Author: Rainer Groh

Control and Stability of Aircraft
One of the key factors in the Wright brothers’ achievement of building the first heavier-than-air aircraft was their insight that a functional airplane would require a mastery of three disciplines:
1. Lift
2. Propulsion
3. Control
Whereas the first two had been studied to some success by earlier pioneers such as Sir George Cayley, Otto Lilienthal, Octave Chanute, Samuel Langley and others, the question of control seemed to have fallen by the wayside in the early days of aviation. Even though the Wright brothers build their own little wind tunnel to experiment with different airfoil shapes (mastering lift) and also built their own lightweight engine (improving propulsion) for the Wright flyer, a bigger innovation was the control system they installed on the aircraft.

1902 Wright glider turn

Fundamentally, an aircraft manoeuvres about its centre of gravity and there are three unique axes about which the aircraft can rotate:
1. The longitudinal axis from nose to tail, also called the axis of roll, i.e. rolling one wing up and one wing down.
2. The lateral axis from wing tip to wing tip, also called the axis of pitch, i.e. nose up or nose down.
3. The normal axis from the top of the cabin to the bottom of landing gear, also called the axis of yaw, i.e. nose rotates left or right.
Aircraft Principal Axes

In a conventional aircraft we have a horizontal elevator attached to the tail to control the pitch. Second, a vertical tail plane features a rudder (much like on a boat) that controls the yawing. Finally, ailerons fitted to the wings can be used to roll the aircraft from side to side. In each case, a change in attitude of the aircraft is accomplished by changing the lift over one of these control surfaces.

For example:
1. Moving the elevator down increases the effective camber across the horizontal tail plane, thereby increasing the aerodynamic lift at the rear of the aircraft and causing a nose-downward moment about the aircraft’s centre of gravity. Alternatively, an upward movement of the elevator induces a nose-up movement.
2. In the case of the rudder, deflecting the rudder to one side increases the lift in the opposite direction and hence rotates the aircraft nose in the direction of the rudder deflection.
3. In the case of ailerons, one side is being depressed while the other is raised to produce increased lift on one side and decreased lift on the other, thereby rolling the aircraft.
Aircraft Control Surfaces By Piotr Jaworski (http://www.gnu.org/copyleft/fdl.html)

In the early 20th century the notion of using an elevator and rudder to control pitching and yawing were appreciated by aircraft pioneers. However, the idea of banking an aircraft to control its direction was relatively new. This is fundamentally what the Wright brothers understood. Looking at the Wright Flyer from 1903 we can clearly see a horizontal elevator at the front and a vertical rudder at the back to control pitch and yaw. But the big innovation was the wing warping mechanism which was used to control the sideways rolling of the aircraft. Check out the video below to see the elevator, rudder and wing warping mechanisms in action.

Today, many other control systems are being used in addition to, or instead of, the conventional system outlined above. Some of these are:
1. Elevons – combined ailerons and elevators.
2. Tailerons – two differentially moving tailplanes.
3. Leading edge slats and trailing edge flaps – mostly for increased lift at takeoff and landing.
But ultimately the action of operation is fundamentally the same, the lift over a certain portion of the aircraft is changed, causing a moment about the centre of gravity.

Special Aileron Conditions

Two special conditions arise in the operation of the ailerons.

The first is known as adverse yaw. As the ailerons are deflected, one up and one down, the aileron pointing down induces more aerodynamic drag than the aileron pointing up. This induced drag is a function of the amount of lift created by the airfoil. In simplistic terms, an increase in lift causes more pronounced vortex shedding activity, and therefore a high-pressure area behind the wing, which acts as a net retarding force on the aircraft. As the downward pointing airfoil produces more lift, induced drag is correspondingly greater. This increased drag on the downward aileron (upward wing) yaws the aircraft towards this wing, which must be counterbalanced by the rudder. Aerodynamicists can counteract the adverse yawing effect by requiring that the downward pointing aileron deflects less than the upward pointing one. Alternatively, Frise ailerons are used, which employ ailerons with excessively rounded leading edges to increase the drag on the upward pointing aileron and thereby help to counteract the induced drag on the downward pointing aileron of the other wing. The problem with Frise ailerons is that they can lead to dangerous flutter vibrations, and therefore differential aileron movement is typically preferred.

The second effect is known as aileron reversal, which occurs under two different scenarios.
- At very low speeds with high angles of attack, e.g. during takeoff or landing, the downward deflection of an aileron can stall a wing, or at the least reduce the lift across the wing, by increasing the effective angle of attack past sustainable levels (boundary layer separation). In this case, the downward aileron produces the opposite of the intended effect.
- At very high airspeeds, the upward or downward deflection of an aileron may produce large torsional moments about the wing, such that the entire wing twists. For example, a downward aileron will twist the trailing edge up and leading edge down, thereby decreasing the angle of attack and consequently also the lift over that wing rather than increasing it. In this case, the structural designer needs to ensure that the torsional rigidity of the wing is sufficient to minimise deflections under the torsional loads, or that the speed at which this effect occurs is outside the design envelope of the aircraft.
Stability

What do we mean by the stability of an aircraft? Fundamentally we have to discern between the stability of the aircraft to external impetus, with and without the pilot responding to the perturbation. Here we will limit ourselves to the inherent stability of the aircraft. Hence the aircraft is said to be stable if it returns back to its original equilibrium state after a small perturbing displacement, without the pilot intervening. Thus, the aircraft’s response arises purely from the inherent design. At level flight we tend to refer to this as static stability. In effect the airplane is statically stable when it returns to the original steady flight condition after a small disturbance; statically unstable when it continues to move away from the original steady flight condition upon a disturbance; and neutrally stable when it remains steady in a new condition upon a disturbance. The second, and more pernicious type of stability is dynamic stability. The airplane may converge continuously back to the original steady flight state; it may overcorrect and then converge to the original configuration in a oscillatory manner; or it can diverge completely and behave uncontrollably, in which case the pilot is well-advised to intervene. Static instability naturally implies dynamic instability, but static stability does not generally guarantee dynamic stability.

Three cases for static stability: following a pitch disturbance, aircraft can be either unstable, neutral, or stable

Longitudinal/directional stability

By longitudinal stability we refer to the stability of the aircraft around the pitching axis. The characteristics of the aircraft in this respect are influenced by three factors:
1. The position of the centre of gravity (CG). As a rule of thumb, the further forward (towards the nose) the CG, the more stable the aircraft with respect to pitching. However, far-forward CG positions make the aircraft difficult to control, and in fact the aircraft becomes increasingly nose heavy at lower airspeeds, e.g. during landing. The further back the CG is moved the less statically stable the aircraft becomes. There is a critical point at which the aircraft becomes neutrally stable and any further backwards movement of the CG leads to uncontrollable divergence during flight.
2. The position of the centre of pressure (CP). The centre of pressure is the point at which the aerodynamic lift forces are assumed to act if discretised onto a single point. Thus, if the CP does not coincide with the CG, pitching moments will naturally be induced about the CG. The difficulty is that the CP is not static, but can move during flight depending on the angle of incidence of the wings.
3. The design of the tailplane and particularly the elevator. As described previously, the role of the elevator is to control the pitching rotations of the aircraft. Thus, the elevator can be used to counter any undesirable pitching rotations. During the design of the tailplane and aircraft on a whole it is crucial that the engineers take advantage of the inherent passive restoring capabilities of the elevator. For example, assume that the angle of incidence of the wings increases (nose moves up) during flight as a result of a sudden gust, which gives rise to increased wing lift and a change in the position of the CP. Therefore, the aircraft experiences an incremental change in the pitching moment about the CG given by
$(\text{Incremental increase in lift}) \times (\text{new distance of CP from CG})$

At the same time, the elevator angle of attack also increases due to the nose up/tail down perturbation. Hence, the designer has to make sure that the incremental lift of the elevator multiplied by its distance from the CG is greater than the effect of the wings, i.e.

$\begin{aligned} &(\text{Incremental increase in lift} \times \text{new distance of CP from CG})_{elevator} \gt \\&(\text{Incremental increase in lift} \times \text{new distance of CP from CG})_{wings} \end{aligned}$

As a result the interplay between CP and CG, tailplane design greatly influences the degree of static pitching stability of an aircraft. In general, due to the general tear-drop shape of an aircraft fuselage, the CP of an aircraft is typically ahead of it’s CG. Thus, the lift forces acting on the aircraft will always contribute some form of destabilising moment about the CG. It is mainly the job of the vertical tailplane (the fin) to provide directional stability, and without the fin most aircraft would be incredibly difficult to fly if not outright unstable.

Lateral Stability

By lateral stability we are referring to the stability of the aircraft when rolling one wing down/one wing up, and vice versa. As an aircraft rolls and the wings are no longer perpendicular to the direction of gravitational acceleration, the lift force, which acts perpendicular to the surface of the wings, is also no longer parallel with gravity. Hence, rolling an aircraft creates both a vertical lift component in the direction of gravity and a horizontal side load component, thereby causing the aircraft to sideslip. If these sideslip loads contribute towards returning the aircraft to its original configuration, then the aircraft is laterally stable. Two of the more popular methods of achieving this are:
1. Upward-inclined wings, which take advantage of the dihedral effect. As an aircraft is disturbed laterally, the rolling action to one side results in a greater angle of incidence on the downward-facing wing than the upward-facing one. This occurs because the forward and downward motion of the wing is equivalent to a net increase in angle of attack, whereas the forward and upward motion of the other wing is equivalent to a net decrease. Therefore, the lift acting on the downward wing is greater than on the upward wing. This means that as the aircraft starts to roll sideways, the lateral difference in the two lift components produces a moment imbalance that tends to restore the aircraft back to its original configuration. This is in effect a passive controlling mechanism that does not need to be initiated by the pilot or any electronic stabilising control system onboard. The opposite destabilising effect can be produced by downward pointing anhedral wings, but conversely this design improves manoeuvrability.
The Dihedral Effect with Sideslip. Figure from (1).
1. Swept back wings. As the aircraft sideslips, the downward-pointing wing has a shorter effective chord length in the direction of the airflow than the upward-pointing wing. The shorter chord length increases the effective camber (curvature) of the lower wing and therefore leads to more lift on the lower wing than on the upper. This results in the same restoring moment discussed for dihedral wings above.
The Sweepback Effect of Shortened Chord. Figure from (1).

It is worth mentioning that the anhedral and backward wept wings can be combined to reach a compromise between stability and manoeuvrability. For example, an aircraft may be over-designed with heavily swept wings, with some of the stability then removed by an anhedral design to improve the manoeuvrability.

From Calvin and Hobbes Daily (http://calvinhobbesdaily.tumblr.com/image/137916137184)

Interaction of Longitudnal/directional and Lateral Stability

As described above, movement of the aircraft in one plane is often coupled to movement in another. The yawing of an aircraft causes one wing to move forwards and the other backwards, and thus alters the relative velocities of the airflow over the wings, thereby resulting in differences in the lift produced by the two wings. The result is that yawing is coupled to rolling. These interaction and coupling effects can lead to secondary types of instability.

For example, in spiral instability the directional stability of yawing and lateral stability of rolling interact. When we discussed lateral stability, we noted that the sideslip induced by a rolling disturbance produces a restoring moment against rolling. However, due to directional stability it also produces a yawing effect that increases the bank. The relative magnitude of the lateral and directional restoring effects define what will happen in a given scenario. Most aircraft are designed with greater directional stability, and therefore a small disturbance in the rolling direction tends to lead to greater banking. If not counterbalanced by the pilot or electronic control system, the aircraft could enter an ever-increasing diving turn.

Another example is the dutch roll, an intricate back-and-forth between yawing and rolling. If a swept wing is perturbed by a yawing disturbance, the now slightly more forward-pointing wing generates more lift, exactly for the same argument as in the sideswipe case of shorter effective chord and larger effective area to the airflow. As a result, the aircraft rolls to the side of the slightly more backward-pointing wing. However, the same forward-pointing wing with higher lift also creates more induced drag, which tends to yaw the aircraft back in the opposite direction. Under the right circumstances this sequence of events can perpetuate to create an uncomfortable wobbling motion. In most aircrafts today, dampers in the automatic control system are installed to prevent this oscillatory instability.

In this post I have only described a small number of control challenges that engineers face when designing aircraft. Most aircraft today are controlled by highly sophisticated computer programmes that make loss of control or stability highly unlikely. Free unassisted “Flying-by-wire”, as it is called, is getting rarer and mostly limited to start and landing manoeuvres. In fact, it is more likely that the interface between human and machine is what will cause most system failures in the future.

References

(1) Richard Bowyer (1992). Aerodynamics for the Professional Pilot. Airlife Publishing Ltd., Shrewsbury, UK.
January 23, 2016
Risk and failure in complex engineering systems

“We must ensure this never happens again.” — Pick Your Favourite Regulator

This is a common reaction to instances of catastrophic failure. However, in complex engineering systems, this statement is inherently paradoxical. If the right lessons are learned and the appropriate measures are taken, the same failure will most likely never happen again. But, catastrophes in themselves are not completely preventable, such that the next time around, failure will occur somewhere new and unforeseen. Welcome to the world of complexity.

Boiled down to its fundamentals, engineering deals with the practical – the development of tools that work as intended. Failure is a human condition, and as such, all man-made systems are prone to failure. Furthermore, success should not be defined as the absence of failure, but rather how we cope with failure and learn from it – how we conduct ourselves in spite of failure.

Failure and risk are closely linked. The way I define risk here is the probability of an irreversible negative outcome. In a perfect world of complete knowledge and no risk, we know exactly how a system will behave beforehand and have perfect control of all outcomes. Hence, in such an idealised world there is very little room for failure. In the real world however, knowledge is far from complete, people and man-made systems behave and interact in unforeseen ways, and changes in the surrounding environmental conditions can drastically alter the intended behaviour. Therefore, our understanding of and attitude towards risk, plays a major role in building safe engineering systems.

The first step is to acknowledge that our perception of risk is very personal. It is largely driven by human psychology and depends on a favourable balance of risk and reward. For example, there is a considerable higher degree of fear of flying than fear of driving, even though air travel is much safer than road travel. As plane crashes are typically more severe than car crashes, it is easy to form skewed perceptions of the respective risks involved. What is more, driving a car, for most people a daily activity, is far more familiar than flying an airplane.

Second, science and engineering do not attempt to predict or guarantee a certain future. There will never be a completely stable, risk free system. All we can hope to achieve is a level of risk that is comparable to that of events beyond our control. Risk and uncertainty arise in the gap between what we know and what we don’t – between how we design the system to behave and how it can potentially behave. This knowledge gap can lead to two types of risk. There are certain things we appreciate that we do not understand, i.e. the known unknowns. Second, and more pernicious, are those things we are not even aware of, i.e. the unknown unknowns, and it is these failures that wreak the most havoc. So how do we protect ourselves against something we don’t even see coming? How do engineers deal with this second type of risk?

The first strategy is the safety factor or margin of safety. A safety factor of 2 means that if a bridge is expected to take a maximum service load of X (also called the demand), then we design the structure to hold 2X (also called the capacity). In the aerospace industry, safety protocols require all parts to maintain integrity up to 1.2x the service load, i.e. a limit safety factor of 1.2. Furthermore, components need to sustain 1.5x the service load for at least three seconds, the so-called ultimate safety factor. In some cases, statistical techniques such as Monte Carlo analyses are used to calculate the probability that the demand will exceed the capacity.

The second strategy is to employ redundancies in the design. Hence, back-ups or contingencies are in place to prevent a failure from progressing to catastrophic levels. In structural design, for example, this means that there is enough untapped capacity within the structure, such that a local failure leads to a rebalancing/redirection of internal loads without inducing catastrophic failure. Part of this analysis includes the use of event and fault trees that require engineers to conjure the myriad of ways in which a system may fail, assign probabilities to these events, and then try to ascertain how a particular failure affects other parts of the system.

Event Tree Diagram

Unfortunately, some engineering systems today have become so complex that it is difficult to employ fault and event trees reliably. Rising complexity means that is impossible to know all functional interactions beforehand, and it is therefore difficult, if not impossible, to predict exactly how failure in one part of the system will affect other parts. This phenomenon has been popularised by the “butterfly effect” – a scenario in which, in an all-connected world, the stroke of a butterfly’s wings on one side of the planet, causes an earthquake on the other.

The increasing complexity in engineering systems is driven largely by the advance of technology based on our scientific understanding of physical phenomena at increasingly smaller length scales. For example, as you are reading this on your computer or smartphone screen, you are, in fact, interacting with a complex system that spans many different layers. In very crude terms, your internet browser sits on top of an operating system, which is programmed in one or many different programming languages, and these languages have to be translated to machine code to interact with the microprocessor. In turn, the computer’s processor interacts with other parts of the hardware such as the keyboard, mouse, disc drives, power supply, etc. which have to interface seamlessly for you to be able to make sense of what appears on screen. Next, the computer’s microprocessor is made up of a number of integrated circuits, which are comprised of registers and memory cells, which are further built-up from a network of logic gates, which ultimately, are nothing but a layer of interconnected semiconductors. Today, the expertise required to handle the details at a specific level is so vast, that very few people understand how the system works at all levels.

In the world of aviation, the Wright brothers were the first to realise that no one would ever design an effective aircraft without an understanding of the fields of propulsion, lift and control. Not only did they understand the physics behind flight, Orville and Wilbur were master craftsmen from years of running their own bike shop, and later went as far as building the engine for the Wright Flyer themselves. Today’s airplanes are of course significantly more sophisticated than the aircraft 100 years ago, such that in-depth knowledge of every aspect of a modern jumbo jet is out of the question. Yet, the risk of increasing specialism is that there are fewer people that understand the complete picture, and appreciate the complex interactions that can emerge from even simple, yet highly interconnected processes.

With increasing complexity, the solution should not be further specialisation and siloing of information, as this increases the potential for unknown risks. For example, consider the relatively simple case of a double pendulum. Such a system is described by chaotic behaviour, that is, we know and understand the underlying physics of the problem, yet it is impossible to predict how the pendulum will swing a priori. This is because at specific points, the system can bifurcate into a number of different paths, and the exact behaviour depends on the nature of the initial conditions when the system is started. These bifurcations can be very sensitive to small differences in the initial conditions, such that two processes that start with almost the same, but not identical, initial conditions can diverge considerably after only a short time.

A double rod pendulum animation showing chaotic behaviour.

Under these circumstances, even small local failures within a complex system can cascade rapidly, accumulate and cause global failure in unexpected ways. Thus, the challenge in designing robust systems arises from the fact that the performance of the complete system cannot be predicted by an isolated analysis of its constituent parts by specialists. Rather, effective and safe design requires holistic systems thinking. A key aspect of systems thinking is to acknowledge that the characteristics of a specific layer emerges from the interacting behaviour of the components working at the level below. Hence, even when the behaviour of a specific layer is governed by understood deterministic laws, the outcome of these laws cannot be predicted with certainty beforehand.

In this realm, engineers can learn from some of the strategies employed in medicine. Oftentimes, the origin, nature and cure of a disease is not clear beforehand, as the human body is its own example of a complex system with interacting levels of cells, proteins, molecules, etc. Some known cures work even though we do not understand the underlying mechanism, and some cures are not effective even though we understand the underlying mechanism. Thus, the engineering design process shifts from well-defined rules of best practise (know first then act) to emergent (act first then know), i.e. a system is designed to the best of current knowledge and then continuously iterated/refined based on reactions to failure.

In this world, the role of effective feedback systems is critical, as flaws in the design can remain dormant for many years and emerge suddenly when the right set of external circumstances arise. As an example, David Blockley provides an interesting analogy of how failures incubate in his book “Engineering: A very short introduction.”

“…[Imagine] an inflated balloon where the pressure of the air in the balloon represents the ‘proneness to failure’ of a system. … [W]hen air is first blown into the balloon…the first preconditions for [an] accident are established. The balloon grows in size and so does the ‘proneness to failure’ as unfortunate events…accumulate. If [these] are noticed, then the size of the balloon can be reduced by letting air out – in other words, [we] reduce some of the predisposing events and reduce the ‘proneness to failure’. However, if they go unnoticed…, then the pressure of events builds up until the balloon is very stretched indeed. At this point, only a small trigger event, such as a pin or lighted match, is needed to release the energy pent up in the system.”

Often, this final trigger is blamed as the cause of the accident. But it isn’t. If we prick the balloon before blowing it up, it will subsequently leak and not burst. The over-stretched balloon itself is the reason why an accident can happen in the first place. Thus, in order to reduce the likelihood of failure, the accumulation of preconditions has to be monitored closely, and necessary actions proposed to manage the problem.

The main challenge for engineers in the 21st century is not more specialisation, but the integration of design teams from multiple levels to facilitate multi-disciplinary thinking across different functional boundaries. Perhaps, the most important lesson is that it will never be possible to ensure that failures do not occur. We cannot completely eliminate risk, but we can learn valuable lessons from failures and continuously improve engineering systems and design processes to ensure that the risks are acceptable.

References
David Blockley (2012). Engineering: A very short introduction. Oxford University Press. Oxford, UK.

December 13, 2015
The Dangers of Outsourcing
“Outsourcing” is a loaded term. In today’s globalised world it has become to mean many things – from using technology to outsource rote work over the internet to sharing capacity with external partners that are more specialised to complete a certain task. However, inherent in the idea of outsourcing is the promise of reduced costs, either through reductions in labour costs, or via savings in overheads and tied-up capital.

I recently stumbled across a 2001 paper [1] by Dr Hart-Smith of the Boeing Company, discussing some of the dangers and fallacies in our thinking regarding the potential advantages of outsourcing. The points raised by Hart-Smith are particularly noteworthy as they deal with the fundamental goals of running a business rather than trying to argue by analogy, or blind faith on proxy measurements. What follows is my take on the issue of outsourcing as it pertains to the aerospace industry only, loosely based on the insights provided by Dr Hart-Smith, and with some of my own understanding of the topic from disparate sources that I believe are pertinent to the discussion.

That being said, the circumstances under which outsourcing makes economical sense depends on a broad spectrum of variables and is therefore highly complex. With that being said let’s delve a bit deeper into the good, the bad and the ugly of the outsourcing world.

Any discussion on outsourcing can, in my opinion, be boiled down to two fundamental drivers:
1. The primary goal of running a business: making money. Taking non-profits aside, a business exists to make a profit for its shareholders. If a business doesn’t make any money today, or isn’t expected to make a profit in the future, i.e. is not valuable on a net present value basis, then it is a lousy business. Any other metric that is used to measure the performance of a business, be it efficiency ratios such as return on capital employed, are helpful proxies but not the ultimate goal.
2. Outsourcing is based on Ricardo’s idea of comparative advantage, that is, if two parties decide to specialise in the production of two different goods and decide to trade, both parties are better off than if they produced both goods for autarchic use only, even if one party is more efficient than the other at producing both goods at the same time.
Using these two points as our guidelines it becomes clear very quickly under what conditions a company should decide to outsource a certain part of its business:
- Another company is more specialised in this line of business and can therefore create a higher-quality product. This can either be achieved via:
  - Better manufacturing facilities, i.e. more precisely dimensioned components that save money in the final assembly process
  - Superior technical expertise. A good example are the jet engines on an aircraft. Neither Boeing nor Airbus design or manufacture their own engines as the complexity of this particular product means that other companies have specialised to make a great product in this arena.
- The rare occasion that outsourcing a particular component of an aircraft results in a net overall profit for the entire design and manufacturing project. However, the decision to outsource should never be based on the notion of reduced costs for a single component, as there is no one-to-one causation between reducing costs for a single component and increased profits for the whole project.
Note, that in either case the focus is on receiving extra value for something the company pays for rather than on reducing costs. In fact, as I will explain below, outsourcing often leads to increases in cost, rather than cost reductions. Under these circumstances, it only makes sense to outsource if this additional cost is traded for extra value that cannot be created in house, i.e. manufacturing value or technical value.

Reducing Costs

Reducing costs is another buzzword that is often used to argue pro outsourcing. Considering the apparent first-order effects, it makes intuitive sense that offloading a certain segment of a business to a third party will reduce costs via lower labour costs and overheads, depreciation and capital outlays. In fact, this is one of the allures of the globalised world and the internet; the means of outsourcing work to lower-wage countries are cheaper than ever before in history.

However, the second-order effects of outsourcing are rarely considered. The first fundamental rule of ecology is that in a complex system you can never only do one thing. As all parts of a complex system are intricately linked, perturbing the system in one area will have inevitable knock-on effects in another area. Additionally if the system behaves non-linearly to the external stimuli, these knock-on effects are non-intuitive and almost impossible to predict a priori. Outsourcing an entire segment of a project should probably be classed as a major perturbation, and as all components of a complex engineering product, such as an aircraft, are inherently linked, a decision in one area will certainly effect other areas of the project as well. Hence, consider the following second-order effects that should be accounted for as a result of outsourcing as certain line of a business:
- Quality assurance is harder out-of-house, and hence reworking components that are not to spec may cost more in the long run.
- Additional labour may be required in-house in order to coordinate the outsourced work, interact with the third party and interface the outsourced component with the in-house assembly team.
- Concurrent engineering and the ability to adapt designs is much harder. In order to reduce their costs, subcontractors often operate on fixed contracts, i.e. the design specification for a component is fixed or the part to be manufactured can not be changed. Hence, the flexibility to adapt the design of a part further down the line is constricted, and this constraint may create a bottleneck for other interfacing components.
- Costs associated with sub-assemblies that cannot be fitted together balloon quickly, and the ensuing rework and detective work to find the source of the imprecision delays the project.
- There is a need for additional transportation due to off-site production and increased manufacturing time.
- It is harder to coordinate the manufacturing schedules of multiple external subcontractors who might all be employing different planning systems, and more inventory is usually created.
Therefore there is an inherent clash between trying to minimise costs locally, i.e. the costs for one component in isolation, and keeping costs down globally, i.e. for the entire project. In the domain of complex systems, local optimisation can lead to fragility of the system in two ways. First, small perturbations from local optima typically have greater effects on the overall performance of the system than perturbations from locally sub-optimal states. Second, locally optimising one factor of the system may force other factors to be far from their optima, and hence reduce the overall performance of the system. A general heuristic is that the best solution is to reach a compromise by operating individual components at sub-optimal levels, i.e. with excess capacity, such that the overall system is robust to adapt to unforeseen perturbations in its operating state.

Furthermore, the decision to outsource the design or the manufacture of a specific component needs to factored into the overall design of the product as a early as possible. Thus, all interfacing assemblies and sub-assemblies are designed with this particular reality in mind, rather than having to adapt to this situation a posteriori. This is because early design decisions have the highest impact on the final cost of a product. As a general rule of thumb, 80% of the final costs are incurred by the first 20% of the design decisions made, such that late design changes are always exponentially more expensive than earlier ones. Having to fix misaligned sub-assemblies at final assembly costs orders of magnitude more than additional planning up front.

Finally, the theory of constraints teaches us that the performance of the overall project can never exceed that of its least proficient component. Hence, the overall quality of the final assembly is driven by the quality of its worst suppliers. This means that in order to minimise any problems, the outsourcing company needs to provide extra quality and technical support for the subcontractors, extra employees for supply chain management, and additional in-house personal to deal with the extra detail design work and project management. Dr Hart-Smith warns that

With all this extra work the reality is that outsourcing should be considered as an extra cost rather than a cost saving, albeit, if done correctly, for the exchange of higher quality parts. The dollar value of out-sourced work is a very poor surrogate for internal cost savings.

Outsourcing Profits

Hypothetically, in the extreme case when every bit of design and manufacturing work is outsourced the only remaining role f0r the original equipment manufacturer (OEM) of the aircraft is to serve as a systems integrator. However, in this scenario, all profits are outsourced as well. This reality is illustrated by a simple example. The engines and avionics comprise about 50% of the total cost of construction of an aircraft, and the remaining 50% are at the OEM’s discretion. Would you rather earn a 25% profit margin on 5% of the total work, or rather 5% profit margin on 25% of the total work? In the former case the OEM will look much more profitable on paper (higher margin) but the total amount of cash earned in the second scenario will be higher. Hence, in a world where 50% of the work naturally flows to subcontractors supplying the engines, avionics and control systems, there isn’t much left of the aircraft to outsource if enough cash is to be made to keep the company in business. Without cash there is no money to pay engineers to design new aircraft and no cash on hand to serve as a temporary buffer in a downturn. If there is anything that the 20th century has taught us, is that in the world of high-tech, any company that does not innovate and purely relies on derivative products is doomed to be disrupted by a new player.

Second, subcontractors are under exactly the same pressure as the OEM to maximise their profits. In fact, subcontractors have a greater incentive for fatter margins and higher returns on investment as their smaller size increases their interest rates for loaned capital. This means that suppliers are not necessarily incentivised to manufacture tooling that can be reused for future products as these require more design time and can not be billed against future products. In-house production is much more likely to lead to this type of engineering foresight. Consider the production of a part that is estimated to cost the same to produce in-house as by a subcontractor, and to the same quality standards. The higher profit margins of the subcontractor naturally result in a higher overall price for the component than if manufactured in-house. However, standard accounting procedures would consider this as a cost reduction since all first-order costs, such as lower labour rate at the subcontractor, fewer employees and less capital tied up in hard assets at the OEM, creates the illusion that outside work is cheaper than in-house work.

Skin in the Game

One of the heavily outsourced planes in aerospace history was the Douglas Aircraft Company DC-10, and it was the suppliers who made all the profits on this plane. It is instrumental that most subcontractors were not willing to be classified as risk-sharing partners. In fact, if the contracts have been negotiated properly, then most subcontractors have very little downside risk. For financial reasons, the systems integrator can rarely allow a subcontractor to fail, and therefore provides free technical support to the subcontractor in case of technical problems. In extreme cases, the OEM is even likely to buy if subcontractor outright.

This state of little downside risk is what NN Taleb calls the absence of “skin in the game” [2]. Subcontractors typically do not behave like employees do. Employees or “risk-sharing” partners have a reputation to protect and fear the economic repercussions of losing their paychecks. On the one hand, employees are more expensive than contractors and limit workforce flexibility. On the other hand, employees guarantee a certain dependability and reliability for solid work, i.e. downside protection to shoddy work. In Taleb’s words,

So employees exist because they have significant skin in the game – and the risk is shared with them, enough risk for it to be a deterrent and a penalty for acts of undependability, such as failing to show up on time. You are buying dependability.

Subcontractors on the other hand typically have more freedom than employees. They fear the law more than being fired. Financial repercussions can be built into contracts, and bad performances may lead to loss in reputation, but an employee, by being part of the organisation and giving up some of his freedom, will always have more risk, and therefore behave in more dependable ways. There are examples, like Toyota’s ecosystem of subcontractors, where mutual trust and “skin in the game” is built into the network via well thought-out profit sharing, risk sharing and financial penalties, but these relationships are not ad hoc and are based on long-term relationships.

With a whole network of subcontractors the performance of an operation is limited by the worst-performing segment. In this environment, OEMs are often forced to assist bad-performing suppliers and therefore forced to accept additional costs. Again from NN Taleb [2],

If you miss on a step in a process, often the entire business shuts down – which explains why today, in a supposedly more efficient world with lower inventories and more subcontractors, things appear to run smoothly and efficiently, but errors are costlier and delays are considerably longer than in the past. One single delay in the chain can stop the entire process.

The crux of the problem is that a systems integrator, who is the one that actually sells the final product, i.e. gets paid last and carries the most tail risk, can only raise the price to levels that the market will sustain. Subcontractors, on the other hand, can push for higher margins and lock in a profit before the final plane is sold and thereby limit their exposure to cost over-runs.

ROE

The return on net assets or return on equity (ROE) metric is a very powerful proxy to measuring how efficiently a company uses its equity or net assets (assets – liabilities; where assets are everything the company owns and liabilities include everything the company owes) to create profit,

$ROE = \frac{Earnings}{Equity}$

The difference between high-ROE and low-ROE businesses is illustrated here using a mining company and a software company as (oversimplified) examples. The mining company needs a lot of physical hard assets to dig metals out of the ground, and hence ties up considerable amount of capital in its operations. A software company on the other hand is asset-light as the cost of computing hardware has exponentially fallen in line with Morse Law. Thus, if both companies make the same amount of profit, then the software company will have achieved this more efficiently than the mining company, i.e. required less initial capital to create the same amount of earnings. The ROE is a useful metric for investors, as it provides information regarding the expected rate of return on their investment. Indeed, in the long run, the rate of return on an investment in a company will converge to the ROE.

In order to secure funding from investors and achieve favourable borrowing rates from lenders, a company is therefore incentivised to beef up its ROE. This can either be done by reducing the denominator of the ratio, or by increasing the numerator. Reducing equity either means running a more asset-light business or by increasing liabilities via the form of debt. This is why debt is also a form of leverage as it allows a company to earn money on outside capital. Increasing the numerator is simple on paper but harder in reality; increasing earnings without adding capacity, e.g. by cost reductions or price increases.

Therefore ROE is a helpful performance metric for management and investors but it is not the ultimate goal. The goal of a for-profit company is to make money, i.e. maximise the earnings power. Would you rather own a company that earns 20% on a business with $100 of equity or 5% on company with $1000 of tied up capital? Yes, the first company is more efficient at turning over a profit but that profit is considerably smaller than for the second company. Of course, if the first company has the chance to grow to the size of the second in a few years time, and maintains or even expands its ROE, then this is a completely different scenario and it would be a good investment to forego some earnings now for higher cashflow in the future. However, by and large, this is not the situation for large aircraft manufacturers such as Boeing and Airbus, and restricted to fast-growing companies in the startup world.

Second, it is foolish to assume that the numerator and denominator are completely decoupled. In fact, in a manufacturing-intense industry such as aerospace, the two terms are closely linked and their behaviour is complex, i.e. their are too many cause-and-effect relationships for us to truly understand how a reduction in assets will effect earnings. Blindly reducing assets, without taking into account its effect on the rate and cost of production, can always be considered as a positive effect as it always increase ROE. In this manner, ROE can be misused as a false excuse for excessive outsourcing. Given the complex relationship in the aerospace industry between earnings and net assets, the real value of the ROE ratio is to provide a ballpark figure of how much extra money the company can earn in its present state with a source of incremental capital. Thus, if a company with multiple billions in revenue currently has an ROE of 20%, than it can expect to earn an extra 20% if it employs an incremental amount of further capital in the business, where the exact incremental amount is of course privy to interpretation.

In summary, there is no guarantee that a reduction in assets will directly result in an increase in profits, and the ROE metric is easily misused to justify capital reductions and outsourcing, when in fact, it should be used as a ballpark figure to judge how much additional money can currently be made with more capital spending. Thus, ROE should only be used as a performance metric but never as the overall goal of the company.

A cautionary word on efficiency

In a similar manner to ROE, the headcount of a company is an indicator of efficiency. If the same amount of work can be done by fewer people, then the company is naturally operating more efficiently and hence should be more profitable. This is true to an extent but not in the limit. Most engineers will agree that in a perfect world, perfect efficiency is unattainable as a result of dissipating mechanisms (e.g. heat, friction, etc.). Hence, perfect efficiency can only be achieved when no work is done. By analogy, it is meaningless to chase ever-improving levels of efficiency if this comes at the cost of reduced sales. Therefore, in some instances it may be wise to employ extra labour capacity in non-core activities in order to maintain a highly skilled workforce that is able to react quickly to opportunities in the market place, even if this comes at the cost of reduced efficiency.

So when is outsourcing a good idea?

Outsourcing happens all over the world today. So there is obviously a lot of merit to the idea. However, as I have described above, decisions to outsource should not be made blindly on terms of shedding assets or reducing costs, and need to factored into the design process as early as possible. Outsourcing is a valuable tool in two circumstances:
1. Access to better IP = Better engineering design
2. Access to better facilities = More precise manufacturing
First, certain components on modern aircraft have become so complex in their own right that it is not economical to design and manufacture these parts in-house. As a result, the whole operation is outsourced to a supplier that specialises in this particular product segment, and can deliver higher quality products than the prime manufacturer. The best example of this are jet engines, which today are built by companies like Rolls-Royce, General Electric and Pratt & Whitney, rather than Airbus and Boeing themselves.

Second, contrary to popular belief, the major benefit of automation in manufacturing is not the elimination of jobs, but an increase in precision. Precision manufacturing prevents the incredibly costly duplication of work on out-of-tolerance parts further downstream in a manufacturing operation. Toyota, for example, understood very early on that in a low-cost operation, getting things right the first time around is key, and therefore anyone on the manufacturing floor has the authority to stop production and sort out problems as they arise. Therefore, access to automated precision facilities is crucial for aircraft manufacturers. However, for certain parts, a prime manufacturer may not be able to justify the high capital outlay for these machines as there is not enough capacity in-house for them to be utilised economically. Under these circumstances, it makes sense to outsource the work to an external company that can pool the work from a number of companies on their machines. This only makes sense if the supplier has sufficient capacity on its machines or is able to provide improved dimensional control, e.g. by providing design for assembly services to make the final product easier to assemble.

Conclusion

After this rather long exposition of the dangers of outsourcing in the aerospace industry, here are some of the key takeaways:
1. Outsourcing should not be employed as a tool for cost reduction. More likely than not it will lead to extra labour and higher costs via increased transportation, rework and inventories for the prime manufacturer, and therefore this extra price should be compensated by better design engineering or better manufacturing precision than could be achieved in-house.
2. Efficiency is not the primary goal of the operation, but can be used as a useful metric of performance. The goal of the operation is to make money.
3. A basic level of work has to be retained in-house in order to generate sufficient cash to fund new products and maintain a highly skilled workforce. If the latter requires extra capacity, a diversification to non-core activities may be a better option than reducing headcount.
4. Scale matters. Cost saving techniques for standardised high-volume production are typically inappropriate for low-volume industries like aerospace.
5. Recognise the power of incentives. In-house employees typically have more “skin in the game” as risk-sharing partners ,and therefore produce more dependable work than contractors.
Sources

[1] L.J. Hart-Smith. Out-sourced profits – the cornerstone of successful subcontracting. Boeing paper MDC 00K0096. Presented at Boeing Third Annual Technical Excellence (TATE) Symposium, St. Louis, Missouri, 2001.

[2] N.N. Taleb. How to legally own another person. Skin in the Game. pp. 10-15. https://dl.dropboxusercontent.com/u/50282823/employee.pdf
November 13, 2015
What Creates Lift – How Do Wings Work?
How airplanes fly is one of the most fundamental questions in aerospace engineering. Given its importance to flight, it is surprising how many different and oftentimes wrong explanations are being perpetuated online and in textbooks. Just throughout my time in school and university, I have been confronted with several different explanations of how wings create lift.

Most importantly, the equal transit time theory, explained further below, is taught in many school textbooks and therefore instils faulty intuitions about lift very early on. This is not necessarily because more advanced theories are harder to understand or require a lot maths. In fact, the theory that requires the simplest assumptions and least abstraction is typically considered to be the most useful.

In science, the simplicity of a theory is a hallmark of its elegance. According to Einstein (or Louis Zukofsky or Roger Sessions or William of Ockham…I give up, who knows), “everything should be made as simple as possible, but not simpler.” Hence, the strength of a theory is related to:
- The simplicity of its assumptions, ideally as few as possible.
- The diversity of phenomena the theory can explain, including phenomena that other theories could not explain.
Keeping this definition in mind, let’s investigate some popular theories about how aircraft create lift.

The first explanation of lift that I came across as a middle school student was the theory of “Equal Transit Times”. This theory assumes that the individual packets of air flowing across the top and bottom surfaces must reach the trailing edge of the airfoil at the same time. For this to occur, the airflow over the longer top surface must be travelling faster than the air flowing over the bottom surface. Bernoulli’s principle, i.e. along a streamline an increasing pressure gradient causes the flow speed to decrease and vice versa, is then invoked to deduce that the speed differential creates a pressure differential between the top and bottom surfaces, which invariably pushes the wing up. This explanation has a number of fallacies:
- There is no physical law that requires equal transit times, i.e. the underlying assumptions are certainly not as simple as possible.
- It fails to explain why aircraft can fly upside down, i.e. does not explain all phenomena.
As this video shows, the air over the top surface does indeed flow faster than on the bottom surface, but the flows certainly do not reach the trailing edge at the same time. Hence, this theory of equal transit times is often referred to as the “Equal Transit Time Fallacy”.

In order to generalise the above theory, while maintaining the mathematical relationship between speed and pressure given by Bernoulli’s principle, we can relax the initial assumption of equal transit time. If we start from a phenomenological observation of streamlines around an airfoil, as depicted schematically below, we see can see that the streamlines are bunched together towards the top surface of the leading edge, and spread apart towards the bottom surface of the leading edge. The flow between two adjacent streamlines is often called a streamtube, and the upper and lower streamtubes are highlighted in shades of blue in the figure below. The definition of a streamline is the line a fluid particle would traverse as it flows through space, and thus, by definition, fluid can never cross a streamline. As two adjacent streamlines form the boundaries of the streamtubes, the mass flow rate through each streamtube must be conserved, i.e. no fluid enters from the outside, and no fluid particles are created or destroyed. To conserve the mass flow rate in the upper streamline as it becomes narrower, the fluid must flow faster. Similarly, to conserve the mass flow rate in the lower streamtube as it widens, the fluid must slow down. Hence, in accordance with the speed-pressure relationship of Bernoulli’s principle, this constriction of the streamtubes means that we have a net pressure differential that generates a lift force.

Flow lines around a NACA 0012 airfoil at 11° angle of attack, with upper and lower streamtubes identified.

Of course, this theory does not explain why the upper streamtube contracts and the lower streamtube expands in the first place. An intuitive explanation for this involves the argument that the angle of attack obstructs the flow more towards the bottom of the airfoil than towards the top. However, this does not explain how asymmetric airfoils with pronounced positive camber at zero angle of attack, as shown in the figure below, create lift. In fact, such profiles were successfully used on early aircraft due to their resemblance to bird wings. Again, this theory does not explain all the physical phenomena we would like it to explain, and is therefore not the rigorous theory we are looking for.

Asymmetric airfoil with pronounced camber [1]

Another explanation that is often cited for explaining lift is that the airfoil pushes air downwards, i.e. there is a net change of momentum in the vertical plane between the leading and trailing edges of the airfoil, and by necessity of Newton’s third law, this creates a lift force. Any object that experiences lift must certainly conform to the reality of Newton’s third law, but referring only to the difference in start and end conditions ignores the potential complexity of flow that occurs between these two stations. Furthermore, the question remains through what net angle the flow is deflected? One straightforward answer is the angle of incidence of the airfoil, but this ignores the upwash ahead of the wing or anything that happens behind the wing. Hence, the simple explanation of “pushing air downwards”, however elegant and correct, is an integral approach that summates the fluid mechanics between leading and trailing edges and leaves little to say of what happens in between. Indeed, as will be shown below, upwash and flow circulation play an equally important role in creating lift.

Indeed, we can imagine a flow around a 2D cylinder shown in the figure below. The flow is symmetric from left-to-right and top-to-bottom and experiences no lift. If we now start the cylinder spinning at the rate $\Omega$ in the clockwise direction shown, the velocity of air increases on the upper surface (reduced pressure) and reduces on the lower surface (higher pressure). This asymmetric flow top-to-bottom therefore creates lift. Note that the rotation of the cylinder has moved the stagnation point towards the rear end of the cylinder (where the bottom and top flows converge) downwards and therefore broken the symmetry of the flow. Hence, in this example, lift is created by a combination of a free-stream velocity and flow circulation, i.e. air is “spun up” and not necessarily just deflected downwards (in this example upwash ahead of the cylinder matches the downwash aft).

Flow around a cylinder

Flow around a rotating cylinder that induces lift

In the example above, lift was induced by creating an asymmetry in the curvature of the streamlines. In the stationary cylinder we had streamlines curving in one direction on the top surface, and by the same amount in the opposite direction on the bottom surface. Rotating the cylinder created an asymmetry in streamline curvature between the top and bottom surfaces (more curvature upwards then curvature downwards). We can create a similar asymmetry in the flow with a stationary cylinder by placing a small sharp-edged flap at the rear edge and positioned slightly downwards. Real viscous flow might not necessarily flow as smoothly around the little flap as shown in the diagram below, but this mental model is a neat tool to imagine how we can morphologically transition from a rotating cylinder that produces lift to an airfoil. This is shown via the series of diagrams below. This series of pictures shows that an airfoil creates a smoother variation in velocity than the cylinder, which leads to a smaller chance of boundary layer separation (a source of drag and in the worst-case scenario aerodynamic stall). A similar streamline profile could also be created with a symmetric airfoil that introduces asymmetry into the flow by being positioned at a positive angle of attack.

The reason why differences in streamline curvature induce lift is addressed in a journal paper by Prof Holger Babinsky, which is free to download. If we consider purely stead-state flow and neglect the effects of gravity, surface tension and friction we can derive some very basic, yet insightful, equations that explain the induced pressure difference. Quite intuitively this argument shows that a force acting parallel to a streamline causes the flow to accelerate or decelerate along its tangential path, whereas a force acting perpendicular to the flow direction causes the streamline to curve.

The first case is described mathematically by Bernoulli’s principle and depicted in the figure below. If we imagine a small fluid particle of finite length l situated in a field of varying pressure, then the front and back surfaces of the particle will experience different pressures. Say the pressure increases along the streamline, then the force acting on the front face pointing in the direction of motion is greater than the force acting on the rear surface. Hence, according to Newton’s second law, this increasing pressure field along the streamline causes the flow speed to decrease and vice versa. However, this approach is valid only along a single streamline. Bernoulli’s principle can not be used to relate the speed and pressures of adjacent streamlines. Thus, we can not use Bernoulli’s principle to compare the flows on the bottom and top surfaces of an airfoil, and therefore can say little about their relative pressures and speeds.

Flow along a straight streamline [2]

However, consider the curved streamlines shown in the figure below. If we assume that the speed of the particle travelling along the curved streamline is constant, then Bernoulli’s principle states that the pressure along the streamline can not change either. However, the velocity vector v is changing, as the direction of travel is changing along the streamline. According to Newton’s second law, this change in velocity, i.e. acceleration, must be caused by a net centripetal force acting perpendicular to the direction of the flow. This net centripetal force must be caused by a pressure differential on either side of the particle as we have ignored the influence of gravity and friction. Hence, a curved streamline implies a pressure differential across it, with the pressure decreasing towards the centre of curvature.

Flow along a curved streamline [2]

Mathematically, the pressure difference across a streamline in the direction n pointing outwards from the centre of curvature is

$\frac{\mathrm{d}p}{\mathrm{d}n} = \rho \frac{v^2}{R}$

where R is the radius of curvature of the flow and $\rho$ is the density of the fluid.

One positive characteristic of this theory is that it explains other phenomena outside our interest in airfoils. Vortices, such as tornados, consist of concentric circles of streamlines, which suggests that the pressure decreases as we move from the outside to the core of the vortex. This observation agrees with our intuitive understanding of tornados sucking objects into the sky.

With this understanding we can now return to the study of airfoils. Consider the simple flow path along a curved plate shown in the figure below. At point A the flow field is unperturbed by the presence of the airflow and the local pressure is equal to the atmospheric pressure $p_{atm}$ . As we move down along the dashed curve we see that the flow starts to curve around the curved plate. Hence, the pressure is decreasing as we move closer to the airfoil surface and $p_B < p_{atm}$ . On the bottom half the situation is reversed. Point C is again undisturbed by the airflow but the flow is increasingly curved as me closer to D. However, when moving from C to D, the pressure is increasing because pressure increases moving away from the centre of curvature, which on the bottom of the airfoil is towards point C. Thus, $p_D > p_{atm}$ and by the transitive property $p_B < p_D$ such that the airfoil experiences a net upward lift force.

Flow around a curved airfoil [2]

From this exposition we learn that any shape that creates asymmetric curvature in the flow field can generate lift. Even though friction has been neglected in this analysis, it is crucial in forcing the fluid to adhere to the surfaces of the airfoil via a viscous boundary layer. Therefore, the inclusion of friction does not change the theory of lift due to streamline curvature, but provides an explanation for why the streamlines are curved in the first place.

A couple of interesting observations follow from the above discussion. Nature typically uses thin wings with high camber, whereas man-made flying machines typically have thicker airfoils due to their improved structural performance, i.e. stiffness. In the figure below, the deep camber thinner wing shows highly curved flow in the same direction on both the top and bottom surfaces.

Deep camber thin wing with high lift [2]

Shallow camber thick wing with less lift [2]

The more shallow camber thicker wing has flow curved in two different directions on the bottom surface and will therefore result in less pressure difference between the top and bottom surfaces. Thus, for maximum lift, the thin, deeply cambered airfoils used by birds are the optimum configuration.

In conclusion, we have investigated a number of different theories explaining how lift is created around airfoils. Each theory was investigated in terms of the simplicity and validity of its underlying assumptions, and the diversity of phenomena it can describe. The theories based on Bernoulli’s principle, such as the equal transit time theory and the contraction of streamtubes theory, were either based on faulty initial assumptions, i.e. equal time, or failed to explain why streamtubes should contract or expand in the first place. The theory based on airfoils deflecting airflow downwards is theoretically accurate and correct (Newton’s third law: changes in fluid momentum over a control volume including the airfoil lead to a reactive lift force), but by being an integral approach it is not helpful in explaining what occurs between the leading and trailing edges of the airfoil (e.g. upwash is also a contributing factor to lift).

A more intricate theory is that curved bodies induce curved streamlines, as the inherent viscosity of the fluid forces the fluid to adhere to the surface of the body via a boundary layer. The centripetal forces that arise in the curved flow lead to a drop in pressure across the streamlines towards the centre of curvature. This means that if a body leads to asymmetric curved streamlines across it, then the induced pressure differential arising from the asymmetry induces a net lift force.

Edits and Acknowledgments

A previous version of this article referenced a misleading and incorrect example of a highly cambered airfoil as a counterexample to the theory of airfoils deflecting airflow downwards and the theoretical explanation using control volumes. Dr Thomas Albrecht of Monash University pointed this error out to me (see the discussion in the comments) and his contribution in improving the article is gratefully acknowledged.

Photo credit

[1] DThanhvp. Photobucket. http://s37.photobucket.com/user/DThanhvp/media/American.jpg.html

[2] Babinsky, H. (2003). How do wings work?. Physics Education 38(6) pp. 497-503. URL: http://iopscience.iop.org/article/10.1088/0031-9120/38/6/001/pdf;jsessionid=64686DBCB81FEB401CFFB87E18DFE6DA.c1
October 10, 2015
The Navier-Stokes Equation

The name we use for our little blue planet “Earth” is rather misleading. Water makes up about 71% of Earth’s surface while the other 29% consists of continents and islands. In fact, this patchwork of blue and brown, earth and water, makes our planet very unlike any other planet we know to be orbiting other stars. The word “Earth” is related to our longtime worldview based on a time when we were constrained to travelling the solid parts of our planet. Not until the earliest seaworthy vessels, which were believed to have been used to settle Australia some 45,000 years ago, did humans venture onto the water.

Not until the 19th century did humanity make a strong effort to travel through another vast sea of fluid, the atmosphere around us. Early pioneers in China invented ornamental wooden birds and primitive gliders around 500 BC, and later developed small kites to spy on enemies from the air. In Europe, the discovery of hydrogen in the 17th century inspired intrepid pioneers to ascend into the lower altitudes of the atmosphere using rather explosive balloons, and in 1783 the brothers Joseph-Michel and Jacques-Étienne Montgolfier demonstrated a much safer alternative using hot-air balloons.

The pace of progress accelerated dramatically around the late 19th century culminating in the first heavier-than-air flight by Orville and Wilbur Wright in 1903. Just 7 years later the German company DELAG invented the modern airline by offering commercial flights between Frankfurt and Düsseldorf using Zeppelins. After WWII commercial air travel shrunk the world due to the invention and proliferation of the jet engine. Until a series of catastrophic failures the DeHavilland Comet was the most widely-used aircraft but was then superseded in 1958 by one of the iconic aircrafts, the Boeing 707. Soon military aircraft began exploring the greater heights of our atmosphere with Yuri Gagarin making the first manned orbit of Earth in 1961, and Neil Armstrong and Buzz Aldrin walking on the moon in 1969, a mere 66 years after the first flight at Kittyhawk by the Wright brothers.

Air and space travel has greatly altered our view of our planet, one from the solid, earthly connotations of “Earth” to the vibrant pictures of the blue and white globe we see from space. In fact the blue of the water and the white of the air allude to the two fluids humans have used as media to travel and populate our planet to a much greater extent than travel on solid ground would have ever allowed.

Fundamental to the technological advancement of sea- and airfaring vehicles stood a physical understand of the media of travel, water and air. In water, the patterns of smooth and turbulent flow are readily visible and this first sparked the interest of scientists to characterise these flows. The fluid for flight, air, is not as easily visible and slightly more complicated to analyse. The fundamental difference between water and air is that the latter is compressible, i.e. the volume of a fixed container of air can be decreased at the expense of increasing the internal pressure, while water is not. Modifying the early equations of water to a compressible fluid initiated the scientific discipline of aerodynamics and helped to propel the “Age of Flight” off the ground.

One of the groundbreaking treatises was Daniel Bernoulli’s Hydrodynamica published in 1738, which, upon other things, contained the statement many of us learn in school that fluids travel faster in areas of lower than higher pressure. This statement is often used to incorrectly explain why modern fixed-wing aircraft induce lift. According to this explanation the curved top surface of the wing forces air to flow quicker, thereby lowering the pressure and inducing lift. Alas, the situation is slightly more complicated than this. In simple terms, lift is induced by flow curvature as the centripetal forces in these curved flow fields create pressure gradients between the differently curved flows around the airfoil. As the flow-visualisation picture below shows, the streamlines on the top surface of the airfoil are most curved and this leads to a net suction pressure on the top surface. In fact, Bernoulli’s equation is not needed to explain the phenomenon of lift. For a more detailed explanation of why this is so I highly recommend the journal article on the topic by Dr. Babinsky from Cambridge University.

Just 20 years after Daniel Bernoulli’s treatise on incompressible fluid flow, Leonard Euler published his General Principles of the Movement of Fluids, which included the first example of a differential equation to model fluid flow. However, to derive this expression Euler had to make some simplifying assumptions about the fluid, particularly the condition of incompressibility, i.e. water-like rather than air-like properties, and zero viscosity, i.e. a fluid without any stickiness. While, this approach allowed Euler to find solutions for some idealised fluids, the equation is rather too simplistic to be of any use for most practical problems.

A more realistic equation for fluid flow was derived by the French scientist Claude-Louis Navier and the Irish mathematician George Gabriel Stokes. By revoking the condition of inviscid flow initially assumed by Euler, these two scientists were able to derive a more general system of partial differential equations to describe the motion of a viscous fluid.

$\rho\left(\frac{\partial\boldsymbol{v}}{\partial t}+\boldsymbol{v}\cdot\nabla\boldsymbol{v}\right)=-\nabla p+\nabla\cdot\boldsymbol{T}+\boldsymbol{f}$

The above equations are today known as the Navier-Stokes equations and are infamous in the engineering and scientific communities for being specifically difficult to solve. For example, to date it has not been shown that solutions always exist in a three-dimensional domain, and if this is the case that the solution in necessarily smooth and continuous. This problem is considered to be one of the seven most important open mathematical problems with a $1m prize for the first person to show a valid proof or counter-proof.

Fundamentally the Navier-Stokes equations express Newton’s second law for fluid motion combined with the assumption that the internal stress within the fluid is equal to diffusive (“spreading out”) viscous term and the pressure of the fluid – hence it includes viscosity. However, the Navier-Stokes equations are best understood in terms of how the fluid velocity, given by $\boldsymbol{v}$ in the equation above, changes over time and location within the fluid flow. Thus, $\boldsymbol{v}$ is an example of a vector field as it expresses how the speed of the fluid and its direction change over a certain line (1D), area (2D) or volume (3D) and with time $t$ .

The other terms in the Navier-Stokes equations are the density of the fluid $\rho$ , the pressure $p$ , the frictional shear stresses $\boldsymbol{T}$ , and body forces $\boldsymbol{f}$ which are forces that act throughout the entire body such as inertial and gravitational forces. The dot is the vector dot product and the nabla operator $\nabla$ is an operator from vector calculus used to describe the partial differential in three dimensions,

$\nabla = \left(\frac{\partial}{\partial x},\frac{\partial}{\partial y},\frac{\partial}{\partial z}\right)$

In simple terms, the Navier-Stokes equations balance the rate of change of the velocity field in time and space multiplied by the mass density on the left hand side of the equation with pressure, frictional tractions and volumetric forces on the right hand side. As the rate of change of velocity is equal to acceleration the equations boil down to the fundamental conversation of momentum expressed by Newton’s second law.

One of the reasons why the Navier-Stokes equation is so notoriously difficult to solve is due to the presence of the non-linear $\boldsymbol{v}\cdot\nabla\boldsymbol{v}$ term. Until the advent of scientific computing engineers, scientists and mathematicians could really only rely on very approximate solutions. In modern computational fluid dynamics (CFD) codes the equations are solved numerically, which would be prohibitively time-consuming if done by hand. However, in some complicated practical applications even this numerical approach can be become too complicated such that engineers have to rely on statistical methods to solve the equations.

The complexity of the solutions should not come as a surprise to anyone given the numerous wave patterns, whirlpools, eddies, ripples and other fluid structures that are often observed in water. Such intricate flow patterns are critical for accurately modelling turbulent flow behaviour which occurs in any high velocity, low density flow field (strictly speaking, high Reynolds number flow) such as around aircraft surfaces.

Nevertheless, as the above simulation shows, the Navier-Stokes equation has helped to revolutionise modern transport and also enabled many other technologies. CFD techniques that solve these equations have helped to improve flight stability and reduce drag in modern aircraft, make cars more aerodynamically efficient, and helped in the study of blood flow e.g. through the aorta. As seen in the linked video, fluid flow in the human body is especially tricky as the artery walls are elastic. Thus, such an analysis requires the coupling of fluid dynamics and elasticity theory of solids, known as aeroelasticity. Furthermore, CFD techniques are now widely used in the design of power stations and weather predictions.

In the early days of aircraft design, engineers often relied on back-of-the-envelope calculations, intuition and trial and error. However, with the increasing size of aircraft, focus on reliability and economic constraints such techniques are now only used in preliminary design stages. These initial designs are then refined using more complex CFD techniques applied to the full aircraft and locally on critical components in the detail design stage. Equally, it is infeasible to use the more detailed CFD techniques throughout the entire design process due to the lengthy computational times required by these models.

Physical wind tunnel experiments are currently indispensable for validating the results of CFD analyses. The combined effort of CFD and wind-tunnel tests was critical in the development of supersonic aircraft such as the Concorde. Sound travels via vibrations in the form of pressure waves and the longitudinal speed of these vibrations is given by the local speed of sound which is a function of the fluids density and temperature. At supersonic speeds the surrounding air molecules cannot “get out of the way” before the aircraft arrives and therefore air molecules bunch up in front of the aircraft. As a result, a high pressure shock wave forms in these areas that is characterised by an almost instantaneous change in fluid temperature, density and pressure across the shock wave. This abrupt change in fluid properties often leads to complicated turbulent flows and can induce unstable fluid/structure interactions that can adversely influence flight stability and damage the aircraft.

The problem with performing wind-tunnel tests to validate CFD models of these phenomena is that they are expensive to run, especially when many model iterations are required. CFD techniques are comparably cheaper and more rapid but are based on idealised conditions. As a result, CFD programs that solve Navier-Stokes equations for simple and more complex geometries have become an integral part of modern aircraft design, and with increasing computing power and improved numerical techniques will only increase in importance over the coming years. In any case, the story of the Navier-Stokes equation is a typical example of how our quest to understand nature has provided engineers with a powerful new tool to design improved technologies to dramatically improve our quality of life.

References

If you’d like to know more about the Navier-Stokes equations or 16 other equations that have changed the world, I highly recommend you check out Ian Stewart’s book of the same name.

Ian Stewart – In Pursuit of the Unknown: 17 Equations That Changed the World. Basic Books. 2013.

August 6, 2015
Engineering – A Manifesto

“Engineering is not the handmaiden of physics any more than medicine is of biology”

What is science? And how is it different from engineering? The two disciplines are closely related and the differences seem subtle at first, but science and engineering ultimately have different goals.

A scientist attempts to gain knowledge about the underlying structure of the world using systematic observations and experimentation. Scientists are experts in dealing with doubt and uncertainty. As the great Richard Feynman pointed out: “When a scientist doesn’t know the answer to a problem, he is ignorant. When he has a hunch as to what the result is, he is uncertain. And when he is pretty darned sure of what the result is going to be, he is in some doubt” [1]. The body of science is a collection of statements of varying degrees of certainty, and in order to allow progress, scientists need to leave room for doubt. Without doubt and discussion there is no opportunity to explore the unknown or discover new insights about the structure and behaviour of the world.

In the same manner, the role of the engineer is to explore the realm of the unknown by systematically searching for new solutions to practical problems. Engineering is less about knowing (or not knowing), and more about doing; it is about dreaming how the world could be, rather than studying how it is. Engineers rely on scientific knowledge to design, build and control hardware and software, and therefore apply scientific insights to devise creative solutions to practical problems.

I bring up this seemingly superfluous topic because even seasoned journalists can confuse, perhaps unwillingly, the differences between the two endeavours. This article in the Guardian about the recent landing of Philae on Comet 67P refers to the great success of “scientists” on multiple occasions, but fails to give due credit to “engineers” by referring to their role only once. So, is landing a machine on an alien body hurtling through space a scientific or an engineering achievement?

There is certainly no straightforward answer to this question. Both scientists and engineers were indispensable in the success of the Rosetta program. However, in paying credit to the fantastic achievement of engineers involved in this space endeavour, I will leave you with this brief letter by three University of Bristol professors, that so poetically captures the essence of engineering:

Landing Philae on Comet 67P from the Rosetta probe is a fantastic achievement (One giant heartstopper, 14 November). A tremendous scientific experiment based on wonderful engineering. Engineering is the turning of a dream into a reality. So please give credit where credit is due – to the engineers. The success of the science is yet to be determined, depending on what we find out about the comet. Engineering is not the handmaiden of physics any more than medicine is of biology – all are of equal importance to our futures.

– Emeritus professor David Blockley, Professor Stuart Burgess, Professor Paul Weaver, University of Bristol

References

[1] “What Do You Care What Other People Think?: Further Adventures of a Curious Character” by Richard P. Feynman. Copyright (c)1988 by Gweneth Feynman and Ralph Leighton.

June 19, 2015
Variable Stiffness Composites

In previous posts I have discussed the unique characteristics and manufacturing processes of a certain type of composite material, namely continuous fibre-reinforced plastics (FRPs). Just like many other composite materials, FRPs combine two or more materials whose combined properties are superior (in a practical engineering sense) to the properties of the constituent materials on their own. What distinguishes FRPs from other composites such as short-fibre composites, nanocomposites or discrete particle composites are the highly aligned, long bundles of fibres typically glass or carbon that are arranged in a specific direction within some resin system.

The biggest advantage of FRPs compared to metals is not necessarily their greater specific strength and stiffness (i.e. strength/density and stiffness/density) but the increased design freedom to tailor the structural behaviour. Metals and ceramics, being isotropic materials, behave in an intuitive way since the majority of the coupling terms in the stiffness tensor vanish. If you a imagine a three-dimensional cube and pull two opposing faces apart then the other two pairs of opposing faces will move towards each other. This phenomenon of coupling between tension and compression is known as the Poisson’s effect and aptly captured by the Poisson’s ratio.

The Poisson’s effect in action

In bending, a similar phenomenon occurs known as anti-clastic curvature. If you have ever tried bending a thin, beam-like structure made out of a soft material e.g. a rubber eraser, you might have noticed that the beam wants to develop opposite curvature in the transverse direction to the main bending axis. The structure morphs into some form of saddle shape as shown in the figure. The phenomenon occurs because the bending moment applied by the person in the picture causes tension in the top surface and compression in the bottom surface in the direction of applied bending. From the Poisson’s effect we know that this induces compression in the top surface and tension in the bottom surface in the transverse direction. By analogy, this is exactly the reverse of the bending moment applied by the hands and so the panel bends in the opposite sense in the transverse direction.

Anticlastic curvature in action (1)

For isotropic materials the fundamental linear constitutive equations between stress and strain eliminate a lot of the possible coupling behaviour. There is no coupling between applied bending moments and twisting. No coupling between stretching/compressing and bending/twisting. And also no coupling between stretching/compressing and shearing. FRPs, being orthotropic materials, i.e. having two orthogonal axes of different material properties, can display all of these effects. Consider a single layer of a continuous fibre-reinforced composite in the figure below. The material axes 1-2 denote the stiffer fibre in the 1-direction and the weaker resin in the 2-direction. If we align the fibres with the global x-axis and apply a load in the x-direction, the layer will stretch/compress along the fibres and compress/stretch in the resin direction in the same way as described previously for isotropic materials. However, if the fibres are aligned at an angle to the x-direction say 45°, and a load is applied in the x-direction then the layer will not only stretch/compress in the x-direction and compress/stretch in the y-direction but also shear. This is because the layer will stretch/compress less in the fibre direction than in the resin direction. This effect can be precluded if the number of +45° layers is balanced by an equal amount of -45° layers stacked on top of each other to form a laminate, e.g. a [45,-45,-45,45] laminate. However, this [45,-45,-45,45] laminate will exhibit bend-twist coupling because the 45° layers are placed further away from the mid plane than the the -45° layers. The bending stiffness of a layer is a factor of the layer thickness cubed and the distance from the axis of bending (here the mid plane) squared. Thus, the outer 45° layers contribute more to the bending stiffness of the laminate than the -45° layers such that the coupling effects do not cancel.

A single fibre reinforced plastic layer with material and global coordinate systems

Using metals, structural designers were constrained to tailoring the shape of a structure to optimise its performance i.e. thickness, length and width, and overall profile/shape. FRPs however add an extra dimension for optimisation by allowing designers to tailor the properties through the thickness and thereby achieve all kinds of interesting effects. For example, forward-swept wings on aircraft have and still are a nightmare due to aeroelastic instabilities like flutter and divergence. Basically, sweeping a wing forward is a neat idea because the airflow over swept wings flows spanwise towards the end furthest to the rear of the plane. Therefore, the tip-stall condition characteristic of backward-swept wings is moved towards the fuselage where it can be controlled more effectively. The drawback is that as the lift force bends the wingtip upwards the angle of attack increases, further increasing the lift and thereby causing more bending, and so on until the wings snap off or fail. Rather than adding more material to the wing to make it stiffer (but also heavier) an alternative solution is to use the bend-twist coupling capability of composite laminates. This was successfully achieved in the iconic Grumman X-29. As the bending loads force the wing tips to bend upward and twist the wing to higher angles of attack, the inherent bend-twist coupling of the composite laminate used forces the wing to twist in the opposite direction and thereby counters an increase in the angle of attack. This is an excellent example of an efficient, autonomous and passively activated control system to prevent divergence failure.

Grumman X-29 with forward-swept wings

In this manner, straight fibre composites allow structural engineers to change the stiffness and strength properties through the thickness in order to tailor the structural behaviour. The concept of variable stiffness composites adds a further dimension to the capability for tailoring. Currently this is achieved by spatially varying the point wise fiber orientations by actively steering individual fibre tows using automatic fibre placement machines. One early application that was considered by researchers was improving the stress concentrations around holes by steering fibres around them.

Automated Fibre Placement machine (2)

This concept can be generalised by aligning fibres with the direction of local primary load paths which could vary across different parts of the structure. Tow steering creates the possibility for designing blended structures by facilitating smooth transitions between areas with different layup requirements. One promising application of variable stiffness composites is in buckling and postbuckling optimisation of flat and curved panels. As a panel is compressed uni-axially the capability of the panel to resist transverse bending loads reduces until a critical level is reached where the panel has lost all capability to sustain any bending loads. At this point known as the buckling load, the fundamental state of compression becomes unstable and the panel buckles outward in a single or multiple waves. It has been found that variable stiffness composites can double the buckling load of flat panels by favourably redistributing the load paths in the fundamental, pre-buckling compression state. Essentially, the middle of the panel where the buckling waves will occur is offloaded, and the edges of the panel are forced to take more load. Thus, the aim is to redirect loads to locally supported regions and remove load from regions remote from supported boundaries. This concept has also been extended to improving aircraft fuselage sections and blade-stiffened panels.

A variable angle tow laminate (3)

This new technology is viewed as a promising candidate for further reducing the mass of future aerospace structures. In fact recently NASA Langley Research Centre announced that they are investing heavily in this capability. The possibility of manufacturing integrated structures with smooth flow of material between components and minimal joints will not only revolutionise stress-based design, but also simplify manufacturing and facilitate entirely new aircraft designs that are currently unfeasible. In trees for example, there is a smooth transition of fibres from the trunk into the branches to strengthen the connecting joint. With the variable stiffness capabilities investigated by NASA we could apply this concept to simplify and even strengthen critical interfaces such as fuselage-wing connections.

References

(1) http://www.astm.org/HTTP/IMAGES/70104.gif

(2) http://csmres.co.uk/cs.public.upd/article-images/Premium-nordenham.jpg

(3) Kim et al. (2012). “Continuous Tow Shearing for Manufacturing Variable Angle Tow Composites”. Composites: Part A, 43, pp. 1347-1356

January 27, 2015
The Airline Metro System

When I was travelling in Chile a short while ago I took a flight from the capital Santiago de Chile to the city of Calama in the Atacama dessert. What was interesting about this flight, was that on its way to Calama the airplane landed for a short stop in Copiapó. Immediately after leaving the runway the doors opened, a couple of people got off and were immediately replaced by others already waiting on the tarmac. I had never seen this metro-style system of operating an airline before and was surprised how efficient this system was being implemented. I was also struck by the albeit ludicrous idea of operating an air-bus (no pun intended) style fixed travel route between major European cities, say London-Paris-Madrid-Rome-Vienna-Berlin-London, with people hopping on and off at their pleasure. How cool would that be?

I understand that the fixed costs of this system would be relatively high, and making any money on the tight margins that airliners are operating on would be incredibly tough. However, research is currently ongoing to realise a similar system for long distance travel. One possibility is exploiting the concept of air-to-air refuelling that has been used by the military and the Air Force One for many years. A collaborative European study Research on a Cruiser-Enabled Air Transport Environment (Recreate) has been running simulations at the National Aerospace Laboratory (NLR) in Amsterdam since 2011. The aim of these simulations is to investigate the technical challenges and potential savings of refuelling airliners in midair.

Leading Boeing 707 refuelling a trailing 747 using a rearward extended boom

This may sound like a fanciful notion but given that airlines have to cut the 2005 carbon emissions in half by 2050 it well worth looking into these radical ideas. In fact, preliminary results of the study show that fuel burn could be reduced by 11% to 23% if airliners could be refuelled by tanker planes. Passenger safety being paramount in civil aircraft the military concepts currently in use will have to be adapted to meet the required reliability standards. In military environments the tanker flies ahead of the aircraft and supplies fuel through a boom from above. To reduce the likelihood of collisions a forward extending boom refuelling from the bottom is the solution preferred by the researchers. In this manner the civil aircraft does not fly in the wake of the tanker, which could affect turbulence and passenger comfort. Furthermore, the responsibility and training remains with the tanker pilots who have better visibility of the refuelling process when flying from the rear.

The researchers also intend to take the concept one step further by exchanging cargo and passengers in midair, thus getting closer to the idea of an airline metro system. This research envisions a new type of large cruising airliner that is fed by much smaller feeder planes. In this scenario, the larger cruisers fly fixed routes over large distances, while the smaller feeders exchange passengers, crew and cargo with the cruiser in midair. One major challenge with the scheme is that the cruiser aircraft will require an incredible durable engine with low fuel consumption. Such a system does not seem to be economically feasible using current chemically fuelled jet engines. The greater amounts of fuel to be stored has to be offset by a larger engine and airframe, which naturally increases the loads on components in turn requiring thicker sections and structures. Thus, with current gas-fuelled engines you are very much caught in the downward payload spiral that is so frustrating in rocketry.

But what if the cruisers are propelled by nuclear engines? Well the efficiency of the system improves significantly. In fact the efficiency gains are so great that a large cruiser could fly continuously for a whole year just on a few litres of gasoline. Powered by nuclear fusion a cruiser could stay airborne for months, and passengers could hop on and off a continuously airborne global fleet of international airlines.

And it turns out that in October 2014 Lockheed Martin’s Skunk Works announced that they could have a prototype fusion reactor ready within five years and a working production engine within ten. The obvious “buts” are that that a fusion process requires temperatures in the millions of degrees in order to separate ions from electrons which creates hot plasma in the process. In fusion the danger is not a nuclear fallout as is the case in fission. The problem with fission engines is that they require shielding to protect passengers and also carry the dangers of spreading radioactive material in the event of a crash. In a fusion engine the difficulty is in stabilising the plasma and safely containing it in the reactor to guarantee the fusion of ions. The Skunk Works are currently working on an eloctro-magnetic suspender system to guarantee a stable reaction. Furthermore, neutrons that are emitted in the fusion process can damage the materials in the containing structure and turn them radioactive. Thus materials that minimise this radioactivity are needed. Finally, the fusion reactors need to be miniaturised from the scale of family houses to something more akin of an SUV. In that event fusion reactors will also become an interesting propulsion method for spaceships and other spacecraft that have limited space for power generation.

While this is all science fiction for now it presents an interesting option for facilitating a global metro-style airline system. And how cool would that be?

January 17, 2015
The Evolution of Airplanes
Adrian Bejan is a Professor of Mechanical Engineering and Materials Science at Duke University and as an offshoot from his thermodynamics research he has pondered the question why evolution exists in natural i.e. biological and geophysical, and man-made, i.e. technological, realms. To account for the progress of design in evolution Prof. Bejan conceived the constructal law, which states that

For a finite-size flow system to persist in time (to live), its configuration must evolve (freely) in such a way that it provides easier access to the currents that flow through it.

In essence a new technology, design or species emerges so that it offers greater access to the resources that flow i.e. greater access to space and time. The unifying driver behind the law is that all systems that output useful work have a tendency to produce and use power in the most efficient manner.

The Lena Delta. Photo Credit Wikipedia [1]

Given Prof. Bejan’s specialty in thermodynamics it is no surprise that the law uses the analogy of a flow system to describe the evolution of design. In nature the branches of rivers carry water, nutrients and sediments to the sea, and if given enough freedom, over time evolve into a river delta that provides a source of life for an entire area. Similarly, our lungs facilitate flow of chemical energy between air and blood and have evolved into a complex multi-branch system that aims to improve the flow of currents within it.

A difficulty in studying natural evolution is that it occurs on a time-scale much greater than our lifetime. However, in a recent study published in the Journal of Applied Physics Prof. Bejan and co-workers show that the shorter technological evolution of airplanes allows us to witness the phenomenon from a bird’s-eye view. Interestingly, as a “flying machine species” the evolution of airplanes follows the same physical principles of evolution that are observed in birds and that can be captured elegantly using the constructal law. For example, the researchers found that
- Larger airplanes travel faster. In particular the flight velocity of aircraft is proportional to its mass raised to the power 1/6, i.e. $V = k M^{1/6}$
- The engine mass is proportional to body mass, much in the same way that muscle mass and body mass are related in animals
- The range of an aircraft is proportional to its body mass, just as larger rivers and atmospheric currents carry mass further, and bigger animals travel farther and live longer.
- Wing-span is proportional to fuselage length (body length), and both wing and fuselage profiles fit in slender rectangles of aspect ratio 10:1
- Fuel load is proportional to body mass and engine mass, and these scale in the same way as food intake and body mass in animals.
This overall trend is depicted nicely in Figure 1 which shows the size of new airplane models against the year they were put into service. It is evident that the biggest planes of one generation are surpassed by even bigger planes in the next. Based on economical arguments it can be assumed that each model introduced was in some way more efficient in terms of passenger capacity, speed, range, i.e. cost-effectiveness than the previous generation of the same size. Thus, in terms of the constructal law the spreading of flow is optimised and this appears to be closely matched with the airplane size and mass. Similarly, Figure 2 shows that both birds and aircraft evolve in the same way in that the bigger fly faster. Thus, the evolution of natural and technological designs seems to have converged on the same scaling rules. This convergent design is also evident in the number of new designs that appear over time. At the start of flight the skies were dominated by swarms of insects of very different design. These were followed by a smaller number of more specialised bird species and today by even fewer “aircraft species”. Combining these two ideas of size and number, it seems that the new are few and large, whereas the old are many and small.

Figure 1. Evolution of airplane mass versus time [2]

Figure 2. Evolution of animal flight speed versus body mass [2]

The key question is why engines, fuel consumption or wing sizes should have a characteristic size?

Any vehicle that moves and consumes fuel to propel it depends on the function of specific organs, say the engines or fuel ducts, that interact with the the fuel. Because there is a finite size constraint for all these organs the vehicle performance is naturally constrained in two ways:
1. Resistance, i.e. friction and increasing entropy within the organs. This penalty reduces for larger organs as larger diameter fuel ducts have less flow resistance and larger engines encounter less local flow problems. Thus, larger is generally better
2. On the flip side the larger the organ the more fuel is required to move the whole vehicle. But the more fuel is added the more the overall mass is increased and the more fuel you need, and so on. This suggests that smaller is better.
From this simple conflict we can see that a size compromise needs to be reached, not too small and not too large, but just right for the particular vehicle. In essence what this boils down to is that larger organs are required on proportionally large vehicles and small organs on small vehicles. Thus, as more and more people intend to travel and move mass across the planet the old design based on small organs becomes imperfect and a more efficient, larger design for the new circumstances is required.

Overall, the researchers conclude that the physical principles of evolution define the viable shape of an aircraft. Thus, the fuselage and the wing must be slender, the fuselage cross-section needs to be round and the wing span must be proportional to the fuselage length. A famous outlier that broke with these evolutionary trends of previous successful airplanes was the Concorde with its long fuselage, massive engines and short wingspan. Rather than attempting to achieve an overall superior solution the designers attempted to maximise speed, and thereby compromised passenger capacity and fuel efficiency. Only 20 units were ever produced and due to lack of demand and safety concerns the Concorde was retired in 2003. Current aircraft evolution manifested in the Boeing 787 Dreamliner, 777X and Airbus A350 XWB are rather based on combining successful architectures of the past and with new concepts, that allow the overall design to remain within the optimal evolutionary constraints. Thus, it is no surprise that in an attempt to make aircraft larger and at the same time more efficient, the current shift from metal to carbon fibre construction is what is needed to elevate designs to a higher level.

References

[1] http://en.wikipedia.org/wiki/Lena_Delta_Wildlife_Reserve#mediaviewer/File:Lena_River_Delta_-_Landsat_2000.jpg

[2] Bejan, A., Charles, J.D., Lorente, S. The evolution of airplanes. Journal of Applied Physics, 116. 2014.
December 9, 2014
Human Fallibility in Aviation II: Case Study

Vanity Fair recently featured an excellent article on Air France Flight 447 that crashed into the Atlantic in 2009. It is a long read, but if you have 30 min to spare it will be a great educational investment.

The author, William Langewiesche, does a good job at weaving multiple aspects of aeronautics, such as cockpit design, ergonomics, the physics of flight and pilot training, into a story that is ultimately about the role of human fallibility in a system that is governed by automation. This is a topic that I find highly fascinating and will only become more pertinent in the future as computers take over increasing number of tasks in the cockpit. In fact, the psychological impact on the pilots and the effect of automation on the piloting profession on a whole remain uncertain.

The article features extensive coverage of the pilots’ conversation and provides a riveting account of what transpired in the cockpit prior to the crash. In this way the article brings to light some of the human misjudgements that ultimately led to the catastrophe. On some occasions I found myself cringing at the incredulity of the events that transpired, futilely hoping that the pilots would turn the situation around and save the 228 passengers onboard, while fully aware that hindsight makes all mistakes appear tauntingly clear.

The reason for the plane crash was a classic case of aerodynamic stall brought on by the pilot climbing too quickly and exceeding the critical angle of attack, depending on the operating conditions in the range of 13-16°. Even when the angle of attack was at an incredible 41°, the aircraft was rolling from side to side, the alarm system was screaming “STALL”, the cockpit was shaking violently due to the turbulent flow separation over the wings and the aircraft was losing altitude at a rate of 4,000 feet per minute, each one a tale-tell signs of aerodynamic stall, the pilots did not know what was happening with the airplane!

What brought the aircraft into this situation in the first place? The pitot static tube used as sensors for the flight speed had been clogged by a hail storm, which automatically took the fly-by-wire system out of the auto-pilot, disabled the automatic stall recovery system and returned the controls back to the pilots. At this point had the pilots continued the modus operandi of keeping the aircraft at the same altitude with the engines at constant thrust, nothing would have happened. It is ironic, that the only thing the pilots needed to do to keep the plane safely in the air was nothing. It is unclear why one of the pilots decided to climb to a higher altitude and especially why this was done so rapidly, but this ultimately triggered the aerodynamic stall of the wings.

William Langewiesche argues that increasing automation “de-skills” pilots, essentially rendering them incapable of flying an aircraft without support systems. I find the following section especially interesting:

“For commercial-jet designers, there are some immutable facts of life. It is crucial that your airplanes be flown safely and as cheaply as possible within the constraints of wind and weather. Once the questions of aircraft performance and reliability have been resolved, you are left to face the most difficult thing, which is the actions of pilots. There are more than 300,000 commercial-airline pilots in the world, of every culture. They work for hundreds of airlines in the privacy of cockpits, where their behavior is difficult to monitor. Some of the pilots are superb, but most are average, and a few are simply bad. To make matters worse, with the exception of the best, all of them think they are better than they are. Airbus has made extensive studies that show this to be true.”

So how has this been dealt with in the past?

“First, you put the Clipper Skipper [daring WW II fighter pilots] out to pasture, because he has the unilateral power to screw things up. You replace him with a teamwork concept—call it Crew Resource Management—that encourages checks and balances and requires pilots to take turns at flying. Now it takes two to screw things up. Next you automate the component systems so they require minimal human intervention, and you integrate them into a self-monitoring robotic whole. You throw in buckets of redundancy. You add flight management computers into which flight paths can be programmed on the ground, and you link them to autopilots capable of handling the airplane from the takeoff through the rollout after landing. You design deeply considered minimalistic cockpits that encourage teamwork by their very nature, offer excellent ergonomics, and are built around displays that avoid showing extraneous information but provide alerts and status reports when the systems sense they are necessary. Finally, you add fly-by-wire control. At that point, after years of work and billions of dollars in development costs, you have arrived in the present time. As intended, the autonomy of pilots has been severely restricted, but the new airplanes deliver smoother, more accurate, and more efficient rides—and safer ones too.”

This essentially causes a shift in the piloting profession…

“In the privacy of the cockpit and beyond public view, pilots have been relegated to mundane roles as system managers, expected to monitor the computers and sometimes to enter data via keyboards, but to keep their hands off the controls, and to intervene only in the rare event of a failure. As a result, the routine performance of inadequate pilots has been elevated to that of average pilots, and average pilots don’t count for much[…]Once you put pilots on automation, their manual abilities degrade and their flight-path awareness is dulled: flying becomes a monitoring task, an abstraction on a screen, a mind-numbing wait for the next hotel.[…] For all three [pilots on Air France Flight 447], most of their experience had consisted of sitting in a cockpit seat and watching the machine work.”

We all know that automation is indispensable going forward. It is too valuable a system and has made aviation the safe mode of transport it is today. However, the issues raised above will need to be addressed within the near future. Possible solutions may be requiring pilots to turn off auto-pilot for a certain number of flights, while another approach may be to improve the machine-human interaction in the cockpit. In either case, I think it is important to point out that catastrophes such as Air France Flight 447 are outliers, black swans, six-sigma events that are not likely to repeat again in the same detail. In fact, the roots of the next catastrophe may lie somewhere completely different and thus are impossible to predict.

References

[1] William Langewiesche, “The Human Factor”, Vanity Fair, October 2014. http://www.vanityfair.com/business/2014/10/air-france-flight-447-crash

October 15, 2014