 6th September 2006
quotequote all
GreenV8S said:
...I still feel that the terminology you have adopted is at best wooly and at worst wrong. I can't see any sensible meaning of the term 'weight transfer' which corresponds to the thing that springs resist...in this context what the springs are resisting is body roll.

NO!!! The springs are resisting weight transfer via the sprung mass, and in so doing restrict body roll.

Without wishing to bicker about dictionary definitions, you need to understand that resist does not mean prevent!

GreenV8S

30,902 posts

300 months

Wednesday 6th September 2006
quotequote all
Sam_68 said:

NO!!! The springs are resisting weight transfer via the sprung mass, and in so doing restrict body roll.

Without wishing to bicker about dictionary definitions, you need to understand that resist does not mean prevent!


rolleyes What do you mean by the term "weight transfer"? To me that's a perfectly clear and unambiguous term which means the movement of weight from one wheel to another. The springs don't resist this, they cause it. At the same time they resist body roll. Look at it this way: what would happen if the springs were removed? Would you get more body roll, or less? Would you get more weight transfer, or less?

PS I do understand the distinction between resist and prevent.