Tyre Loading and
Co-Efficient of Friction - The Reason Why Wedge Allows Us to Balance Handling
For a given size of tyre
contact patch, the amount of cornering force it can generate depends on the vertical load
(or weight on the tyre) and the co-efficient of friction (ie "sticky" tyres are
better). As we increase the load on the tyre, it turns out that the the relationship
between vertical load and force that can be applied before slippage occurs is not linear.
This is because the co-efficient changes with the vertical load applied. In particular, if
you apply twice the load to the tyre, you do not get twice the cornering force.
The significance of this is crucial to our understanding of vehicle dynamics:
Two tyres equally loaded will always
generate more cornering force than two tyres carrying the same weight, unequally
distributed between them.
So it is evident that weight transfer hurts grip in cornering and braking - we would like
to have tyres equally loaded. Weight transfer to the rear of the car will help grip
for acceleration though.
Weight transfer will happen, and there is little we can do about
it. But we can apportion weight transfer between wheel pairs pretty much as we like,
so that we can balance the car.
Where's Total Weight Transfer Come From?
I've left this last, because it is so disarmingly simple that it
can appear to diminish the importance of suspension tuning. Of course, your car must
be designed to maximise grip, within the restrictions of your class of racing. But
if you are not winning races, you can be sure the drivers that are winning, have got cars
that do a lot of things a little bit better than yours - drivability and response that
comes from suspension tuning.
In roll, the cornering force, generated horizontally at the tyre
contact patches, can be represented by a single cenripetal force at ground level. The
opposing inertial reaction (or centrifugal) force is what we feel when sitting inside the
motor car, and can be represented by a single force acting at the centre of gravity.
These horizontal centripetal/centrifugal forces generate a roll
moment, outward from the centre of the corner, with a lever arm equal to the height of the
centre of gravity from the ground.
This moment acts through the body, suspension and tyres and finally shows up as weight
transfer at the tyre contact patches (as we have discussed from the beginning). In
steady state cornering, the vertical forces (vertical force couple) generate a moment
equal to the weight transfered times the track of the vehicle (the measurement between the
two contact patches).
So you can see that the total amount of weight transferred in roll is dictated by only
1. Cornering force (go faster, and you transfer more weight)
2. The height of the centre of gravity
3. Track width
Any other affects you can dream up have only a miniscule effect on weight transfer - less
than 2% for a race car eg horizontal movement of the CG in roll.
In particular, total weight transfer in steady state does not
Your springs and shocks. (Go Karts have no springs, yet transfer weight like crazy.)
Your anti-roll bars.
Your amount of body roll in the corners.
We can tune the car to (as detailed in page 1.):-
1. Apportion weight transfer between wheel pairs. The stiffer
wheel pair transfers a greater percentage of the total weight transfer.
2. Control the timing of weight movements - the response of the race car. This
is very, very important (as discussed in detail throughout this web site). The
weight transfer is constantly changing as we traverse the race track. The
stiffer wheel pair not only transfers more weight, but transfers weight faster, so that we
have inumerable possible combinations of spring, antiroll bar and shock settings to
produce any one desired effect. Note that we can also change front and rear wheel
pair stiffness by changing roll centre heights.
Total weight transfer in pitch can be considered the same as
roll, turned through 90 degrees. It is dictated by three things:
1. Braking force, or acceleration force, generated at the
2. The height of the centre of gravity.
3. Wheel base.
For pitch, stiffness distribution still applies, except this time
we consider the relative stiffness between RH and LH wheel pairs. We can wedge or
de-wedge the car under braking or acceleration. This is a key tuning aid for
speedway, but generally undesirable for road racing. So we not only run the same
springs and shock settings RH and LH sides, but spend considerable time on the weight
scales getting the car "square". But for shock tuning, we can use what are effectively assymetrical set ups.
Unfortunately, total weight transfer reduces cornering power
(what a shame).
Wider track will always increase cornering power, a reason to resrict it in many classes
Low centre of gravity will always help cornering power on smooth bitumen. Not always the
case for speedway cars. Some times they move the CG up, to create more roll. The resulting
positive camber change can cut the outside edges of the tyres into the dirt, for more
grip. Note that weight transfer is NOT a factor in why they do this!
We can influence balance by moving the CG forward or back
(changing the front vs rear weight distribution).
Interestingly, your inside wheels ARE very important when cornering, up to the point where
you are going so fast you're up on two wheels.
Remember when you might throw a couple of cement bags in the back of the old ute to
improve handling? The extra weight on the tyres will improve grip for cornering -
but at a cost. The extra mass of the cement bags must be accelerated, and de-accelerated
(braking) constantly, to the overall detriment of performance, and extra cost in fuel
consumption. The lighter vehicle will also corner faster, because even at a constant
speed in the corner, you are still accelerating the mass to make it go round the curve.
Race car teams will never add mass to the car to improve cornering. They will adjust the
set up of the car to take best advantage of the minimum practical mass of the car (or
minimum allowed by the rules.)
So how can you add weight to the tyres to improve grip? The answer, of course, is
aerodynamic down-force. The downside is aerodynamic drag. But we only have to look at any
form of motor racing where aero aids are allowed to see that the trade off is worth it -
we get considerable improvement in overall car speed (lap times). In some categories, race
teams spend easily as much time and money to gain aero advantage, as they do an engine
advantage (and probably a lot more.) The whole chassis and suspension is designed around
what downforce can be achieved. There are a a few articles on the net about race car
aerodynamics - see insideracingtechnology.com
Formula Ford is one of the few national categories where aero aids are not allowed. Also
engine output is restricted. So the aim of FF car designers is to run at the minimum
allowed weight, reduce aero drag, and maximise mechanical grip.
The same criteria apply to nearly all amateur racing, short track speedway, and rallying.
For performance road cars, there is little advantage in aero downforce. It seems that
after-market aero kits don't work. (Track tests have been done to confirm this. How could
you get the ride height and the front splitter low enough?)
It is interesting to consider the new sports cars recently released - the Celica and MR2
Toyotas, and the Honda S2000 and Intergra R. They have gone all out to reduce weight (yet
still retain a stiff chassis). The engines produce more power (naturally aspirated) by
designing for much higher rpm than previously. If they could get any usefull downforce,
they'd have aero kits. It is true, however, that some performance cars, such as the
Audi TT, have rear spoilers to reduce rear lift at very high speed.
There is more to handling than weight transfer. We can find
more factors by consider movements of the race car in yaw - rotation about the
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