Aero Handbook

Introduction to Sub-Aero

Design Methods

Manufacturing Methods

General Advice

Sub-Aero History

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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.

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

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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 ${\rho }_1{A}_1{V}_1={\rho }_2{A}_2{V}_2$. Because we assume incompressible flow, the density ($\rho$) 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 $F_{net}=\rho (V_{out}^2{A}_{out}-V_{in}^2{A}_{in})=({\dot{m}}_{out})V_{out}-({\dot{m}}_{in})V_{in}$, 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 $F_{net}=\dot{m}v$ 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

$P_1+\frac{1}{2}\rho v_1^2+\rho g{h}_1=$ 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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