Engineered with perfection, the loud and aggressive Formula One (F1) racecar is the ultimate racing machine.Its reputation has been defined by its amazing speed and handling characteristics, which are for the most part, a product of its aerodynamic features.The success of these features relies primarily on the appropriate and efficient harnessing of drag and downforce – both of which are ruled by physical principles explained by Bernoulli’s equation.

1.1Bernoulli's Equation

Investigated in the early 1700s by Daniel Bernoulli2, his equation defines the physical laws upon which most aerodynamic concepts exist.This now famous equation is absolutely fundamental to the study of airflows.Every attempt to improve the way an F1 car pushes its way through molecules of air is governed by this natural relationship between fluid (gas or liquid) speed and pressure.There are several forms of Bernoulli's equation, three of which are discussed, in the succeeding paragraphs: flow along a single streamline, flow along many streamlines, and flow along an airfoil.All three equations were derived using several assumptions, perhaps the most significant being that air density does not change with pressure (i.e. air remains incompressible).Therefore they can only be applied to subsonic situations.Being that F1 cars travel much slower than Mach 1, these equations can be used to give very accurate results.1

Low speed fluid flow along single or multiple streamlines is interpreted in Figure 1.The presumptions regarding the application of Bernoulli's equation to this scenario are listed in the figure.In this situation, there exists a relationship between velocity, density and pressure.As a single streamline of fluid flows through a tube with changing cross-sectional area (i.e. an F1 air inlet), its velocity decreases from station one to two and its total pressure equals a constant.With multiple streamlines, the total pressure equals the same constant along each streamline.However, this is only the case if height differences between the streamlines are negligible.Otherwise, each streamline has a unique total pressure.

As applied to flow along low speed airfoils (i.e. F1 downforce wings), airflow is incompressible and its density remains constant.Bernoulli's equation then reduces to a simple relation between velocity static pressure.1

(pressure) + 0.5(density)*(velocity)2 = constant

This equation implies that an increase in pressure must be accompanied by a decrease in velocity, and vice versa.Integrating the static pressure along the entire surface of an airfoil gives the total aerodynamic force on a body. Components of lift and drag can be determined by breaking this force down.

In order to discuss lift and downforce, it may be helpful to provide an additional explanation of the relationship that occurs with the above form of Bernoulli's equation.If a fluid flows around an object at different speeds, the slower moving fluid will exert more pressure on the object than the faster moving fluid.The object will then be forced toward the faster moving fluid.8A product of this event is either lift or downforce, each of which is dependent upon the positioning of the wing's longer chord length.Lift occurs when the longer chord length is upward and downforce occurs when it is downward.

The remarkable speed of the F1 racecar is achieved from the careful combination of its powerful engine and expertly crafted aerodynamic body features.In the early years of F1 design, the engine was the primary variable in determining the racing success of a car.Applicable engine technology had far exceeded the maturity of vehicle aerodynamics.Those historic years embodied a simple algorithm. Speed was nearly a direct function of horsepower.Although still improving almost annually, engine performance levels among the cars of each racing season today have comparable performance – record speed achievements now hinge on a different design issue – aerodynamics and drag plays a major role.F1 aerodynamics engineer, Will Gray, has noted that "Top speed is determined other factors [car weight, fuel strategy, and good low-end engine power], but the main factor which separates the victors from the valiants in this area is aerodynamic performance – too much drag and you're pulling unwanted air along with you

One form of drag occurs as air particles pass over a car's surfaces and the layers of particles closest to the surface adhere.The layer above these attached particles slides over them, but is consequently slowed down by the non-moving particles on the surface.The layers above this slowed layer move faster.As the layers get further away from the surface, they slow less and less until they flow at the free-stream speed.The area of slow speed, called the boundary layer, appears on every surface, and causes one of the three types of drag, Skin Friction Drag.

The force required to shift the molecules out of the way creates a second type of drag, Form Drag.Due to this phenomenon, the smaller the frontal area of a vehicle, the smaller the area of molecules that must be shifted, and thus the less energy required to push through the air.With less engine effort being taken up in the moving air, more will go into moving the car along the track, and for a given engine power, the car will travel faster.Another factor that plays a role in aerodynamic efficiency is the shape of the car's surfaces.The shape over which air molecules must flow determines how easily the molecules can be shifted.Air prefers to follow a surface rather than to separate from one.Interestingly, researchers of aerodynamics have found the 'teardrop' shape, round at the front and pointed at the back, to be most efficient at propelling through air while providing a suitable surface for the air to easily move across.With this shape there is little or no separation.It is important to note that sharp frontal areas, rounded ends, sharp curves or sudden directional changes in a shape should be avoided since they tend to cause separation, which increases drag

F = 0.5CdAV2,

whereF - Aerodynamic drag

Cd- Coefficient of drag

D- Air density

A- Frontal area

V- Object velocity

Interestingly, modern F1s are reported to have Cd values of about 0.83 with corresponding CdA[m2] values near 1.2.1 These values are approximately double of those for the modern Ford Sierra, an ordinary family sedan.This is primarily due to three reasons.The first is that regulations specify features that deter from the ability of a designer to achieve relatively low drag coefficients (i.e. open cockpits and running exposed wheels).The second reason is likely due to be the fact that F1 cars rely on a balance between drag and downforce in which drag is often sacrificed for necessary downforce.In order to make up for the speed losses due to drag, engine power is increased if possible.Lastly, unlike family sedans, low fuel consumption is not a paramount concern.Therefore, drag coefficients are allowed to be somewhat large, especially since the importance of other factors (i.e. downforce) takes priority.

Downforce, or negative lift, pushes the car onto the track.5It is accomplished by use of an airfoil mounted such that its longer cord length is facing downward.As air flows over the airfoil, as seen in Figure 6, a low-pressure region is created on the under side of the wing.A high-pressure region then develops on the upper side of the wing, creating a downward force.This pressure difference causes the net downforce.

Downforce is necessary for maintaining speed through corners.8Due to the fact that the engine power available today can overcome much of the opposing forces induced by drag, design attention has been focused on first perfecting the downforce properties of a car then addressing drag.

The teardrop shape, previously discussed, displays ideal aerodynamic properties in an unconstrained flow and is well suited for aeronautical applications.However, when this shape is incorporated into the design of an F1 vehicle, it is subjected to constrained flow, which causes different flow behaviors.This is due to the simple fact that these cars are very close to the ground.The presence of the ground prevents the formation of a symmetrical flow pattern (See Figure 4).1The results of this flow behavior are an unfavorable increased drag coefficient and generation of a very favorable down force.Fortunately, the downforce created is highly valuable and the increased drag can be overcome with array of aerodynamic strategies