Cornering compliance

[WilO]

As part of my ongoing efforts to understand vehicle directional control, I've been trying to gain an understanding of cornering compliance. It's not going well.

My limited understanding of the concept is that many factors are included, such as roll steer, camber effects, aligning moments (more about that later), but could be simplistically characterized as the rate of change of vehicle sideslip.
I'd appreciate any input from those who know more than I (ie., everyone).

I do understand that understeer effects on the front axle add to the cornering compliance, while understeer effects on the rear axle subtract from the cornering stiffness. I have to admit I'm accustomed to considering understeer as an overall vehicle characteristic, not independently at front and rear axles.
This begins to get into control systems stuff, I think...I have read that understeer, rear axle understeer in particular, shortens vehicle response time (raises the system natural frequency).

I apologize for the length of this post, and my sincere appreciation to anyone who replies.

Wil

[Jersey Tom]

Cornering compliance at an axle is indeed the summation of all the effects from cornering stiffness, load transfer effects, roll-steer, etc.

Understeer is not evaluated at each axle.. it is the front-to-rear difference in cornering compliances. You are correct in that all other things being equal, increasing understeer (say by moving some cornering compliance off the rear axle and to the front) will indeed reduce the system response time to yaw inputs.

Can see this pretty easily if you put together a 2DOF bicycle model vehicle simulation in your software of choice. Could be MATLAB, or even Excel. Doesn't require tire data or any BS like that, just assign an arbitrary cornering compliance rate to each axle and play around with it.

Hope that helps.

[WilO]

JT, thank you for the reply.
I had thought that I'd read that understeer effects at the front and rear axles add and subtract to the cornering compliance, perhaps I'm wrong. Given that cornering compliance has units of degrees/g, I can't help but wonder if cornering compliance is somewhat analogous to (or is affected by) a net aligning moment.

Thanks again for reading and replying.

Wil

[Jersey Tom]

Other way around. Understeer... or really any measure of lateral balance, is a comparison of how the front and rear axes are behaving relative to each other. Makes no sense to have understeer at one axle. I can't even conceive what it would mean.

In any event cornering compliance is in deg/G, yes. Isn't really analogous to aligning torque... though aligning torque does enter the picture to contribute to cornering compliance.

Think of it this way. Take a car. Cut it in half, or just think of one half of the car. It has a given mass, so to accelerate it laterally at a given rate requires a defined amount of force. Ultimately that force comes from steering the tires. So the question is, how much do have to steer the tires per G of acceleration. If there's aligning torque that strains the suspension and wants to steer the tires out of the turn, it will require more steer (or sideslip really) to make up for it.

So, there is a cornering compliance at each axle. If you have to "slide" the front more than the rear - understeer. Otherwise, oversteer.

In a way, you could also say there's a cornering compliance for the entire car - how much would the car sideslip to counter some external lateral force disturbance for example. But that's a separate topic.

[WilO]

Tom,
Thanks again for the help; your explanation helped clarify things a great deal.
I'm wondering if what Bundorf/Leffert may have been getting at with respect to 'understeer' effects at the rear axle refers to the front axle being 'fixed', while some change takes place at the rear axle that contributes to understeer.
Just my half-baked thought.
I was able to find a copy of an earlier paper by Bundorf, it seems to be a little clearer, along with your input I might have this sorted out soon.

Thanks again.

Wil

[fastback33]

Other way around. Understeer... or really any measure of lateral balance, is a comparison of how the front and rear axes are behaving relative to each other. Makes no sense to have understeer at one axle. I can't even conceive what it would mean.

In any event cornering compliance is in deg/G, yes. Isn't really analogous to aligning torque... though aligning torque does enter the picture to contribute to cornering compliance.

Think of it this way. Take a car. Cut it in half, or just think of one half of the car. It has a given mass, so to accelerate it laterally at a given rate requires a defined amount of force. Ultimately that force comes from steering the tires. So the question is, how much do have to steer the tires per G of acceleration. If there's aligning torque that strains the suspension and wants to steer the tires out of the turn, it will require more steer (or sideslip really) to make up for it.

So, there is a cornering compliance at each axle. If you have to "slide" the front more than the rear - understeer. Otherwise, oversteer.

In a way, you could also say there's a cornering compliance for the entire car - how much would the car sideslip to counter some external lateral force disturbance for example. But that's a separate topic.

FFS, they should just write that in a book and call it done. I know it is much more complex than just your explanation JT, but overall that just saved me a couple months of reading and trying to understand everything. (okay bit of an exaggeration but you get my point.)

[Jersey Tom]

I know it is much more complex than just your explanation JT

You'd be surprised. Easiest thing to do in vehicle dynamics is over-complicate things. In any event, glad I could be helpful.

[WilO]

I thought I'd share some of the information regarding cornering compliance that I received from a 'specialist' on the topic, having a control systems background:

Cornering compliances are the net front and rear axle sidelip derivatives at a given level of steady state lateral acceleration, in units of degree per g.

There are 11 recognized cornering compliance terms:
Tire stiffness normalized by weight (front and rear)
Lateral force steer and camber (f and r)
Aligning moment steer and camber (f and r)
Overturning moment steer and camber (f and r)
Roll steer and camber (f and r)
Net aligning moment, the sum of all the SATs acting on the vehicle as a whole.

An effect which reduces the axle sideslip rate of change is positive in sign, obviously any effect which increases the derivative is considered negative. Positive effects are understeering, negative effects oversteering.

If DF is the front cornering compliance, and DR the rear, DF-DR is the net vehicle understeer, while DF+DR is an indicator of the vehicles response time, and the sum divided by the product is a measure of the system damping.

It was pointed out that trying to quantify vehicle performance based on understeer is absurd; a car with a DF of 5 and a DR of 3 has an understeer value of 3, so also does a bus with having values of DF10 and DR7...

[Jersey Tom]

It was pointed out that trying to quantify vehicle performance based on understeer is absurd

Agreed. Which is why it hasn't been done in decades. Lots of SAE papers on this topic. Some better than others.

[ubrben]

The best bang for buck methodology I've come across is the Milliken Moment Method. You basically characterise your car by three terms; Directional Stability (moment (usually restoring) to a pure sideslip input), control moment (destabilising yaw moment due to pure steer input with zero sideslip), and limit balance (resultant yaw moment with all tyre capacity used)

These three numbers are speed dependent, so for a car with significant aero you need to do the calculation a few times for low and high speed corners. A circuit analysis will tell you what speeds are relevant.

I like it because you stop thinking as directly about understeer and oversteer, and you stop obsessing about lap time simulations as well. A good MMM simulation, plus DaveW's rig to get the dampers right has won us championships.

Ben

[hardingfv32]

Are you allowed to state what "DaveW's rig" rig is?

Brian

[DaveW]

This.

[WilO]

Brian, a fairly lengthy thread on the topic of multi-post rigs can be found a few pages back in this forum.

@DaveW: fantastic pic for a number of reasons.

[FW17]

Are articulated steering allowed in F1?

What will be the possible +ve and -ve of a articulated steering system in a race car?

[Tim.Wright]

I can only think of negatives. More weight, more complexity, loss of chassis stiffness, packaging nightmare x10^69, slow response, steering inertia force affecting the overall vehicle balance.

Tim