Basic Suspension Dynamics: What is a roll moment?
Roll moments, roll centres, inertial loads, mass centres, roll axes - let’s step into the Ghetto Engineering lecture theatre. Please, take your seats, buckle in...
My recent interview with suspension tuning legend Graeme Gambold was quite a hit with you. (If you missed it, you can do your Gambold homework here >> )
Some people did express states of confusion and the odd intracranial bleed over some of the basics of kinematic dynamics. So let’s demystify that here and now.
In this report, we’re going to talk about three-dimensional space, and how you’ll never think about moving through it the same way again. First, you need a few minutes of beer garden basics before we can get into the properly hard stuff.
You can move six ways in 3D space. They’re called ‘degrees of freedom’. There’s no other way to move in 3D space (without going ‘sci-fi’).
There’s three ‘straight line’ degrees of freedom: Forwards and backwards is one, side-to-side is two, and up/down is three. Cars have controls for forwards/backwards and side-to-side. Up/down is more or less just a matter of following the road as it meanders up and down hills.
When you do something as simple as following a right-hand curve, you’re actually doing three things at the same time. You’re moving forwards, and to the right, and rotating in yaw. Most people don’t think about it like this, just physicists and engineers.
If you don’t do all three things, and by just the perfect amount, you don’t get there. That’s called ‘crashing’, so getting it right is important.
Now, let’s talk about inertial forces, AKA virtual forces.
Inertia is what happens when you kick a brick and it breaks your toe, because it really doesn’t want to start moving and it pushes back.
It’s Newton’s first law of motion. Everything wants to continue to do what it’s already doing unless external forces act on it.
And then there’s the second law of motion, when external forces act, it causes acceleration. And acceleration can act forwards, backwards, up, down, side-to-side, and in roll, pitch and yaw. All at the same time, if you’re in a fighter jet that goes divergent on all three axes, which is quite confusing.
In a car, it plays out like this. In a drag race, you nail the accelerator and the nose comes up in the air, your head gets thrown back, right? That’s inertia. It’s not a real force - it’s a virtual force.
A brainy French dude named Jean le Rond d’Alembert had a neat hack for Newton’s second law for this. He essentially said the sum of forces acting on a system, minus the time derivative of the momentum, was zero if the mass didn’t change. It converts accelerating frames of reference into static ones for analysis by imposing virtual forces of (-m.a) upon them.
What that means is in the case of a drag race, your head is not really thrown back - is just wants to stay where it was - while the car shunts itself forwards.
What you’re feeling, essentially, is a virtual inertial force in the opposite direction. If you hit the brakes suddenly, at speed, you get the inverse effect - your head wants to keep going. But another force is acting upon it.
Your head gets pushed forward - only, not really. It just seems that way, subjectively, thanks to d’Alembert. The nose dives down, right? Same thing, only it’s a reverse virtual force. You’re just accelerating in the other direction.
The rotating backwards and forwards in pitch is in response to inertial loads.
This happens when you corner in your car. Turn left, your head goes right. Turn right, your head goes left - seemingly, anyway.
It’s really just the inertia of your head and body which want to go straight ahead, hence Newton’s first and second laws. The car starts moving to the right. It feels like you’re being pushed left, because of d’Alembert’s principle.
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Kinematics: the foundations of roll moment
Take any object - a person, a car, a fighter jet, a hammer - literally everything has a mass centre, or mass centroid.
That object has a mass centre and you can figure it out on every plane - the ‘x’, the ‘y’ and the ‘z’. Cars essentially have two mass centres, one at the back and one at the front, both around the axles, which affect the roll performance at the front and rear.
The roll centre is the central point on the vehicle around which the mass centres pivot. If you’re tuning the suspension on a vehicle in R&D, like Graeme Gambold, you need to know where the roll centre of the car is so you can figure out how it’s going to roll based on speed and the radius of the bend is.
But the roll centre, the second big thing you need to know, is a geometric point where the pivoting takes place in a corner. Roll centre is typically just above the road. The rear roll centre is generally a bit higher than the roll centre, ditto at the front.
Roll moment is just a torque; a turning effect, like a spanner applying turning force over a certain length of a spanner.
It’s essentially the applying of force over a certain distance, which tips the body over.
The force is determined by the length of the corner and how much force is applied through that roll centre.
In electric vehicles, there’s a profound effect on the spanner because a big heavy battery goes down low, and sits further back in the vehicle. It essentially stiffens the car up because the ‘spanner’ is so much shorter and the weight has increased.
All the suspension hardpoints are unchanged and the mass centre has changed dramatically on an EV based on an internal combustion platform. This explains the inherent suspension compromise on those modified vehicle platforms, and it will make dedicated EV-only platforms a key design aspect of future models.
Roll moment is just the turning force applied through the roll centre. Congratulations if you understood all of this - you passed.
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