AirShaper

For more on AIRBUS:
- Part 1 - Aviation challenges: https://youtu.be/IgowvQZ3JtE
- Part 3 - America's Cup Aerodynamics (1/2): https://youtu.be/ZcD9iA9DPrI
- Part 4 - America's Cup Aerodynamics (2/2): https://youtu.be/AdGuENBuZ-Y

In this second video in our series 'AIRBUS talks' we dive into the different methods that are used to design a modern airplane:
- CFD (computational fluid dynamics): aerodynamic simulations running on high-performance computers
- Wind tunnel testing: using scaled models inside a wind tunnel to analyze multiple set points
- Flight testing: flying the real airplane to map its behaviour, performing reject take-off scenario's, stall angle detection, ...

AIRBUS gives us insights into the benefits of these methods:
- CFD: it's possible to simulate the real Reynolds number - the real speed & size of the airplane
- Wind tunnel testing: you can analyze multiple setpoints over a single campaign
- Flight testing: the one & only end evaluation

Most of the efforts are focused on cruise flight, as this represents 90% of the operating regime of the plane.

We also zoom in on the challenges of keeping the Reynolds number the same. AIRBUS even goes as far as working with different gases at low temperature & pressure to get the same Reynolds number as the real aircraft! They've performed tests at DNW (German-Dutch Wind tunnels), ETW (European Transonic Wind Tunnel), DLR (Deutsche Luft & Raumfahrt) and more.

Coming up next:
How AIRBUS was and is involved in the America's Cup!


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The AirShaper videos cover the basics of aerodynamics (aerodynamic drag, drag & lift coefficients, boundary layer theory, flow separation, reynolds number...), simulation aspects (computational fluid dynamics, CFD meshing, ...) and aerodynamic testing (wind tunnel testing, flow visualization, ...).

We then use those basics to explain the aerodynamics of (race) cars (aerodynamic efficiency of electric vehicles, aerodynamic drag, downforce, aero maps, formula one aerodynamics, ...), drones and airplanes (propellers, airfoils, electric aviation, eVTOLS, ...), motorcycles (wind buffeting, motogp aerodynamics, ...) and more!

For more information, visit www.airshaper.com

AIRBUS Talks - Aircraft Design Tools

For more on AIRBUS:
- Part 2 - Aircraft design tools: https://youtu.be/G60rTDR6CPw
- Part 3 - America's Cup Aerodynamics (1/2): https://youtu.be/ZcD9iA9DPrI
- Part 4 - America's Cup Aerodynamics (2/2): https://youtu.be/AdGuENBuZ-Y

'AIRBUS TALKS' is a series of 4 videos with Julián Maldonado: he explains the ins & outs of aviation design and the America's Cup boats they help design.

Part 1: Aviation Challenges

In this first video, Julian explains the modern challenges in aviation and how they plan to tackle these.

About Julian Maldonado:
- Has been working at AIRBUS for 15 years
- 10 years on aerodynamics: CFD, wind tunnel testing, flight testing
- 2 years on flight dynamics: A320neo, flight test identification
- 3 years on aircraft performance: project manager

Typical general aviation challenges - related to the aerodynamics:
- Safety first
- Reduce emissions: CO2, NOx, Noise

Aerodynamic focus points:
- Laminar flow: reducing turbulence & drag
- Improving the lift/drag ratio: improve performance & optimize the trajectory

Improving the overall drag of the airplane:
- Winglets: 2% drag reduction. Applied to every flight, this has a huge impact.
- Laminar flow: the BLADE project focuses on improving laminarity on the wings to reduce the drag.

Coming up next:
Simulation techniques, wind tunnel testing & flight testing


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The AirShaper videos cover the basics of aerodynamics (aerodynamic drag, drag & lift coefficients, boundary layer theory, flow separation, reynolds number...), simulation aspects (computational fluid dynamics, CFD meshing, ...) and aerodynamic testing (wind tunnel testing, flow visualization, ...).

We then use those basics to explain the aerodynamics of (race) cars (aerodynamic efficiency of electric vehicles, aerodynamic drag, downforce, aero maps, formula one aerodynamics, ...), drones and airplanes (propellers, airfoils, electric aviation, eVTOLS, ...), motorcycles (wind buffeting, motogp aerodynamics, ...) and more!

For more information, visit www.airshaper.com

AIRBUS Talks - Part 1/4 - Aviation Challenges

For more information on sports car aerodynamics:
- 300 MPH custom Lamborghini: https://youtu.be/N9kMQBBMUdM
- Porsche Taycan - part 1: https://youtu.be/K2jgsgihZ_w
- Porsche Taycan - part 2: https://youtu.be/kyHjWGnrByQ

In this video, we’re analyzing how aerodynamics impact the performance of rally cars.

Surprisingly enough, in many ways the aerodynamics of rally cars are far more complex than in Formula One, where the cars enjoy some of the world’s smoothest and grippiest bits of tarmac. That’s quite a big contrast to rally cars, where driving in a straight line without wheel spin, drifting or jumping is a rare occasion.
So, where do you start if you want to optimize the aerodynamic performance? The hard reality is that you’ll have to look at multiple scenario's and strike a delicate balance between aerodynamic performance in each of those.

Let's take this 2016 Skoda Rally car in normal setup (regular ride height) and straight-line driving at 40 m/s as the reference. As shown by these red clouds, which indicate where a drag-increasing wake is created, this clearly isn’t the most streamlined car out there:

The rooftop air intake disturbs the air to such an extent that in its wake the center of the rear wing loses pressure and performance. And those wheel arches cause a lot of separation of the airflow at the sides of the car.

But enough on theoretical straight-line driving – it almost never happens, it’s time to start jumping & drifting!

If we increase the car's ride height by 15cm, which is not uncommon just before or during a jump, then the drag on the car increases by 16% and the downforce is cut in half! As you can imagine, losing downforce and grip just before take-off can be quite tricky for the launch. And once you’re flying, you’re slowing down quite a lot because of the drag!

Massive changes in ride height like this are one of the main reasons it’s difficult to boost rally car performance by using underfloor aerodynamics, diffusers and so on: the downforce they generate is extremely sensitive to changes in ride height. And perhaps even more important, that change of downforce can be more pronounced at the front or the rear, changing the aerodynamic balance and thus the handling & stability of the car.

Next, let's look at drifting. Obviously, there's enough debate going on already as to whether you'll be faster or not when drifting. When it comes to aerodynamics, the drag on this car increased by 43% at a moderate drift angle of 15°! That would slow you down quite a lot. But there's good news as well:

The entire car starts acting like a giant wind shield, with the wind hitting the outer side flank. This generates around 100kg of lateral force pushing the car back into the corner.

And, interestingly, the wake of the rooftop air intake is no longer affecting the rear wing, which is now happily creating downforce, so it seems that this car really comes together in the corners.



Note: the 3D model of the rally car used in this video was a public one from hum3D.com and is not an official model from Skoda: it serves mainly to highlight general rally car challenges and not to make official claims to the performance of this car in question.

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The AirShaper videos cover the basics of aerodynamics (aerodynamic drag, drag & lift coefficients, boundary layer theory, flow separation, reynolds number...), simulation aspects (computational fluid dynamics, CFD meshing, ...) and aerodynamic testing (wind tunnel testing, flow visualization, ...).

We then use those basics to explain the aerodynamics of (race) cars (aerodynamic efficiency of electric vehicles, aerodynamic drag, downforce, aero maps, formula one aerodynamics, ...), drones and airplanes (propellers, airfoils, electric aviation, eVTOLS, ...), motorcycles (wind buffeting, motogp aerodynamics, ...) and more!

For more information, visit www.airshaper.com

Rally Car Aerodynamics - Side Slipping through the Air

For more information on sports car aerodynamics:
- Gordon Murray T50: https://youtu.be/FSaI6STYIQA
- 300 MPH custom Lamborghini: https://youtu.be/N9kMQBBMUdM
- Porsche Taycan - part 1: https://youtu.be/K2jgsgihZ_w
- Porsche Taycan - part 2: https://youtu.be/kyHjWGnrByQ

In this video, we’ll cover the advanced aerodynamic features of the upcoming Lotus Evija electric hypercar.

From a distance, the Lotus looks relatively normal, at least for a hypercar. But the closer you get, the more hidden channels you discover. At the front, underneath the hood, the air is guided between the wheels and the center of the car, to exit a bit further downstream at the sides of the car. The air that has chosen to go on top of the hood, tumbles down to the flanks to enter the air intakes on the side of the car to exit at the back.

We didn’t yet obtain a 3D model of the Evija, but we have something that comes quite close. The Aquilo is a concept car I designed 10 years ago, featuring roughly the same channels. Let’s have a look at how they help to improve aerodynamic performance.

In this concept, the air enters the car in the middle and then splits left & right to exit on the sides. This helps to reduce the virtual frontal area of the car, something Lotus refers to as aerodynamic porosity. This same porosity can be seen at the back, where large channels take the air in on the sides and spit it back out at the rear. This air helps to fill the low-pressure bubble at the back of the car, greatly reducing the wake it leaves behind, as shown by these red pressure clouds. This helps a great deal to reduce the drag of the car and thus increases range and top speed.

Beyond reducing drag, the channels in the Aquilo are meant to split the air left & right in an asymmetric way. This generates lateral forces to help the car corner faster. The concept was patented and later on referenced to in patents of Ferrari and Toyota. So perhaps the Lotus Evija hasn’t revealed it’s full potential yet, let’s see what the future brings!

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The AirShaper videos cover the basics of aerodynamics (aerodynamic drag, drag & lift coefficients, boundary layer theory, flow separation, reynolds number...), simulation aspects (computational fluid dynamics, CFD meshing, ...) and aerodynamic testing (wind tunnel testing, flow visualization, ...).

We then use those basics to explain the aerodynamics of (race) cars (aerodynamic efficiency of electric vehicles, aerodynamic drag, downforce, aero maps, formula one aerodynamics, ...), drones and airplanes (propellers, airfoils, electric aviation, eVTOLS, ...), motorcycles (wind buffeting, motogp aerodynamics, ...) and more!

For more information, visit www.airshaper.com

Hypercar Aerodynamics - 2000hp Lotus Evija

For more videos on motorbike aerodynamics:
- Motorbike wheelies: https://youtu.be/M2Z_GuLHmHs
- MV Agusta - MotoGP - part 1: https://youtu.be/BUkaejkHRn8
- MV Agusta - MotoGP - part 2: https://youtu.be/fGNdMaVft_w
- Damon motorcycles - electric motorbikes: https://youtu.be/asYdvFfzHTs

In this video, we’ll discuss the motorbike aerodynamics with together with Joseph Katz, author of the famous book “race car aerodynamics”, professor at the San Diego State University and passionate motorbike rider.
Before we move on to the interview, let’s summarize some basic aspects of motorbike aerodynamics and how they differ from cars:

First of all, the drag: the frontal area, which is the area when looking at an object from the front, is much smaller for a motorbike. But to get the total drag on an object, you need to multiply this frontal area by the drag coefficient, which is much, much larger for a motorbike, offsetting the benefit of the smaller frontal area: it is filled with exposed bits of geometry like the wheels, brakes, and so on, and the surface the air needs to follow is hardly a smooth one: it’s full of abrupt changes like the end of the wind shield causing the flow to detach. And then there’s the rider, a massive disturbance to the air. So, the drag coefficient of a motorbike is easily double or more than that of a modern-day car.
Second of all, the centre of pressure, which is the point where the total sum of the pressure is acting, is quite high above the ground. With respect to the contact point of the rear wheel on the ground, this tends to push the motorbike backwards, lowering contact pressure on the front wheel, which reduces steering control. As the aerodynamic drag force increases with the square of velocity, this can become problematic at high speeds. So, trying to get the center of pressure as low as possible is crucial for motorbikes. A low rider position is a good start. Another way to balance things is to create down force on the front wheel to counteract this back-flipping moment on the bike.

In the interview, we cover the following topics:
- Effects of leaning on aerodynamics
- Engine performance
- AMA superbikes
- Rider position
- Rear tire wear
- Active aerodynamics
- Wind tunnel testing
- Centre of pressure
- Ducati wings
- Lateral forces
- Helmet vibration
- Better engine performance via RAM air


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The AirShaper videos cover the basics of aerodynamics (aerodynamic drag, drag & lift coefficients, boundary layer theory, flow separation, reynolds number...), simulation aspects (computational fluid dynamics, CFD meshing, ...) and aerodynamic testing (wind tunnel testing, flow visualization, ...).

We then use those basics to explain the aerodynamics of (race) cars (aerodynamic efficiency of electric vehicles, aerodynamic drag, downforce, aero maps, formula one aerodynamics, ...), drones and airplanes (propellers, airfoils, electric aviation, eVTOLS, ...), motorcycles (wind buffeting, motogp aerodynamics, ...) and more!

For more information, visit www.airshaper.com

Motorbike Aerodynamics - 10 mph faster with Joseph Katz

Open wheels, exposed components and a constantly moving rider makes optimising motorcycle aerodynamics a huge challenge. But there are many techniques engineers use to refine the designs of motorbikes, helmets and suits and the rider has an important role to play too.

How to improve Motorcycle aerodynamics

For more information about race car aerodynamics:
- Porsche GT4 racing: https://youtu.be/JkdoXKfc2hU
- Race car aerodynamics: https://youtu.be/GApwSjKYUpQ

In this video we’ll explain how you can build aero maps for your own race car.

What are aero maps?
In general, a map is a tool to visualize or store the relationship between different variables. Like the altitude of a terrain in function of longitude and latitude. Or, in case of a race car, the aerodynamic drag, lift and balance in function of the setup of the car, like the ride height at the front and the rear, the angle of a wing, and so on. So in general, aero mapping can be described as the “mapping” of the relationship between geometric parameters of the car on one hand, and the effect on aerodynamic properties on the other hand.

What do you use them for?
When the time has come to race, every second matters: not only for lap times, but also for setting up the car prior to and during the race. Aerodynamics are crucial for the dynamic behavior & performance of the car. For example, the aero balance describes how the down force is distributed between the front and rear axle. Shifting this balance can help mitigate oversteer for example. Another aspect is the cornering performance: when the circuit is filled with high-speed corners, you need more down force. But on circuits with long straights, the drag penalty associated with high-down force settings will slow you down over the course of a lap. Having a clearly mapped relationship available between the setup parameters of the car and the aerodynamics is essential to setup or modify the car on race day – when there is no room for trial & error.

Where can you get these aero maps?
“Ok, you have me convinced, I need aero maps. Where do I buy one?” Unfortunately, it’s not that easy, for a number of reasons:
a. You could ask the manufacturer, but quite often the aero maps are not shared, or the ones that are shared are not always accurate or useful.
b. You could also consider building your own aero maps in a wind tunnel: it can result in highly accurate maps, but requires large budgets as a proper tunnel with moving floor costs thousands of euros per hour, not even taking the cost of preparation & data processing into account.
An interesting budget-friendly way of building aero maps is to run CFD, or computational fluid dynamics simulations on the different setups of your car. Let’s have a look at how this can be done.


Building an aero map through simulations
To illustrate the process of aero mapping we’ll be using this public 3D model of the 2016 Audi R8 LMS. We changed the ride height of this car by 20mm in two steps and then mapped two important aerodynamic properties.

First, the drag and down force. As you can see, increasing the ride height of the car doesn’t impact the aerodynamic drag much but it significantly reduces the down force. This is because you reduce the speed up of the air underneath the car, helped by the splitter at the front and the diffuser at the back. So lowering the car would actually be a better idea in terms of aerodynamics, giving you extra down force at hardly any drag penalty, so why didn’t we?
Well, in most race classes there is a lower limit to the ride height of the car, so you wouldn’t be allowed. And, if you lower the car too much, you can actually block or choke the flow underneath the car, losing that precious down force.

But down force is more complicated than just a single number. As mentioned before, the aero balance describes the distribution of down force between the front and rear axle. Too much on the front will make the front wheels grip nicely but allows the back to lose grip easily, resulting in oversteer. So, it’s important to tweak the balance properly and amongst many things, align it with the weight distribution of the car itself. In this example, we can see that increasing the ride height of the car, also shifts the aerodynamic balance backwards. To counter this, you may need to play with the front splitter or the angle of attack of the rear wing, or the rake of the car, if allowed by regulations.

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The AirShaper videos cover the basics of aerodynamics (aerodynamic drag, drag & lift coefficients, boundary layer theory, flow separation, reynolds number...), simulation aspects (computational fluid dynamics, CFD meshing, ...) and aerodynamic testing (wind tunnel testing, flow visualization, ...).

We then use those basics to explain the aerodynamics of (race) cars (aerodynamic efficiency of electric vehicles, aerodynamic drag, downforce, aero maps, formula one aerodynamics, ...), drones and airplanes (propellers, airfoils, electric aviation, eVTOLS, ...), motorcycles (wind buffeting, motogp aerodynamics, ...) and more!

For more information, visit www.airshaper.com

Race car aerodynamics #3 - Aero mapping

Aero maps visualise the relationship between downforce, drag and ride height. Engineers use aero maps to tune the set-up of a race car to achieve maximum downforce and optimum aero balance in the corners where the most lap time can be found.

How aero maps can improve race car performance

To learn more about the Tesla Semi Aerodynamics: https://youtu.be/Km1NHe0ZsVo

---What is Vecto---
Within the quest to limit climate change, the pressure on heavy duty transport has been rising, and with good reason: trucks, buses and coaches together produce around a quarter of all CO2 emissions from road transport in the European Union. To ensure that the most fuel-efficient vehicle combinations are brought onto the market, the European Union developed the “Vehicle Energy Consumption calculation Tool”, or VECTO in short, a mandatory tool since January 2019 for new trucks & buses in a number of categories. Based on input parameters like rolling resistance, air drag, masses and inertias, gearbox friction, auxiliary power and engine performance, it simulates fuel consumption and CO2 emissions based on standardised driving cycles. So how do you obtain all these parameters?


---What is Vecto AirDrag---
Based on constant speed track tests and a massive set of measurement data, Vecto AirDrag allows you to calculate the air drag Cd*A, based based on force measurements:
- Constant forces, that do not change with velocity (rolling resistance, bearing losses, and so on)
- Air drag force, which scales with the square of the velocity
To obtain the split between these forces, you can measure the force at 2 different velocities. If you then fit a curve through both low-speed and high-speed tests, including a constant and a quadratic term, you can isolate both components.
***The Track***
Tests are executed on a proving ground test track, with two straight parts running in opposite direction. Data is logged throughout the entire test, but it’s only the data captured on these straights that counts.
 
***Measurements***
- On the vehicle
High-accuracy DGPS data
Front axle rpm & torque (left and right)
Wind speed & direction above the truck measured using an anemometer mounted on a pole
Ambient temperature on the truck
- At the fixed weather station on the proving ground
Ground temperature and
Air pressure & humidity are measured.

 
***Data evaluation***
Once all the tests have been performed and the data has been gathered, the constant speed tests are processed in 8 steps:
1: the instantaneous velocity readings are corrected using the average velocity over a test section.
2: the forces acting on the truck are calculated, based on the torque readings from the shafts and the engine or cardan speed. These are then corrected:
- the force for climbing or descending is compensated for based on the road gradient & vehicle mass.
- the correct air density is calculated using the temperature at the vehicle and pressure & humidity at the fixed weather station
3: validity criteria are applied to each constant speed test (speed & temperature ranges, ...)
4: CdA(beta) is calculated for each test by fitting a curve through the data.
5: result averaging per heading and then across headings.
6: extra checks (on rolling resistance, ...).
7: CdA(beta) conversion to CdA(0°) based on empirical data / vehicle type.
8: anemometer drag correction

---Optimizing for efficiency--
As you can imagine, running these tests requires large budgets & a lot of preparation effort, so you want to get it right the first time around. To know up front how changes in aerodynamics will impact vehicle efficiency, you can run aerodynamic simulations: 12--these allow you to calculate the CdA for each design concept and quantify the effects of replacing mirrors by camera’s, shielding the wheels, reducing the gap between tractor and trailer, and so on.
You can then use the engineering mode of Vecto to assess the effect of these differences in aerodynamic coefficient on total vehicle efficiency. Once you’re comfortable enough with the predicted efficiency gains, you can move on to real physical testing, using the declaration mode of Vecto for the final analysis.

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The AirShaper videos cover the basics of aerodynamics (aerodynamic drag, drag & lift coefficients, boundary layer theory, flow separation, reynolds number...), simulation aspects (computational fluid dynamics, CFD meshing, ...) and aerodynamic testing (wind tunnel testing, flow visualization, ...).

We then use those basics to explain the aerodynamics of (race) cars (aerodynamic efficiency of electric vehicles, aerodynamic drag, downforce, aero maps, formula one aerodynamics, ...), drones and airplanes (propellers, airfoils, electric aviation, eVTOLS, ...), motorcycles (wind buffeting, motogp aerodynamics, ...) and more!

For more information, visit www.airshaper.com

Cutting truck & bus emissions - The Vecto AirDrag Tool

In this video, we’ll guide you on how to select the right simulation for your project.

In theory, the advice is simple: go for the one with the highest resolution, as it results in the highest accuracy & the most useful data. But in practice, this is also the most expensive & time-consuming solution, so the real question is:
“Within a given budget & timeframe, how can I improve the aerodynamics the most?”

For example, should I run 10 simulations at low resolution or one at high resolution? The answer is to select the right resolution for the right purpose. 

But first, let’s explain what exactly resolution means for aerodynamic simulations:
Very similar to the pixels of a digital photograph, which form a 2D grid or mesh, a flow simulation uses a 3D mesh, featuring small blocks around your 3D model to calculate the aerodynamics. For more details on this, watch our separate video on computational fluid dynamics using the link in the description below or at the end of this video. Most important aspect: the higher the resolution, the smaller these 3D blocks become and the more accurate the flow simulation will be. That brings us to the first guideline on how to select the right resolution, the 3D model you’re analyzing.

3D model
Let’s compare the effect of low, medium and high resolution on the same object, in this case, a Formula E car. At low resolution, the global mesh looks quite ok but in areas, with small details like the wheels the mesh is quite rough. Depending on how accurately you want to capture the flow around these details, the mesh resolution needs to increase accordingly.
So if you’re interested in the global flow around a smooth object, a low resolution might be enough for a first idea. But if you’re interested in the flow around small details on a large 3D model, you may want to go for a high resolution.

Accuracy
Next up is the accuracy. Your shape may be simple, like an airfoil, but to accurately analyze lift & drag forces, you still need a high resolution. So if you’re simply interested in learning about the order of magnitude of forces, like the difference between 1 or 10 Newtons of lift, a low resolution might do. But if you’re looking to make more accurate force estimations, to know whether the lift on your airfoil is 6 or 6.5 Newtons, you’ll need a high resolution.

Design phase
Finally, it also depends on the design phase of your project. If you’re in the very initial phase, you first want to gain basic insights and not spend all your budget on simulations just yet. So a low resolution might be enough to provide you with those first valuable learnings and relative ranking between concepts. But as you progress towards more detailed models with smaller differences, the resolution needs to evolve accordingly.

This means you could for example run 10 simulations at low resolution to determine the main design direction during the concept phase, run 5 simulations at medium resolution when you’re detailing a selected number of designs and finish off with 3 simulations at high resolution to tweak the last bits of performance before releasing the design for physical wind tunnel testing or production. 

So in conclusion, a low resolution might be enough if you’re working on simple, early-stage 3D models and just need a ball-park estimate on the forces and the flow field. But if you’re looking to make accurate force predictions on complex 3D model towards the end of your design process, you’re better off with a high resolution.

Last but not least: talk about it. If you’re not sure how to approach things, just get in touch and we’ll see how we can help!

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The AirShaper videos cover the basics of aerodynamics (aerodynamic drag, drag & lift coefficients, boundary layer theory, flow separation, reynolds number...), simulation aspects (computational fluid dynamics, CFD meshing, ...) and aerodynamic testing (wind tunnel testing, flow visualization, ...).

We then use those basics to explain the aerodynamics of (race) cars (aerodynamic efficiency of electric vehicles, aerodynamic drag, downforce, aero maps, formula one aerodynamics, ...), drones and airplanes (propellers, airfoils, electric aviation, eVTOLS, ...), motorcycles (wind buffeting, motogp aerodynamics, ...) and more!

For more information, visit www.airshaper.com

Choosing your Simulation - Accuracy vs Speed vs Cost

To learn more about adjoint shape optimization: https://youtu.be/cZAhPQFINZ8

In this video, we’ll explain the basic principles of CFD or computational fluid dynamics.


Modeling involves the continuous mathematical functions that you use to describe the real flow. In reality, that flow is the result of many different laws of physics working together. To limit computational effort, it’s a matter of selecting only the ones that have a substantial impact on your flow topic: if you’re calculating the aerodynamic force on a wing, for example, there’s little use in taking the gravitational pull of the moon into account, as the effect is negligible. So, defining correct & relevant models is important to limit the modeling errors:

In case of fluid mechanics, the most important model is a set of partial differential equations called the “Navier Stokes” equations. These basically apply the laws of Newton for every small bit of the fluid, stating the dynamic balance between the forces acting on it and the change in its momentum. This conservation of momentum, together with the conservation of mass, allows you to describe the flow field.

For some very simple cases, like laminar flow through a pipe, there are analytical solutions: the entire flow field can be described using continuous mathematical functions. These allow you to calculate the exact velocity & pressure for any given location in the flow field at an infinite resolution.

But for anything more complex than these very simple cases, we don’t have such an analytical solution. That means we need to break down reality into small blocks for which we do have a solution. These blocks can be finite elements or finite volumes, also called cells. Think of it as the difference between analog and digital photography, where a complex image is described by simple pixels, each having just one color.

This process of breaking down a large continuous flow field into small cells is called meshing. For each of these cells, we can approximate the continuous Navier-Stokes equations by discrete algebraic equations. These allow us to calculate the pressure & velocity at the center of each cell, which is called the node, based on the values of velocity & pressure of the surrounding nodes.

The higher the order of these discrete approximations, the more surrounding nodes are included. This “reach” is called the computational molecule, resulting in a set of algebraic equations for each node. As the value of one node depends on the value of neighboring nodes and vice versa, the equations are connected. This means you need to solve them simultaneously by putting them together in a big matrix.

But before we discuss how to solve this matrix, we need to talk about the discretization error: “The difference between the exact solution of the governing equations and the exact solution of the discrete approximation”. The more cells you apply, the smaller this error. But this also increases the number of equations you need to solve, and with meshes typically containing millions of cells, this quickly becomes very expensive. So you’re best off applying small cells to locations where the flow is complex, and large cells where the flow is less curvy, typically further away from the object.

Once you have defined your mesh and your matrix of equations, it’s time to solve them. It’s possible to find the exact solution of this matrix problem through a direct method like Gauss elimination or LU decomposition. But this is very costly in terms of computational power and why bother solving the equations down to computer accuracy level, when your discretization error is much bigger anyway?

This is where faster iterative methods come in: they start by “guessing” an initial solution, which could even just be a standstill flow field, or “zero velocity” for every point. Then they linearize the equations around that point and improve the solution through iteration. If you iterate long enough, the flow field will converge to a stable solution, reducing the iteration error. The difference between this solution and the direct solution of the equations is called the iteration error.


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The AirShaper videos cover the basics of aerodynamics (aerodynamic drag, drag & lift coefficients, boundary layer theory, flow separation, reynolds number...), simulation aspects (computational fluid dynamics, CFD meshing, ...) and aerodynamic testing (wind tunnel testing, flow visualization, ...).

We then use those basics to explain the aerodynamics of (race) cars (aerodynamic efficiency of electric vehicles, aerodynamic drag, downforce, aero maps, formula one aerodynamics, ...), drones and airplanes (propellers, airfoils, electric aviation, eVTOLS, ...), motorcycles (wind buffeting, motogp aerodynamics, ...) and more!

For more information, visit www.airshaper.com

Computational Fluid Dynamics Explained

Computational Fluid Dynamics is used in many industries to model and optimise the behaviour of fluids. Based on the Navier Stokes equations, there are three steps to computing flow, modelling, discretisation and linearisation.

Our Latest Videos Gain aerodynamic insight by watching our videos