“Aerodynamics are for people who can’t build engines.”
– Enzo Ferrari 1960
Aerodynamics determine both the downforce and the drag acting on an F1 car during a race and although every aspect of the design is critical, aerodynamics is now widely accepted as the most crucial. The downforce which the car creates forces the tyres into the track and increases the frictional force between the tires and the track, increasing grip and in turn allowing the car to accelerate quicker and corner at higher speeds.
As the performance of F1 cars has rapidly increased so too has the importance of aerodynamics. In 1960 Enzo Ferrari said “Aerodynamics are for people who can’t build engines.” Although this statement was defendable in 1960, when the top F1 cars produced 290hp, this could not be further from the truth for today’s top teams whose cars produce in excess of 900hp [1][2]. The downforce created by the aerodynamics is essential to harness the immense power that the power units are now capable of producing and to retain speed through the corners. In fact, the aerodynamics of modern F1 cars are so effective that at top speed, that they create enough downforce to theoretically be capable of driving on the roof of a tunnel.
The wing of an F1 car utilises the same physics as the wings on a plane, only in reverse. Whereas wings on a plane create lift, the wings on an F1 car produce a downforce, forcing the car into the track. Bernoulli’s principle states that, for an incompressible fluid, when an increase in speed occurs, the pressure decreases simultaneously. The wing of an F1 car is shaped such that the air passing below the wing travels faster than the air passing above. According to Bernoulli’s principle this creates a pocket of low pressure beneath the wing, sucking it down towards the track [3].
Downforce
Fluids can generally be considered as incompressible for speeds up to mac 0.3. [4] for air this value is just over 230mph which is almost the top speed of an F1 car,. For this reason we will make the approximation that in this context air is incompressible and Bernoulli's principle can be applied
In addition to the explanation provided by Bernoulli, we can apply Newton’s third law of motion which states that for every action there must be an equal and opposite reaction[3]. If our two interacting bodies are the wing and the air then if the wing experiences a downwards force, the air must experience an equal force upwards and therefore be deflected upwards. The greater the speed of the car, the greater the mass of air deflected upwards and thus a larger downforce results. Deflecting a greater mass of air upwards can also be achieved by using a curved surface or by inclining the wing (attack angle), using a combination of the two increases the lift coefficient F and maximises the downforce. The cars also have a diffuser at the rear which aids in equalising the pressure of the faster flowing air which has passed under the car, this prevents a low pressure bubble at the rear of the car which would exert a force backwards.
Approximating the Coefficient of Lift
The coefficient of lift is dependent on both the shape and the angle of attack of the wing. For thin wings with small angles of attack (<10 degrees) the coefficient of lift is directly proportional to the angle of attack. At angles of attack exceeding this, a layer of the fluid which the wing is moving through builds up and effectively changes the shape of the wing resulting in a loss of this proportionality [5][8]. At this point the coefficient of lift rapidly decreases and is known as the stalling point of the wing [6]. It is mathematically very hard to approximate the relationship of coefficient of lift and angle of attack past this point and is usually experimentally determined.
Drag
The drag force is such that it acts to oppose the direction of motion and therefore slows the car down so is undesirable.
The drag force has a quadratic dependence on velocity and a linear dependence on both surface area and the coefficient of drag. The drag coefficient is a dimensionless number that is experimentally determined and depends on the shape of the surface and the material of the surface [7].
The reduction in drag extends beyond just reducing the surface area of the car but also to creating aerodynamically shaped body parts and directing air away from un-aerodynamically shaped parts. The front wing for example is shaped such that it deflects air away from un-aerodynamically shaped wheels.
Lift Induced Drag
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There is, however, a trade-off between creating downforce and increasing drag. If the wing is inclined at a greater angle it deflects more air upwards, creating a larger downforce. However, this also increases the component of the force directed parallel to the direction of motion of the car, this is due to the increase of the surface area parallel to motion which results in an increased drag force, slowing the car down. For this reason, F1 cars employ drag reduction systems (DRS) which allows the driver to adjust the angle of the wing in order to gain a speed advantage on the straights however F1 rules greatly limit the use of DRS. Therefore, it is important that the correct compromise between downforce and drag is met. For a slower track with lots of tight corners such as Monaco more downforce and a greater angle is beneficial whereas for a faster, straighter track such as Monza less drag and a lesser angle is an advantage.
As discussed above, generating lift requires a differential of air pressures above and below the wing, this means that around the wing ends vortices are created which disrupt air flow and reduce the lift created as well as increasing the drag force on the car. To reduce this turbulence, the wings have vertical end plates. This effect disappears for a wing with an infinite aspect ratio, however F1 cars have strict legislation limiting the wingspan on wings and by decreasing the chord of the wing, we forgo lift force as seen above [6].
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Here we can see the trade-off between lift coefficient and drag coefficient for small angles of attack.
Combining Zero Lift Drag and Lift Induced Drag
To determine the total drag force which the car will experience we must combine both the zero lift drag and the lift induced drag. We therefore substitute the coefficient of induced drag into the equation for drag force to attain an equation for the induced drag force.
The total drag force is a combination of both the lift induced drag force and the zero lift drag force, which are simply added together.