uploaded 8/1/2000
Difference Between Weight and Downforce
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Forces in a Corner
We're trying to understand why a heavier car corners slower
but aerodynamic downforce helps a car corner faster. The previous
article in this series explained that friction, described by
the equation Ff=Cf x Fv, improves as downforce increases helping
the tires generate grip. Now we're going to look at how the weight,
or mass, of the car affects cornering.
Sir Isaac Newton, 16421727, a British philosopher and mathematician,
is famous as the discoverer of gravity. The popular story is
that he was napping under an apple tree and, when wakened by
a hit on the head from a falling apple, came up with the realization
that there must be a force on the apple that made it fall toward
the ground and clunk him on the head. Silly story or not, Newton
formulated some basic relationships between mass and forces and
the acceleration of bodies that are the foundation of all the
engineering sciences. Isaac Newton is to engineering what Albert
Einstein is to nuclear physics.
Newton made the extraordinary observation that a body at rest
(motionless) will remain at rest unless some force acts upon
that body. That's Newton's First Law of Motion. His Second Law
of Motion says that a body will accelerate when acted on by a
force. The acceleration is larger if the force is larger and
smaller if the mass of the body is bigger. The Second Law of
Motion is represented by the equation:
F=MA,
which reads F equals M times A. F is the force, M is the mass
of the body, and A is the acceleration of the body caused by
the force.
But we're interested in racecars and in addition to accelerating
in a straight line they turn corners. Race tires generate lateral
forces which cause the car to accelerate toward the center of
the arc of the turn. If the mass (M) is going on a circular arc,
we can express A as the square of the speed (V2) divided by the
radius of the curve. The equation for Newton's Second Law is
now:
Fc=MV2/R
The force, Fc, is popularly called the centrifugal force.
It's what keeps the string tight when you swing a weight on a
string. The force on the string goes up the faster you spin the
weight and goes down as you make the string longer. The weight
of the car is just like the weight on the string and the tires
on a cornering car are holding the string!
Look at this equation, Fc=MV2/R, and think about a car going
around a corner. If M gets bigger, Fc has to be bigger so that
the equals sign is still right. That means the heavier the car,
the more force it takes to hold the car in the arc. The faster
the car, the bigger V gets and, at the same time, Fc gets larger
for the same arc. A tighter corner means a lower value for R,
which means Fc has to be bigger.
This is just a basic equation for what you already know. A
lighter car corners faster and a smaller arc (tight turn) is
a slower corner. You also know it takes more force to corner
fasteryou can feel it. Notice that cornering force is proportional
to the square of the speed. For the same arc, cornering at 60
mph takes four times the force as 30 mph (60 times 60 =3,600
which is four times 30 times 30 or 900).
These two equations, Ff=CfFv and F=MA, are what modern racing
is all about. F=MA or its arc equivalent, Fc=MV2/R, tells you
we need a light car with a powerful engine. Ff=CfFv says you
need sticky tires, good suspension (to keep the tires in constant
contact with the road), and all the downforce you can generate.
