Any discussion of chassis design will come round to roll centres sooner or later. Invariably, if that discussion happens on the HAMB, someone will chip in with the comment that worrying about roll centres is splitting hairs and that the enquirer is best advised to stick with the tried and trusted and not break his head trying to understand how or why it works. However many of us have the kind of nature to take that as a challenge, one is still hard pressed to find someone who will actually explain what the whole roll centre thing is all about: so here it is. Chassis tuning is all about varying the distribution of lateral weight transfer between the front and rear axles. The great thing about a pneumatic rubber tyre is, the more weight one puts on it, the squishier it becomes. To some extent putting more weight on a tyre has the same effect as putting less air in it. The contact patch at the bottom of the tyre is capable of twisting further away from the direction the wheel is pointed, the more weight one puts on it, or the less air pressure one puts in it. We call this difference between the direction the contact patch is pointing and the direction the wheel is pointing a slip angle. (The term is traditional but it is hard to get one's head around because it doesn't really involve slipping. A better term might be something like "twist angle", as it has more to do with tyre deformation. The confusion has led to misuse of the old term drift, which used to mean an attitude different to its direction of travel adopted by a car due to slip angles without loss of traction, and not a controlled slide as the term is more often used today.) Because the total weight transfer at any given lateral acceleration is a function of vehicle mass, track width, and CG height, it is pretty much locked into the design by the time it gets to tuning the chassis; but that means that adding weight transfer at one end (front or rear) will automatically take the same amount of weight transfer away from the other end. That is to say, by adding weight transfer at one end for the purposes of chassis tuning one cannot increase the total amount of weight transfer. Hence, most chassis tuning happens by adding weight transfer at the end which is behaving better, in order to take weight transfer away from the end that is behaving worse. For example, excessive oversteer is counteracted by a stiffer front anti-roll bar which, by loading the outside front wheel more, causes the outside rear wheel to be loaded less. (Yes, front anti-roll bars are also used to reduce understeer, but that is by reducing roll as such and thereby reducing front-wheel camber gain with roll. The fact that it works and is a common fix on Morris Minors, for instance, causes endless confusion about how weight transfer distribution works.) When subject to lateral acceleration in cornering, weight will be transferred from the inside wheels to the outside wheels of a vehicle. The extent of this transfer will be equal to the inertial torque about the tyre contact patches, i.e. vehicle mass times lateral acceleration times CG height, divided by the lateral torque arm represented by the vehicle's track. But this total weight transfer consists of two components, because the vehicle consists of two components, the sprung mass and the unsprung mass. That the weight transfer of the unsprung mass works just like the overall weight transfer should be easy enough to understand: unsprung mass x G's x CG height of the unsprung mass / track. Here we see the real reason for wanting to get rid of unsprung mass, rather than the usual reason about inertia over bumps resulting in loss of traction. The more unsprung mass there is, the more weight transfer is locked in and not distributable between front and rear by working with roll stiffness and such. But note that just as important as reducing the amount of unsprung mass is ensuring that the CG of the unsprung mass is as low as one can get it. If one could devise a live axle with the pumpkin hanging below the axle, it might be as good as a lighter axle. Where roll centres come in is with the fact that weight transfer of the sprung mass comes about in two ways: due to lateral inertia of the sprung mass acting on the unsprung mass at the front and rear roll centres; and due to the resistance to rotation of the sprung mass about the roll axis (which is an imaginary line connecting the front and rear roll centres). Simply put, the more one has of the one the less one has of the other, and the proportion depends on the height of the roll centres. The extent of weight transfer due to lateral inertia of the sprung mass is given by: sprung mass x G's x RC height / track. The extent of weight transfer due to resistance to rotation of the sprung mass is: sprung mass x G's x (sprung mass CG height - RC height) / track. It is generally easier to change the front or rear roll stiffness by using stiffer or softer anti-roll bars than it is to change roll centre heights. That is why the conventional wisdom in chassis tuning has been to favour roll centres as close as possible to road level, thus to render a chassis as responsive as possible to changes in front or rear roll stiffness. It has also increased the importance of a torsionally rigid vehicle structure, as this approach effectively comes down to using the entire vehicle structure as a rotating shaft to relay weight transfer to one axle or the other. On a simple, flexible, but relatively light hot-rod frame one soon runs up against the limitations imposed by the lack of rigidity, which is why I'd argue that the best-handling hot rod might not be the all-independent chassis one might expect. That would require some sort of departure from the conventional wisdom; but that is another discussion. Low roll centres have other advantages, though, especially the reduction of lateral displacements over bumps, resulting in a less jittery ride and better composure on bumpy surfaces. I've crunched some numbers by way of comparison. It will be noticed that all the above formulae contain "mass x G's / track", so for comparison purposes one can replace all that with a constant, call it "A", and express the results in terms of percentages rather than absolute values. Then all we need to know is a few heights. Let's assume a typical early Ford hot rod. For argument's sake let's say the unsprung mass is 10% of the total. The CG of the unsprung mass is 10" above the ground; the CG of the sprung mass is 20" above the ground; the CG of the two together is therefore 19" above the ground; and the roll centres are both 12" above the ground. In order not to cloud the issue I shall not introduce different values for front and rear, but that is what one would eventually be looking at. Total lateral weight transfer would be: 19 x A Weight transfer of unsprung mass would be: 0.1 x 10 x A = 1 x A (5.263%) Weight transfer due to lateral inertia of sprung mass would be: 0.9 x 12 x A = 10.8 x A (56.842%) Weight transfer due to resistance to rotation of sprung mass would be: 0.9 x (20-12) x A = 7.2 x A (37.895%) Note that 1 + 10.8 + 7.2 = 19. These figures indicate that only about 38% of the weight transfer will be responsive to changes in roll stiffness at the front or rear. If the base weight transfer distribution is 50:50 the greatest bias one would be able to induce one way or another would be 69:31, and that fairly large differences in roll stiffness would be required to induce any given bias. If the base distribution is already biased, e.g. due to a heavy rear axle and tall rear tyres running relatively low pressure, there might not be enough adjustment there to keep the tail under control, especially if one factors in the limitations of the frame's flexibility, and moreover requires a reasonably comfortable ride. Let's see what happens when one reduces the roll centre heights to 2½": Weight transfer due to lateral inertia of sprung mass would be: 0.9 x 2.5 x A = 2.25 x A (11.842%) Weight transfer due to resistance to rotation of sprung mass would be: 0.9 x (20-2.5) x A = 15.75 x A (82.895%) This allows one an adjustment range of up to a 9:91 bias either way (given a 50:50 base distribution); and if the adjustment required is around the middle of that, a small difference in roll stiffness will go a long way. But generally the forces pertaining to roll resistance would be somewhat greater than with the higher roll centres, and the torsional demands on the frame will be somewhat more onerous. That is, unless one can get past the torsional rigidity thing, but that, too, is another discussion.
Oh wow. Can you tell me if Henry Ford had it "right" with his cross-sprung wishbone suspensions? Say ala 1932 Ford. Now how about if we flatten the springs, drop the front axle, and install 16x5.00 and 16x7.00 tires?
Henry actually achieved something quite interesting, doubtless purely by accident. The early transverse-leaf suspensions have two roll centres at each end. The car can roll quite a lot without the springs coming into play at all, about instant centres defined by the spring shackles and normally located a short distance below the road. The instant centres migrate with roll to self-correct to a certain extent, so the car doesn't keel over and rest on its bump stops. Only after a certain amount of roll does the spring gradually start to have an effect, and the second roll centre near the middle of the spring come into play. The advantage of this is that torsional rigidity is a non-issue as long as one drives mildly enough that the lateral accelerations on the chassis are small. If you flatten the springs the shackles go closer to vertical, and the first roll centres move lower below the road. The lateral motion of the frame with roll becomes greater and the self-correcting effect becomes less pronounced, to the extent that you'll need a lateral locating device like a Panhard bar, which will impose a single roll centre definition. That means that the spring always has an effect on roll. And that means that torsional rigidity of the frame starts to become a factor. If instead you take care to use a shorter spring, the shackle angles are maintained: but chances are that the whole purpose of the exercise is going to involve pushing the chassis to lateral accelerations way over the abovementioned self-correcting range. Short answer: the transverse leaf set-up isn't nearly as crude as it looks, but it has fairly severe limits. I'm disappointed in the rest of you guys! No small furry animals with baked foods on their heads?!
I liked it, but just to be on the safe side, can you give us examples of sprung and unsprung components (to calculate the mass), or how can we differentiate between the two types of mass?
Fopelaez, simple way to look at spring weight vs unsprung weight is to just look at your vehicle in parts, anything that is attached to the spring and touches the ground is unsprung weight, anything that attaches to the spring and doesnot touch the ground is sprung weight . To account for any part that contact both like the shock and spring itself, the weight is divided in half between unsprung and sprung.
Unsprung components are items like tire, wheel, brakes and the axles themselves. Edit: Dick types faster and explains better Here's a handy dandy little gizmo that anyone could make and IMO anyone interested in roll centers, instant centers, sprung vs unsprung or spring rates should have. http://www.jalopyjournal.com/forum/showthread.php?t=588650 Gary this roll center thread goes right along with your thread a while back . http://www.jalopyjournal.com/forum/showthread.php?t=573296&highlight=scale
In other words, everything that moves up and down when the car bounces on its springs is sprung mass. Everything that stays put when the car bounces on its springs is unsprung mass. Some things are attached to the sprung mass at one end and to the unsprung mass at the other. The springs themselves are a classic example. Conventionally one would consider half their mass sprung and half their mass unsprung, but sometimes that isn't quite true. Some of these components have a greater concentration of mass at one end than at the other. For example, a split wishbone is heavier at the axle end than at the frame end, so it's probably about 60% unsprung / 40% sprung. Or an anti-roll bar: most of the bar simply rotates about its own axis, so one would only be considering the mass of the free ends when deciding how much of the bar's mass is sprung and how much unsprung. Or an extreme example: a Vespa scooter's engine and gearbox ride on the rear swingarm, but the entire mass of the engine and gearbox isn't unsprung mass. Not even half is unsprung mass, because the assembly rotates about a point near the engine/gearbox's centre of gravity. Knowing the actual figures isn't nearly as important as understanding the principles, so that the principles can inform good design decisions. I did some math in the original post to illustrate how much roll centre heights influence the effect of roll stiffness, but once one understands that principle one doesn't need to do a lot of math to make good design decisions about locating roll centres.
O/T; Ned Ludd, I tried posting a comment on new urbanism on your blog, but it kept flicking back to email detail request. Fine argument, esp. on land deprivation as a cult. Thanks for this thread too- nice chunky tech, over my head some, but I can work on it. Thanks DICK SPADARO.
Well written Ned. I would argue that the unsprung weight on a 32 highboy is closer to 20 percent than ten.. My 32 weighs exactly 1000KGs, and Im damn sure the diff, brakes and front end weigh a hell of a lot more than 100 KGs.
Thanks Spoggie. I don't know why it should do that, it's letting spammers through just fine! PM me your e-mail address, and I'll check if the blog isn't treating it with suspicion. That is entirely probable! though 1000kg is light for a Deuce, even fenderless. I'd expect more of them to be around 1100-1200kg. I plucked the figure of 10% out of thin air, purely for argument's sake: I think one would be quite pleased if one could achieve it in reality.
well written and informtive.but i really dont care lol. when i build a frame i dont look for roll centers. i just put things where i need them. seems to work out pretty darn good!
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