In our discussion of weight transfer, we
explored the ever changing loading and unloading of the tyres, and movements of the race
car around axes in the horizontal plane - roll, pitch and warp.
Rotations of the Race Car about the Yaw Axis
For a race car to be cornering in steady state neutral steer, we
consider the centrifugal force, acting at the centre of gravity, to be
balanced by the cornering forces of the front and rear tyres.
If front cornering force was to be reduced, we say the car
and if rear cornering force reduces, we say the car oversteers.
This is the intuitive model that most of us start with, when we
consider vehicle dynamics.
So it appears not unreasonable, that the resultant cornering
the tyres, should have a turning torque around a vertical axis through
the centre of gravity - the yaw axis.
As this is a race car, we are talking optimum performance - we
to use all the available tyre force. From our knowledge of weight
transfer, we know that tyre loading determines the size of that force.
And that force can be in any direction, depending on the combination
of braking, cornering or acceleration. To help in our thoughts on
setting up race cars, it is usefull to consider all the components of those
forces, and their contribution to oversteer or understeer torque around the centre of
Best way to do this is to look at an analysis done by Paul Van
Valkenburg in his book Race Car Engineering & Mechanics 1992, page
74. His calculations are for a typical mid-engined 1600 lb race car.
The results are plotted graphically, with total rear tyre thrust on the X
axis, and turning torque around the CG on the Y axis. The two
directions of rotation are shown as, up for oversteer and down for understeer.
Some of the factors contributing to understeer stay fairly
with increasing rear tyre thrust. These are front tyre drag and reduced
co-efficient of friction on front tyres (front tyres smaller on this car).
Our set up is front stiff, so we build some increasing wedge (understeer)
with increasing cornering force from the thrust of the rear tyres.
Most interesting to me is what he shows happening with front to
load transfer. Both increased rear tyre load and reduced front tyre load
contribute to understeer in a big way - more at the front than back, and
a lot more than the lateral load transfer alone. See my wedge
for acceleration while cornering - it shows part of this effect.
The two contributors to oversteer are - cornering traction
the rear tyres are being used up with increasing thrust, and the locked
axle oversteer effect (this car has a locker, rather than a limited slip
But it is the net torque around the CG, that
produces actual understeer
or oversteer. The car in Paul's calculations, has quite a bit of throttle
off understeer. To maintain a constant speed in the corner it needs
about 300 lbs of rear tyre thrust. From 500 lbs to about 1200 lbs of
thrust it has quite a nice flat area in the net torque curve, representing
steady light understeer, almost neutral steer, which the driver would
experience as balanced and requiring very little steering input. The
cornering traction loss really starts to rise fast from 1200 lbs onwards,
and the handling balance quickly moves into oversteer at about 1500
lbs. The locked rear axle effect has been fairly constant up to this
point, but now really comes into play as inside rear tyre capability is
used up. Increased thrust after this point goes into the outside tyre, causing
oversteer torque on the CG.
So lets look at some conclusions:
1. There is no such thing as an all understeering or all
car. It depends entirely on how it is being driven. In testing, we need
both driver and race engineer to be very clear about what is happening,
and where in the corner phase, before we attempt to improve the set up
of the race car.
2. Before we do any serious tuning, we need the car balanced in the
mid-corner steady state phase, with just the right amount of mild understeer, that leaves
room for the coming increase of rear tyre thrust on corner exit.
We probably then need to improve overall grip using tyre temperature
checks to assess the correct dynamic camber, change the static cambers to suit, assess the
best working pressures for the tyres, and check that tyre
temps are in a good operating range. Then re-balance the car again,
because it has probably changed!
3. If we had a powerfull car with a limited slip diff, it
tuning possibilities. If we have a locker, we need to tune around it's
known performance characteristics, as in V8 Supercars for instance.
4. If we were to add suitable aerodynamic downforce, the
have a lot more traction in fast corners. So the cornering traction loss
curve would remain flatter, and the steeply increasing increasing
oversteer torque from this effect would be delayed much longer.
Also, inside rear tyre would not get used up, so locked axle curve would
stay flat too. Result - cornering speed much faster.
5. We should not use downforce to solve a handling
problem. If we
just added wing to a poor chassis set-up, we would give away heaps
of potential performance. Set up for mechanical grip and balance first,
then optimise downforce. Of course, we must be applying a baseline
set up for downforce the whole time, because a big increase in downforce
might change the ride height of the car sufficiently for the suspension
geometry to change the balance of the car.
6. The transient effects we have been looking at are so
quick lap times. The driver must be able to use up all the available
traction of the tyres as often as possible. The responses of the car
must be as linear as possible - no sudden surprises. So drivability
is more important than ultimate grip.
7. Data acquisition systems, as commonly available to
teams, will not be able to break down your set up problem into all the
effects you need to consider. We still have to use our own knowledge
and judgement to decide what changes to test. Paul Haney has
interviewed some race car engineers. They seem to be saying that data
helps with most set up problems, but that the driver is the best sensor
we have for determining balance.
A Comprehensive View of Race Vehicle Dynamics
For professional race teams, data acquisition has a allowed a more detailed
analysis of what is happening with race car set up than what we have discussed here.
A Race Car Engineer, Claude Rouelle, has been presenting seminars showing how Pi
Research data acquisition might be used to address set up problems.
Instead of just one centre of gravity (or more correctly, centre
of mass), he shows how to calculate two - centre of mass for the sprung mass and unsprung
Rouelle differentiates between "elastic weight
transfer" and "geometric weight transfer." Geometric forces go through the
suspension links into the chassis as soon as tire forces begin. Because the instantaneous
center of rotation of the suspension is probably below the center of mass there is a roll
moment that wants to rotate the chassis about that center of rotation. The springs and
dampers control the timing of those "elastic" forces, but they build up after
the start of the geometric forces. Rouelle shows how to calculate all these forces
using the data acquisition.
You can read Paul Haney's article and interview with Claude
Rouelle by clicking on this link: www.insideracingtechnology.com/nwclaud.htm
Suspension Geometry and Wheel Alignment.
We have re-printed a good article from Grass Roots Magazine:
"Castor, Camber, Toe"
Further Reading on Vehicle Dynamics.
(It helps to read someone else's view, to formalise
your own understanding of the basics.)
For my own understanding I am indebted
to the brilliant articles by Mark Oritz writing in "Race Car Engineering", and
Paul Haney's book, "Inside Racing Technology". The interviews with
Engineers and Team Owners are great.
Visit autospeed.com for great articles on performance cars:
We link to Autospeed elsewhere on this site to interesting
articles on supension development.
Read "The Physics of Motorsport" by
Richard Bowen, a lecturer at Durham University: http://www.dur.ac.uk/~dph0rgb/PoM/pom/pom.html
As Richard says at the outset, this is a simplified view of
vehicle dynamics. It only takes a few minutes to click through his article.
There are equations, and his conclusions are spot on.
"The Trans Am & Corvette Chassis"
articles on handling theory:
There is quite a lot here, some good explanations, especially on
tires and tyre temp readings. These articles
are for speedway. So not all is relevant to road racing.
The acclaimed "Physics of Racing" Series,
by Brian Beckman:
Too many equations for me. Also, if the maths gets too
complex to include in the article, Brian does not cover
some important areas, e.g. combination pitch and roll.
"Weight Transfer": http:www.//rc-racing.com/docs/1997/aug/Weight-Transfer.html
Very good stuff. And the're racing radio controlled cars!
You better just hope they don't move into your series.
Go to the Suspension index and they have a glossary of terms
related to vehicle dynamics topics.
The Shock Articles (if you havn't read them on the way through).
for Analysing Suspension Set Up Problems
Bringing all the concepts together.
Smithees can help with all race car setup problems, contact us