Veronica Foreman is a payload engineer at the small-satellite launch provider Virgin Orbit. Before starting her career at Virgin Orbit, Veronica earned several academic accolades including an Outstanding Undergraduate Researcher Award at Georgia Tech, and a Best Masters Thesis award at MIT. What I find especially impressive about her Masters work on small-satellite constellations is that Veronica considered both the design of constellations, as well as the economic and policy challenges to small-satellite mission success.
As Virgin Orbit’s mission is to be the premier dedicated launch service for small satellites, Veronica has seemingly found the perfect place for her expertise and passion. One of the key features of Virgin Orbit’s launch design is its air-launching system that drops the rocket (LauncherOne) from the wing of a Boeing 747 (Cosmic Girl), providing a movable launchpad. As Veronica explains in this episode, this capability provides Virgin Orbit unique advantages in terms of providing a dedicated launch service for small satellites. In this episode of the Aerospace Engineering podcast, Veronica and I discuss:
Virgin Orbit’s vision
the unique advantages and challenges of an air-launched rocket system
some of Virgin Orbit’s key engineering technologies
and the growing importance of satellite constellations
Mark Crouchen is the managing director of Rockwood Composites, a company in the UK that specialises in manufacturing complex composite components using compression and bladder moulding. These manufacturing processes use fibre mats of carbon fibre, glass fibre, Kevlar, or any other material, which are pre-impregnated with a resin matrix and then placed in a mould, where they are cured at elevated temperature with the addition of external or internal pressure.
The team at Rockwood has been supplying the aerospace, defense, medical and nuclear industries for over 25 years, with customers ranging from Leonardo Helicopters and the McLaren Formula 1 team to Safran and Facebook’s Aquila internet drone. In 2018, Rockwood won the Innovation in Manufacture award at the Composite UK industry event for their innovative use of advanced composite materials on the Tokomak ST40 nuclear fusion reactor. Composite materials have many benefits in terms of their excellent strength and stiffness at low weight. However, there is a common misconception that metal or ceramic components can easily be replaced one-to-one with composite components. The performance of any composite component is closely linked to the quality of the manufacturing process, and designing and manufacturing quality components is an area where Rockwood Composites particularly excel. In this episode of the podcast, Mark and I talk about:
his background in engineering
the types of structures that Rockwood Composites manufacture
why composites manufacturing is a challenge
and the special solution Rockwood found for the Tokomak ST40 fusion reactor
Oliver Family is the Overall Aircraft Design Leader of the Airbus E-Fan X demonstrator. The E-Fan X is a hybrid-electric technology demonstrator being developed by Airbus, Rolls-Royce and Siemens based on a British Aerospace 146 regional airliner. The driver behind the E-Fan X demonstrator is that current aircraft designs have converged to a near-optimum, and with existing technologies, it is difficult to meet the stringent sustainability goals in terms of CO2/NOX emissions and reductions in noise. New technologies, such as electrification, are therefore required to achieve these goals.
As we have seen on other episodes of the podcast, electrification of aircraft is currently a hot topic with new start-up companies promising to disrupt and revolutionise the regional aircraft market. In this environment, one may assume that incumbents like Airbus are too slow to react to a changing technology landscape. As you will hear in this episode, nothing could be further from the truth. The E-Fan X project is structured as a separate entity within Airbus with the explicit mission of challenging Airbus’ legacy business. As you will hear, the consequences of integrating an electric propulsion system on a regional aircraft run much deeper than mere calculations about battery power density and battery longevity. In fact, it’s the secondary effects that we rarely think, hear and read about, such as thermal management of batteries; the interaction between pilots and new control systems; and the challenges of new certification protocols, that are especially challenging. So in this episode, Oliver and I discuss:
what exactly the E-Fan X demonstrator aims to achieve
the main technical and economic challenges of electric aircraft
and how electrification widens the design envelope for engineers
“We need to get going into the future in terms of clean aviation” — Kim-Tobias Kohn
On this episode of the podcast I speak to Kim-Tobias Kohn who is a lecturer in Aerospace Engineering at the University of the West of England. Beside his main vocation, Kim is also an avid pilot and runs an electric skateboard startup company. Kim has garnered attention in the media and from aerospace societies in the UK for his unique university project of building an electric glider with his undergraduate students. For obvious reasons, building an electric passenger aircraft that can replace current fuel-powered airliners is significantly more challenging than replacing gasoline cars with electric vehicles. However, there is a growing grass-roots initiative developing in the UK that is attempting to solve some of the regulatory and technical challenges to realise this vision of electric aviation.
So in this episode Kim and I talk about:
the unique regulatory framework for experimental aircraft in the UK known as the E-conditions
the major technical hurdles that need to be overcome to make electric aviation a reality
how the UAV/drone sector is opening doors for larger-scale electric aviation
his university project of building an electric glider
his dreams for a student-led design, build and fly competition for electric aircraft
“If you’re trying to put these structures into orbit, every gram counts. Not just every pound but every gram…So you are making structures that are operating at their margins.” — Dr Chauncey Wu, NASA Langley Research Center
Today’s conversation features Dr Chauncey Wu, who is a research engineer at NASA Langley Research Center in Hampton, Virginia. Chauncey has worked at NASA for more than 30 years, predominantly in the field of structural mechanics, and has been responsible for designing and testing a number of space structures that have been launched into space. Some examples of his work include structural analyses on the LITE telescope that was launched into space in 1994, as well as the optimisation of rocket propellant tank structures, and conceptual design studies of lunar lander vehicles and habitat structures for the colonisation of the Moon. In this wide-ranging conversation, we discuss:
Chauncey’s path to NASA as an undergraduate student
The history of NASA and the cultural shift compared to its predecessor, the NACA
The reason why rocket science is so hard
Chauncey’s recent research on a new type of lightweight composite material: tow-steered composites, which could be a game-changer for rocket booster designs
I am happy and excited to announce a new project on the Aerospace Engineering Blog. To go along with the usual blog posts, I will now be releasing regular podcast episodes that feature conversations with engineers and researchers in industry and academia to reveal their fascinating real-world stories of innovation, and provide a glimpse into the future of the industry by discussing cutting-edge research and promising new technologies. This episode is just a quick primer of what I have in mind, and the first “real” episode will be released in a couple of days.
A very important parameter when designing jet engines is specific power — the amount of power output divided by the mass of the engine. In general, a good heuristic to keep in mind when designing anything that moves is that maximising the power output per unit mass leads to a more efficient design. Afterburning is an exception to this rule. Yes, afterburning provides more thrust and therefore provides more bang for every gram of jet engine, but it is terribly fuel inefficient.
Afterburning, sometimes also called reheat, is a means of increasing the thrust of a jet engine in order to improve aircraft take-off and climb performance, to accelerate beyond the sound barrier, or in a military setting, for improved combat performance. Of course, we could simply increase the thrust by building a bigger and more powerful engine, but this naturally leads to a greater frontal area that impedes the oncoming flow, and therefore increases drag. Even though afterburning is incredibly fuel-inefficient, it is the best solution for enabling massive amounts of additional thrust at the switch of a button. This means an engine can be run in two modes – a fuel efficient, low thrust configuration and a fuel-inefficient, high-thrust configuration.
Effect of afterburning during take-off and climbing [1]
From conservation of momentum we know that the thrust of a jet engine is governed by the mass flow rate, , and the difference between the entry and exit velocities of air into, , and out of, , the jet engine.
For a fixed airspeed , this means that the level of thrust depends on both the exit jet velocity of the gases and the mass of air flowing through the engine per second. So to produce high levels of thrust we can either accelerate the exhaust gases to a greater velocity, or just increase the amount of air that is being sucked into the engine. Early turbojets attempted to maximise the exit jet velocity in order to create more and more thrust. The downside of this approach is that it decreases the efficiency of the engine. The propulsive or Froude efficiency of a jet engine is defined by the power output divided by the rate of change of kinetic energy of the air. The kinetic energy of the air represents the power input to the system. The power output is the product of force output, i.e. the thrust and the resulting air speed . Although this is an approximation, this equation summarises the essential terms that define aircraft propulsion. So, power output is
and the rate of change in kinetic energy is
such that the propulsive efficiency is
This means that for a fixed airspeed , the efficiency can be increased by reducing the jet exit velocity . However, decreasing the jet exit velocity decreases the thrust unless the mass flow rate is increased as well. Note that the advantage of increasing the mass flow rate is that it does not have an effect on the propulsive efficiency.
Schematic Diagram of Turbofan Engine
High bypass-ratio turbofan engines, which are the most common in modern airliners, are designed around this second principle – the big fan at the front sucks in tons of air, but because this flow bypasses the combustion chamber, it is not accelerated to a high exit velocity. The advantages of this design is that increasing the bypass ratio yields better fuel efficiency which means that turbofans can be operated over long periods (great for long-haul commercial passenger flights).
The downside, of course, is increased size and induced drag, which is a nightmare for nimble fighter aircraft. In fighter aircraft you want a small and compact engine that provides tons of thrust. Fuel efficiency is typically of secondary concern. Therefore, an afterburner naturally addresses the first principle we discussed above – accelerating the exhaust gases to higher velocity. This generally means that we can shrink the size of the engine and decrease the bypass ratio to provide better aerodynamic performance.
Schematic of afterburning components and functionality at the tail end of a jet engine [1]
As shown in the figure above, afterburning is achieved by injecting extra fuel into the hot exhaust gases that are being expelled by the turbine stage. The gas inside the jet engine is highest just before entering the turbine (just after combustion), and this turbine entry temperature is often the limiting design driver of the entire jet engine. Today, the turbine entry temperature is actually greater than the melting point of the metal used to make the turbine blades, but clever single-casting manufacturing methods and intricate cooling ducts inside the turbine blades guarantee that the blades do not creep excessively. To further limit the turbine entry temperature the combustion just prior to the turbine stage typically occurs at an oxygen-rich ratio such that sufficient oxygen is present in the hot gases flowing through and exiting the turbine. The hot jet exiting the turbine contains sufficient uncombusted oxygen that spraying more fuel into the jet pipe, and igniting the ensuing fuel-oxygen mix with a little spark raises the temperature to about 1700°C, and the related increase in the pressure forces the gases through the exhaust nozzle at increased velocity.
The hot jet from the turbine flows into the jet pipe at a velocity of around 250 m/s to 400 m/s, and this velocity is far too high to guarantee stable combustion in the jet pipe. Just prior to the jet pipe, the cross-sectional area of the exit portion to the turbine increases to diffuse the flow to lower velocities. However, because the standard injection rate of kerosene at a good fuel-to-oxygen mixture is only around 1-2 m/s, the kerosene would be rapidly blown away even by the diffused jet stream. To prevent this a vapour gutter is placed just prior to the fuel injection nozzles that spins the jet into turbulent eddie currents, thereby further slowing down the hot turbine exhaust gases and allowing for a better mixture of fuel and jet stream. A common misconception is that due to the high temperature of the gases exiting the turbine (around 700°C), the fuel-oxygen mixture in the jet pipe would combust spontaneously. Cooler combustion flames can develop at these temperatures, but because of the atmospheric pressure differences between ground level and altitude, a design that spontaneously combusts at ground level would never do so at altitude. To guarantee a stable and smooth reaction over a wide range of mixture ratios and flying altitudes, a high-intensity spark is needed.
Two-position nozzle [1]Variable-area nozzle [1]
To allow the jet to operate without afterburning, the jet pipe is fitted with a two-position or a variable-area propelling nozzle as shown above. When afterburning is not being used, the nozzle remains in its closed configuration, but opens when afterburning is initiated to increase the exit area and prevent pressure from building up in the jet pipe that can adversely affect the operation of the turbine. A two-position nozzle has two “eyelids” that can be moved irrespective of the other in order to open or close the nozzle area. A variable-area nozzle consists of multiple flaps situated side-by-side in a ring arrangement around the exit nozzle and hinged to the outer casing. The nozzles can rotate into or out of the flow by rotating rollers that are actuated by a camtrack and a linear actuator (operating ram). When afterburning is initiated, a fuel control unit determines the correct amount of fuel to flow into the jet pipe to provide the correct balance between increased jet pipe pressure and the pressure ratio across the turbine. The pressure ratio across the turbine is crucial for efficient operation of the jet engine as it provides the energy to operate the compressor stages. Therefore, the control system can automatically vary the nozzle exit area in order to maintain the correct pressure ratio across the turbine – the higher the degree of afterburning, the greater the build-up of pressure in the jet pipe, and thus, the greater the required nozzle area to reduce the load on the turbine.
Thrust and fuel consumption
The increase in thrust is a function of the increase in jet pipe temperature as a result of afterburning. For a perfectly efficient system, the relationship between the temperature ratio before and after fuel is burnt, and the thrust increase is nearly linear in the typical operating range with temperature ratios of 1.4 to 2.2. Within this range we can expect a 40% increase in thrust for a doubling of the temperature in the jet pipe. Thus, if afterburning raises the jet pipe temperature from 700°C (973 K) to 1500°C (1773 K) this results in a thrust increase of around 36%.
In a static test bed, thrust increases of up to 70% can be obtained at the top end, and at high forward speeds, several times this can be achieved. The lower the temperature exiting the turbine and the greater the extent of uncombusted oxygen, the greater the temperature increase in the jet pipe due to afterburning.
As is to be expected, afterburning naturally incurs a fuel consumption penalty, and this is why afterburning is typically constrained to short bursts. The aim of the compressor in a classic jet engine is to raise the pressure of the incoming air to the optimal pressure for efficient combustion. After expansion by the turbine stage, the gases are at a lower degree of compression, and therefore the fuel is not burnt as efficiently as in the combustion chamber between compressor and turbine. For a 70% increase in thrust the fuel consumption can easily double, but of course this increased fuel consumption is balanced by an improved performance in terms of take-off and climb. This means that the increased fuel consumption is balanced by the time saved to cover a desired distance or operating manoeuvre.
The inspiration of this post and the diagrams have all been taken or inspired by [1] Rolls-Royce (1996). The Jet Engine. Rolls Royce Technical Publications; 5th ed. edition (Amazon link). For anyone interested in jet engine design this is a beautiful book, describing lots of intricate details about jet engine design and presenting the information in an intuitive and visually pleasing manner using diagrams as used throughout this post. I can not recommend this book enough.
Aeroelasticity is the study of the interactions between dynamic, inertial and aerodynamic forces that arise when a body is immersed in airflow. The unique challenge of aeroelasticity is to analyse how vibrations, static deflections and lift and drag forces combine, and to make sure that any interaction of these three forces does not lead to inferior aircraft performance or even failure.
The triangle in the figure below is known as Collar’s triangle and each vertex shows one of the forces mentioned above. When all three forces interact simultaneously we are in the realm of aeroelasticity and common failure modes include wing flutter and buffeting. When inertial and elastic forces combine in the absence of aerodynamic forces we are in the classical domain of structural dynamics and essentially dealing with any sort of mechanical vibration that you would experience on any piece of moving machinery. The interaction of inertial forces and aerodynamic forces gives rise to aerodynamic stability problems. How does an aircraft react to small disturbances – do the oscillations dampen out or do they get worse over time? Finally, the interaction of aerodynamic forces and elastic forces can give rise to a phenomenon known as divergence, which is an effect where twisting of the wing becomes theoretically infinite and can cause wings to twist off.
The Collar Triangle defining aeroelasticity as “the study of the mutual interaction that takes place within the triangle of the inertial, elastic, and aerodynamic forces acting on structural members exposed to an airstream, and the influence of this study on design.”
The two most dramatic aeroelastic effects are flutter and divergence. Flutter is a dynamic instability, often of the wing, caused by positive feedback between the wing’s deflection and the aerodynamic lift and drag forces. The flutter speed is the airspeed at which the wing, or any other part of the structure, starts to undergo simple harmonic motion – much like the simple to and fro motion of a simple pendulum – and this vibration occurs with zero net damping. Zero net damping means that there is no dissipation of energy (think of a pendulum swinging for eternity) and so any further decrease in net damping will result in self-oscillation – the structure is basically forcing itself to vibrate more and more, which at some point, will naturally lead to failure.
As we all know, the lift force acting on a wing will tend to bend it upwards, but what is less well-known is that this lift force can also cause the wing to twist. This is because the centre of pressure, the point where the total sum of the lift pressure field is assumed to act on an airfoil, is not necessarily coincident with the shear centre, the point through which a bending load needs to be applied to get pure bending without any twisting. Imagine holding a ruler in one hand and pushing up on it with your other hand. If you apply the load along the central axis of the ruler, the ruler will only bend, but if you apply the load at one of the two sides you can see the ruler bend and twist ever so slightly. Most of the time, the shear centre of an airfoil is not coincident with the centre of pressure, and so a lift force produces both bending and twisting. A critical phenomenon called divergence can occur when this twisting of a wing increases the angle of attack, which consequently increases the lift force further or creates further mismatch between shear centre and centre of pressure, so that a feedback loop ensues until the wing diverges or essentially shears off. In fact, one of the Wright Brothers’ main rivals in the race to being the first at heavier-than-air flight was Samuel Langley, whose prototype plane crashed into the Potomac river in Washington D.C., and this is now believed to have occurred as a results of torsional divergence. Furthermore, torsional divergence was a large problem with many WWI fighter planes and required a lot of additional stiffening of the wings.
Forward-swept wings
One of the domains where divergence is particularly pernicious is in forward-swept wings. Simply put, wing sweep delays the onset of shock waves over the wings and therefore reduces the associated rise in aerodynamic drag caused by boundary layer separation. In slightly more detail, as air flows over a curved object, such as an aircraft wing, it accelerates due to centripetal forces and this means that an aircraft travelling slightly slower than Mach 1.0 (the speed of sound) can develop pockets of supersonic flow over areas with high local curvature, typically the wings or the canopy. For thermodynamic reasons,supersonic flows terminate in a shock wave which results in a sudden increase in the density of the air. This effect disturbs the smooth flow over the wing and creates vortices behind the aircraft, which means it is a form of parasitic drag. Sweeping the wing reduces the curvature of the body as seen from the airflow by the cosine of the angle of sweep. For example, a 45 degree sweep reduces the effective curvature by around 70% () compared to the straight-wing case. As a result, this increases the airspeed at which supersonic pockets start to form by about 30%, such that the aircraft can reach speeds much closer to Mach 1 before shocks occur.
Another way to think about the effect of sweep is to imagine the airflow over the wing as shown in the figure below. The effect of sweeping is such as to break the airflow into a component normal to the wing chord (“normal component”), and one along the span of the wing (“spanwise component”). The maximum curvature of the wing occurs along the wing chord, and the normal velocity component for the swept wing () is always less than the normal component for a straight wing ().
The figure above highlights another critical aspect of swept wings: the spanwise component. On a backward-swept wing the spanwise flow is outwards and towards the tip, while on a forward-swept wing it is inwards towards the root (see the figure below). Firstly, with the air flowing inwards towards the fuselage, wingtip vortices and the accompanying drag are reduced. Wingtip vortices form when the higher pressure air underneath the wing is sucked up onto the lower pressure top surface of the wing, thereby reducing the effective lift-generating surface of the wing. On most modern backward-swept airliners, winglets and sharklets prevent this phenomenon from occurring. Forward-swept wings similarly minimise this effect by re-routing some of the flow towards the wing root, and therefore allow for a smaller wing at the same lift performance. The second advantage of forward-swept wings is that shockwaves tend to develop first at the root of the wing, rather than towards the tips, and this helps to reduce tip stall. Aerodynamic control surfaces such as ailerons are typically located near the tips of the wings, because the further outboard, the greater their effect on controlling the rolling action of the plane. Tip stall essentially renders these ailerons useless, and therefore jeopardises the pilot’s control over the aircraft. As a result, the dangerous tip stall condition of a backward-swept design becomes a safer and more controllable root stall on a forward-swept design, providing better manoeuvrability at high angles of attack.
For all their merits, forward-swept wings suffer from one detrimental flaw – divergence. In a forward-swept wing configuration, the aerodynamic lift causes a twisting force that rotates the leading edge upward, causing a higher angle of attack, which in turn increases lift, and twists the wing further. With conventional metallic construction, additional torsional stiffening is typically required which adds weight, and is therefore sub-optimal in terms of aircraft performance.
Enter the Grumman X-29
The Grumman X-29 was an experimental aircraft developed by Grumman in the 1980’s, and flown by NASA and the US Air Force. The X-29 tested a forward-swept wing, canard control surfaces, and computerised fly-by-wire control to counter balance the various aerodynamic instabilities created by its airframe. From my perspective, the most important innovation, however, was the novel use of composite materials to control the aeroelastic divergence of forward-swept wings. At the time, composite materials were popular in the high-performance aircraft community as a means of creating stiff and strong structures at very low weight. In fact, composites were mainly used to save weight. However, the X-29 showcased a second advantage of this new material over classic metallic structures – multi-functionality.
Metals are isotropic materials, meaning that their stiffness is the same in all directions. The relationship between stress and strain along one direction of an aluminium panel is the same as in any other direction. Because composite materials are a union of stiff fibres held together by a resin matrix, we can manufacture panels that are stiffer in one direction than in another. This is because the composite material will be very stiff along the fibre direction but relatively compliant perpendicular to the fibre direction. In most fibre-reinforced composite materials, such as fibreglass and carbon fibre, this variation in stiffness is restricted to the plane of a single sheet of material known as an orthotropic lamina.
Consider one such layer of a continuous fibre-reinforced composite in the figure above. 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 along the fibres and compress in the resin direction (or vice versa). However, if the fibres are aligned at an angle to the x-direction (of say 45°), and a load is applied in the x-direction, then the layer will not only stretch in the x-direction and compress in the y-direction but also shear. This is because the layer will stretch 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 plus the distance from the axis of bending (here the mid-plane) squared. Thus, even if the +45° and -45° layers have the same thickness, the outer 45° layers contribute more to the bending stiffness of the [45,-45,-45,45] laminate than the -45° layers do. Therefore, stretching-shearing coupling is eliminated in a [45,-45,-45,45] laminate as the number of +45° and -45° layers is the same, but bend-twist coupling will occur because the +45° layers are further from the mid-plane than the -45° layers.
Let’s now apply this effect at a wing level, i.e. a layup is used for the top wing surface and a layup for the bottom wing surface. At the global wing level, the layup is balanced because we have an equal number of and layers, but the layers are further away from the wing mid-plane than the layers. This means that the bending stiffness is dominated by the layers, and the wing will twist when it bends.
In the Grumman X-29, this bend-twist coupling was successfully exploited to prevent divergence in the forward-swept wings. As aerodynamic lift forces the wing tips to bend upward, the forward-swept wing wants to twist to higher angles of attack, but the inherent bend-twist coupling of the composite laminates forces the wing to twist in the opposite direction and thereby counters an increase in the angle of attack – divergence is avoided!
Bend-twist coupling in Grumman X-29 wings. Both top and bottom wing skin may have the same number of +theta and -theta fibre angles, but if the +theta angles are further from the wing mid-plane then they will dominate the bending behaviour and cause the leading edge to twist down as the wing bends up.
The Grumman X-29 is an excellent example of an efficient, autonomous and passively activated control system. 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 capability is an example of elastic tailoring, and remains one of the most under-exploited advantages of composite materials. As the big aircraft manufacturers overcome the initial hurdles of using composites on a large scale with the 787 Dreamliner and A350-XWB, expect more and more of these multi-functional capabilities of composites to find their way onto aircraft components.
After Germany and its allies lost WWI, motor flying became strictly prohibited under the Treaty of Versailles. Creativity often springs from constraints, and so, paradoxically, the ban imposed by the Allies encouraged precisely what they had actually wanted to thwart: the growth of the German aviation industry. As all military flying was prohibited under the Treaty, the innovation in German aviation throughout the 1920’s took an unlikely path via unmotorised gliders built by student associations at universities.
Before and during WWI, Germany had been one of the leading countries in terms of the theoretical development of aviation and the actual construction of novel aircraft. The famous aerodynamicist Ludwig Prandtl and his colleagues developed the theory of the boundary layer which later led to wing theory. The close relationship of research laboratories and industrial magnates, like Fokker and Junkers, meant that many of the novel ideas of the day were tested on actual aircraft during WWI. Part of the reason why Baron von Richthofen, the Red Baron, became the most decorated fighter pilot of his day, was because his equipment was more technologically advanced than that of his opponents; a direct result of a thicker cambered wing that Prandtl had tested in his wind tunnels.
Given this heritage, it comes to no surprise that German students and professors soon found a way around the ban imposed at the Treaty of Versailles. For example, a number of enthusiastic students from the University of Aachen formed the Flugwissenschaftliche Vereinigung Aachen (FVA, Aachen Association for Aeronautical Sciences). These students loved the art and science of flying and intended to continue their passion despite the ban. Theodore von Kármán, of vortex street and Tacoma Narrows bridge fame, was a professor at the Technical University of Aachen at the time and remembers the episode as follows:
One day an FVA member approached me with a bright idea.
“Herr Professor,“ he said. “We would like your help. We wish to build a glider.”
“A glider? Why do you wish to build a glider?”
“For sport.” the student said.
I thought it over. Constructing a glider would be more than sport. It would be an interesting and useful aerodynamic project, quite in keeping with German traditions, but in view of postwar turmoil it could be politically quite risky … On the other hand, motorised flight was specifically outlawed in the Treaty of Versailles, and sport flying was not military flying. So rationalizing in this way, I told the boys to go ahead.
What von Kármán was not aware of at the time was that he was helping to lay the foundation for an important part of the German air force during WWII. The lessons learned in improving glider design would be directly applicable to military aeronautics later on.
Glider development in itself is a topic worth studying. The French sailor Le Bris constructed a functional glider in 1870, but the most famous gliders of the 19th century were all built by Otto Lilienthal. Lilienthal became the first aviator to realise the superiority of curved wings over flat surfaces for providing lift. Lilienthal conducted some rudimentary wing testing to tabulate the air pressure and lift for different wing sections; data which inspired, but was then superseded by the Wright brothers’ experiments using their own wind tunnel. In the USA, Octave Chanute is famous for his work on gliders and for many years he served as a direct mentor to the Wright brothers, who themselves built a number of successful gliders to optimise wing shapes and control mechanisms.
After the first successful motor-powered flight in 1903, interest in gliders largely subsided, but was then revived by collegiate sporting competitions organised by German universities. Oskar Ursinus, the editor of the aeronautics journal Flugsport (Sport Flying), organised an intercollegiate gliding competition in the Rhön mountains, a spot renowned for its strong upwinds. So work began behind closed doors in many university labs and sheds. Von Kármán’s school, the University of Aachen, built a 6 m (20 foot) wing-span glider called the Black Devil, which was the first cantilever monoplane glider to be built at the time. As a result of the cantilever wing construction, the design abandoned any form of wire bracing to stabilise the wing and relied purely on internal wing bracing, as had been pioneered by Junkers in 1915. In this regard, the glider was already more advanced than most of the fighters in WWI that were based on the classical bi-plane or even trip-plane design held together by wires and struts.
The Black Devil sailplane, designed by Wolfgang Klemperer
By early 1920 the Black Devil was ready to compete. At this point the students faced a new logistical challenge — how were they going to transport the glider a 150 miles south through three military zones (British, French and American), when shipping aircraft components was strictly forbidden?
As reckless students they of course operated in secret. The Black Devil was dismantled into its components, packed into a tarpaulin freight car and then driven through the night. Of this episode von Kármán recounts that,
On one occasion during the journey we almost lost the Black Devil to a contingent of Allied troops. Fortunately the engineer and student guard received advance notice of the movement, disengaged the car holding the glider, and silently transferred it to a dark sliding until the troops rode past.
Overall, the trip took six hours and the teams from Stuttgart, Göttingen and Berlin were already in attendance.
Lacking any motorised aircraft to launch the gliders, two rubber ropes were attached to the nose of the glider and then used as a catapult to launch the glider off the edge of a hill. Once in the air, it was the role of the pilot to manoeuvre the plane purely by shifting his/her body weight to balance the glider in the wind. In 1920, Aachen managed to win the competition with a flight time of 2 minutes and 20 seconds. Not a new revolution in glider design, but proving the aerodynamics of their concept plane nevertheless. A year later, an improved version of the Black Devil, the Blue Mouse, flew for 13 minutes, breaking the long-held record by Orville Wright of 9 minutes and 45 seconds. Some great videos of the early flights at the Wasserkuppe in the Rhön mountains exist to this day.
The Blue Mouse glider flying at the Wasserkuppe in the Rhön mountains.
In the following years, von Kármán and his scientific mentor and aerodynamics pioneer Ludwig Prandtl gave a series of seminars on the aerodynamics of gliding, which were attended by students and flying enthusiasts from all over the country. Among the attendees was Willy Messerschmitt, an engineering student at the time, whose fighters and bombers later formed the core of the Nazi air force during WWII. Even established industrialists, German royalty and other university professors attended the talks. As a result of this broad and democratic dissemination of knowledge and the collaborative spirit at the time, innovations began to sprout quickly. One of the main innovations was efficiently using thermal updrafts in combination with topological updrafts to extend the flying time. In 1922, a collaborative design team from the University of Hannover built the Hannover H 1 Vampyre glider, which first extended the gliding record to 3 hours and then to 6 hours in 1923. The Vampyr was one of the first heavier-than-air aircraft to use the stressed-skin “monocoque” design philosophy and is the forerunner of all modern gliders.
Aircraft Glider Vampyr
The collegiate sporting competitions continued until the early 1930’s. The Nazis soon realised that the technical knowledge gained in these sporting competitions could be used in rebuilding the German air force. Due to the lack of a power unit and limited control surfaces, the student engineers and industrialists had been forced to design efficient lightweight structures and wings that provided the best compromise in terms of lift, drag and attitude control. Most importantly, the gliders proved the superiority of single long cantilevered wings over the limited double- and triple-wing configuration used during WWI. The internal structure of the wing allowed for much lighter construction as the size of the aircraft grew, the parasitic source of drag induced by the wires and struts was eliminated, and the lift to drag ratio was dramatically improved by the long glider wings. Tragically, some pioneers took these concept too far and lost their lives as a result. While the lift efficiency of a wing is increased as the aspect ratio (length to chord ratio) increases, so do the bending stresses at the root of the wing due to lift. As a result, there were a number of incidents where insufficiently stiffened wings literally twisted off the fuselage.
On the importance of glider developments von Kármán reflects that,
I have always thought that the Allies were shortsighted when they banned motor flying in Germany … Experiments with gliders in sport sharpened German thinking in aerodynamics, structural design, and meteorology … In structural design gliders showed how best to distribute weight in a light structure and revealed new facts about vibration. In meteorology we learned from gliders how planes could use the jet stream to increase speed; we uncovered the dangers of hidden turbulence in the air, and in general opened up the study of meteorological influences on aviation. It is interesting to note that glider flying did more to advance the science of aviation than most of the motorised flying in World War I.
We can only speculate how von Kármán must have felt after leaving Germany in the 1930’s, partly due to his Jewish heritage, and witness from afar how the machines he helped to develop wreaked havoc in Europe during WWII.
References
The quotes in this post are taken from von Kármán’s excellent biography The Wind and Beyond: Theodore von Karman, Pioneer in Aviation and Pathfinder in Space by Theodore von Kármán and Lee Edson.
On November 8, 1940 newspapers across America opened with the headline “TACOMA NARROWS BRIDGE COLLAPSES”. The headline caught the eye of a prominent engineering professor who, from reading the news story, intuitively realised that a specific aerodynamical phenomenon must have led to the collapse. He was correct, and became publicly famous for what is now known as the von Kármán vortex street.
Theodore von Kármán was one of the most pre-eminent aeronautical engineers of the 20th century. Born and raised in Budapest, Hungary he was a member of a club of 20th century Hungarian scientists, including mathematician and computer scientist John von Neumann and nuclear physicist Edward Teller, who made groundbreaking strides in their respective fields. Von Kármán was a PhD student of Ludwig Prandtl at the University of Göttingen, the leading aerodynamics institute in the world at the time and home to many great German scientists and mathematicians.
Von Karman and JATO Team
Although brilliant at mathematics from an early age, von Kármán preferred to boil complex equations down to their essentials, attempting to find simple solutions that would provide the most intuitive physical insight. At the same time, he was a big proponent of using practical experiments to tease out novel phenomena that could then be explained using straightforward mathematics. During WWI he took a leave of absence from his role as professor of aeronautics at the University of Aachen to fulfil his military duties, overseeing the operations of a military research facility in Austria. In this role he developed a helicopter that was to replace hot-air balloons for surveillance of battlefields. Due to his combined expertise in aerodynamics and structural design he became a consultant to the Junkers aircraft and Zeppelin airship companies, helping to design the first all-metal cantilevered wing aircraft, the Junker J-1, and the Zeppelin Los Angeles.
Furthermore, von Kármán developed an unusual expertise in building wind tunnels — a suitable had not originally exist when he first started his professorship in Aachen and was desperately needed for his research. As a result, he became a sought after expert in designing and overseeing the construction of wind tunnels in the USA and Japan. Von Kármán’s broad skill set and unique combination of theoretical and experimental expertise soon placed him on the radar of physicist Robert Millikan who was setting up a new technical university in Pasadena, California, the California Institute of Technology. Millikan believed that the year-round temperate climate would attract all of the major aircraft companies of the bourgeoning aerospace industry to Southern California, and he hired von Kármán to head CalTech’s aerospace institute. Millikan’s wager paid off when companies such as Northrup, Lockheed, Douglas and Consolidated Aircraft (later Convair) all settled in the greater Los Angeles area. Von Kármán thus became a consultant on iconic aircraft such as the Douglas DC-3, the Northrup Flying Wing, and later the rockets developed by NACA (now NASA).
Von Kármán is renowned for many concepts in structural mechanics and aerodynamics, e.g. the non-linear behaviour of cylinder buckling and a mathematical theory describing turbulent boundary layers. His most well-known piece of work, the von Kármán vortex street, tragically, reached public notoriety after it explained the collapse of a suspension bridge over the Puget Sound in 1940.
The von Kármán vortex street is a direct result of boundary layer separation over bluff bodies. Immersed in fluid flow, any body of finite thickness will force the surrounding fluid to flow in curved streamlines around it. Towards the leading edge this causes the flow to speed up in order to balance the centripetal forces created by the curved streamlines. This creates a region of falling fluid pressure, also called a favourable pressure gradient. Further along the body, where the streamlines straighten out, the opposite occurs and the fluid flows into a region of rising pressure, an adverse pressure gradient. The increasing pressure gradient pushes against the flow and causes the slowest parts of the flow, those immediately adjacent to the surface, to reverse direction. At this point the boundary layer has separated from the body and the combination of flow in two directions induces a wake of turbulent vortices (see diagram below).
Boundary layer separation over cylinder
The type of flow in the wake depends on the Reynolds number of the flow impinging on the body,
where is the density of the fluid, is the impinging free stream flow velocity, is a characteristic length of the body, e.g. the diameter for a sphere or cylinder, and is the viscosity or inherent stickiness of the fluid. The Reynolds number essentially takes the ratio of inertial forces to viscous forces , and captures the extent of laminar flow (layered flow with little mixing) and turbulent flow (flow with strong mixing via vortices).
Flow around a cylinder for different Reynolds numbers
For example, consider the flow past an infinitely long cylinder protruding out of your screen (as shown in the figure above). For very low Reynolds number flow (Re < 10) the inertial forces are negligible and the streamlines connect smoothly behind the cylinder. As the Reynolds number is increased into the range of Re = 10-40 (by, for example, increasing the free stream velocity ), the boundary layer separates symmetrically from either side of the cylinder, and two eddies form that rotate in opposite directions. These eddies remain fixed and do not “peel away” from the cylinder. Behind the vortices the flow from either side rejoins and the size of the wake is limited to a small region behind the cylinder. As the Reynolds number is further increased into the region Re > 40, the symmetric eddy formation is broken and two asymmetric vortices form. Such an instability is known as a symmetry-breaking bifurcation in stability theory and the ensuing asymmetric vortices undergo periodic oscillations by constantly interchanging their position with respect to the cylinder. At a specific critical value of Reynolds number (Re ~ 100) the eddies start to peel away, alternately from either side of the cylinder, and are then washed downstream. As visualised below, this can produce a rather pretty effect…
This condition of alternately shedding vortices from the sides of the cylinder is known as the von Kármán vortex street. At a certain distance from the cylinder the behaviour obviously dissipates, but close to the cylinder the oscillatory shedding can have profound aeroelastic effects on the structure. Aeroelasticity is the study of how fluid flow and structures interact dynamically. For example, there are two very important locations on an aircraft wing:
the centre of pressure, i.e. an idealised point of the wing where the lift can be assumed to act as a point load
the shear centre, i.e. the point of any structural cross-section through which a point load must act to cause pure bending and no twisting
The problem is that the centre of pressure and shear centre are very rarely coincident, and so the aerodynamic lift forces will typically not only bend a wing but also cause it to twist. Twisting in a manner that forces the leading edge upwards increases the angle of attack and thereby increases the lift force. This increased lift force produces more twisting, which produces more lift, and so on. This phenomenon is known as divergence and can cause a wing to twist-off the fuselage.
A different, yet equally pernicious, aeroelastic instability can occur as a result of the von Kármán vortex street. Each time an eddy is shed from the cylinder, the symmetry of the flow pattern is broken and a difference in pressure is induced between the two sides of the cylinder. The vortex shedding therefore produces alternating sideways forces that can cause sideways oscillations. If the frequency of these oscillations is the same as the natural frequency of the cylinder, then the cylinder will undergo resonant behaviour and start vibrating uncontrollably.
So, how does this relate to the fated Tacoma Narrows bridge?
Upon completion, the first Tacoma Narrows suspension bridge, costing $6.4 mill and the third longest bridge of its kind, was described as the fanciest single span bridge in the world. With its narrow towers and thin stiffening trusses the bridge was valued for its grace and slenderness. On the morning of November 7, 1940, only a year into its service, the bridge broke apart in a light gale and crashed into the Puget Sound 190 feet below. From its inaugural day on July 1, 1940 something seemed not quite right. The span of the bridge would start to undulate up and down in light breezes, securing the bridge the nickname “Galloping Gertie”. Engineers tried to stabilise the bridge using heavy steel cables fixed to steel blocks on either side of the span. But to no avail, the galloping continued.
On the morning of the collapse, Gertie was bouncing around in its usual manner. As the winds started to intensify to 60 kmh (40 mph) the rhythmic up and down motion of the bridge suddenly morphed into a violent twisting motion spiralling along the deck. At this point the authorities closed the bridge to any further traffic but the bridge continued to writhe like a corkscrew. The twisting became so violent that the sides of the bridge deck separated by 9 m (28 feet) with the bridge deck oriented at 45° to the horizontal. For half an hour the bridge resisted these oscillatory stresses until at one point the deck of the bridge buckled, girders and steel cables broke loose and the bridge collapsed into the Puget Sound.
After the collapse, the Governor of Washington, Clarence Martin, announced that the bridge had been built correctly and that another one would be built using the same basic design. At this point von Kármán started to feel uneasy and he asked technicians at CalTech to build a small rubber replica of the bridge for him. Von Kármán then tested the bridge at home using a small electric fan. As he varied the speed of the fan, the model started to oscillate, and these oscillations grew greater as the rhythm of the air movement induced by the fan was synchronised with the oscillations.
Indeed, Galloping Gertie had been constructed using cylindrical cable stays and these shed vortices in a periodic manner when a cross-wind reached a specific intensity. Because the bridge was also built using a solid sidewall, the vortices impinged immediately onto a solid section of the bridge, inducing resonant vibrations in the bridge structure.
Von Kármán then contacted the governor and wrote a short piece for the Engineering News Record describing his findings. Later, von Kármán served on the committee that investigated the cause of the collapse and to his surprise the civil engineers were not at all enamoured with his explanation. In all of the engineers’ training and previous engineering experience, the design of bridges had been governed by “static forces” of gravity and constant maximum wind load. The effects of “dynamic loads”, which caused bridges to swing from side to side, had been observed but considered to be negligible. Such design flaws, stemming from ignorance rather than the improper application of design principles, are the most harrowing as the mode of failure is entirely unaccounted for. Fortunately, the meetings adjourned with agreements in place to test the new Tacoma Narrows bridge in a wind tunnel at CalTech, a first at the time. As a result of this work, the solid sidewall of the bridge deck was perforated with holes to prevent vortex shedding, and a number of slots were inserted into the bridge deck to prevent differences in pressure between the top and bottom surfaces of the deck.
The one person that did suffer irrefutable damage to his reputation was the insurance agent that initially underwrote the $6 mill insurance policy for the state of Washington. Figuring that something as big as the Tacoma Narrows bridge would never collapse, he pocketed the insurance premium himself without actually setting up a policy, and ended up in jail…
If you would like to learn more about Theodore von Kármán’s life, I highly recommend his autobiography.
