Aero Handbook

Introduction

Hello and welcome to the Georgia Tech Motorsports Sub-Aero Handbook! Building race cars is hard, as SuperFastMatt showed with Car 7 . Doing so on a team of students that has completely new members every four years is near impossible. This document intends to make that task slightly less daunting by officially documenting best practices in an organized and efficient manner. While it is impossible to document all the knowledge currently on our sub-system, my hope is to get as close as possible. To future members, please update this. What we consider best practices now are not optimal, and there are far better solutions out there for nearly everything we do. Once you find the better solution, add it, but document what we did prior to avoid regression.

General Sub-Aero terms

Airfoil: The cross-sectional shape of a wing which generates a pressure differential on either side.
Biplane: An airfoil or system of airfoils above the main airfoil system in a wing.
Camber: The curvature of an airfoil.
Chord Length: The distance from the LE to the TE of an airfoil.
Coefficient: Normalized, dimensionless quantity describing interaction between a system and fluid.
Count: One thousandth of a coefficient. Note: There is no standardized, universal definition of a count, so it is important to define.
Free Stream: The state of air infinitely ahead of a given aerodynamic system such that it is not affected by the system.
Leading Edge (LE): The front edge of an airfoil.
Mainplane: The first, primary airfoil in a system/series of airfoils.
Ply: A layer of fiber in a composite material.
Ply Schedule: The construction of a composite skin as defined by individual plys.
Sandwich Panel: A composite board made of fibers on either end of a core material.
Secondary: The airfoil immediately preceding the mainplane.
Span Length: The length of an airfoil along its width (perpendicular its chord).
Tertiary: The airfoil immediately preceding the secondary airfoil.
Trailing Edge (TE): The rear edge of an airfoil.
Up/Down/In/Out Wash: The movement of air in a respective direction.
Yaw: The crosswind experienced by the system, represented by an angle
or
the angular difference in the car’s velocity and wind speed brought on by rotation through a corner.
Core: The central section of sandwich panel; usually a honeycomb-shaped material or foam.

General Resources

Design Reviews: These are always good places to start, as their real benefit is documentation. Design binders can be helpful as a single document outlines an entire design cycle, but sometimes they are done in different formats. Progress throughout a design cycle should be documented in preliminary, intermediary, and final design reviews. More importantly, these should show concepts that didn’t work and why they didn’t work to prevent repeating mistakes.

Mechanical/Manufacturing Resources

Easy Composites: Tons of well-made videos on everything composites, including layups and mold design.
FibreGlast: similar to Easy Composites but in article format.
Guides and Resources: From our very own Sub-Composites.
LittleMachineShop: Good source for using metal, including determining what size drill bit to use.

Aerodynamic Resources

Kyle.Engineers: Former F1 Aerodynamicist turned Youtuber with tons of great videos analyzing different racecars, including an FSAE car.
NASA: Great introductory articles on different topics in aerodynamics, both theoretical and applied.
No One Can Explain Why Planes Stay in the Air: An explanation of why we have no concise, physical (non-math based), and general explanation of airfoil theory.

Introduction to Aerodynamic Theory

What We Try to Do

Race cars are built from the tires up; therefore, everything on a racecar is intended to manipulate the tires to make the car accelerate faster. Their grip is a product of the normal force and the coefficient of friction, both of which are constantly changing. Increasing the normal force allows for faster acceleration; however, simply adding mass adds inertial forces that slow the car down. Therefore, we want to increase the force pushing the tires down without increasing mass. There lays the goal of aerodynamics: using the car’s air speed to push it into the ground without adding much mass.

Aerodynamics has two downsides: drag and weight. The package must be designed to work efficiently, meaning the ratio of downforce to drag is high (somewhere between 2 and 3). While we have found an efficiency of 2 to still be beneficial versus having no aero, increasing efficiency can gain many points. F24 has an efficiency of 2.6 and F25 around 2.2. Secondly, as with anything on a racecar, reducing weight directly results in a faster car. F24’s full aero package weighed about 35 pounds; F25’s around 48 (see the lessons learned section for why).

Key Concepts, Equations, and Assumptions

Incompressible Assumption

As with any gas, air is compressible. However, fluid mechanics becomes far more complex with varying density, so a constant density is assumed. At the speeds we run (<70mph), the variation in density is very low. This allows for easier intuition and less computationally heavy simulations.

Steady State Assumption

Steady state means a system does not change with time, whereas transient means it does. Of course, a racecar is constantly changing, so there are transient effects; however, we assume the added computing power needed to simulate transience outweighs the performance gains. Taking a time average of high energy airflow is generally considered accurate.

Conservation of Mass

Imagine air passing through a sealed tube. The amount of mass passing through two cross sections of the tube must be equal. This is because mass cannot be created or destroyed. The mass flow, or mass of air passing through per time, at section A1 must equal section A2, giving the equation $ρ_{1} A_{1} V_{1} = ρ_{2} A_{2} V_{2}$ . Because we assume incompressible flow, the density ( $ρ$ ) may be dropped, and the equation then gives the conservation of volumetric flow in volume per time. To balance the equation, $v_{2}$ must be greater than $v_{1}$ because $A_{1}$ is greater than $A_{2}$ . Conversely, if $A_{2}$ were greater than $A_{1}$ , as in a diffuser, the air would slow down. This equation for conservation of mass may be derived from Reynold’s Transport Theorem if you are interested.

Conservation of Momentum

Newton’s Third Law provides a simple way to intuit aerodynamics: conservation of momentum. For every action, there is an equal and opposite reaction. When the car pushes air up, the air pushes the car down and creates downforce – momentum transfer. This can be derived from Reynold’s Transport Theorem for Momentum, which, for a control volume with one inlet and one outlet at constant density, simplifies to $F_{n e t} = ρ (V_{o u t}^{2} A_{o u t} - V_{i n}^{2} A_{i n}) = ({\dot{m}}_{o u t}) V_{o u t} - ({\dot{m}}_{i n}) V_{i n}$ , where F and V are vectors.

For example, take air moving under a wing to be a control volume. Assume the velocity and area at the inlet and outlet of the control volume are the same. As air enters the control volume, it moves horizontally. As it leaves the control volume, it moves vertically. Applying the above equation with the given assumptions means $F_{n e t} = \dot{m} v$ forward and up, so the force acting on the wing is down and back, creating equal amounts of downforce and pressure drag.

Bernoulli's Equation

$P_{1} + \frac{1}{2} ρ v_{1}^{2} + ρ g h_{1} =$ Bernoulli's Constant

Bernoulli’s Equation relates speed to static pressure along a streamline, or the path of an air particle. We assume variations in the gravity term to be negligible. Bernoulli’s constant is the total pressure along a streamline. To balance the equation, pressure and velocity must be inversely proportional to each other; therefore, as one increases, the other decreases. In the pipe example above, the pressure at point 2 would be less than the pressure at point 1 because velocity increases from point 1 to point 2.

Types of Pressure and Force

Bernoulli's Equations may be expressed as:

Static Pressure + Dynamic Pressure + Gravitational Pressure = Total Pressure

Static Pressure: Static Pressure is what we measure as acting on surfaces and is what creates downforce. It can be directly measured with pressure taps with inlets normal to airflow, such as sticking through a surface, normal to it.
Dynamic Pressure: Dynamic Pressure is the pressure associated with the movement of air and represents kinetic energy. It can be measured through a pressure tap oriented tangent to airflow. Think if it as the pressure a wall perpendicular to airflow would feel as air particles constantly collide with it, transferring their kinetic energy to the wall.
Gravitational Pressure: Gravitational Pressure is pressure due to the depth of the fluid. Because air is light and the change in elevation is very small, we often ignore variations in gravitational pressure.
Body Forces: A body force acts on the entire fluid. Gravity or magnetic forces are examples of a body force.
Surface Forces: This is what we care about. These act on the surfaces against the fluid, such as a wing.
Lift: The component of the aerodynamic force pushing the system up. In our case, lift is negative
Pressure Drag: The component of the aerodynamic force, excluding skin friction, which pulls the system backwards.
Skin Friction: The shear force between the boundary layer (defined below) and respective surface, slowing the air down and leading to drag.

Putting it All Together: How a Wing Works

A clear, intuitive, physical interpretation of how wings work is surprisingly difficult, and many common explanations are wrong or misleading. While we have been able to model lift mathematically, an intuitive explanation is still under debate.

A leading intuitive explanation states that air molecules begin by moving tangent to the airfoil surface. As the surface curves downward, the tangent motion of the air creates a vacuum, pulling the molecule back down to the wing and causing it to follow the airfoil’s shape again. This explanation accounts for the conservation of momentum, by turning the air, and the cause of the low-pressure region. It also states the high velocity seen on the low-pressure side is simply a byproduct of the lower pressure, rather than the cause of low-pressure, based on Bernoulli’s principle. However, this theory does not account for why flow separation occurs – if the tangential motion creates a vacuum, wouldn’t aggressive curvature just create a stronger vacuum which pulls the molecules to the surface with increased force?

This Article gives other theories and explains the difficulty of finding a concise and general theory.

Incorrect Airfoil Theories

Equal Transit Theory

Described in this article, the Equal Transit Theory states two molecules hitting the LE at the same time will meet at the TE at the same time. Therefore, the molecule moving along the longer side must travel at a higher speed and, according to Bernoulli’s Principle, create lower pressure. However, symmetric airfoils or angled flat plates create lift, which this theory does not explain. Furthermore, the assumption the two molecules meet at the TE is unfounded.

Skipping Stone Theory

The skipping stone theory states molecules colliding with the high-pressure side of an airfoil impart their momentum to the airfoil, generating lift. This theory completely ignores the low-pressure side, which we know is responsible for the bulk of the lift generated. This is further described in this article.

Venturi Theory

The Venturi theory, described in this article, claims air is squeezed at the leading edge causing the airfoil to act as a narrowing pipe. As the “pipe” narrows, it speeds up the air due to the conservation of mass and, according to Bernoulli’s Principle, creates low pressure. However, this still does not account for flat airfoils, like an angled plate creating lift. Further, the assumption that air is constricted to create the pipe effect is unfounded.

Other Aerodynamic Phenomena

Adverse Pressure Gradients and Flow Separation

An Adverse Pressure Gradient means air flows from low to high pressure. The upstream pressure peak seen on airfoils and diffusers generates such flow. Flow energy is necessary to overcome adverse pressure and allow molecules to follow the surface’s shape. Flow separation occurs when the air does not have enough energy to overcome the relatively higher pressure, causing it to detach from the surface and expand the boundary layer. This image shows gauge pressure, such that the green is negative gauge (relative) pressure and decreasing magnitude represents an increase in absolute (gauge + atmospheric) pressure.

Boundary Layers and the "No Slip Condition"

The No-Slip Condition states that the infinitesimally thin layer of air in contact with a surface has no relative velocity to the surface – that is, the air sticks to it. Moving further from the surface, the air slowly approaches the free stream velocity.

Laminar Versus Turbulent Flow

Laminar flow follows very smooth, predictable streamlines whereas turbulent flow is unsteady and unpredictable. Turbulent boundary layers, however, have much better flow attachment due to their higher energy. The region between laminar and turbulent flow is called transitional, but is not important for us.

Flow Detachment

Flow Detachment occurs when the curvature of a surface is overly aggressive such that the boundary layer grows very large and turbulent, preventing the air above from following the surface’s shape. This is also called stalled airflow. Because downforce is generated by turning the air upward, air not following a surface’s shape prevents downforce generation. The stalled air generates vortices, or eddies, which in turn generate drag.

Vorticity

A vortex is an aerodynamic structure rotating about a line, such that the air has very high angular velocity. In the center, the line or point has very low pressure which constantly pulls the air in; however, the air’s linear momentum prevents it from reaching this low-pressure point. These effects result in a stable, low-pressure, high energy flow structure.

Vortex Characteristics

Low Pressure: Vortices generally create low-pressure regions. Vortices forming along the low-pressure side of an airfoil can create additional lift or downforce.
High Flow Attachment: Vortices cling to surfaces better than laminar airflow such that they support flow attachment. This is due to their high energy.
High Drag: Vortices generate high amounts of drag due to the high energy they take to form.

Tip Vortices

Top vortices form at the ends of wings and are caused by the pressure differential on either side of the wing. Air wants to move from the high-pressure side to the low-pressure side. In doing this, it curls around the end of the wing, creating a vortex. These reduce lift and increase drag.

Aerodynamic Tools

Airfoils

An airfoil is the cross-sectional portion of a wing, shaped to create a high- and low-pressure side. For a downforce generating airfoil, the bottom side is low pressure as it sucks the wing downward.

Diffusers

Diffusers suck in air, driving high speed flow at their inlet. Conservation of mass requires air to slow through the diffuser as its cross-sectional area increases. This image shows the pressure across the diffuser’s surface. The diffuser sucks air from the floor, driving high speed flow across the flat bottom. Because Bernoulli’s Principle states high speed flow creates low static pressure, the floor experiences low pressure, as shown by the blue. The diffuser inlet experiences the highest velocity – this effect can be seen by the deep blue pressure peak. As the air travels through the diffuser and slows down, the pressure map shows increasing pressure.

For a more intuitive understanding, conservation of momentum may still be applied: the diffuser gradually turns the air upwards, so the air must impart a reactionary force downward on the car.

Venturi Tunnels

While similar to diffusers, Venturi Tunnels squeeze the air at the inlet to create a stronger pressure peak. The inlet collects air and then forces it through a choke point before it is sucked and expanded through the diffuser. Venturi tunnels generally have stronger performance than simple diffusers but are more complex to design and may require a longer chord length.

An intuitive reason they create more downforce than a diffuser is because the lower suction peak draws in more air, generating more momentum transfer as more mass flow is accelerated upward.

Endplates

As previously discussed, wings generate tip vortices due to the pressure differential on either side. These vortices cause high drag and reduce downforce, so preventing them creates a better wing. Endplates help accomplish this by preventing airflow at the wing’s tip from the high-pressure side to the low-pressure side. Without this airflow, the vortex does not form. Oversized endplates experience poor yaw performance and limit the amount of air the wing may affect, thus limiting downforce generation.

Gurney Flaps

Gurney Flaps are small, flat plates at a wing’s trailing edge oriented normal to the chord. They create a turbulent region behind them. The air comes off the wing and continues flowing smoothly along the border of this region, making the unsteady region act as an extension of the wing. This may be seen on the second image, where the boundary layer – the green portion along the surface – continues along the grey region behind the Gurney Flap.

Gurney Flaps effectively increase the chamber and chord length of an airfoil while supporting flow attachment. Downsides include large drag generation due to the turbulent flow they cause.

Slot Gaps

As previously discussed, flow detachment occurs when the boundary layer does not have enough energy to continue flowing through the adverse pressure gradient. Slot gaps delay flow attachment by injecting high energy flow into the boundary layer. The image above shows flow detachment near the TE of the first airfoil, indicated by the blue flow which doesn’t follow the upward curve of the TE. However, after the slot gaps there is high speed flow following the curvature of the secondary airfoil, showing strong flow attachment.

Vortex Generators

Vortex generators are another way to promote flow attachment by injecting high energy flow into the boundary layer. They can also be thought of as blocking the existing boundary layer while mixing in freestream air.

VGs on Airfoils

The image above is a total pressure plot of a rear wing. Total pressure is a way to visualize flow energy and therefore boundary layers. The red indicates lower energy and white/grey high energy. The black circle features a vortex generator. Prior to the VG, there is a clearly stressed, red boundary layer; afterwards, there is a high energy, white boundary layer.

VGs on Undertrays

In-Washing Endplate Vents

In-washing vents are holes in the endplate which allow ambient air flow into the low-pressure region below the airfoil, promoting flow attachment at the expense of air expansion. The top image shows two of these vents on F26’s RW endplate

The lower image shows a shear stress (skin friction) plot from the perspective of standing behind the car looking forward. High shear stress indicates strong flow attachment. The circled region is immediately inboard of the endplate vent and exhibits higher shear stress than the segments toward the center of the wing.

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Goal Setting

Integration

Having aero in FSAE is often looked at as a nice to have. This makes it easy to get pushed around.

Set up integration bounding boxes early in the design cycle. This gives a clear space to work in. If someone breaks this agreement, you have something to point to.
Catch things early. If some interference between parts gets caught in manufacturing, aero almost always is the one to end up cutting. Constantly check for interference with other sub-systems in CAD during design and ensure you are using accurate and updated references. Ask respective leads if the CAD is correct. Once again, doing so will give someone to point to if their CAD ends up being wrong. 38’s undertray has holes for the lower control arm, upper control arm, exhaust, and oil pan because nobody checked CAD.
People like numbers. A failure of 38’s design cycle was not giving other sub-systems data to show why we wanted certain integration points – hence reverting to the front dampers being mounted on top of the nose.

CAD

Computation Fluid Dynamics (CFD)

Oooooh boy, aren’t you excited to run your first CFD! First off pal, you don’t “run a CFD”, you run a sim, so that’s strike one. So you don’t use up your other two strikes and blow up our sim computers, here’s some detailed instructions on our CFD environment setup, automation, and use. Below is a workflow of the process used in completing a CFD simulation. In red are the parts that are not currently automated by the sim queue.

“Pre-processing” (Geometry Preparation, Meshing, Physics Setup)

Geometry Preparation

How do we begin the simulation process of an aerodynamic part? We first look to the part itself in CAD. There are some rules of thumb that should be followed for all aerodynamic parts that are to be imported into CFD and ran in a simulation.

Sharp Edges: Avoid geometry with any sharp edges. The rule of thumb in this case is not to create an edge that has a thickness of less than two millimeters. If that sounds like a lot, go outside to whatever car is in shop now and measure the thickness of the trailing edge. Not only are sharp edges impossible to achieve on car, they cause issues with the mesh. More gory details in the mesh portion of this section, but in layman’s terms your surface will become a big grid, and when the grid is touching (like at a sharp edge) bad math things happen and your sim gets sad.
Closed Surfaces: Either one of two types of bodies should be used inside of a CFD simulation. Solid bodies work well, as they will behave as just that, a surface with a closed-out region. The second type is a surface that has either been thickened or closed entirely. Do not use a lone surface body in a CFD sim. This essentially acts as a really long sharp surface. You can check if your surface is closed if you are given the option to make it a solid body when you knit the final part together.
Export Type: Export your parts as parasolids (.x_t). Our software reads these geometry files best. STEP files may also be used.

Meshing

Meet Siemens Simcenter STAR-CCM+, the official name of our CFD software. Most referred to as star, this software is industry standard for automotive aerodynamics. You might hear a ton about meshing jargon from those in industry or otherwise because of how important it is to get right for a correct simulation. Don’t worry, this section discretizes the most important things to get right about your mesh.

Before that, though, the user should understand that star (or at least our use of it) utilizes an automated mesher. There is software dedicated to creating custom meshes from scratch like pointwise. The automated mesher in star is highly customizable and renowned for it’s ability. We should be fine.

Cell Density: The most obvious parameter to adjust in you mesh is your cell density. Lower densities will allow for faster solutions but finer meshes will be more accurate. A “mesh convergence study” of sorts was conducted a while ago which allowed us to land on our current density settings. Truth is, though, we make the cell density as small as possible where we can without sacrificing accuracy. No exact math here, just be mindful of reducing cell density in aerodynamic parts
Y+: FILL THIS IN

Interpreting CFD Results

CFD, and simulations and tests in general, have two categories of outputs: qualitative and quantitative. Qualitative includes graphs and other non-numerical data. Quantitative is strictly numerical and objective. Qualitative CFD results are pressure maps of the car's surface or surrounding airflow, while qualito tative results include parameters such a $C_{l}$ or CoP. Below are several important outputs to interpret CFD results:

Pressure Coefficient: This gives normalized static pressure – what actually acts on the aerodynamic surfaces to create lift or drag.
Skin Friction Coefficient: This gives normalized shear stress. In fluid mechanics, shear stress is the stress acting between layers of a fluid or between a surface and the fluid. High skin friction is indicative of strong flow attachment.
Total Pressure Coefficient: This gives a normalized sum of static and dynamic pressure and may be used to interpret the total energy in the fluid. The total energy is helpful in understanding whether a wing is receiving clean airflow or whether a boundary layer is attached.
Velocity: While helpful in understanding the flow field, velocity is included in the total pressure coefficient and has a strong correlation with pressure, so looking at velocity on its own may not always be helpful.