# AI Propeller Design Optimization using CAESES and AirShaper


## Introduction
In the world of propeller design, achieving optimal efficiency and performance is paramount.
In this blog, Simon Hauschulz (project engineer at FRIENDSHIP SYSTEMS) explains how a combination of AI and CFD helped win a recent propeller design competition hosted by popular YouTuber <ExternalLink href="https://www.youtube.com/user/RCtestflight">RCTestflight</ExternalLink>. With the help of powerful design and simulation tools <ExternalLink href="https://www.caeses.com">CAESES</ExternalLink> by <ExternalLink href="https://www.friendship-systems.com">FRIENDSHIP SYSTEMS</ExternalLink> and <ExternalLink href="https://www.airshaper.com">AirShaper</ExternalLink> we created two high-performance propellers that demonstrated remarkable efficiency. Here's how we did it and how these tools played a crucial role in our success.



## Objective

The primary goal of the competition was to design propellers that could achieve maximum efficiency across a wide range of operating speeds.
Efficiency can mean very different things depending on the application: for some, it's the top speed of a boat for a given available power, for others it may be the efficiency at one or multiple specific operating conditions, and so on.
In this case, Daniel from RCTestflight introduced a unique efficiency parameter that combined maximum speed with low-speed efficiency into a single objective function. This comprehensive approach provided a more thorough evaluation of propeller performance compared to traditional single-point objectives, making the challenge both complex and rewarding.


### Method

In short, AirShaper CFD simulations were used to analyze large numbers of 3D models generated by CAESES. The results were fed into a CAESES surrogate model which was then used to predict the best possible design.

This process involved several key steps:
1. **Parametric Model**: We developed a parametric model for both conventional and Toroidal propellers using CAESES.
2. **Design Space Exploration** We explored the design space using a Design of Experiments (DoE) approach utilizing the <ExternalLink href="https://en.wikipedia.org/wiki/Sobol_sequence">Sobol sequence</ExternalLink>.
3. **CFD Simulations**: Using AirShaper's <ExternalLink href="https://en.wikipedia.org/wiki/API">API</ExternalLink>, which seamlessly connects CAESES to the CFD tool, we ran the simulations at different speeds for each design
4. **Surrogate Model**: We used the CFD results (torque and thrust) within CAESES to train surrogate models. With these surrogate models we are able to generate the open-water diagram for any design in the considered design space.
5. **Optimization and Validation**: With the information from the open-water diagram, each design can be evaluated over the whole operating range and the single objective function can be evaluated. A gradient-based optimization was used to find the optimal design.

### Parametric Propeller Model for the Design Space Exploration

Parametric models were created for both the Toroidal and conventional propeller.
Such models allow for what is called Design Space exploration. We explored various design configurations based on the following parameters:

- Toroidal Propeller Paremeters

| Absolute Chord Length | Relative Blade Position | Absolute Pitch |
| -------------- | -------------- | -------------- |
| <img src="/assets/images/toroidalChordScaling.gif" alt="Happy" width="200" /> | <img src="/assets/images/toroidalBladeOffset.gif" alt="Laugh" width="200" /> | <img src="/assets/images/toroidalPitchShape.gif" alt="Surprised" width="200" /> |

| Blade Pitch Distribution | Blade Pitch Back vs Front | AoA at the tip |
| -------------- | -------------- | -------------- |
| <img src="/assets/images/toroidalPitchOffset.gif" alt="Happy" width="200" /> | <img src="/assets/images/toroidalDeltaPitch.gif" alt="Laugh" width="200" /> | <img src="/assets/images/toroidalDeltaAoAtip.gif" alt="Surprised" width="200" /> |



- Conventional Propeller Parameters

| Max Chord Length Change | Max Chord Length Radial Shift | Maximum Pitch Change |
| -------------- | -------------- | -------------- |
| <img src="/assets/images/conventionalDeltaMaxChord.gif" alt="Happy" width="200" /> | <img src="/assets/images/conventionalShiftMaxChord.gif" alt="Laugh" width="200" /> | <img src="/assets/images/conventionalDeltaPitch.gif" alt="Surprised" width="200" /> |

| AoA at the Tip | Rake at Blade Tip | Radial Range of Tip Rake |
| -------------- | -------------- | -------------- |
| <img src="/assets/images/conventionalDeltaAoAtip.gif" alt="Happy" width="200" /> | <img src="/assets/images/conventionalTipRake.gif" alt="Laugh" width="200" /> | <img src="/assets/images/conventionalTrRange.gif" alt="Surprised" width="200" /> |


The limits for the training data set were determined by realistic operational ranges (for example avoiding pitch angles which would lead to stall anyway) and physical constraints (e.g. blades falling off the hub, geometrical interferences between blades and maximum diameter).

### API Link to Run CFD Simulations

Through the API, the CAESES software communicated directly with AirShaper to launch simulations for each design option and to obtain the resulting torque & thrust values.
This integration greatly improved the efficiency, streamlining the process of uploading models, defining parameters, and retrieving results.

### AirShaper Results

AirShaper's intuitive interface and advanced visualization tools helped us understand the flow patterns around the propellers.
This allowed us to maintain a "physical feeling" with the propellers being analyzed, understanding how flow structures evolved during the optimization process.

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### Creating the Surrogate Models

The results from AirShaper were fed back into CAESES to create surrogate models for thrust and torque at three different speeds. By interpolating the output of the surrogate models, we created the curves for the thrust coefficient $K_T$ and the torque coefficient $K_Q$. Having this information and knowing the ship resistance for any speed, we can now calculate the propeller efficiency over the whole operating range for any design within the design space without running a CFD simulation.

### Optimization
The surrogate models allow the evaluation of any design in the considered design space within seconds. Therefore, the actual optimization run can be carried out in just a few minutes instead of hours or days which is the case for a direct optimization approach where each design has to be evaluated by a CFD simulation.

### Efficiency Gains and Design Differences

- Toroidal propeller: the optimization resulted in a 21% improvement over the baseline which was loosely based on FIENDSHIP SYSTEMS' <ExternalLink href="https://www.wageningen-b-series-propeller.com/show/app/wageningen">Wageningen B-Series App</ExternalLink>.
- Conventional propeller: the optimization resulted in a staggering 58% improvement over the baseline propeller used as the benchmark by Daniel!
And even as new & improved designs from the community came in, this design still had a 7% higher efficiency compared to the second best 3D printed design in the competition.


## Winning Designs
We've open sourced the AirShaper CFD simulations of the winning designs:
- <ExternalLink href="https://app.airshaper.com/simulations/bestdesign_j12">Toroidal proppeller</ExternalLink>
- <ExternalLink href="https://app.airshaper.com/simulations/designlab1_07_des0000_v325 ">Conventional proppeller</ExternalLink>

## Toroidal vs. Conventional Propeller
Our conventional propeller outperformed our Toroidal propeller by 24%. However, we do not intend this to be a conclusive assessment whether conventional or Toroidal propellers are better and believe this is very much a question of the specific application case and requirements a design is targeting. But it shows that the design of a good conventional propeller is easier than the design of a good Toroidal propeller. Especially when limiting the simulation resources, the apparent advantage of having more degrees of freedom with the Toroidal propeller becomes a disadvantage. As the number of variable parameters has a direct influence on the number of simulations needed to achieve a sufficient exploration of the design space.

## Conclusion

The success of our propeller design project highlights the importance of using advanced design and simulation tools. [CAESES](https://www.caeses.com/) by [FRIENDSHIP SYSTEMS](https://www.friendship-systems.com/) and [AirShaper](https://www.airshaper.com/) were instrumental in helping us achieve remarkable results in the competition. As technology continues to advance, leveraging these powerful tools will be essential for developing innovative and high-performance components.

The process can be applied for both hydrodynamic & aerodynamic propellers and even far beyond propellers as well. Basically any parametric model can be used to explore a design space and build a surrogate mode, through the AirShaper API, to find the optimum solution.

Interested?
Drop [Simon Hauschulz](mailto:hauschulz@friendship-systems.com) of Friendship Systems or [Wouter Remmerie](mailto:wouter@airshaper.com) of AirShaper an email!

AI Propeller Design Optimization

# OpenFOAM Convergence detection

## Problem statement

In addition to monitoring residuals, a common method to assess whether a
simulation has converged is to look at the forces on an object.
Especially for external aerodynamics, the drag, lift and lateral forces
are usually of great interest (towards drag and lift coefficient,
efficiency and power estimates, ...). It therefore makes sense to
monitor these properties and wait until they are stable before starting
the averaging.

OpenFOAM already provides such functionality through run-time
control function objects. These allow, for example, to terminate
the simulation as soon as the averaged drag coefficient is within a
certain specified tolerance for a given number of steps. However, these
parameters need to be determined manually for each case, making it
difficult to use towards automation.

The open-source library presented here has been developed to provide
fully automated convergence detection and averaging of OpenFOAM output
data but is generally applicable to any data output for which
convergence needs to be detected. It's been designed to automatically
scale to the amplitude and length of the provided data, eliminating user
input.

## Suggested solution

### Convergence detection

The theory behind the library is to mimic "human behaviour" to assess
whether a curve has converged or not, following these steps:

- Normalization When we evaluate a curve as a human, we do so looking
 at its proportions: how much does it oscillate versus the total
 height, for how long has the curve been flat versus the total length
 of the curve, etc. So we look at relative properties, which can
 mathematically be represented by normalizing the curve on both the
 horizontal axis (the number of iterations n) and the vertical axis
 (the force in this case, but this could be any parameter). In this
 library, we use the average force value of the last 50 percent of
 iterations (a window size of 0.5) to normalize the entire curve (and
 we do this again for each iteration). Fig. 1 illustrates this.

<ImageWithCaption
 src="/assets/images/normalization.jpg"
 alt="Figure 1: Normalization"
 width="475"
 height="140"
 positionCenter={true}
/>

- Gradient calculation Once we have normalized the curve, we want to
 assess when the curve has "stabilized. That means that the last bit
 of the curve somehow needs to have been "stable enough" for "long enough". For each iteration, we fit a straight line through the last 50 percent (a window size of 0.5) of the normalized curve and store the gradient of this curve. Fig. 2 illustrates this.

<ImageWithCaption
 src="/assets/images/curve_fitting_and_gradient.jpg"
 alt="Figure 2: Curve fitting and gradient calculation"
 width="400"
 height="64"
 positionCenter={true}
/>

- Threshold This "running gradient" then indicates how stable the
 curve is (looking backwards) for each iteration. As we are working
 with a normalized curve, we can then define an absolute threshold
 value (irrespective of the magnitude of the force or the number of
 iterations) for this gradient to be within before we label a
 simulation as converged. We have chosen to evaluate this running
 gradient for the last third (so a window size of 0.33) of the curve.
 Fig. 3 illustrates this.

<ImageWithCaption
 src="/assets/images/threshold_analysis.jpg"
 alt="Figure 3: Threshold analysis"
 width="238"
 height="154"
 positionCenter={true}
/>

### Averaging

Dynamic window sizing - Once convergence has been detected, the
simulation will start to average. A modified version of the conversion
detection method will detect when the averaging has taken long enough to
provide a reliable averaged value / reliable averaged fields -- see Fig.
4 (the yellow bar indicates the convergence detection, the green one the
averaging window).

<ImageWithCaption
 src="/assets/images/dynamic_sizing.jpg"
 alt="Figure 4: Dynamic sizing"
 width="238"
 height="154"
 positionCenter={true}
/>

This detection method differs from the convergence detection method in
the following ways:

- Normalization is frozen and the horizontal axis index will grow
 beyond 1. The longer a simulation runs, the lower the gradient value
 will become (as you divide by an ever-increasing index).

- The threshold values for the gradient are more strict (+-0.025
 versus +-0.075).

- The evaluation window is now the entire length since the convergence
 point (versus a 0.5 window for the convergence detection), as there
 is no need any more to ignore initial oscillations. The whole
 averaging window needs to feature a stable curve.

Re-start - In the background, this convergence detection method keeps
running: sometimes, after convergence has been detected, the curve can
go up or down and the gradient can "exit" the threshold band again. Fig.
5 illustrates how at point A the curve seemed to have converged
(looking back at a flat part) but then suddenly rose (see the orange
dot). In that case, the state of the simulation will again be set to
"not converged" until the convergence criterion is met again (at point B
in the curve below). That also means averaging will be stopped until
convergence is reached again.

<ImageWithCaption
 src="/assets/images/restart_convergence_detection.jpg"
 alt="Figure 5: Re-start of convergence detection"
 width="250"
 height="77"
 positionCenter={true}
/>

## Code description

The principles laid out above have been implemented in the repository. The main parameters are described below (for OpenFOAM v2112, but also compatible with v2312):

- windowNormalization - default value 0.5: This parameter determines
 the length of the window used for normalizing the curve. Default
 value is 0.5, meaning that the entire curve will be divided by the
 averaged value of the last 0.5 (or 50 percent) of the curve.

- windowGradient - default value 0.5: This parameter determines the
 length of the window used to calculate the gradient. The default
 value of 0.5 means that the gradient will be fitted through the last
 0.5 (or 50 percent) of the curve.

- windowGradientAveraging - default value 0.99: Same as above, but for
 the averaging phase (once convergence has been detected). Nearly the
 entire window is used here, since convergence has already been
 detected and the curve is in a "steady" phase (i.e. the initial
 oscillations are gone). • windowEvaluation - default value 0.333:
 This parameter determines the length of the window used to evaluate
 the running gradient. The default value of 0.333 means the algorithm
 will evaluate the last third of the curve (to see if the gradient
 was within the specified threshold within that window).

- windowEvaluationAveraging - default value 0.333: Same as above, but
 for the averaging phase (once convergence has been detected).

- thresholdConvergence - default value 0.075: This is the threshold
 value within which the gradient needs to be during the evaluation
 window. The default value is 0.075 for convergence detection,
 meaning the gradient needs to remain within [-0.075 0.075] before
 convergence is detected. • thresholdAveraging - default value 0.025:
 Same as above but for the averaging phase. The default value of
 0.025 is more stringent compared to the one for convergence, to get
 reliable averaged values and fields.

- iterationMaxConvergence - default value 4000: This is a hard stop to
 detect convergence. The default value is 4000 iterations to force
 averaging.

- iterationMaxAveraging - default value 2000: The averaging will be
 stopped after 2000 iterations, whether it detected completion or
 not. So in total, a simulation will never run for more than
 4000+2000=6000 iterations.

- iterationMinConvergence - default value 200: A simulation will run
 for at least 200 iterations before convergence can be detected.

- iterationMinAveraging - default value 200: The averaging window will
 be at least 200 iterations long.

- forceStabilityFactor - default value 2: During averaging, there is a
 check to see if the forces go outside the [0.5*average ;
 2*average] range. If this happens, it indicates a run-away of
 forces and the simulation is likely going to crash.

## Examples

Fig. 6 illustrates the convergence detection and dynamic sizing of the
averaging window for a real industrial case. Mind this graph represents
the "second" CFD run, on the adaptively refined mesh. It started from
the mapped fields from the first, coarse mesh and therefore the initial
oscillations are fairly limited. This illustrates the method works well
even on a fairly irregular force graph, with a varied "frequency"
content.

<ImageWithCaption
 src="/assets/images/convergence_example.jpg"
 alt="Figure 6: Convergence detection and averaging window sizing example on a real industrial case."
 width="490"
 height="326"
 positionCenter={true}
/>

Interesting links:

<ExternalLink href="https://github.com/airshaper/openfoam-convergence-detection">
 Github repository
</ExternalLink>

OpenFOAM Convergence detection

World’s most aerodynamic suits - Interview with Deanna Panting, founder of Qwixskinz.

Free Speed: how properly designed clothing can make Olympic athletes faster.

Wind tunnels are one of the most important tools in an aerodynamicist’s armoury. They bridge the gap between real world aerodynamic testing and CFD simulation, allowing aerodynamicists to test physical parts in a more controlled environment. But how do wind tunnels work and what techniques should you use to achieve reliable and accurate results?

- ###### [A brief history](#windtunnelhistory)
- ###### [How does a wind tunnel work?](#howwindtunnelswork)
- ###### [Moving the air](#windtunnelmovingair)
- ###### [Cooling the air](#windtunnelcooling)
- ###### [Conditioning the flow](#windtunnelconditioning)
- ###### [Accelerating the flow](#windtunnelacceleratingflow)
- ###### [The test section](#windtunneltestsection)
- ###### [Scale models](#windtunnelscalemodels)

---

## A brief history <a name="windtunnelhistory"></a>

During the 19th century, research into aerodynamics was largely aimed at manned flight. The physical testing at this time involved a whirling arm, often gravity powered, which rotated a test object through the air. It was eventually realised that this rotation generated a circular wake that affected the accuracy of the results, so a new testing approach was required.

In response, Frank Wenham built the world’s first wind tunnel in 1871 [1] which was a 12ft (3.7m) long tube with a fan blowing air along its length. As aircraft and ground vehicles continued to develop, so did the capabilities of wind tunnel testing and by 1916, the Wright Brothers were utilising a larger tunnel with improved flow velocity and quality.

<ImageWithCaption
 src="/assets/images/wright-brothers-wind-tunnel.jpeg"
 alt="Side view of a long red, thick tube acting as a scale wind tunnel"
 caption={
 
 The 1916 Wright Brothers wind tunnel. CREDIT:{' '}
 <ExternalLink href="https://www.nationalmuseum.af.mil/Visit/Museum-Exhibits/Fact-Sheets/Display/Article/196756/wright-brothers-1916-wind-tunnel/">
 National Museum of the United States Airforce
 </ExternalLink>
 
 }
 width="700"
 height="408"
 positionCenter={true}
/>

Aeronautical engineering continued to progress quickly and by 1920, NACA were building a 5ft (1.5m) wind tunnel based on a British Royal Aircraft Establishment (RAE) tunnel [2]. However, the need for better measurement techniques to match scientific understanding meant these tunnels quickly became obsolete. 

Over the last 100 years, aircraft have developed into faster and larger vehicles, so to conduct accurate testing, wind tunnels have had to evolve too. The <Link href="/blog/nasa-full-size-wind-tunnels">largest wind tunnel in the world</Link> is currently NASA’s Ames Research Center which can test aeroplanes with wing spans of up to 100ft (30.5m) [3]. While the accuracy of results now means that wind tunnels can be used to test anything from space shuttles to athletes. 

<ImageWithCaption
 src="/assets/images/nasa_space_shuttle_wind_tunnel_test.jpeg"
 alt="Silver space shuttle scale model in the test section of a scale wind tunnel"
 caption={
 
 A space shuttle under test in a NASA wind tunnel. CREDIT:{' '}
 <ExternalLink href="https://www.nasa.gov/mission_pages/shuttle/flyout/unflyable.html">
 NASA
 </ExternalLink>
 
 }
 width="700"
 height="394"
 positionCenter={true}
/>

---

## How does a wind tunnel work? <a name="howwindtunnelswork"></a>

Whether it is a plane or a racecar, fundamentally it is an object moving through air. However, to replicate the behaviour of the airflow around an object, wind tunnels flip this around and move air over a fixed object. 

Wind tunnels come in a range of layouts, sizes and speeds to cater for the many different applications of wind tunnel testing. The most common is the closed loop wind tunnel, variations of which form the basis of most aeronautical and automotive facilities. To understand the basics of wind tunnels, let's consider a subsonic, pressurised wind tunnel such as the <ExternalLink href="https://www.onera.fr/en/windtunnel/testing-capabilities">ONERA wind tunnel in France</ExternalLink>. 

<ImageWithCaption
 src="/assets/images/onera-wind-tunnel.png"
 alt="Schematic showing the closed loop layout of the F1 wind tunnel at ONERA in plan view"
 caption={
 
 The layout of the subsonic continuous pressurized closed-loop wind tunnel at ONERA. CREDIT:{' '}
 <ExternalLink href="https://www.onera.fr/fr/windtunnel/f1-subsonic-wind-tunnel-pressurized-high-reynolds-number-high-efficiency">
 ONERA
 </ExternalLink>
 
 }
 width="600"
 height="565"
 positionCenter={true}
/>

This type of tunnel circulates a mass of air around a closed-loop circuit and flows high speed air over the object in the test section. This object could either be a scale model or full-size vehicle. This wind tunnel loop can be broken down into four main areas:
- Fan
- Cooling
- Flow conditioning
- Test section

<YouTubeEmbed
 videoId="L1AYo9Mk1EI"
/>

---

## Moving the air <a name="windtunnelmovingair"></a>

At the heart of the wind tunnel is the fan, which needs to be extremely powerful to achieve the flow velocity required at the test section. This results in large, multi-bladed fans with variable speed and sometimes variable pitch propellors. They can be over 15m (49ft) in diameter and are driven by electric motors rated up to 10MW. The larger the fan, the higher its efficiency but the more difficult it is to build and house.

<ImageWithCaption
 src="/assets/images/volkswagen-wind-tunnel-main-fan.jpeg"
 alt="Front view of the main fan in the Volkswagen wind tunnel with an engineer crouching infront for scale"
 caption={
 
 The main fan of the Volkswagen wind tunnel in Wolfsburg. CREDIT:{' '}
 <ExternalLink href="https://uk.motor1.com/news/185851/volkswagen-wind-tunnel/">
 Motor1
 </ExternalLink>
 
 }
 width="700"
 height="394"
 positionCenter={true}
/>

---

## Cooling the air <a name="windtunnelcooling"></a>

As the air moves around the wind tunnel, it generates friction with the walls. This, together with the pressurised nature of the majority of wind tunnels causes the air to increase in temperature. To make sensitive measurements, temperature control is very important for both the air flow and the instrumentation. This is why tunnels of this nature have very powerful cooling systems, usually liquid based, and a radiator matrix through which the air flows.

---

## Conditioning the flow <a name="windtunnelconditioning"></a>

To maximise the flow at the test section, the air needs to travel around the circuit as efficiently as possible and minimise any losses. To help the air turn round corners efficiently, a series of aerofoil-section vanes are fitted to each corner to help bend the flow through 90 degrees with minimal loss in velocity. 

<ImageWithCaption
 src="/assets/images/icing-research-tunnel-turning-vanes-2.png"
 alt="Close up photo of large aerofoil-shaped turning vanes at the corner of a the Icing Research Wind Tunnel"
 caption={
 
 The main fan of the Volkswagen wind tunnel in Wolfsburg. CREDIT:{' '}
 <ExternalLink href="https://www.nasa.gov/specials/irt360/">
 Icing Research Tunnel
 </ExternalLink>
 
 }
 width="500"
 height="365"
 positionCenter={true}
/>

After the air has turned the final corner, it enters the settling chamber where the flow is conditioned to be as straight and turbulent free as possible. This is achieved using a honeycomb structure where tubes force the flow to be parallel and minimise swirl. The air then passes through a series of mesh screens which help to reduce variations in longitudinal flow velocity and break up an eddy currents. 

<ImageWithCaption
 src="/assets/images/wind-tunnel-flow-conditioning.png"
 alt="Diagrams with arrows showing the direction of airflow as it moves through honeycomb structures and mesh screens"
 caption={
 
 Diagrams showing how the flow is conditioned through honeycomb (left) and mesh screens (middle and right)
 
 }
 width="900"
 height="233"
 positionCenter={true}
/>

---

## Accelerating the flow <a name="windtunnelacceleratingflow"></a>

The last stage the air has to go through before entering the test section is a Venturi. Shrinking the diameter of the wind tunnel down to the cross sectional area of the test section, accelerates the flow to the required test speed. Downstream of the test section, the cross section is progressively increased through a diffuser expanding the flow and slowing it down again.

---

## The test section <a name="windtunneltestsection"></a>

The test object is mounted in the <Link href="/videos/wind-tunnel-test-section/L1AYo9Mk1EI">wind tunnel test section</Link>. If the object is an aircraft, it will be mounted via a sting in some manner, typically from the rear. The sting is used to run instrumentation connections to and from the model and to move it through different test attitudes whilst measuring loads.

<ImageWithCaption
 src="/assets/images/aeroplane-scale-model-z-sting-mount.jpeg"
 alt="Silver scale model of an aeroplane mounted in the wind tunnel test section via a Z sting mount"
 caption={
 
 Scale model aircraft mounted in the wind tunnel test section via a Z sting mount. CREDIT:{' '}
 <ExternalLink href="https://www.onera.fr/en/windtunnel/model-support">
 ONERA
 </ExternalLink>
 
 }
 width="700"
 height="500"
 positionCenter={true}
/>

If the object is a full scale ground vehicle, it will usually sit on load measuring pads or a rolling road. The latter is more accurate as it allows the wheels to rotate at speeds that match the tunnel speed. Whereas, scale model road vehicles are often suspended just above the ground. In either case, the interaction with the ground plane is essential to model as the vehicle operates in a boundary layer in the real world that must be replicated in the wind tunnel. 

<ImageWithCaption
 src="/assets/images/daimler-truck-wind-tunnel-smoke.jpg"
 alt="Perspective view of a red lorry cabin in an open section wind tunnel with oncoming air visualised with smoke"
 caption={
 
 Smoke testing a full-size lorry cabin which is sitting on load measuring pads. CREDIT:{' '}
 <ExternalLink href="https://media.daimlertruck.com/marsMediaSite/en/instance/ko/Product-Pictures.xhtml?oid=45626421">
 Daimler Truck
 </ExternalLink>
 
 }
 width="700"
 height="421"
 positionCenter={true}
/>

---

## Scale models <a name="windtunnelscalemodels"></a>

It is relatively unusual to test at full scale as the costs associated with a large enough facility are prohibitive. Therefore, companies often opt for <Link href="/videos/scale-model-wind-tunnel-testing/qqYiz1eo-F4">scale model wind tunnel testing</Link>. This allows aerodynamicists to make quick iterations during test programmes, the parts are faster and cheaper to manufacture and scale models are overall easier to work on. 

Scale models are typically 10-50% of full size, depending on the application. Large aircraft models are at around 10%, while road cars are often at 50% scale. But regardless of the scale, wind tunnel models are highly accurate with refined external geometries and a high standard of build quality to minimise the effect of any discontinuities on the results.

Internally, the models are full of instrumentation. This could include the load balance, which is responsible for measuring the lift and drag forces as well as the yaw, pitch and roll moments. Pressure tappings will be implemented on the surface of the model to measure static pressure, all of which have to be connected via rubber tubing to a pressure scanner.

<ImageWithCaption
 src="/assets/images/scale-model-instrumentation.jpeg"
 alt="Silver scale model of an aeroplane with the external geometry removed so that the instrumentation and pressure tubing cables are visible"
 caption={
 
 An example of the instrumentation inside a scale model of an aeroplane. CREDIT:{' '}
 <ExternalLink href="https://www.nlr.org/article/high-tech-wind-tunnel-models-creating-competitive-edge/">
 Netherlands Aerospace Centre (NLR)
 </ExternalLink>
 
 }
 width="700"
 height="359"
 positionCenter={true}
/>

The wind tunnel itself will also have a range of measurement techniques available. The forces on the model may be measured through the floor or the sting, rather than inside the model. While there are a a number of flow visualisation techniques such as <Link href="/videos/how-wind-tunnels-work-measurement-techniques-piv-pressure-taps-force-balance-pressure-probe/yA9FdqJdiKk">Particle Image Velocimetry (PIV)</Link>, smoke jets and flow visualisation paint. These help aerodynamicists visualise the behaviour of the flow to further their understanding.

---

### Interesting links:

- <ExternalLink href="https://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-are-wind-tunnels-58.html">What Are Wind Tunnels?</ExternalLink>

- <ExternalLink href="https://www.youtube.com/watch?v=KC0E0wU6inU&ab_channel=SauberMotorsport">How Wind Tunnels work - F1 explained - Sauber F1 Team</ExternalLink>

---

### References

[1] <ExternalLink href="https://history.nasa.gov/SP-440/ch1-3.htm">Wind Tunnels of NASA. Chapter 1 - Whirling Arms and the First Wind Tunnels</ExternalLink>
[Online]. NASA. 

[2] Smith, Y. 2015. <ExternalLink href="https://www.nasa.gov/the-nacas-first-wind-tunnel">The NACA's First Wind Tunnel</ExternalLink>
[Online]. NASA. 

[3] 1992. <ExternalLink href="https://www.nasa.gov/centers/langley/news/factsheets/WindTunnel.html">NASA's Wind Tunnels - IS-1992-05-002-LaRC</ExternalLink>
[Online]. NASA. 

---

How does a Wind Tunnel work?

Did you know that only one fifth of the world’s ocean floor has been successfully mapped? Although this is a substantial improvement from 2017, where 6% was mapped, there is still an abundance of unchartered waters to explore [1]. Fortunately, the recent surge of development around Autonomous Underwater Vehicles (UAVs) has transformed these vessels into advanced research tools that are helping oceanographers understand the depths of our oceans and how to protect these oceanic habitats from climate change.

- ###### [What is an AUV?](#whatisanauv)
- ###### [The importance of hydrodynamic efficiency](#importanceofhydrodynamicefficiency)
- ###### [Case study: Using CFD to reduce AUV drag](#uavreducingdragcasestudy)

---

## What is an AUV? <a name="whatisanauv"></a>

A AUV is a torpedo shaped vessel that can manoeuvre itself close to the sea floor. Some of the latest designs are 1.5-5.5m (5-18ft) long and weigh between 20-1,400kg (45-3,000Ibs) [2]. They utilise sonar technology such as multibeam and side scanning systems that can map the seabed in 3D at much higher resolutions than could previously be achieved with other submarines. AUVs are also instrumented with fluorometers, turbulence sensors, magnetometers and water-quality sensors and all the data collected is stored onboard until the AUV reaches the surface.

<ImageWithCaption
 src="/assets/images/ecomapper-auv-diagram.png"
 alt="AUVs are often equipeed with a variety of sensors and measurement equipment to maximise the amount of data that can be colected during a mission"
 caption={
 
 The layout and features of the Ecomapper AUV. CREDIT:{' '}
 <ExternalLink href="https://www.usgs.gov/media/images/ecomapper-autonomous-underwater-vehicle-auv">
 USGS
 </ExternalLink>
 
 }
 width="700"
 height="190"
 positionCenter={true}
/>

AUVs travel through water via propellors or fixed hydrofoils, depending on the design. Propellor AUVs are typically used for seabed surveys whereas hydrofoil AUVs are more suited for offshore studies. The former uses spinning angled blades to create an area of low pressure above the blades and an area of high pressure below the blades. This pressure difference generates forward thrust.

A hydrofoil AUV uses variable buoyancy propulsion instead. This is where a pump moves internal weights back and forth to alter the vessel’s buoyancy. Its hydrofoils generate lift and glide forward as it rises due to its buoyancy and falls due to gravity.

---

## The importance of hydrodynamic efficiency <a name="importanceofhydrodynamicefficiency"></a>

AUVs are typically powered by onboard batteries and therefore, like any electric vehicle, the available battery capacity defines the speed at which the AUV can travel and the range of the mission. Smaller AUVs are only capable of deploying for several hours, whereas AUVs with larger batteries can survey for several days with survey speeds around 1-2m/s (2-4mph) [2].

<ImageWithCaption
 src="/assets/images/auv-battery.jpg"
 alt="A semicircular tray of battery packs and wiring of a typical UAV"
 caption={
 
 The layout of a typical AUV battery. CREDIT:{' '}
 <ExternalLink href="https://www2.whoi.edu/staff/nforrester/project-auv-li-ion-battery-systems/">
 Woods Hole Oceanographic Institution
 </ExternalLink>
 
 }
 width="700"
 height="351"
 positionCenter={true}
/>

To increase the range of the battery and therefore the potential duration of missions, engineers are focusing on maximising the efficiency of UAV design. One of the key techniques to achieving this is to optimise the shape of the vessel’s body to minimise drag. This means there is less drag for the motor to overcome, demanding less energy from the battery and enabling the AUV to travel for longer. Extending the length of missions will allow researchers to explore more remote places such as underneath ice formations.

- <Link href="/blog/electric-vehicle-aerodynamics-improving-range">
 How can aerodynamics improve the range of electric vehicles?
 </Link>

---

## Case study: Using CFD to reduce AUV drag <a name="uavreducingdragcasestudy"></a>

<ExternalLink href="https://www.airflowsciences.com/resources/case-studies">
 Airflow Sciences Corporation
</ExternalLink>
, a USA-based fluid dynamics engineering firm, were tasked with optimising the hydrodynamics
of a new AUV concept. The main goal was to optimise the shape of the hull to generate
the least amount of drag. To achieve this, a number of CFD tools were used to evaluate
different designs and establish the one with the highest performance.

The first stage involved simulating the flow of a variety of hull shapes in 2D. This allowed a quick comparison between different designs and visually showed the behaviour of surface pressure and where the flow separates. As expected, the shape with the more gradual curvature showed much less flow separation, as shown below.

<ImageWithCaption
 src="/assets/images/surface-pressure-distribution-auv-concepts.png"
 alt="Side view of the surface pressure distribution of two different AUV hull designs in 2D"
 caption={
 
 The surface pressure distribution of two different AUV hull concepts in 2D
 
 }
 width="700"
 height="470"
 positionCenter={true}
/>

The hull design with the most potential was then developed into a 3D model and simulated in CFD using the web-based app <Link href="/pricing">AirShaper</Link>. This software automatically creates the mesh, runs the CFD simulation and consolidates the results into a PDF report which includes a range of plots such as total pressure, surface pressure, and velocity streamlines.

<YouTubeEmbed videoId="O_DNDxCtI_I" />

However, as this AUV design was a new concept and therefore there was no experimental data to use as a benchmark, Airflow Sciences decided to use several CFD solvers to analyse the results.

‘We felt AirShaper was a cost-effective way to obtain a comprehensive analysis of the OpenFOAM k-omega turbulence model,’ explains Robert Mudry, President and Airflow Sciences Corporation. ‘We wanted to validate the AirShaper results, but with no data available to compare against, we decided to run the same mesh, boundary conditions and turbulence model in two other independent CFD solvers; <ExternalLink href="https://www.azorecfd.com">Azore</ExternalLink> and Fluent.’

<ImageWithCaption
 src="/assets/images/auv-airflow-sciences-drag-coefficient-diagram.png"
 alt="Diagram showing the AirShaper drag coefficient of the Airflow Sciences AUV design on a scale with other notable objects"
 caption={
 
 AirShaper calculated the drag coefficient of the Airflow Sciences AUV
 design to be 0.133
 
 }
 width="700"
 height="176"
 positionCenter={true}
/>

The results from the AirShaper simulation are shown below and the predicted drag coefficient of the optimised hull design was 0.133 in AirShaper, 0.128 in Azore and 0.143 in Fluent. ‘There was minimal difference in drag forces between the different CFD solvers and the variance of the drag coefficient figures was within an acceptable margin of error. This gave us confidence in the AirShaper software as well as in our hull design.’

<ImageWithCaption
 src="/assets/images/auv-airflow-sciences-surface-pressure-velocity-streamlines.png"
 alt="CFD screenshots showing a coloured surface pressure contour plot on the left and coloured velocity streamlines on the right"
 caption={
 
 The surface pressure contour plot (left) and velocity streamline plot
 (right) from the AirShaper report
 
 }
 width="700"
 height="197"
 positionCenter={true}
/>

Furthermore, as AirShaper also provided the numerical simulation files, Airflow Sciences could then conduct more detailed analysis as well as create custom graphics and videos using Azore.

‘We appreciate the opportunity to collaborate with Wouter Remmerie and the AirShaper team,’ concludes Mudry. ‘The simulation process using the AirShaper interface was straight-forward, the results were obtained quickly, and the report complete. We also liked the ability to import the OpenFOAM CFD results into the Azore post-processing software to create additional results in our corporate format. We are looking forward to more Airflow-AirShaper joint projects in the future.’

<YouTubeEmbed videoId="u3DXTrkba9g" title="Animated pathlines of an AUV" />

---

### Interesting links:

- <ExternalLink href="https://www.sciencedirect.com/topics/earth-and-planetary-sciences/autonomous-underwater-vehicle">
 An overview of Autonomous Underwater Vehicles
 </ExternalLink>

- <ExternalLink href="https://www.youtube.com/watch?v=4aaPZ80Yo4s&ab_channel=TNO">
 The benefits of Autonomous Underwater Vehicles
 </ExternalLink>

---

### References

[1] 2020. <ExternalLink href="https://www.unesco.org/en/articles/nearly-fifth-worlds-ocean-floor-now-mapped">Nearly a fifth of world's ocean floor now mapped</ExternalLink>. [Online]. Unesco.

[2] <ExternalLink href="https://www.vims.edu/research/units/legacy/cornwallis/auv/index.php">What is an AUV?</ExternalLink>. [Online]. VMS Virginia Institute of Marine Science.

---

Reducing the drag of an AUV with AirShaper

Hydrofoil Design - America's Cup Technology for Commercial Products

Technology - Can it improve lives?

Safety is of paramount importance when travelling in the air. This makes certifying an aircraft a long and detailed process. However, over the last few decades, Computational Fluid Dynamics (CFD) has become instrumental in streamlining flight certification. The capabilities of high performance computing along with the flexibility of open source software and improvements in solver accuracy has made the latest CFD codes a viable alternative to expensive wind tunnel testing. 

We sat down with David Solar, Head of General Aviation (GA) and Vertical Take-off and Landing (VTOL) Department at EASA to hear his thoughts on the use of CFD in passing aircraft EASA regulations.

- ###### [What is certification?](#whatiscertification)
- ###### [The history of certifying aircraft](#certificationhistory)
- ###### [The dangers of test flying](#testflyingdangers)
- ###### [How are today's aircraft certified?](#certifyingtodaysaircraft)
- ###### [The structural integrity testing pyramid](#structuraltestingpyramid)
- ###### [Certifying the use of CFD](#certifyingcfd)
- ###### [Could the future of certification be simulation only?](#simulationonlycertification)
- ###### [Extreme configurations at the limit of separation](#extremeconfigurations)

---

## What is certification? <a name="whatiscertification"></a>

Certification is where governing bodies work with manufacturers and operators to ensure that an aircraft and its components are designed, manufactured and modified for safety throughout its life cycle. These governing bodies include the European Union Aviation Safety Agency (EASA), the UK’s Civil Aviation Authority (CAA) and the Federal Aviation Administration (FAA) in the United States. Each authority defines a set of regulations which a new aircraft or operation needs to comply with. So to prove the airworthiness of new developments, manufacturers have to conduct comprehensive testing programmes. 

---

## The history of certifying aircraft <a name="certificationhistory"></a>

Before Computer Aided Design (CAD) and Finite Element Analysis (FEA), flight certification had to rely on many physical flight tests. For example, the certification of the Anglo-French Concorde supersonic transport project in 1960 required six development airframes which flew for 5,127 hours [1]. Although, this project was arguably the most ambitious of it’s time.

<ImageWithCaption
 src="/assets/images/1960-concorde-101.jpg"
 alt="Side view of a white 1960s Concorde G-AXDN (101) on a runway"
 caption={
 
 Twenty Concorde were built of which six were used solely for development and certification. CREDIT:{' '}
 <ExternalLink href="https://www.heritageconcorde.com/airframe-detail">
 Heritage Concorde
 </ExternalLink>
 
 }
 width="700"
 height="421"
 positionCenter={true}
/>

Fast forward to 2014 and certification of the Airbus A350 was achieved with five aircraft and only 2,600 hours of flying [2]. Whilst the A350 may not have been the technical leap of Concorde, it arguably exists in a much more stringent regulatory era.

<ImageWithCaption
 src="/assets/images/airbus-a350.jpg"
 alt="A white Airbus A350 on a runway"
 caption={
 
 The Airbus A350 was first certified in 2014. CREDIT:{' '}
 <ExternalLink href="https://www.airbus.com/">
 Airbus
 </ExternalLink>
 
 }
 width="700"
 height="439"
 positionCenter={true}
/>

---

## The dangers of test flying <a name="testflyingdangers"></a>

Historically, test pilots have been revered due to the hazardous nature of their work. "Flight tests were only experimental and the risks pilots were taking was a big unknown at the time, which is why their life expectancy was short in some cases," explains Solar. 

"Now however, it has evolved significantly. Whilst there is always a risk to the first flight of an aircraft, simulations give us some confidence in how the aircraft will perform aerodynamically as well as it's landing qualities." 

- <Link href="/cases/optimization/cessna">Using CFD to optimise the efficiency of a Cessna winglet</Link> 

The risk of flight tests was demonstrated by the loss of the prototype BAC 1-11 and its seven crew members in 1963. The test was investigating the aircraft’s characteristics during stall and the high angle of attack lead to the wings blocking airflow to the control surfaces on the high tail. This resulted in deep stall, which is a specific risk to this type of aircraft. Sadly, this was not well understood at the time and was unrecoverable. 

<ImageWithCaption
 src="/assets/images/bac1-11-prototype.png"
 alt="Side view of the BAC 1-11 prototype in the air"
 caption={
 
 Understanding aircraft behaviour around stall with modern CFD and simulation might have been able to prevent the loss of the prototype BAC 1-11. CREDIT:{' '}
 <ExternalLink href="https://www.baesystems.com/en/heritage/bac1-11">
 BAE Systems
 </ExternalLink>
 
 }
 width="700"
 height="394"
 positionCenter={true}
/>

---

## How are today's aircraft certified? <a name="certifyingtodaysaircraft"></a>

The EASA type-certification process has four main steps [4]. How a manufacturer goes about completing these steps will vary, but is always after discussion and agreement with EASA. 

- Technical Familiarisation and Certification Basis

- Establishment of the Certification Programme

- Compliance Demonstration 

- Technical Closure and Issue of Approval 

The first two phases start before there is a completed design or a physical aircraft. CFD is used extensively to optimise the key performance characteristics of an aircraft, according to the specific requirements of the project. Presenting the concept and the CFD results to EASA, the two parties can come to an agreement about the exact nature of the certification process. This will be unique to each aircraft. 

Once the certification programme has been agreed, the next stage is Compliance Demonstration and Technical Closure and Issue of Approval. This is where the manufacturer needs to demonstrate that an aircraft meets the requirements of its type approval. Generally, this comes down to proving its structural integrity and illustrating it has suitable flight characteristics.

---

## The structural integrity testing pyramid <a name="structuraltestingpyramid"></a>

From a structural point of view, manufacturers are required to document every step of the design process from materials coupon testing to full aircraft flights. In modern aircraft, a blend of simulation and physical testing is used to make this process as efficient as possible.

<ImageWithCaption
 src="/assets/images/structural-integrity-testing-pyramid.png"
 alt="Infographic showing the importance of testing and simulation from level 1 materials to level 6 full scale aircraft"
 caption={
 
 Modern certification requires physical testing and simulation to work hand in hand. CREDIT:{' '}
 <ExternalLink href="https://www.appluslaboratories.com/global/en/what-we-do/service-sheet/aerospace-structural-testing">
 Applus Laboratories
 </ExternalLink>
 
 }
 width="700"
 height="442"
 positionCenter={true}
/>

CFD plays a key role in the process by generating flight load cases for the different sign-off criteria. Take-off, landing, cruise, stall and even taxiing will present different loads to different parts of the airframe. Even with a physical aircraft it is difficult to measure these loads, so CFD is used extensively to help engineers decide how to test each part.

- <Link href="/blog/airshaper-validation-study">Validating AirShaper with physical testing</Link> 

<ImageWithCaption
 src="/assets/images/aircraft-physical-testing.jpg"
 alt="Front view of a Boeing 787 Dreamliner during a physical rig test"
 caption={
 
 Physical confirmation testing of extreme load cases is based on CFD and FEA studies. CREDIT:{' '}
 <ExternalLink href="https://www.wired.com/2010/03/boeing-787-passes-incredible-wing-flex-test/">
 Wired
 </ExternalLink>
 
 }
 width="700"
 height="433"
 positionCenter={true}
/>

---

## Certifying the use of CFD <a name="certifyingcfd"></a>

Simulation tools are now used so frequently to support the certification process, regulatory bodies have had to specify the requirements of suitable CFD and FEA software packages. This ensures that only reliable and accurate codes are used by manufacturers to model scenarios and assess the flightworthiness of an aircraft. 

In 2020, EASA issued a <ExternalLink href="https://www.easa.europa.eu/en/proposed-cm-s-014-modelling-simulation-consultation">Notification of a Proposal to issue a Certification Memorandum</ExternalLink> on the subject of modelling and simulation. As well as demonstrating their aircraft is fit to fly, manufacturers also have to show that the analysis tools are accurate enough to calculate relevant load cases. 

<ImageWithCaption
 src="/assets/images/easa-cfd-regulations.png"
 alt="Screenshot of section B4 of EASA CM-S-014 regulations covering CFD"
 caption={
 
 EASA CM-S-014 highlights the potential sources of inaccuracy in a CFD simulation. CREDIT:{' '}
 <ExternalLink href="https://www.easa.europa.eu/en/proposed-cm-s-014-modelling-simulation-consultation">
 EASA
 </ExternalLink>
 
 }
 width="750"
 height="455"
 positionCenter={true}
/>

---

## Could the future of certification be simulation only? <a name="simulationonlycertification"></a>

Simulation and physical testing is the accepted way of design and certifying a modern aircraft. For the future, the likelihood of simulation completely replacing physical testing is a constant topic of discussion. 

"Simulations are becoming more complex and we are pushing the boundaries with physical testing, but will we ever certify an aircraft using simulation only?" questions Solar. "I'm not sure it will ever happen, actually. I think we must always check the results in the real world to validate the models, maybe less extensively than before in some areas, but for the extreme cases and conditions this needs to be checked by physical testing."

<ImageWithCaption
 src="/assets/images/cfd-of-airplane-wing-engine-flap.jpg"
 alt="Colourmap CFD comparison of the surface flow of an aiplane wing, engine and flap"
 caption={
 
 Complex flow regimes like engine/wing/flap interactions are still too variable in CFD to fully sign-off. CREDIT:{' '}
 <ExternalLink href="https://arc.aiaa.org/doi/pdfplus/10.2514/1.J059869">
 AIAA
 </ExternalLink>
 
 }
 width="700"
 height="426"
 positionCenter={true}
/>

Physical testing also allows every detail of the design to be assessed because it requires real parts. Whereas CFD simulations often involve simplified models that may not capture all the intricacies of vortex generators and small gaps, which could affect the overall aerodynamics. 

---

## Extreme configurations at the limit of separation <a name="extremeconfigurations"></a>

Aircraft flight characteristics are of most interest to regulators at the extremes of performance, particularly in low-speed stall conditions and high speed transonic flow. 

<ImageWithCaption
 src="/assets/images/contrails-on-high-lift-airplane-wing.jpg"
 alt="Close up shot of contrails on a high lift airplane wing configuration in the air"
 caption={
 
 Contrails demonstrate vortices and heavily worked flow on a high lift wing configuration. CREDIT:{' '}
 <ExternalLink href="https://aerocorner.com/blog/how-flaps-work/">
 Aerocorner
 </ExternalLink>
 
 }
 width="700"
 height="466"
 positionCenter={true}
/>

"There are still some configurations which are very difficult to simulate," highlights Solar. "Low speed is when you have the most complex wing configuration with perhaps single slotted, double slotted, triple slotted flaps, some slots with different extensions and multiple transitions usually with a high angle of attack. We can run simulations on a very small portion of the wing, but to simulate the full aircraft accurately requires a high amount of computing power which is the limit at the moment."

Computing power will continue to increase, making that last goal of a full aircraft simulation possible in the future. For now, CFD is a key contributor to aircraft safety, fitting alongside the other real world testing capabilities of modern aircraft manufacturers.

---

### Interesting links:

- <ExternalLink href="https://ntrs.nasa.gov/api/citations/20210015404/downloads/NASA-CR-20210015404%20updated.pdf">NASA Guide for Air Certification by Analysis</ExternalLink>

- <ExternalLink href="https://ntrs.nasa.gov/api/citations/20200002394/downloads/20200002394.pdf">NASA Computational Study of a Generic T-Tail Aircraft</ExternalLink>

- <ExternalLink href="https://www.baesystems.com/en-uk/heritage/bac1-11">BAE Systems Heritage BAC1-11</ExternalLink>

- <ExternalLink href="https://flightsafety.org/asw-article/discoveries-on-ice/">NASA flight research into icing</ExternalLink>

- <ExternalLink href="https://www.easa.europa.eu/en/document-library/type-certificates">Database of EASA Type Certificate Datasheets</ExternalLink>

---

### References

[1] <ExternalLink href="https://www.heritageconcorde.com/airframe-detail">The Concorde Fleet - Breakdown of each air frame built</ExternalLink>. [Online]. Heritage Concorde. 

[2] <ExternalLink href="https://www.airbus.com/en/products-services/commercial-aircraft/the-life-cycle-of-an-aircraft/test-and-certification">Test and Cetification</ExternalLink>. [Online]. Airbus. 

[3] <ExternalLink href="https://www.easa.europa.eu/en/proposed-cm-s-014-modelling-simulation-consultation">Proposed CM-S-014 Modelling & Simulation – for consultation</ExternalLink>. [Online]. EASA. 

[4] <ExternalLink href="https://www.easa.europa.eu/en/domains/aircraft-products/aircraft-certification">Aircraft certification</ExternalLink>. [Online]. EASA.

[5] 2007. <ExternalLink href="https://www.easa.europa.eu/sites/default/files/dfu/CS-25_Amdt%203_19.09.07_Consolidated%20version.pdf">Certification Specifications for Large Aeroplanes CS-25</ExternalLink>. [Online]. EASA.

[6] 2016. <ExternalLink href="https://www.easa.europa.eu/en/document-library/product-certification-consultations/equivalent-safety-finding-cs-25251b-vibration">Equivalent Safety Finding CS 25.251(b) - “Vibration / buffeting”</ExternalLink>. [Online]. EASA.

---

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