Warning, roll theory inside...

[JohnL]

String wrote:
“Exactly how low are you? If you're getting close to the bump stops then I'll bet your problem is the front roll centre location. Increasing the front roll couple relative to the rear will result in worse steering feel, especially on turn-in; a feeling of perpetual understeer and tyre-rollover - sound familiar?”

String’s statement above (and a similar one in another thread a week or so ago) brings up something of some importance to an understanding suspension behaviour, ‘roll theory’. This isn’t only to do with body roll, but is also fundamental to the manner(s) in which weight transfer occurs.

Many of you won’t find this topic of much interest as it’s quite esoteric and (pseudo) theoretical, so please don’t read it and then chime in with something like “blah blah blah’. You were warned!

I don’t pretend that all the following blather is 100% correct or gospel, I’m only putting up some of my personal understanding for discussion, if anyone’s interested…

Before I really begin, we need to be aware that starting to talk about roll centres etc is like opening a big can of very wriggly and slippery worms. ‘Roll theory’ is to do with geometric roll centres (GRC) locations, weight transfer etc. and is very complex and hard to get your head around. If anyone thinks they might have a handle on it by having read what’s written about it in the more commonly available chassis dynamics books, then they’re wrong. The explanations in such books are invariably very simplistic, sometimes wrong and at the very least somewhat misleading. Even professional suspension engineers can struggle with roll theory, and it’s a topic of much discussion and disagreement among them.

I don’t pretend to understand roll theory particularly well, but it is something I’ve read a lot about and given a great deal of (headache inducing) thought to while trying to understand kart chassis behaviour (and yes IMO the fundamental principles are the same, though some will argue…). It’s one of those things where to understand X you need to understand Y and also Z, but to understand Y you need to already have some understanding of Z, but to understand Z you need to understand Y. To understand Y or Z (and thus understand X), you need to incrementally zero in on both, building on the understanding bit by bit (and even then you can’t be sure you’re getting it right). There are a number of simple things going on when weight is transferring, but the interactions between them become complex.

By the way, before I go on (and on and on…), unless I say otherwise, all the following is referring to the suspension at a single axle line, i.e. either the front suspension or the rear suspension.

Oh, and it’s long!

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String,
The lower the GRC the lower the geometric roll stiffness becomes, not higher (as I think you were suggesting?).

As you lower the chassis, the suspension arms (wishbones etc) become angled downward (from the uprights to chassis mounting points). This causes the ‘instant centres’ of the ‘virtual swing arms’ (points in space defined by suspension geometry, of which there is one per corner on an independent suspension) to become lower, and as a result the GRC also lowers. The CG also lowers, but the GRC height above ground relative to the CG height above ground becomes lower more than the CG height does.

When lowering the chassis, if this lowering of the GRC(s) occurs equally at both ends, then the geometric ‘roll couple’ (relative front / rear roll stiffnesses) will remain unaltered (though roll stiffness will tend to decrease at both ends of the chassis). If you lower the front but not the rear then only the front GRC lowers and the geometric roll couple will become biased more toward the rear and geometric roll stiffness will decrease at the front. This will tend to improve turn in and decrease understeer because lateral weight transfer will now be greater and faster at the rear than at the front because front roll stiffness is now less than it was.

Despite what most people have probably read or heard or think, the first thing we need to understand is that the GRC is NOT the point around which the chassis actually ‘rolls’, except at the very instant the chassis begins to ‘see’ a weak lateral acceleration (in theory, but in reality as soon as ANY lateral acceleration is occurring the point around which the chassis is actually rolling has moved away from the GRC to some degree).

The location of the point around which the chassis mass (i.e. all sprung weight) actually rolls IS influenced by the location of the GRC, but once the chassis starts to ‘see’ lateral acceleration we get some immediate ‘geometric’ weight transfer and the chassis also attempts to simultaneously ‘roll’ around another centre located at the outer contact patch (as weight transfer begins to transfer through the springs etc), it attempts in some degree to ‘pole vault’ through the spring (and ARB and damper) over the outer contact patch.

As such the chassis is attempting roll around two points, which it can’t do because it’s a rigid structure (or should be!), so it ends up rolling around a point located in space that is an ‘average’ of the two points, the location of which depends on the relative ‘strengths’ both points may have at any given moment. The point around which the chassis actually rolls will be at a point located somewhere on a line drawn between the GRC and outer contact patch, and the point’s location on this line will move either way along the line depending on the strength of lateral acceleration.

The exact location in space of the actual centre of chassis roll is determined by the location of the GRC, the location of the outer contact patch, and the strength of the lateral acceleration, and changes dramatically with changes in lateral acceleration.

Weight transfers through two ‘vectors’; ‘geometric’ and ‘elastic’. The elastic vector involves WT through the springs, ARBs, and dampers (though dampers only, but importantly, influence transient weight transfer when the suspension is either deflecting or ‘undeflecting’, not in static state when the suspension has taken a ‘set’, though spring and ARB rates do affect static state WT). The geometric vector involves how much weight transfers through the articulated suspension members themselves (i.e. wishbones etc), instead of through the springs etc.

However, if the value of either the geometric OR elastic vector is zero, i.e. if geometric roll stiffness is zero, OR, no springs etc exist (as with a ‘wobble beam’ tractor front axle, where the beam pivot is also by default the GRC), then regardless of the strength of lateral acceleration all WT will be occurring through the other vector that has a value higher than zero (but this is rarely the case in the real world where both vectors typically have some value above zero).

If the GRC is located at ground level then it’s value will be zero (i.e. there is zero geometric roll stiffness), and all WT will occur ‘elastically’ through springs etc. If the GRC is at the same height as the CG, then the value of the geometric vector will be 100%, and no WT will occur elastically even if the springs etc are quite stiff (i.e. WT will occur entirely via the geometry through the linkages, and body roll will be zero). Most commonly WT occurs through a combination of geometric and elastic vectors.

The value of lateral acceleration affects the ratio of how much weight is transferring elastically and geometrically whenever WT is occurring through both vectors. If the value of either the geometric or elastic vectors is zero then lateral acceleration won’t affect the ratio, no weight will transfer through the vector with a value of zero.

In the real world with WT occurring through both vectors, the ratio of WT through the geometric and elastic vectors varies constantly (except when a steady cornering state is reached, when nothing at all is in a state of change). This is because suspension deflection causes the location of the GRC to change (be changing), and because as lateral acceleration changes the degree to which the chassis is attempting to ‘pole vault’ through the springs over the outer contact patch changes. The chassis attempts to ‘pole vault’ through the vector of the springs etc., which deflect under this load, carrying more WT the more the outer spring compresses (and the inner spring ‘decompresses’).

It’s important to understand that it does matter how much weight is transferring at any moment through either vector, because WT through the geometric vector is ‘instantaneous’ (i.e. it occurs at the same rate that lateral acceleration increases), and WT through the elastic vector is ‘slow’ (i.e. it lags behind the increase in lateral acceleration until a steady state is achieved). It’s important to note that stiffer spring, ARB and damper rates increase the speed at which WT occurs elastically (though unless the springs are 100% rigid WT never becomes ‘instant’ through the elastic vector), and chassis flex (or lack of) will also have an affect.

The different rates at which weight is transferring (at any given moment) through the geometric and elastic vectors, and how this is occurring at either end of the chassis relative to the other end, has very large implications for transient handling characteristics.

If you have say a low GRC location at the front (i.e. low front geometric roll stiffness) relative to the rear (i.e. higher rear GRC location), then you will get a lesser and slower WT at the front than at the rear, particularly in the earlier parts of the corner before lateral acceleration has built to a higher level (because as lateral acceleration increases the influence of GRC location on WT decreases and the influence of the elastic vector increases).

This will tend to give better turn in and early corner behaviour, i.e. reduce transient understeer, and is why front GRC locations are typically designed to be lower than rear GRC locations. However, as the lateral acceleration increases the influence of the geometric roll stiffness tends drop off (less so it’s the rear end of an old Beetle or Corvair etc. which have a very high rear geometric vector value with the majority of WT occurring geometrically most of the time), and the elastic vector becomes more influential (i.e. as acceleration increases, an increasingly greater % of WT occurs elastically and less geometrically), so the relative front / rear spring rates (and ARB rates etc) more strongly governs front vs. rear WT ratio, and thus what % of weight is transferring front vs rear at higher accelerations.

This is also partially affected by the fact that the GRC location typically becomes lower and moves laterally inward (lateral position also affects geometric roll stiffness) during body roll motion, but it’s largely to do with the elastic vector increasing in strength as the outer spring and ARB compresses.

Because of all this, the elastic vector more strongly affects understeer / oversteer at higher lateral accelerations than the geometric vector does, being why most manufacturers tend to fit softer rate springs (etc) on the rear, i.e. to increase near / at the limit understeer. This is also advantageous for RWD cars getting the power to the ground at corner exit because more WT is occurring at the front than at the rear.

So, (typically) production and racing cars tend to have lower front / higher rear geometric roll stiffness (by means of GRC location) to encourage good turn in and limit transient understeer, and most production cars tend to have higher front / lower rear spring rates etc to limit at / near the limit oversteer (i.e. to encourage understeer).

Congratulations for coming this far with me, don’t say I didn’t warn you! There’s a fair bit more to this subject, but I think that’s more than enough for now. This is hard stuff to understand, probably just as hard to explain, and at least some of my understandings may be suspect. I’ve tried to be as clear as I can be, so don’t shoot me if you think I’ve got some of it wrong!

[hisoka]

good post~scared me a bit
just thought id add pic of roll centre adjuster

[JohnL]

good post

Thanks.

~scared me a bit

Sorry about that! I started writing intending to keep it much shorter, but it just grew and grew. I almost didn't post it because it became so long winded.

just thought id add pic of roll centre adjuster
[/IMG]

Probably a very good thing to use with any significant chassis lowering. Something similar for the rear would probably be a good thing too.

A lot of racing cars have a number of alternative suspension member attachment points on the chassis to allow GRC adjustment. I think V8 Touring Cars can raise or lower the Watts Linkage (on the rear suspension) for rear GRC adjustment.

[SuperDave]

Since my car (non Honda) as far as I know lacks roll centre adjustment, would lifting the rear suspension result in a similar corner entry effect? As it is raising the CG of the rear above whatever the factory GRC is. I always link things back to weight transfer as that is what I used to simplify everything in carting days.

[JohnL]

SuperDave,
At least with a double wishbone suspension (and most other types), raising the rear will theoretically raise the rear instant centres (of the virtual swing arms) and thus the GRC will also be raised to some degree (i.e. rear geometric roll stiffness will increase), and it will also raise the CG.

However, the CG will rise less for X rise in rear chassis height than it will for X rise in front chassis height. This is because FWD cars are usually front heavy with the CG significantly closer to the front than the rear. You shouldn't think in terms of the front and rear having seperate CGs (as implied by your statement; "As it is raising the CG of the rear"), as there is only one CG.

So, in theory the answer should be yes. My personal experience with my CB7 Accord when I raised the rear (highest perch setting on the rear Konis, leaving the front on the lowest perch) is that it felt like turn in and early corner understeer was slightly improved, but I couldn't say with certainty that it wasn't a placebo affect created by the fact that this is what I was expecting to happen...

In karting (and with cars too), weight transfer (and just how this is occuring at the front vs at the rear) is incredibly important, almost the be all and end all. With karts (but not cars to any significant degree) we also have the added factor (complication) of mechanical weight jacking from the steering geometry (i.e. high caster angles accompanied by huge scrub radius) causing the OF and (more importantly) the IR to become very 'light' at turn in, which is what allows the diffless kart to actually turn (if it weren't for this jacking effect karts would suffer drastic turn in understeer).

It's not that weight transfer is "used to simplify everything in karting", but that most peoples concept of how weight transfer occurs is quite simplistic.

[bennjamin]

fantastic discussion here guys.

pity 99% of the members here (including myself to a degree) lower their car and mod their suspension for looks or mainstream attention. The terms discussed will never pop into our heads

[trism]

how do thicker/thinner swaybars come into play with roll centre adjustment?

[SuperDave]

SuperDave,
At least with a double wishbone suspension (and most other types), raising the rear will theoretically raise the rear instant centres (of the virtual swing arms) and thus the GRC will also be raised to some degree (i.e. rear geometric roll stiffness will increase), and it will also raise the CG.

Failed to mention I have lame rear beam suspension. One day When I get enough time at the track I'll raise the rear by 15mm between runs to see what effect it has on lap times. Being a beam rear end there wont be any effect upon alignment due to this.

Are there any resources you would recommend for reading into this further? I have always wanted to know more in this field of suspension set up. I believe I have a strong understanding of the other suspension area, and always want to know more.

I would give you more rep, but it wont let me. Apparently I have to share

[JohnL]

how do thicker/thinner swaybars come into play with roll centre adjustment?

They don't alter the the location of the two GRCs in any way (i.e. the one one front GRC and one rear GRC). ARBs (anti roll bars) directly affect the 'elastic' roll stiffness, not the 'geometric' RS.

It could be argued that, if you have greater elastic roll stiffness (stiffer ARB or springs) then the rate (speed) with which elastic RS becomes the dominant vector of weight transfer (with increasing lateral acceleration and as the degree of weight transfer increases) and geometric RS becomes less influentuial will be increased, i.e. the more quickly weight transfer will start to transfer more through the springs, ARB etc than geometrically.

In any case, a stiffer ARB at a single axle line will increase and speed up the amount of elastic weight transfer at that axle line, and decrease it (to an equal but opposite degree) at the other axle line (even though the suspension at this axle kine remains unchanged).

With increased elastic RS, initial axle line roll stiffness at turn in will still mostly be the geometric RS (before springs , ARBs load up significantly), but elastic weight transfer just after turn in should be sped up and increased by stiffer ARBs or springs.

Remember that the geometric vector transfers (whatever % of total weight transfer that is transferring geometrically at any given moment) at the same rate as the increase in lateral acceleration, so sudden changes in 'G' force will to some degree see abrupt changes in dynamic weight distribution that will aggravate the change in 'G' force (read loss of grip at an axle line). So, cars with a very high GRC (e.g. rear suspension on Beetles etc) can be very unforgiving near / at the limit because a lot of weight can be transferring geometrically even at higher lateral accelerations.

It's generally good to have lower geometric RS (lower GRC location) as this allows more weight to be transferring elastically at / near the limit, and since the elastic vector transfers weight 'slowly' (compared to the geometric vector), any sudden change in acceleration ('G' force) will not be accompanied by such an abrupt change in dynamic weight distribution, so the handling will tend to be at least somewhat more forgiving (i.e. less abrupt loss of grip with more warning to the driver). There's a bit of a 'chicken and egg' thing here I think.

Note that if X weight is transferring, then (unless the CG and GRC are at the same height, or, the GRC is at ground level and on the centreline, or, the springs are rigid, in which case suspension geometry effectively ceases to exist), that some % of weight will, be transferring geometrically and some elastically, and these %s will always add up to 100% of the total weight transfer at that axle line.

It's interesting to note that if the GRC is say at ground level (for ease of example just because ground level and on the centreline gives zero GRS), but hypothetically offset to one side then this will either increase or decrease the value of the GRS and the ELS (elastic RS).

Example, if the GRC is offset toward the inside (of the chassis and corner), then GRS will be less than zero, it will actually be negative. This won't alter the amount of weight being carried on each contact patch, but will change how much load is being carried via the springs and how much carried by the suspension members (wishbones etc).

In this example more weight will be carried on the outside spring and less on the inside spring. This would also affect weight carried by the suspension linkages, with less being carried by the outside linkageslinkages and more by the inside linkages.

Note that this does have a real world affect because the GRC typically moves inward when cornering because the angles of the suspension linkages change, causing the virtual swing arm to become shorter on the outside suspension and longer on the outside suspension.

Some people might wonder how more or less lateral suspension linkages can carry vertical weight, but they can. When you jack the car up the wheels move closer together, but when you lower the car it won't lower to the original level because the tyres have grip and refuse to 'scrub' laterally to allow original ride height. This means more weight is being carried by the 'lateral' suspension members and less by the springs (which will be somewhat extended over their length at static ride height). In fact this weight (force) is being reacted into the chassis through the same geometry that defines the GRC.

Similar (but more complex) affects occur when cornering, causing some changing % of weight transfer to be transferred through the linkages (i.e. geometrically) and not the springs.

I suppose I should describe the 'virtual swing arm', since it's important to understanding GRC location (among other things).

Looking at the front suspension(s) head on, if we draw lines along the lateral axis of each wishbone pair, then the point at which those axes intersect (which will be a point 'in space', not a physical part of the vehicle) is the 'instant centre' of the 'virtual swing arm'. The instant centre is the point around which the hub moves (in an arc) with suspension deflection, as if it were the real pivot point of a real swing axle.

That's all OK and good, but the instant centre moves around a lot as the suspension deflects (unless it really is a real swing arm suspension, in which case it's location is static regardless of deflection), moving up / down and laterally depending on the exact geometry of the suspension linkages.

This change in instant centre location is what governs the 'camber curve' with suspension travel (i.e. how much and in what manner the camber changes with suspension deflection), as well as other things such as lateral contact patch 'scrub' with deflection (how much the contact patch moves laterally relative to the chassis, which is another reason not to have a very high GRC as this creates too much lateral contact patch scrub).

Once we know (on paper) the location of the two ICs (one per side), we can locate the GRC by drawing lines from the centres of each contact patch to the IC of that side of the suspension, and where these two lines intersect is the location of the GRC.

If you can imagine how the ICs must move around with deflection (with dramatic changes in suspension arm angles), you start to see how difficult it can be for designers to keep the GRC in a relatively stable position with body roll. This is probably one of the most important things for the designer to achieve, as abrupt changes in GRC location create abrupt changes in distribution of weight transfer and thus can cause tricky transient handling.

Mess with the suspension geometry a lot and you can easily create significant problems in this regard, and is at least one good reason to reduce body roll motion with heavily modded suspensions (read lowered more than just a bit), i.e. limiting roll motion limits the degree to which the GRC can move erratically, even if the basic eometry has been stuffed up!

Sorry, too long again! As you might be gathering by now, this is a very complex area of chassis dynamics, but it lies at the heart of how well a truly good handling car behaves.

[JohnL]

Failed to mention I have lame rear beam suspension. One day When I get enough time at the track I'll raise the rear by 15mm between runs to see what effect it has on lap times. Being a beam rear end there wont be any effect upon alignment due to this.

Are there any resources you would recommend for reading into this further? I have always wanted to know more in this field of suspension set up. I believe I have a strong understanding of the other suspension area, and always want to know more.

In principle, beam axles are very good for the rear end (not the front though). If they are well designed (i.e. good linkage geometry), then the GRC will tend to be more or less in the right place for a rear suspension (i.e. higher than the front GRC). They tend to be very simple and robust, easy to set up and deal with, but probably not quite as good as a really well designed independant rear end.

They don't allow much camber change on the loaded wheel (beyond the 'axle tilt' you get due to vertical tyre deflection and IR lift, but you can tweak their static camber to account for this), so give good camber control with body roll.

The old BMC Mini had a rather poor stock rear suspension (trailing arms that placed the rear GRC at ground level), and one of the more common changes often made for racing (if rulles allowed) was the installation of a beam rear end.

The best beam rear ends use four radius rods for longitudinal location and a Watts Linkage for lateral location (Panhard rods allow some lateral movement with deflection, whereas Watts Linkages don't).

DeDion rear ends are in effect a beam axle (like a live axle but with the diff mounted on the chassis rather than in the axle, to save unsprung weight and prevent axle wind lifting the RR and losing traction at that wheel), and were used on many very good handling RWD cars over the years (my old Alfetta had one, a very nice handling car), being very common in 'formula' racing in the 40s and 50s.

Beam axles are typically a bad bet for the front end as it's almost impossible to design them so that the GRC is as low as you'd really want, which is probably the main reason that they were abandoned so long ago for front suspensions (with some more modern aberations such as the Panther Lima).

Having said that, I can recall at least one Australian racing car ('Welsor' clubman) that was reasonably successful in the 80s using a rather sophisticated front beam, the details of which I don't know. There is a kind of lateral linkage that can be used to give quite low GRC locations on beam axles called the 'Mumford Linkage', but it's very complex and rather fragile from what I hear, not a very practical proposition, especially when you can more easily use a fully independant design probably to better effect.

Speedway sprint cars also use front beams succesfully, but they are very developed for a very very particular application (I'm not sure that good turn in behaviour is all that important for a car basically steered sideways on opposite lock and with the throttle?).

It's a bit hard (for me) to say whether raising your rear end will improve your lap times or not. If raising the rear end of a rear beam axled car that has the axle located with a Panhard rod, then this will change the angle of the PR, which can increase the lateral axle displacement with suspension movement (best avoided). PRs should be horizontal in the static position.

There are probably a number of things that could interact to make an in theory 'improvement' work less well in real life, which doesn't necessarily mean that X change was wrong, but that other things may also need to be changed to make the most of change X. It's always a good thing to get the CG as low as possible and set up the car around that (though failure to do this well may result in the car being faster at a higher CG height). Only with karts is it intrinsically possible for the CG to be too low, but these are very idiosyncratic vehicles with very specific requirements.

Resources? Most of my own 'understanding' (right or wrong) comes from my own thinking, being sparked off by what I've read in the more common books (when some of the authors propositions didn't make complete sense to me) such as Fred Puhn's 'How To Make Your Car Handle' (and some others I can't recall), from discussions on internet forums with knowledgable people involved in karting, and from a relatively lengthy on-line correspondance with a professional suspension engineer (the head chassis engineer at TVR cars UK) who found my ideas on roll theory of interest when he ran across them on ekartingnews.com.

Probably the most authoritative book on chassis dynamics would be one that I haven't yet read; 'Race Car Vehicle Dynamics' by Milliken and Milliken. This is more or less 'The Bible' for suspension designers, but not light reading from what I hear. It's on my book wish list, but it's not a cheap tome (and I'm a cheap reader!).

[EGB18CT]

gotta also be careful if your adding one of the roll center adjusters it may also raise the upper wishbone/camber arm and hit the fender on compression, solution to this is if you have multi height adjustable coilovers at the cuffs to actually lower the coils without compromising the compression of the spring/damper. Read this on H-T the other day as ill be getting one of these soon.

[string]

Probably the most authoritative book on chassis dynamics would be one that I haven't yet read; 'Race Car Vehicle Dynamics' by Milliken and Milliken. This is more or less 'The Bible' for suspension designers, but not light reading from what I hear. It's on my book wish list, but it's not a cheap tome (and I'm a cheap reader!).

PM me when you give up trying to find a copy just like I did.