Brian Beckman
physicist and member of
No Bucks Racing Club
P.O. Box 662
Burbank, CA 91503
©Copyright 1991
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 straight-line 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 50-50, 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 50-50 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 G-analyst 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.