Aerodynamics is an important component in the design of vehicles. The shape of
the vehicle helps the engine puncture through the air instead of pushing it
aside. But then what do the air wings or spoilers do? If anything they increase the
drag force making the engine more inefficient, right? Well yes, but there is something else.
To understand the effects of an air wing let s first understand the physics of banking a curve.
When the car travels in a straight line the traction force between the
road and the tires points in the same direction as the direction of travel.
However, when the wheels are turned there is an additional component generated which
points perpendicular to the direction of travel. This component is the Centripetal Force, Fc in
this case, which is needed for circular motion. If Fc is not high enough, meaning the traction
force between the tires and the road is less than M times V-squared over R then the car would slide
off the road in an attempt to keep moving in a straight line as noted in Newton' s First Law.
From the circular motion formula we can notice that if we increase the velocity
of the car we would have to increase the radius of the curve as well to keep the
car from sliding off which explains why the curves on highways are much milder
with large radii compared to the urban roads. However in a real world scenario we don t really
have control over these parameters. Unless we eject a passenger mid drive, the mass of
the car is pretty much fixed. Same applies for the radius of the curve.
So we are essentially left with only two
parameters to play with. Either decrease the velocity or increase the traction. The easiest
way to make the curve safely would be to reduce the travel speed. A reduction in the speed would
decrease the needed centripetal force which would decrease the chances of sliding off
the road. But that defeats the purpose right? The objective is the travel faster and safer.
So as we already saw, the traction between the tires and the road provides the centripetal force
needed for the car to stay on the road. As long as this friction force is larger than the needed
centripetal force then we don't have a problem. However, when we go faster we, need more
centripetal force to stay on the road and from the friction equation it seems that the only thing we
can increase is the Normal force since we don t have much control over the friction coefficient.
To increase this limit, the wheels need to be pushed harder against the road. Adding mass can
do this, but heavier vehicles require a more powerful engine and are harder to control. So
we need some virtual weight that will allow the car to have more traction, without the negative
effects of actually adding the extra mass. This is where the wing comes into play. A wing
can generate downforce solely through clever aerodynamics. The engine will have to work
only slightly harder to overcome the added drag from the wing which is not a problem for racing
cars since fuel economy is not really an issue. But the down force is where the real benefit lies,
the tires friction is proportional to the normal force, adding aerodynamic downforce
to the weight component increases the adhesion to the road. The larger normal force avoids
wheel slipping or sliding off the road and allows for maximum possible acceleration.
But how much difference does the wing actually make? The answer is not simple,
it's highly dependent on parameters such as the mass of the vehicle, the friction coefficient,
radius and superelevation of the curve but also the shape of the wing and angle
of attack and so on. But for regular non-racing cars, the wing doesn't make a huge difference.
We will simulate a typical non-racing vehicle in this Case Opel Astra. The red vector represents
the direction and magnitude of the centripetal force and in green vector is the velocity.
If we quickly sum up the forces acting on the car while it's banking a curve we can
solve for the maximum allowed velocity as a function of the rest of the parameters.
If we enter parameters as specified by The Ministry
of Transportation of British Columbia for a 100km/h design speed the minimum radius
of a curve is 440m with 6% superelevation. Furthermore, the mass of the vehicle can be
taken as 1200kg and the coefficient of friction at 0.8 which would represent ideal conditions.
Solving for the maximum safe velocity with a wing we get 244km/h compared to 225km/h for without
a wing. However keep in mid this analysis is oversimplified and assumes equal weight acting on
all wheels and absolutely perfect road conditions. For icy roads, the coefficient of friction can
drop as low as 0.1 which dramatically changes the result. Regardless of that, the main point is that
installing a wing to a regular non-racing car is somewhat stupid because the effects of it are more
drastic for higher speeds and low mass vehicles. One place where the wing plays a huge role is
formula 1. The low mass of the vehicle and high velocities make the effects of aerodynamics very
important. Maybe in a future video we will explore how much difference the aerodynamic
components make on a formula 1 vehicle. If you liked this video and want to see
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