For my old buddies from the "other" forum

[Oscar Aguilera]

We had some people say a Kart had a roll center and some say it couldn't. (I say it does)

What is the difference in a car lifting the inside rear wheel and when a Kart does the same?

I ask this question because some opinions say that a kart is not sprung.

Where is my buddy John Learmouth?

[Paul Kish]

IMHO...

Weight transfer is directional. The sore spot to me is does each individual part on the kart/car transfer weight directionally or is the starting point for all weight transfer the cg? I think that both are true. If it ain't nailed down its going to go its own way initially. The driver is the only sprung weight on the kart. The driver is moble and sprung weight up untill the point that the drivers weight against the seat, steering wheel etc, effects the kart. So there is the sprung weigh of the driver on the kart and the rest of the kart is for all practicality not sprung.

As far as roll centers go they are meaning less unless the weight that is going to transfer directionally does something for you of makes something "roll".

The only thing we have to understand is the direction the weight is going to go and what restrictions if any are being placed on the transfering weight being able to "move" something. Unless the transfering weight will "move" something, again roll centers are meaning less.

Beyond that the transfered weight will do things for the kart that are, sort of, intangable. Like adding to the grip of a particular tire or flexing a chassis, or putting two or more parts of the kart in conflict with each other.

To net it out roll centers on a kart or a car for that matter are meangless. What matters is "THE DIRECTION THAT THE WEIGHT IS GOING TO TRAVEL" and how that weight is going to operate the chassis. It doesn't really matter if you cannot put a neat drawing or fine math to it, all that matters is the "direction" the weight will go.

And the only significant sprung weight on the kart is the driver.

Now if yer debating how to draw a picture of it and how to do the math then that's a whole different ball game. Have fun, ya got a tough row to hoe.

This is all IMHO and ain't necessarly right.

[ October 12, 2001: Message edited by: Paul Kish ]

[John Learmonth]

Hi Oscar old mate (we don’t have ‘buddies’ here in Oz, we have ‘mates’!),

Ah …… roll centres, one of my favourite sources of headaches!! I could be wrong of course, but I agree with you. I can’t really see (even with karts) how roll centres (2 off, defining a ‘roll axis’) cannot exist, despite with karts the very real problem of actually defining their location.

Assuming they do exist (which I do, for good reason I think!) then by the very nature of a kart chassis they must be very mobile points in space (the front roll centre more so than the rear, because of the greater chassis deflection at the front). A car’s geometric and actual roll centre locations will also change with suspension deflection (laterally as well as vertically), but generally less so than a kart’s will because on a car the actual suspension linkage and its geometry will be more defined and ‘finite’ (even taking into account that the ‘effective swing arm’ length will change with deflection) than the ‘suspension’ geometry on a kart (ie despite any movent of the car suspension, the actual linkages will remain fixed in actual length, and their points of articulation remain stable), whereas a kart’s ‘suspension linkages’ will be less defined and ‘infinite’ (effectively change in actual length and their points of articulation vary with loading).

As with a car, parts of the kart are unsprung, and parts are sprung. The chassis has its own form and geometry that acts as ‘suspension’, and just as a car’s suspension geometry defines the car’s roll centre locations, so must the kart’s chassis geometry. It may be desirable with a kart and not with a car, but when either lifts a wheel I don’t think there’s any intrinsic difference in the way in which a kart does this and the way in which a car does it (whether this is the inside rear, inside front, or both inside wheels). Its still the ‘suspension’ deflection, and the geometry of that deflection that will dictate what wheel lifts / unloads under whatever particular dynamic conditions.

Whenever there is a moving object / mass with inertia (which will be the case with every moving physical object), and that inertia is resisted by a force that is offset from the direction in which that object is travelling and ‘wishes’ to continue to travel in, then the movement of that object will be influenced by that offset force in a manner that will cause the object to change direction and that change of direction will involve the object in moving in an arc or arcs around a centre or centres. These arcs of movement will be seen as the mass moving around a centre that is the centre of the cornering arc in the horizontal plane, and as the mass moving in an arc that is a ‘roll centre’ in the vertical plane. I think all vertical movements of the inertial mass in an arc can be described in terms of ‘roll’, whether or not the text books may call it ‘roll’, or ‘pitch’ or whatever, basically these will be manifestations of similar phenomena.

A single roll centre can only exist if there is only a single point of resistance to the inertia of the moving mass, and since this is never the case with any vehicle with more than one wheel on the ground then there must be two roll centres (defining a ‘roll axis’) around which the mass of the major masses of any four, three or two wheeled vehicles moves in vertical arcs.

At each end of the car or kart there will be two points that can resist the inertia of the moving mass (ie the contact patches). If only one of the contact patches at either end of the vehicle is in contact with the track, then that point will become the point of resistance around which the mass will move in a vertical arc, but if both contact patches are in contact with the track then the point around which the mass will move in an arc will be an average of the resistances generated by both of these contact patches.

When there are two contact patches in contact with the track at an end of the kart (or car), then where the average point of these two resistances (contact patches) will be located in space at any point in time will depend on the geometry of the path through which the forces involved are leveraged between the mass and the resistances (ie the ‘suspension geometry’), which will cause the roll centre to be located somewhere between the contact patches, but may also cause the roll centre to be located at a height either above or below the contact patch height.

This is why I conceive of a kart having a diagonal roll axis, ie because when the inside rear is unloaded there is only one point of resistance at the rear (the outside rear), which becomes the rear roll centre, and there will usually still be two contact patches in contact with the track at the front, and the front roll centre will be somewhere between these two contact patches. Additionally I think the actual roll centre (as opposed to the purely geometric roll centre) will be biased toward the contact patch with the greatest actual grip (which will depend on a number of factors), which will be one reason why the front roll centre is closer to the inside front early in the corner and closer to the outside front later in the corner.

I know a lot of people will disagree with how I conceive this to work, and admit that I may not be thinking of roll centres in exactly the same manner as is commonly accepted in the automotive world. I do think however that the common conception of how roll centres are defined is only part of the true picture of how they work in the real world (ie I don’t think geometry is the be all and end all of defining the actual point around which a mass will ‘roll’). This is all oversimplifying and leaving a LOT of stuff out, but unfortunately I find myself lacking the articularity (is that a word?!) to adequately explain the complex nature of how I perceive all this to function (and believe me I’ve tried!).

I expect many will think this all to be just a lot of hot air and theoretical bull****, and even some of those who don’t might think my ideas are wildly off track, but I do think the location of roll centres and the manner in which those roll centres move has a great deal to do with how any chassis behaves, and is a major part of why some chassis work better than others, why some chassis are easier to drive than others, why some are easier to set up than others, and why some work well in certain conditions and others don’t, ie Paul I disagree with you, roll centres are not “meaningless”, they are VERY important! (I just wish I understood the exact nature of their behaviour better!).

[ October 14, 2001: Message edited by: John Learmonth ]

[ October 14, 2001: Message edited by: John Learmonth ]

[Oscar Aguilera]

G'day Mate, indeed! Any Whacker knows that ther is nothing but Bull**** on the Chassis forum.

Let me Texas size simplify, my down under buddy.

I think that the roll center in the front only deviates from the center of the kart up to the point where something bends in the front end. Be it the chassis or the spindle. Forming that arc that a suspended car has. But suspensions stop at the chassis where they connect. The bending in a car is far less noticable and I think most people negate the fact ath they bend as well when doing the Center Roll stuff. (Isn't that why they invented monoq... chassis?

I think that the rear roll center raises and moves (as the driver controls this with his body wieght whether he knows it or not) to the left or right up until the bending stops. In some cases it is the axle, and in some it is the chassis. Tire wear dictates what needs to be changed to bend more or less.

I was starting to miss your long disertations. Ever since you wrote that front end geometry stuff you checked out on us, huh?

[Bryan Mappe]

Some simple thoughts from a simple mind (all you engineers take it easy on me ).

Isn't the defintion of roll center something akin to "The amount the car's (kart's) front end rolls (leans) due to cornering forces, compared to its static (standing still) angle."?

If so, common sense tells me a kart has a roll center, unless your frame is so stiff nothing flexes and you are just sliding sideways through the corner on the tires contact patches. Of course, you would have to get rid of the inflated rubber tires also to eliminate all "flexing" parts.

And yes, on the race car in my garage the frame would flex, hopefully so minute that it is not measureable. The goal is to have the stiffest frame possible so you can control the dynamics of cornering with your suspension design.

[Chuck Bunnell]

This sounds like a trick question to pull John back out of the woods, (or Aussie equivalent), where he was hiding. I think you just need to adjust your point of view here. If a kart or any other vehicle rolls in some fashion during cornering, it has to have a physical roll center. You may not be able to simply or easily describe it's location, but that doesn't mean it doesn't exist. It just means a "simple" kart ain't so simple after all.

We can answer the suspension question the same way. The chassis is designed to deflect as are the tires and therefore we are suspended. Just not in the traditional sense. How dark is dark? How small of suspension travel can we have and still be considered suspended. I guarantee you that we are suspended and would not be able to drive much faster than 10 mph if we weren't.

[Dave Embry]

quote:

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Originally posted by Oscar Aguilera:


Where is my buddy John Learmouth?

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hahaha!! "LearMOUTH" !!! haha!

[Oscar Aguilera]

quote:

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Originally posted by Dave Embry:


hahaha!! "LearMOUTH" !!! haha!

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That was a typo, but it is funny

[John Learmonth]

quote:

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Originally posted by Dave Embry:


hahaha!! "LearMOUTH" !!! haha!

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Dave, I've been called worse things! I get that mispelling all the time, and others, so didn't bother to correct it.

[Paul Kish]

Oscar/John

Roll centers and leverage.

We race LTO karts and I have found that it makes a big difference where the outside rear bearing casset is mounted.

I don't net things out very well but to net it out... All other things being equal the farther away from the outside rear tire contact patch the bearing casset is located the lower the cg should be to be.

I think the first reason is because as the bearing casset is moved closer to the outside rear tire the flex of the axle between the outside rear bearing casset decreases.

Secondly and I think more importantly the flex of the axle/chassis towards the inside rear tire increases as the bearing casset is moved towards the contact patch of the outside rear tire. I think that increase in flex raises the rear ROLL CENTER of the kart. The raising of the rear roll center also raises the cg of the weight that is transfering to the outside. That in turn will direct more weight toward above the contact patch of the outside rear tire and tend to make that tire want to roll over. And to compensate for that you will need to run a lower cg when the position of the outside bearing casset is moved away from the contact patch of the outside rear tire.

Where did all that go and how do I relate it to roll centers? It means to me that it looks like that at least the rear roll centers are not immediatly fixed or defined. They only become fixed and defined once the inside rear tire is unloaded to what ever point it is going to unload. It means to me that at least the rear roll centers are constantly raising and lowering. It also looks to me that they must be defined at rest and at their maximum movement to be usefull. You need to know where they are at rest so you can place static weight to start them moving. You don't necessarly need to know where they will be when the stop raising but you need to be able to define the mechanics of the chassis so you can control how much they raise. That way your chassis can efficiently start the roll center raising up and run out of leverage when the inside rear is unloaded.

I sure hope some of what I wrote makes some sence to someone out there.

John, I hope I finially see a logical reason to be concerned about roll centers, at least rear roll centers. We race LTO karts so I am only thinking of the kart having just one roll center. But I think there are really two. One is created at the rear when the kart turns left and the other is created when the kart turns right. The light bulb that went on for me was that I could possibly use chassis design and static weight placement to make it easy to initiate or start the roll center moving. And that realizing that they were going to move, specifically in the direction of up, I also can see chassis design and again weight placement limiting their upward height. To me that is really great, the thought of being able to do that. Make it easy for the chassis to start running and then put a govener on it.

Thinking out loud some more about it.... I think there is a relationship between the location of the outside rear tire patch, the location of the outside bearing casset, the cg and the length/height of the lever to the vcg from the outside rear tire contact patch. Maby... if you can calculate the lever length and position with the kart at rest and then calculate its length with the inside rear tire unloaded or raised slightly you could define the arc the roll center is taking and there by define the roll center. In other words the tire patch can be difined, and the actual cg can be defined. Just define it with the kart at rest and again with the kart inside rear unloaded. Then every point in between will be the arc the roll center is taking. Oooops... just though of one problem. Yes you can define the arc of the roll center but now how are you going to place that arc in space between the cg and the outside rear tire contact patch? At least you will know or did I just define that it, the roll center, is going to have to be located somewhere between the cg and the outside rear contact patch????

[Tim Lewis]

OK, this one is more closely related to cars...I can run with for a little while.

Roll center is a term that is somewhat misnamed. Even a car when there is not question as to where is it located, it is not the 'magical' point about which the car rolls. It is simply a way of seperating which part of the overturning moment is taken by the spring and which is taken by the suspension links. A car that has both r.c.'s at ground level takes all of the roll load in the springs while one with higher r.c.'s distributes it between the springs and the wishbones.

Without sprung masses, unsprung masses, and linkages between them, we cannot have r.c.'s.

I can visualize the rear 'suspension' easily. The rear is essentially a swing arm with the sprung mass starting at the bearing carriers and the linkage being the bit of axle between the hub and bearing. In this case (like a VW bug or old Corvair), the R.C. would be defined by drawing a line from the contact patch of the rear tires through the bearing carriers. The point where these two lines intersect will be the R.C. The wider the track, the lower the R.C. It will always be above axle hieght, though.

The front is a little tougher for me to visualize. It get's pretty fuzzy as to what is sprung and unsprung. Unsprung is generally defined the stuff that moves vertically when the tire hits a bump. For a kart, that is going to be practically everything, including the driver.

I'm not convinced that a roll-center has any real meaning on a kart. Yes, the chassis flexes, but the tires themselves are probably the biggest contributors of cushion between the surface of the road and your bum. Having said that, my kart rides bumps better with a soft axle and a wide rear track so the tires are certainly not the only player.

So what does it all mean? I don't know...that's why I had the other post.

Tim Lewis

[Larry Hayashigawa]

I have watched this debate go on the karting website and now here. So I am going to throw my two cents in.

Most non-kart race cars have a rigid body/chassis. A roll center is the point in space where the rigid body/chassis rolls about when cornering. There are two defined roll centers, a front roll center and a rear roll center, which are in plane with the front wheel and rear wheel centerlines. These are picked for convenience, as the roll centers can be determined by analysis of the suspension geometry) For a myriad of reasons the front and rear suspension geometries are different and therefore the roll centers are at different heights. The line between the front roll center and the rear roll center is the roll axis and is the axis that the rigid body/chassis rotates about. Roll centers also move as the chassis rolls.

Roll centers are used by non kart race car designers to determine how much load is transferred to the tires during cornering acceleration. Steady state weight transfer can be calculated as function of lateral acceleration by knowing the suspension geometry and the spring rate.

It's difficult to do this for a kart using roll center techniques because there is no roll center (no rigid body rolling about a specific point in space)and there is no discrete spring element.

All this leads me to cast my vote that there is no roll center on a kart.

Although, just writing about this made me think a little more on the topic. There is a roll center/axis on a kart though. It happens when the kart goes up on two wheels. The roll center is the outside tires and the rigid body is the kart and the driver rotating about the outside tires.

[John Learmonth]

Tim Lewis said:

> Roll center is a term that is somewhat misnamed. Even a car when there is not question as to where is it located, it is not the 'magical' point about which the car rolls. It is simply a way of seperating which part of the overturning moment is taken by the spring and which is taken by the suspension links. <

Tim, I’m not completely certain, but I suspect what you say may well be correct, ie that a geometric roll center isn’t the point of actual roll, but largely the point defining how much weight transfers via roll or via roll stiffness. I am sure that the geometric roll center at least has a large influence on the location of the point of actual roll. I suspect that mechanical rigidity of the load path has as much influence on the location of the ACTUAL point of roll as does the geometric ‘roll center’.

> A car that has both r.c.'s at ground level takes all of the roll load in the springs while one with higher r.c.'s distributes it between the springs and the wishbones. <

And if the roll center and the CG occupy the same point in space then the overturning moment will transfer weight entirely ‘through’ the linkages and not at all through the spring (100% roll stiffness). To add further to this, I think the reason this is 100% roll stiffness is not so much because the two points (CG and RC) occupy the same point in space, but that the roll center is located ON the line between the contact patch and the CG. No matter where along this line (ie at the CG or at the contact patch, or anywhere between these points) the roll center may be located, the result will be 100% roll stiffness.

Assuming this to be correct, we can see that increased roll stiffness will come not only from raising the roll center closer to the CG height (or lowering the CG closer to the roll center), but also from moving the roll center laterally closer to the outside contact patch. I think that a karts rear roll center is located quite low early in the corner, at or very close to the outside rear contact patch. In the first half or so of the corner this will give a high roll stiffness at the rear, even though the roll center is low. I think the front roll center is also low, but very much farther from the outside front contact patch, giving a very low roll stiffness at the front (possibly even negative roll stiffness, if such a thing is possible).

> Without sprung masses, unsprung masses, and linkages between them, we cannot have r.c.'s. <

I can’t agree that karts don’t have sprung and unsprung masses, or that there aren’t linkages between them. I think there are some parts of the kart that you can safely consider to be 100% unsprung, such as the tyres, wheels and the outer ends of the axles. There will be parts of the chassis that can safely be considered to be (for all intents and purposes) effectively 100% sprung, such as the seat, but more importantly most of what it contains, ie the majority of the driver’s body mass. Between these sprung and unsprung masses there are ‘linkages’ that are to greater or lesser degrees flexible members acting as ‘suspension’. Some % of the mass of these ‘suspension’ members will be sprung and some % will be unsprung (which is the same with a car’s suspension components, including springs).

I don’t think any of this is inherently different to the sprung and unsprung masses of a car chassis. It should be kept in mind that a car will have some masses that are 100% unsprung (wheels, tyres, hubs etc), and some that are 100% sprung (chassis, motor, driver etc), AND that some % of the suspension linkages will be both sprung and unsprung, just like the ‘suspension’ on a kart. The only inherent difference here is that a car’s suspension linkages are of fixed length, and the points to which they are attached to the main unsprung masses are stable, whereas a karts ‘suspension’ linkages are of variable ‘length’ and the location of the points to which they are effectively ‘attached’ to the main unsprung masses are not stable.

Just because a karts ‘suspension’ linkages are not easily definable compared with a car suspension (and even if you can define them, the moment you flex the chassis the definition changes), doesn’t mean that the flexible members allowing the wheels to move up and down relative to the CG are not bone fide suspension linkages that act in every way like bone fide suspension with real and active roll centres. This ‘vagueness’ of the linkage simply means that the geometry of the suspension is variable, and as a result of this variability the location of the roll centers will also be variable (as are the roll centers on a car, just not to the same degree).

> I can visualize the rear 'suspension' easily. The rear is essentially a swing arm with the sprung mass starting at the bearing carriers and the linkage being the bit of axle between the hub and bearing. In this case (like a VW bug or old Corvair), the R.C. would be defined by drawing a line from the contact patch of the rear tires through the bearing carriers. The point where these two lines intersect will be the R.C. The wider the track, the lower the R.C. It will always be above axle hieght, though. <

Assuming you were correct here, this would place the rear roll center very high up indeed. The roll center on the type of swing axle rear end used on the VW or Corvair is located above the transaxle, placing the roll center very close to the actual CG (the actual reason Ralph didn’t like the Corvair!). What you are suggesting would I think be even more extreme because the bearing hangers are wider apart (relatively) than the swing axle pivots on the two cars mentioned, ie there would be every chance the rear roll center would actually be above the CG, which would make for interesting handling to say the least!

I tend to only think of the rear as having ‘suspension’ from about mid corner to exit. Before that when the inside rear is only lightly or actually un loaded, then nearly all the chassis flex (‘suspension’ movement) is happening up front. When weight starts to transfer more rearward and the rear starts to flex more, I think you must consider that the rear virtual swing arm is much longer than from the contact patch to the bearing hanger. However I strongly suspect that as weight transfers to the rear and the inside rear reloads that the rear roll center migrates from near the outside rear contact patch to nearer the inside rear contact patch (which I think would go hand in hand with the VSA being much longer than you suggest).

Keep I mind that when the inside rear is unloaded, that the inside rear ‘suspension’ geometry isn’t doing anything and can’t have any affect on the location of the rear roll center. If only one contact patch on an axle line is in contact with the track surface then the roll center must be at that contact patch. This would be the same for cars as for karts (or motorcycles, bicycles).

> The front is a little tougher for me to visualize. It get's pretty fuzzy as to what is sprung and unsprung. Unsprung is generally defined the stuff that moves vertically when the tire hits a bump. For a kart, that is going to be practically everything, including the driver. <

I don’t think you should be thinking about sprung and unsprung so much as where and how the ‘suspension’ articulates. It’s the geometry of the chassis, the geometry changes that occur when the chassis flexes, and the mechanical rigidities if various chassis members that will determine the location (and movement) of the two roll centers, not so much what is sprung and unsprung weight.

When a kart wheel hits a bump it won’t rise vertically, but in an arc (and it can deflect a considerable amount, especially a front wheel). The location of the instant center of this arc will have a lot to do with the ‘suspension’ geometry, but I don’t think the arc will necessarily be identical from hitting a bump as it will be from ‘G’ force flexing the chassis. When a wheel moves in an arc in response to hitting a bump or the chassis being flexed by ‘G’ force, the arc’s instant center won’t necessarily be located along any axle line, but more than likely to some degree will be behind the axle line for a front wheel and in front of the axle line for a rear wheel.

> I'm not convinced that a roll-center has any real meaning on a kart. Yes, the chassis flexes, but the tires themselves are probably the biggest contributors of cushion between the surface of the road and your bum. Having said that, my kart rides bumps better with a soft axle and a wide rear track so the tires are certainly not the only player. <

There’s a lot going on, and I think roll centers are at the very heart of how the chassis works. I don’t think this is about having a comfy ride though!

[John Learmonth]

Larry Hayashigawa said:

> Most non-kart race cars have a rigid body/chassis. A roll center is the point in space where the rigid body/chassis rolls about when cornering. There are two defined roll centers, a front roll center and a rear roll center, which are in plane with the front wheel and rear wheel centerlines. These are picked for convenience, as the roll centers can be determined by analysis of the suspension geometry) For a myriad of reasons the front and rear suspension geometries are different and therefore the roll centers are at different heights. The line between the front roll center and the rear roll center is the roll axis and is the axis that the rigid body/chassis rotates about. Roll centers also move as the chassis rolls. <

Larry, I don’t think it’s the ‘rigid body’ so much as the masses housed within the rigid body structure that ‘rolls’. A car’s ‘body’ itself may well have very little mass (especially a well designed racing car), but be a very rigid structure. The main unsprung masses (represented by the CG) will be more or less immobile within this rigid structure, so it’s easy to confuse the roll of the body with the roll of the masses.

It’s because the CG is immobile within the rigid body that the roll centers (as seen at the axle lines) are easily envisaged (referenced against the body structure where it intersects the axle lines), but I think the roll centers still have more to do with the points / axis around which the CG of mass is ‘rolling’ than about what the chassis structure itself is doing, although the movement (roll, or whatever movement) of the car body will exactly match that of the CG, but only because the mass is rigidly contained within the body. It’s because the kart doesn’t have a rigid body extending to the axle lines that it’s hard to ‘see’ the roll centers on a kart (not the location so much as the very existence thereof).

Imagine a single seat racing car with a completely rigid body / chassis that envelopes the driver, engine etc, but the suspension on this car is actually similar to a kart suspension grafted onto the rigid body, and attached at points very close to the middle of the chassis. Would this car not have roll centers? It would be perfectly feasible to build such a car, and similar types of suspension have been used before. This suspension would be geometrically very similar to a front beam axle suspended on and located by long quarter elliptic springs (but somewhat more sophisticated). The rear suspension would be not dissimilar either.

The difference with a kart chassis is that the rigid body doesn’t exist, but the masses that make up the kart / driver / engine unit do. I think it’s the collective CG of these masses that must be considered to effectively be (or seen as) the ‘body’ that rolls around the roll axis. The fact that the rigid body doesn’t exist doesn’t mean the flexible chassis doesn’t act as suspension, or that any suspension doesn’t have geometry. It only means that the suspension geometry is infinitely variable, which means the location of the roll centers is also infinitely variable.

With all this ‘variability it’s amazing that karts don’t all handle like a bowl of jelly (jello for you yanks), but I think its actually desirable and necessary that a kart’s roll centers do change position, but only if they move from where you want them to be to where you want them to be from moment to moment. If they move to where you don’t want them to be or move too quickly or too slowly then you’ll have a problem.

We don’t have enough information to accurately plot the roll centers from the ‘suspension’ geometry, but if we could locate the CG and observe the movement of this point (relative to the chassis) under dynamic conditions, then we would be able to plot the roll centers from the arc movement of the CG. Pity this is at least as difficult as plotting the roll centers from the suspension geometry!!

It should be understood that a real three dimensional object rotating or ‘rolling’ (which is rotation around an offset axis) can’t rotate / roll around a single point, so there cannot be less than two roll centers. It should also be understood that the CG can and will roll from side to side and from front to back, and that a combination of lateral / longitudinal roll will constitute a roll axis that is to some degree diagonal.

> Roll centers are used by non kart race car designers to determine how much load is transferred to the tires during cornering acceleration. Steady state weight transfer can be calculated as function of lateral acceleration by knowing the suspension geometry and the spring rate. <

Steady state weight transfer is a function of the direction of the ‘G’ force (relative to the chassis), CG height, and the horizontal distance from the CG to the contact patches. Roll centers and spring rates will have an effect on transient weight transfer, ie how quickly and to what degree weight will transfer between contact patches under changing dynamic conditions. Transient transfer is hugely important.

> It's difficult to do this for a kart using roll center techniques because there is no roll center (no rigid body rolling about a specific point in space)and there is no discrete spring element. <

It may be difficult, but this doesn’t mean ‘ipso facto’ that roll centers don’t exist on karts. The CG of mass will still move in reaction to force, and the nature of this reactive movement will depend on the direction of that force and the nature of any resistances to that force.

> All this leads me to cast my vote that there is no roll center on a kart. <

I agree, there can be no SINGLE roll centre, there must be two!

> Although, just writing about this made me think a little more on the topic. There is a roll center/axis on a kart though. It happens when the kart goes up on two wheels. The roll center is the outside tires and the rigid body is the kart and the driver rotating about the outside tires. <

Ah….it isn’t so obvious as it first seems is it?! Once you start seriously thinking about roll centers on karts, you’ll start having bad nights sleep and headaches, if you don’t then you’re just not thinking about it properly!

If you concede that the two outside contact patches define a roll axis when the kart is ‘bicycling’, then I think you would have to agree that whenever the inside rear is lifted (or even just unloaded) that the OR contact patch must define the rear of the roll axis. If the IR is lifted, but the IF isn’t, then this must mean that the front roll center is located elsewhere than at the OF contact patch, and the only place this somewhere can be is to the inside of the OF, ie somewhere between the OF and IF. If you agree with this then you must see that the roll axis is diagonally oriented most of the time (but not at all times). This has a great bearing on the levels of roll / roll stiffness at the front or rear, and on how the kart unloads / reloads the inside rear in changing dynamic conditions.

Must be bed time, hope I can sleep!

[Steve F]

I'm with Larry on this one, karts dont have the physical components to even determine where the front and rear roll centers would be. Great discussion on car-theory though.

Steve Frank