# Formula 1 Aerodynamics – Basics of Aerodynamics and Fluid Mechanics, part I

Aerodynamics is only a single field of overall fluid mechanics, but there are some specifics about the flow of all-surrounding air around objects – or objects flowing through the air! To understand F1 aerodynamics and the tools teams use to shape their cars in the best way, we bring you a unique article covering the basics of fluid mechanics, which those fond of aerodynamics should find useful.

## General Fluid Properties

Fluids, for starters – are both liquids and gasses (even plasma – ionised gas). Even though their motion is mostly different, it has fundamental similarities. One distinctive property of fluids is that they are a continuous volume filling out the space given to them – liquids take the shape of the space, while gas takes over the entire volume of course.

To investigate fluid motion, fluids are theoretically divided into **fluid parcels** – volume of fluid small enough that all the physical properties of fluid inside it are the same and large enough that it can be considered a continuum. This definition is very important for CFD meshing before simulations, which will be covered in later articles.

*Figure 1 – Example of 6-million-cell CFD mesh on a showcase F1 car, credit Nick Perrin and SimScale GmbH*

Physical properties of fluids are density, compressibility, viscosity, thermal conductivity and capillarity. Aside from capillarity, all properties of air as a fluid are very important in motorsport.

**Density** is simple enough – the mass of given fluid dived by the volume it takes up. Density is in general a function of pressure and temperature. **Compressibility** of fluid is directly related to its density. In general, gasses are compressible and liquids aren’t. Of course, liquids are compressible in reality, but conditions for that are extreme and are of no interest in aerodynamics. For air, it is considered incompressible at air speeds bellow roughly 400-450km/h, but from that point on **compressibility effect** (abrupt and exponential drag increase) is minimal until air speed is close (some 80+ percent) to speed of sound.

**Viscosity** is a very important property of fluid, as it is directly related to surface friction and drag – higher viscosity means bigger drag. Simply put – viscosity is the stickiness of a fluid, i.e. the property of fluid to stick to the surface it is in contact with. Peanut butter is highly viscous compared to water for example, while water is highly viscous compared to air. Viscosity shouldn’t be confused with capillarity, even though these two properties have similar consequences sometimes.

*Figure 2 – illustration of different viscosity effect on 1D fluid flow*

**Thermal conductivity** is a very obvious property for a fluid, or a solid in fact. This property is important for heat transfer in cooling systems. Air, relative to other materials and fluids, is a great thermal insulator – so not good for cooling at all. But it is abundant and therefore logical choice for a natural heat sink, therefore cars need large radiators to cool power train components and brakes need large brake ducts to feed them air that takes away the heat. Water (sometimes oil) is used as a medium in radiators between air and heat sources in the car.

## Fluid Mechanics – Statics, Kinematics and Dynamics

Fluid mechanics is theoretical field of general mechanics, aimed at understanding that fluid’s motion. It is differentiated further to fluid statics, kinematics and dynamics.

**Fluid statics** is the simplest field, determining the forces, pressure and other properties of standing fluid. As air surrounding us is standing still (ignoring the wind at the moment) and cars pass through it, aerostatics is not that interesting to us.

What is interesting is **International Standard Atmosphere**, a set of averaged values for air temperature and pressure in atmosphere, starting at 0m above sea level. Temperature and pressure determine other air properties (density and viscosity) and at 0m above sea level we have

*T=288.15K (15°C),*

*p=101325Pa,*which gives us air density

*rho=1.225kg/m3.*

These are theoretical values of course, but important for initial CFD settings for example. In reality these vary slightly from race to race, day to day and even hour to hour, but are the same for all cars in a race of course.

**Fluid kinematics** studies the motion of fluid, without needing to know the cause (or effect) of this motion. This motion is called flow, sometimes current (e.g. air current, water current). One of the most important terms coming from fluid kinematics is streamline. **Streamline** defines a vector line of velocity field connecting all the different fluid parcels whose velocity direction is tangent to the streamline. In other words, streamline is a line that an air particle is taking during its motion.

Another important and often heard term is vorticity. **Vorticity** is a (pseudo)vector field describing local spinning motion around some point, and in our case it is spinning motion of a fluid. Spinning motion is often found in fluid motion, especially around an F1 car – be it a vortex or an eddy (to be defined in section about turbulent flow). Vortex is a region of a fluid where the flow revolves around an axis line, be it straight or curved. In general, these axis lines are parallel to stream lines of non-revolving flow.

*Figure 3 – Wingtip vortex created by crop-duster*

Vorticity is also important for understanding circulation. **Circulation** (of velocity vectors) is very important in aerodynamics, as a precursor for creating (and understanding) lift around objects. It describes revolving motion of fluid around a closed contour and it is essential for Magnus effect – rotating cylinder perpendicular to fluid flow will create lift. In practice, it is often neglected since understanding how F1 or motorsport aerodynamics works can and is easily explained without it.

**Fluid dynamics** is the largest field of fluid mechanics, as it studies causes and effects of fluid motion to its surroundings, interactions and forces caused by it. In fluid dynamics, there is a big difference between theoretically ideal fluids and real fluids, so there are several levels of fluid simplification between them – introduced to better understand different effects of different properties of real fluids. Naturally, we’ll get straight to the most important aspects of real fluids as race cars go through air and not an ideal, two-molecular gas.

## Some Governing Equations

Even though the most often mentioned equation of fluid mechanics is Navier-Stokes equation, it is far from being the only one and it is important to understand how science (and humanity) got to the point of being able to predict fluid behaviour.

To begin with, we have **ideal gas law** – *pV=nRT.* This shows us correlation between pressure, volume and gas temperature. In the same volume, pressure will rise with temperature rise and vice versa. At the same pressure, volume will expand with temperature rise and vice versa. For instance, this is basic for understanding tyre pressure correlation to overheating those tyres, but is also important for understanding effects of air going trough radiator core on internal aerodynamics.

From general law of mass conservation (in a closed system, its mass must remain identical at all times) comes the **continuity equation** in its form for fluids. In its general (integral) form this equation leaves room for a lot of scenarios depending on fluid density. In our case, air is considered practically incompressible and therefore it can be brought to a simple form – mass flow of air is constant in a single streamtube (a bundle of streamlines) and is equal to air velocity in local cross section times its surface.

This is an important equation for understanding the basic principle of slots in wings – the air velocity trough a single cross section with variable height will change reversely proportionate to slot height. In other words – convergent slot will accelerate the flow, divergent slot will decelerate it.

*Figure 4 – Example of air velocity increase with a convergent slot in rear wing*

The other well-known equation is **Bernoulli equation**, giving us a correlation between fluid velocity, pressure and geodesic height in multiple cross sections of a closed system. Since all cars run at the same geodesic height in a single race and all cars are only one meter high, this effect can be neglected in understanding overall flow structures. This leaves us with air velocity, pressure and temperature as main governing factors for air flow structures around the car.

Bernoulli equation tells us, in short, that high velocity reduces pressure in a closed system and lower velocity increases it. Coupled with continuity equation, this gives us a basic principle of wing slots, for example – in front of convergent slot there will be an increase in pressure on top of the wing and behind the slot will there be a decrease in pressure on bottom of the wing. This corresponds to general pressure distribution on race car wings (reverse of aircraft wings, of course), so slots are naturally used a lot in race car aero packages – and lately more and more aside from wings. Downside of slots is drag increase (coming with downforce increase of course), so they are used carefully and in a different way for different applications.

*Figure 5 – Example of air pressure drop with a convergent slot and upwash of BMW Sauber F1.08*

rear wing, credit Sauber F1 Team

rear wing, credit Sauber F1 Team

Second Newton’s law also has its application in fluid mechanics, in **law of momentum conservation in a continuum**. Momentum change in fluid flow is equal to sum of all forces acting on the fluid. For example, this explains upwash of air coming off the rear wing on the car – in air’s reference frame the wing is acting on it with downforce, so air’s reaction is upward movement. These equations take into account viscous stress in fluid and are called **Navier equations.**

Stokes introduced an assumption for correlation between tangent stress in fluid and its viscosity. Coupled with Navier equations, we have **Navier-Stokes equations** that describe motion of fluid flow. Navier-Stokes equations take into account all effects and properties of real fluids, including energy dissipation (into heat, sound etc.) in real systems. This is why they are not typical conservation equations. In general, they can be described as:

*Inertial forces = Mass forces + Pressure forces + Viscous forces*

**Computational Fluid Dynamics (CFD)** software solves these equations in every single cell of model geometry mesh, iteratively, a few dozen hundred times, coupled with different turbulent models. Since number of mesh cells can get as big as 200 million for an F1 car, it’s obvious why it takes so long and takes so many resources to accurately calculate just one single simulation. In spite of this, teams run 50-200 simulations per week – not all of them are full car simulations of course.

In part II of this article, we will discuss remaining important subjects:

- Laminar and Turbulent Flow
- Boundary Layer
- 1D, 2D and 3D Flows
- Total, Static and Dynamic Pressure

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