Most autocrossers and race drivers learn early in their
careers the importance of balancing a car. Learning to do it
consistently and automatically is one essential part of becoming a
truly good driver. While the skills for balancing a car are commonly
taught in drivers' schools, the rationale behind them is not usually
adequately explained. That rationale comes from simple physics.
Understanding the physics of driving not only helps one be a better
driver, but increases one's enjoyment of driving as well. If you know
the deep reasons why you ought to do certain things you will remember
the things better and move faster toward complete internalization of
the skills.
Balancing a car is controlling weight transfer using throttle,
brakes, and steering. This article explains the physics of weight
transfer. You will often hear instructors and drivers say that
applying the brakes shifts weight to the front of a car and can induce
oversteer. Likewise, accelerating shifts weight to the rear, inducing
understeer, and cornering shifts weight to the opposite side,
unloading the inside tires. But why does weight shift during these
maneuvers? How can weight shift when everything is in the car bolted
in and strapped down? Briefly, the reason is that inertia acts through
the center of gravity (CG) of the car, which is above the ground, but
adhesive forces act at ground level through the tire contact patches.
The effects of weight transfer are proportional to the height of the
CG off the ground. A flatter car, one with a lower CG, handles better
and quicker because weight transfer is not so drastic as it is in a
high car.
The rest of this article explains how inertia and adhesive forces
give rise to weight transfer through Newton's laws. The article begins
with the elements and works up to some simple equations that you can
use to calculate weight transfer in any car knowing only the
wheelbase, the height of the CG, the static weight distribution, and
the track, or distance between the tires across the car. These numbers
are reported in shop manuals and most journalistic reviews of cars.
Most people remember Newton's laws from school physics. These are
fundamental laws that apply to all large things in the universe, such
as cars. In the context of our racing application, they are:
The first law: a car in straightline motion at a constant speed
will keep such motion until acted on by an external force. The
only reason a car in neutral will not coast forever is that friction,
an external force, gradually slows the car down. Friction comes from
the tires on the ground and the air flowing over the car. The tendency
of a car to keep moving the way it is moving is the inertia of the
car, and this tendency is concentrated at the CG point.
The second law: When a force is applied to a car, the change in
motion is proportional to the force divided by the mass of the car.
This law is expressed by the famous equation ,
where
is a force,
is the mass of the car, and
is the acceleration, or change in motion, of the car. A larger force
causes quicker changes in motion, and a heavier car reacts more slowly
to forces. Newton's second law explains why quick cars are powerful
and lightweight. The more
and the less
you have, the more
you can get.
The third law: Every force on a car by another object, such as
the ground, is matched by an equal and opposite force on the object by
the car. When you apply the brakes, you cause the tires to push
forward against the ground, and the ground pushes back. As long as the
tires stay on the car, the ground pushing on them slows the car down.
Let us continue analyzing braking. Weight transfer during
accelerating and cornering are mere variations on the theme. We won't
consider subtleties such as suspension and tire deflection yet. These
effects are very important, but secondary. The figure shows a car and
the forces on it during a ``one g'' braking maneuver. One g means that
the total braking force equals the weight of the car, say, in pounds.
In this figure, the black and white ``pie plate'' in the center is
the CG.
is the force of gravity that pulls the car toward the center of the
Earth. This is the weight of the car; weight is just another word for
the force of gravity. It is a fact of Nature, only fully explained by
Albert Einstein, that gravitational forces act through the CG of an
object, just like inertia. This fact can be explained at deeper
levels, but such an explanation would take us too far off the subject
of weight transfer.
is the lift force exerted by the ground on the front tire, and
is the lift force on the rear tire. These lift forces are as real as
the ones that keep an airplane in the air, and they keep the car from
falling through the ground to the center of the Earth.
We don't often notice the forces that the ground exerts on objects
because they are so ordinary, but they are at the essence of car
dynamics. The reason is that the magnitude of these forces determine
the ability of a tire to stick, and imbalances between the front and
rear lift forces account for understeer and oversteer. The figure only
shows forces on the car, not forces on the ground and the CG of the
Earth. Newton's third law requires that these equal and opposite
forces exist, but we are only concerned about how the ground and the
Earth's gravity affect the car.
If the car were standing still or coasting, and its weight
distribution were 5050, then
would be the same as .
It is always the case that
plus
equals ,
the weight of the car. Why? Because of Newton's first law. The car is
not changing its motion in the vertical direction, at least as long as
it doesn't get airborne, so the total sum of all forces in the
vertical direction must be zero.
points down and counteracts the sum of
and ,
which point up.
Braking causes
to be greater than .
Literally, the ``rear end gets light,'' as one often hears racers say.
Consider the front and rear braking forces,
and ,
in the diagram. They push backwards on the tires, which push on the
wheels, which push on the suspension parts, which push on the rest of
the car, slowing it down. But these forces are acting at ground level,
not at the level of the CG. The braking forces are indirectly slowing
down the car by pushing at ground level, while the inertia of the car
is `trying' to keep it moving forward as a unit at the CG level.
The braking forces create a rotating tendency, or torque, about the
CG. Imagine pulling a table cloth out from under some glasses and
candelabra. These objects would have a tendency to tip or rotate over,
and the tendency is greater for taller objects and is greater the
harder you pull on the cloth. The rotational tendency of a car under
braking is due to identical physics.
The braking torque acts in such a way as to put the car up on its
nose. Since the car does not actually go up on its nose (we hope),
some other forces must be counteracting that tendency, by Newton's
first law.
cannot be doing it since it passes right through the cetner of
gravity. The only forces that can counteract that tendency are the
lift forces, and the only way they can do so is for
to become greater than .
Literally, the ground pushes up harder on the front tires during
braking to try to keep the car from tipping forward.
By how much does
exceed ?
The braking torque is proportional to the sum of the braking forces
and to the height of the CG. Let's say that height is 20 inches. The
counterbalancing torque resisting the braking torque is proportional
to
and half the wheelbase (in a car with 5050 weight distribution),
minus
times half the wheelbase since
is helping the braking forces upend the car.
has a lot of work to do: it must resist the torques of both the
braking forces and the lift on the rear tires. Let's say the wheelbase
is 100 inches. Since we are braking at one g, the braking forces equal
,
say, 3200 pounds. All this is summarized in the following equations:
With the help of a little algebra, we can find out that
Thus, by braking at one g in our example car, we add 640 pounds of
load to the front tires and take 640 pounds off the rears! This is
very pronounced weight transfer.
By doing a similar analysis for a more general car with CG height
of ,
wheelbase ,
weight ,
static weight distribution
expressed as a fraction of weight in the front, and braking with force
,
we can show that
These equations can be used to calculate weight transfer during
acceleration by treating acceleration force as negative braking force.
If you have acceleration figures in gees, say from a Ganalyst
or other device, just multiply them by the weight of the car to get
acceleration forces (Newton's second law!). Weight transfer during
cornering can be analyzed in a similar way, where the track of the car
replaces the wheelbase and
is always 50%(unless you account for the weight of the driver). Those
of you with science or engineering backgrounds may enjoy deriving
these equations for yourselves. The equations for a car doing a
combination of braking and cornering, as in a trail braking maneuver,
are much more complicated and require some mathematical tricks to
derive.
Now you know why weight transfer happens. The next topic that comes
to mind is the physics of tire adhesion, which explains how weight
transfer can lead to understeer and oversteer conditions.
