# What is a roll center? (steady state cornering in a vehicle)

by hari00968
Tags: cornering, handling, physics, roll center, vehicle
 P: 10 I'm studying the chapter 'Steady State Cornering', from the book 'Fundamentals of Vehicle Dynamics' (by Gillespie). The concept of a 'roll center' seems to be very important here, especially after the 'roll axis' is defined (line joining the front and rear roll centers). But I don't understand what a roll center is, in the first place, can somebody please help me out?
P: 566

 The SAE's definition of the force based roll center is, "The point in the transverse vertical plane through any pair of wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll".
 The significance of the roll center can only be appreciated when the vehicle's center of mass is also considered. If there is a difference between the position of the center of mass and the roll center a moment arm is created. When the vehicle experiences angular acceleration due to cornering, the size of the moment arm, combined with the stiffness of the springs and anti-roll bars (anti-sway bars in some parts of the world), dictates how much the vehicle will roll.
What is it you don't understand exactly?
 Sci Advisor PF Gold P: 1,474 see - Race car suspension Class - below ..in this forum
P: 10
What is a roll center? (steady state cornering in a vehicle)

@jack_action
 The SAE's definition of the force based roll center is, "The point in the transverse vertical plane through any pair of wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll.

 The significance of the roll center can only be appreciated when the vehicle's center of mass is also considered. If there is a difference between the position of the center of mass and the roll center a moment arm is created. When the vehicle experiences angular acceleration due to cornering, the size of the moment arm, combined with the stiffness of the springs and anti-roll bars (anti-sway bars in some parts of the world), dictates how much the vehicle will roll.
The second part is perfectly clear, but I'm having trouble with the first part. Generally, wouldn't the Roll Center simply be the center of mass of the sprung mass? Any force that doesn't pass through it would have a moment about the COM, resulting in a tendency to roll right?

The book also says
 The roll center can also be thought of as the point on the body at which a lateral force application will produce no roll angle, and it is the point around which the axle rolls when subjected to a pure roll moment.
Now where is the axle coming into the picture now? I thought the RC is a property of the sprung mass? And also, the roll center seems to be really close to the ground in diagrams, like, completely away from the body.
 P: 10 @ranger_mike I tried reading it, but it seems really complicated, was unable to follow it, as I haven't done any courses on vehicle dynamics/suspensions, everything seems new to me. Isn't there a simpler explanation?
 P: 566 Let's look at a really simple suspension. In the next picture, you can see that the tractor has a simple solid axle for the front wheels. There are no springs, the axle is just rotating about the pin at the center (There is no suspension at all for the rear axle). The pin is the roll center of the front axle. In this particular (really simple) suspension, no matter how the «sprung» mass (the tractor frame) is positioned with respect to the «unsprung» mass (the front axle), the roll center position is always clearly known. Now, this tractor is not built for cornering, but let's imagine that the rear axle is built the same way and that there are left & right springs between each axle and the tractor frame. The roll axis would be the imaginary line linking both rear and front pins. If that tractor would be under lateral acceleration, the centrifugal force (ma) would act at the center of gravity of the sprung mass. The distance between the center of gravity and the roll axis would create the moment arm for the centrifugal force. That moment (or couple) would begin a rotation of the sprung mass around the roll axis. This rotation (or this moment) will be opposed by the moment created by the spring force and how far it is from the roll center. These moments will be balanced when the rotation stops to a certain angle. The larger the lateral acceleration, the larger the final angle. Now imagine that the pins are moved high enough that the roll axis goes through the center of gravity. In such a case, there will be no moment created since the moment arm length is zero. Hence there will be no rotation initiated and the tractor would stay perfectly parallel to the ground under any amount of lateral acceleration. For more complex suspensions (with more links), the position of the roll center depends on the position of each link. Since those links are constantly moving, the roll center is also constantly moving. And that's where the fun begins in suspension design ...
 Sci Advisor PF Gold P: 1,474 hari00968 - I agree that the subject is not simple..nothing is that one can not touch or see.. Jack Action did a pretty good job of explaining it.. I suggest you use the Search mode on this forum to look up the following posts.. . Centre of gravity of a car Mar11-09, 04:22 PM Race car physics Dec29-08, 11:31 AM circular motion of car on banked track, with friction Dec28-08, 04:47 AM Tire Slip Coefficient Apr2-10, 07:57 AM ifin you REALLY want to learn about this..we all are hear to help...there are so many people contributing to these posts, with so much valuable experience..it is one of the best kept secrets on the net today...
 P: 10 @jack_action That was beautiful man, thanks a lot! I still don't get how you calculate the position of the RC in more complex situations, but I think I understand the concept, how it works, and why it's so important. I'm finally able to make some progress with my book. Looking forward to the 'fun' you were talking about, I think that comes somewhere in the next chapter! Thanks again!
 P: 10 @ranger_mike I agree, I love the website, it's the biggest find of my summer vacation! Great work by you guys. Looking forward to learning lots more. Race car physics is something I'm looking forward to in particular.
 P: 563 Download the free demo of Circle Track Analyzer found here: http://performancetrends.com/download.htm#rcc and play with it for a while. There are other programs out there but this is a good start.
 Sci Advisor PF Gold P: 1,474 this is the ONE tool any crew chief has to have,,,yo ucan not fix it if you don't know what its doing and the dynamic software will show you the tires caster, camber going thru the turns.. good one mender... hari00968 welcome to the forum and look forward to your input.. rm
 P: 2 @jack action: that was an awesome explanation! i am trying to model a truck's cabin suspension here. since the cabin alone does not have a wheel or an axle i am having trouble using the existing logic for multi bars and independent suspensions to it. this is the case: it has a COD at all 4 points. in the front, the COD is connected to the frame and the cab via revolute joints and there's a torsion bar between them. in the rear the COD is again connected in the same way but there's an additional panhard bar for lateral loads. that's pretty much it. my question is: should i consider this as in independent suspension system (though the truck frame will hardly allow much lateral movement) or should I consider the frame as some kind of a beam? And then how do I find the roll center. PS: instinctively i feel it is merely the center point of the COD itself.. thanks in advance!
P: 173
 Quote by hari00968 @jack_action That was beautiful man, thanks a lot! I still don't get how you calculate the position of the RC in more complex situations, but I think I understand the concept, how it works, and why it's so important. I'm finally able to make some progress with my book. Looking forward to the 'fun' you were talking about, I think that comes somewhere in the next chapter! Thanks again!
the roll center for a suspension is the istant center of rotation between the vehicle body and the ground and it can be find using principles of the instant center of rotation (e.g. the Kennedy arnold theorem)

 Related Discussions Engineering, Comp Sci, & Technology Homework 2 Engineering, Comp Sci, & Technology Homework 2 Electrical Engineering 1 Engineering, Comp Sci, & Technology Homework 0 Introductory Physics Homework 4