Vehicle Dynamics for Drivers


Here's a preview of one of the topics in our new training course "A Physical Understanding of Race Car Handling".

It's due for release next week.  If you're on our email list,  I'll let you know when you can buy it. (Get on the list at the bottom of the page.)

Topic 1.3  Vehicle Dynamics for Drivers

Vehicle Dynamics Engineers have developed a theoretical model of how car handling works.  It’s based on the mathematics of what’s known as the “Bicycle Model” (or single-track model). 

The model greatly simplifies the otherwise complex array of forces and motions involved as the driver controls the speed and path of the race car negotiating a corner.

Vehicle dynamics engineers generally work only with the car, and do not consider the input of the driver.  To some extent, this explains why vehicle dynamics engineers have not been more involved in the discussion about driver control.  They do seem to consider it outside their field.  However, Damian Harty changed all that in his book “The MultiBody Systems Approach to Vehicle Dynamics” – Mike Blundell and Damian Harty.  He has written in detail about the driver’s relationship with the car.  His work is the basis for most of what you see here in this course.  

Most advances in vehicle handling have come from engineers using the Bicycle Model, and related software, to analyze the problem. 

(Note the centre of gravity (CG), also known as the centre of mass (M).

The front and rear axles are collapsed into one tyre front, and one rear.  The term "bicycle" is a misnomer really.  The forces and so-called "moments" (see next topic) exist in the ground plane only.   The bicycle model refers only to the dynamics of a four wheel vehicle, and is unrelated to a two wheel vehicle.

The model is very simple, yet so powerful in predicting the dynamic behavior of a four wheel vehicle.

For more details on the role of classical vehicle dynamics in modern race car development, see our blog:
https://www.suspensionsetup.info/blog/race-car-design-testing-virtual-prototypes-real-drivers

Further into the course, we have some descriptive diagrams, based on the bicycle model, to show you what's happening at the tyres.  It helps us better understand how the forces and "moments" work in creating the motion of the race car.  (We describe what moments are all about in the next topic.)

The "Attitude Angle" (Vehicle Slip Angle or Body Slip Angle)

Vehicle dynamics engineers use the bicycle model as the basis for developing the handling characteristics for road and race cars alike. 

The key value of interest is the Body Slip Angle.  The body slip angle is also known by other various names, such as attitude angle, side slip angle, vehicle slip angle, float angle, beta angle and probably many others. 

I like the term "attitude angle".  To me, it is more descriptive.  I used it years ago, when I first started writing on vehicle dynamics.  But others have not used it, so I have reverted to talking about the body slip angle.

You will probably have heard of tyre slip angles, but the body slip angle as an important concept, may be new to you.  So please read this topic carefully, and let me know by writing in the comments about anything you see differently, or where you need clarification.  (Comments only available in the course, not available in this blog.)

Vehicle dynamics and engineering design is all about control of the Body Slip Angle.  This is the angle β in the bicycle model diagram.  It's the angle that shows how much the car has rotated around a vertical axis through the centre of gravity, at that point in time, while the tyres continue to grip the road.

If the car loses grip and starts to spin, the body slip angle becomes larger.  The car spins around a vertical axis through the centre of gravity. 

In driving on loose surfaces (speedway or rally driving) the drivers may control the race car at much larger body slip angles, now very evident to any outside observer.

The body slip angle is the same attitude angle we were looking at in the previous topic. We showed this in the course as a couple of photos Senna's Lotus.  The photo showing the attitude angle is below:

The rotation of the car the driver can feel in corner entry is the body slip angle building up, as the tyres build up lateral grip.

The rotation feeling we are talking about is just a blip in time - it is the body of the car rotating on the tyres just a few degrees, while the tyres continue to grip the road. 

It's got nothing to do with the rotation of the car in the corner as we see it from outside of the car.  The driver feels this bulk rotation in the corner as a straight line G force, not rotation - as simply the lateral force of cornering. The driver feels lateral G building up in corner entry and letting go in corner exit.  There is plenty coming up in the topics ahead, to clarify this important distinction.

Showing you how and when you feel this rotation - the rate of increase of the body slip angle - is a major part of this course.  Traditionally in racing, the nature and importance of this rotation and the body slip angle in car control, has not been recognized.

In the course, whenever we are talking about rotation the driver can feel, we are talking only about feeling the rate of change of the body slip angle.

Below is the outline of a generic closed loop control system, such as might be used for an electronic stability control system.  There is an array of sensors required of course, and some complicated calculations.  But the intention, control of the body slip angle, is simple, and highly effective.  Stability of the the vehicle can be maintained, even in extreme maneuvers, where the driver might otherwise lose control .

In vehicle dynamics engineering, the above closed loop system will operate with the measured output from the "body slip angle sensor" being more than expected, or less than expected.  The "controller" element of the stability control system making the necessary adjustments to the car via the ABS brakes.

Now let's consider how this closed loop control system could work in our driver/car relationship with the driver as the controller.

The racing driver obviously doesn't have access to the inputs, or the computing power in the same way.  Driver control of the body slip angle remains the objective.  But the driver has no accurate visual on what the body slip angle is.

In cornering, the key sensing for the racing driver in closed loop control of the racing car is the subtle rotation of the body of the car on the tyres. The feeling is associated with the rate of increase of the body slip angle in corner entry.  The driver has almost instant feedback on the balance of the car, or as we shall see, "agility" vs "stability".

In controlling the race car up to the point of corner entry, the driver is operating in largely an open loop fashion, controlling the race car based on visual cues.  In judging corner entry speed and line through the corner, your visual perception remains dominant, of course.

But once into the corner entry phase and beyond, there is one aspect of a closed loop control system available to the driver.  The driver can respond almost instantly to the subtle rotation, the build up of the body slip angle. 

The rotation feeling is a simple measure of how much of the grip availability you are using up.  If you feel the car rotating too fast (ie it's nervous, too agile), then you can correct accordingly, or if you feel the rotation too slow or not at all, then your mission is to push harder until you can feel it.

"The Driver Counter Steers in Time to Regain Control of the Car by Feeling the Rotation."   

As a first step in appreciating if this is possible, ask yourself, "How else could the driver respond so readily in counter steering to control oversteer?" 

Ask yourself, "How do I get the message to make the control adjustments to the car that I need during the cornering phase?" 

A driver might say. "I can see the body slip angle looking forward through the windscreen."  Or, "I can see the path tightening as the car oversteers, and the path widening as the car understeers." (eg) "I noticed I missed the apex."  Or, "I feel the lateral G building up, as grip increases in corner entry."  Or, "I feel the weight transfer, the roll and pitch of the car."

All of the above feedback is useful, of course.  And nothing beats being able to see where your going in terms of controlling the cornering line.  But you won't generally see the body slip angle with your eyes in any useful way.

"If you have to wait until you see the oversteer with your eyes, it's already too late."  Martin Brundle

In the video below, you can see the body slip angle change (rotation) through the windscreen at times.  Might be useful when the rotation is slow - below the threshold of feeling, say when the car is 4 wheel drifting on corner exit.  The motions of the car slow down.  Everything is more easily manageable on the throttle.  When 4 wheel drifting, ie the front and rear tyres fully saturated together, the rate of change of body slip will probably be too slow to feel.  You may be on visual control only.  You'll see the path tightening, or the car running wider than expected and adjust the throttle accordingly.

But at other times, when you are trying to build up grip as quickly as possible, only the rotation feeling from rate of change of the body slip angle can explain the speed with which the driver takes corrective action in racing. The driver can respond almost instantly to oversteer about to happen. 

However, for you to be convinced, I must show you everything I've got to support the premise that you feel the rotation.  It's such a subtle, nuanced thing.  In the topics following, I can explain how it works by showing you the forces and so-called "moments" acting on the vehicle in a very simple way.  You'll see what's happening at the tyres.

A Lap with Jamie Whincup Driving (see video)

Once the racing driver has made the first closed loop control adjustment to the car, closed loop control may be continuous for the whole of the corner, up to the point where you get to full acceleration on corner exit.  Corner entry could transition to corner exit without the steering wheel being stationary long enough for the car to stabilize on the suspension, as necessary for us to have a true mid corner phase.  This is pretty much how it happens in this video:

In this video, in any one corner, Jamie Whincup is making 3, 4 or 5 control adjustments with the steering wheel based on the rotation he is feeling. 

The multiple adjustments at the steering wheel, happen particularly when the driver is operating at the limit of grip, in a low grip environment.  But of course, for quick lap times, the race car will still be driven as straight as possible (and we don't know if lowest lap time is the objective here.  They may be just mucking around, or maybe JVG  is trying to get Jamie to drift the car.)

Notice the rotation is felt primarily in the oversteer direction.  If no rotation is felt, push harder is the basic precept.

This is a key finding in this course, that is not generally recognized by racing drivers.  I will be presenting heaps of evidence as how this incredibly simple idea can be so important to you in your driving.

Gravel rally driving on a super low grip surface can involve an even greater number of control adjustments, often with very fast movements of the steering wheel.  Some of the steering wheel movements are driver induced so as to get some rotation happening, so that the driver can feel the car.

It's with an understanding of the vehicle dynamics involved, that we can fully appreciate the potential of driver sensing with this one simple motion of the car.  We can vastly simplify our view of what's happening.

A Breakthrough? Or Not? 

There is only one source I know of with sufficient detail to back up our premise about the importance of the body slip angle in car control for racing drivers.  We rely heavily on the work of Damien Harty.  Without the insights in his book, "The Multibody Systems Approach to Vehicle Dynamics", we would not have been able to produce this course.  But as we introduce the course, other drivers, and those with expertise in this field, are able to shed further light on various aspects.

There are going to be changes as we go along.  This is all too new for that not to be the case. I will very much appreciate your advice on any errors or additions you see needed.

Driving and Driver Feedback

Hopefully, we are agreed.  It is a breakthrough - the start of something bigger to come. 

This is knowledge that could influence your driving for the better, no matter what level you're at - grassroots, through to pro driver, when you:

  • Understand what's happening at the tyres.
  • Know what motions of the car are useful to you for feedback.
  • Study the rotation you can feel at a deep level, then focus on what you are sensing in some test sessions.  It's always been there.  You'll just be refining it, then putting it back into your subconscious.  

To be expert at driver feedback, you need a physical understanding of car control and how the car turns the corner, and the experience necessary to discern differences between tyres and set-ups - which you do by comparison.  Test one set-up back to back with another. 

With the comparison process, drivers can build up incredible sensitivity.  (All backed up by what is the quickest, of course.) 

On the other hand, for racers with little experience, even if you doubt your ability to sense the difference, if you are comparing meaningful changes to the set up, you will notice the difference.

The insights you need about driving are different from the specifics of knowing what to do with suspension set-up.  It's not necessary to know about the suspension tuning, if others can make the changes necessary, based on your feedback. 

However, for most grass roots racers, you don't have the technical people who can do set-up.  Our course, "Get More Grip and Better Balance", is your best guide as to what to do.  You can get yourself and your team up to speed fast.  Learn the suspension set-up priorities for your race car, at your level of grass roots racing - beginner through to highly experienced.

What's Ahead? 

In the topics ahead, we'll look at how the car turns a corner via the forces acting at the tyre contact patches. 

But before we do that, coming up next is a practical demonstration of how you can feel the rotation we are talking about.  It's a simple step steer exercise.  Click through to the next topic.

This is the end of Topic 1.3 in the course.  To get onto our mailing list, please enter your name and email address below: