Aerodynamics

Introduction This article will discuss some important principles of aerodynamics, and their application to flight and Formula 1. Section 1 will deal with lift and downforce, explaining how these are maximised using aerodynamics. Section 2 will consider the reduction of drag using similar principles. 1. Lift and Downforce Key to maximising vertical forces in aerodynamics is the wing shape (Figure 1), usually characterised by one curved and one straight edge (although it does not have to be straight, as we shall see). Air pressure is lower along the curved edge than the straight edge, establishing a vertical force due to pressure gradient. With the curved edge at the top, the wing is forced upwards, creating the lift desired in aeroplanes. With the curved edge at the bottom, the wing is forced downwards, creating the downforce desired in racing cars. I will now investigate how the curved edge produces a lower pressure. 1.1 The pressure gradient along curved streamlines¹ Consider the streamlines shown in Figure 1. Naturally, the streamlines are curved when the air flows over the curved edge. A streamline is defined as the path a particle would take if released in the air flow. Curved streamlines mean that the path is curved. That means that a centripetal force is acting in the region. The only force existing around the wing is pressure. So the centripetal force must arise from a pressure gradient, with lower than atmospheric pressure as we approach the centre of curvature. In other words, pressure is lower close to the curved edge than it is further away from the wing. This pressure gradient creates a vertical force on the wing. 1.2 Lift Aeroplane wings (Figure 2) have a curved top edge with the centre of curvature beneath the wing. This means that the pressure is lower directly above the wing than elsewhere, forcing the wing upwards. Similarly, the top surface of bird wings (Figure 3) curves downwards, creating an upward force on the top surface. However, bird wings differ from aeroplane wings in that the lower surface is also curved downwards. Hence a second pressure gradient is established, with higher pressure close to the lower surface. This results in even greater lift. Aeroplanes sacrifice this extra lift due to the structural weakness of a curved bottom surface.

1.3 Downforce² The opposite effect is desired in Formula 1 cars. Downforce is used to increase the car's maximum speed when driving around corners. Figure 4 shows a car with wings which are beneath their centre of curvature. Again, the pressure gradient is established with lower pressure towards the centre of curvature - that is, lower than atmospheric pressure close to the bottom surface of the wing. This pressure gradient forces the wing downwards. Consequently, the reaction force from the ground on the car also increases. This results in greater friction, which is proportional to reaction force. When driving around corners, cars depend on friction to act as a centripetal force. The greater the friction, the greater the maximum velocity during the turn. This is why downforce is so important in Formula 1.

2. Drag Along with generating lift or downforce, minimising drag is one of the most important considerations for engineers designing the shape of an aeroplane or race car. In this section, I will discuss the causes of drag, and hence explain how the shapes of vehicles are used to reduce this force. 2.1 Turbulence The main form of drag is caused by turbulence in the air flow. Turbulent flow is lower pressure than laminar flow³. If a moving vehicle leaves an area of turbulent air behind it, a horizontal pressure gradient is established. This creates a horizontal force, pushing the vehicle from areas of higher to lower pressure - i.e. a force opposing the direction of motion. Turbulence is caused by sharp changes in the direction of the air flow (Figure 5). The best shape for a vehicle to reduce this kind of drag is a teardrop shape, with a round edge at the front and a point at the rear.?

2.2 Applications of the teardrop shape Neither an aeroplane nor a Formula 1 car ever has a perfect teardrop shape. This is prevented by the wings which deviate from the shape; safety considerations (crash structures in cars, as well as the structural weakness of a thin point at the rear)² and other features which are important for control of the vehicle (tails of planes etc). However, the streamlined shape can be seen in several features of these vehicles². These are generally the features which are most likely to produce drag and which do not contribute to the creation of lift/downforce. Conclusion The main forces in aerodynamics are produced by pressure gradients. The most important structure for maximising vertical forces is the curved wing shape, which causes a pressure gradient to act as a centripetal force due to the curving of streamlines. An important aspect of reducing drag is the teardrop shape, which sustains laminar flow and so reduces horizontal pressure gradients. References 1. H. Babinsky How Wings Work, Physics Education 38 497 2003 2. Personal correspondence with D. Mackenzie, F1 engineer 3. M. Crawford et al. Physics in Context, 2001 4. https://howthingsfly.si.edu/aerodynamics/pressure-drag accessed 05/12/14