Weight and Downforce
by Paul Haney
You may be wondering why, if aerodynamic downforce can increase cornering speed, does a lighter car corner faster? Why is vertical load provided by aerodynamics different than vertical load provided by weight? Those are good questions! We~ll start answering them by talking about friction.
Friction
Friction supplies the resistance to sliding that we use everyday. Without friction we couldn~t walk or crawl and nails wouldn~t hold.
Consider a block of some material, a cube about an inch on a side. The block is lying on a surface, say a table. The block has some weight because of gravity. We~ll call that weight Fv, the vertical force, because it acts straight down. If you push on the block with a force (F) parallel to the table, you can make it slide on the surface. If you push hard, it will slide right off the table. If you push against it very lightly, it won~t move.
Intuitively, you know a block of wood will slide with a lighter push than a hunk of rubber, and the wood block will also be easier to move than a block of lead. Why is that?
This force needed to overcome friction is bigger if the block weighs more, but it also depends on the properties of the surfaces in contact~their coefficient of friction. The equation that describes this is:
Ff = Cf x Fv. That reads: Friction force equals the Coefficient of friction times the vertical Force.
You can see from this equation that the friction force is larger when Cf is larger. Cf is why you have to push a rubber block harder than a wood block. Rubber sliding on anything has a higher Cf than wood sliding on that same material.
Fv, the vertical force, is why it takes more force to slide a lead block than a wood one. The lead is heavier and so Fv is bigger than with a wood block of the same size.
How about some numbers? Rubber has a relatively large friction coefficient when tested on most surfaces. Let~s say it~s 0.8. If the rubber block weighs 1 pound, then the vertical force is 1 pound, and it~s going to take 0.8 pounds of force to push the block at a steady speed. That came from this calculation: 0.8 (Cf) times 1 pound (Fv) = 0.8 pound (Ff).
Let~s add some vertical force to the block. We could just place a piece of lead on top of the wood block but that wouldn~t be very interesting. Instead, let~s put an upside-down wing on top of the block, blow some air over the wing, and produce a downforce of 9 pounds. Now, Fv is 10 pounds (1 pound of weight and 9 pounds of aero force), and it takes 8 pounds to move the block. That came from the calculation: 0.8 (Cf) times 10 pounds (Fv) = 8 pound (Ff).
You~re right, there~s some aero drag force too but, since we~re in control here, we can rotate the wing and blow the air at right angles to the path of the block. Then, drag forces don~t act in the same direction as the friction forces and don~t affect our numbers. Anyway, we~ve got downforce in excess of the weight of the block and gained a lot of friction force without adding weight to the block. What about the weight of the wing? OK, we made the wing out of Unobtanium which has no weight.
These calculations show we can add downforce to a racecar with a wing and get more friction force from the tires, but it doesn~t answer the part of the question about why a lighter car can corner faster than a heavier car. We~ll answer that in the next installment of this series.
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, 1642-1727, 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 ofthe 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 faster-you 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...