We want aircraft that are fuel efficient but can also fit at airport gates and take off before hitting the ends of the runways. We want them built tough enough that parts don’t break off during emergency maneuvers, but light enough that we’re not wasting fuel by hauling around unnecessary weight.
Optimization software encodes these goals and adjusts the airplane design to find the version that best delivers. However, the field has conventionally accepted a trade-off: optimization programs that include multiple disciplines – aerodynamics and structures, for instance – could only be done with relatively crude, low-fidelity simulations. This is in part because the more detailed, true-to-life simulations require intensive computing power to run, and the computing time increases with every variable to be explored.
The work of Joaquim Martins, a professor of aerospace engineering at U-M, has been dedicated to breaking that trade-off, knitting high-fidelity simulations together in an efficient way so that an aircraft can be optimized through aerodynamic shape and underlying structure at the same time. His group’s computational framework, known as MACH, is currently used at Embraer, Aerion Supersonic and is under consideration at Airbus. At NASA, researchers have been using some of the ideas from MACH in a more general purpose framework that can fold in many more design considerations such as propulsion and controls.
“Quim and his group are, no doubt, at the cutting edge of airplane design optimization based on high-fidelity numerical modeling,” said Eli Livne, a professor of aeronautics and astronautics at the University of Washington, Seattle, and Editor-in-Chief at the American Institute of Aeronautics and Astronautics Journal of Aircraft. “I value Quim’s work highly, and so do many others.”
Martins’ group has used the technique to improve a variety of wing designs, such as optimizing the shape and structure of wings on a Boeing 777 based on real routes flown by that aircraft. They have explored futuristic blended-wing-body aircraft, which resemble manta rays.
“They’ve taken really complex software pieces and developed them but also found a way to glue them together so that we can do these types of difficult problems,” said Jason Hicken, an associate professor of mechanical, aerospace and nuclear engineering at Rensselaer Polytechnic Institute. Like Martins, Hicken works on the math underlying high-fidelity, multidisciplinary design optimization algorithms.
For now, the arena for optimization is in improving existing designs. But perhaps its most interesting promise is the potential to identify new designs. One study from Martins’ group was an optimization program looking for the best wing cross-section, or airfoil, that would minimize drag while producing enough lift.
“So here we start with a circle, we have a simulation of the flow around the circle coming this way,” said Martins. “Basically, our optimization figures out a shape that’s a lot lower drag, more streamlined, and eventually converges to this shape.”
The screen displayed a shape vaguely resembling the silhouette of a blue whale, known as a supercritical aerofoil.
“This shape was invented by NASA a few decades ago. And it took several years to invent this. Now, with an optimizer, we can get that same shape in a few hours. A few decades later though,” he noted with a laugh, “but with no preconceived notion of what it should look like.”
The aesthetic of efficiency
As a PhD student, he dreamed of software that could start with a sphere and mold it into an ideal flying machine. Design may one day be constrained only by what we need aircraft to do, rather than our existing ideas of what an airplane looks like.
For now, however, there is too much about aircraft design that can’t be quantified. Yet even with humans doing the bulk of the design, today’s aircraft are almost entirely prescribed by function.
“I think that more than any other engineering system, it’s really about efficiency and not aesthetics,” said Martins. Aircraft require so much energy to stay aloft that even a fraction of a percent in improved efficiency matters.
And yet, he finds the result beautiful, an echo of the sharks and dolphins he used to draw as a child growing up on the island of Faial in the Azores, a volcanic archipelago 1000 miles off the coast of Portugal. The trip to the mainland was two hours by plane or a few days by boat, so he understood the importance of aircraft in connecting the world.
As a teenager, Martins weighed career options of fighter pilot or aerospace engineer, settling on engineering when he realized that he would prefer a technical career to the airline pilot lifestyle that would likely follow his retirement from the military.
He attended Imperial College London for his undergraduate degree, and he appreciates their aerospace engineering teaching philosophy to this day. In particular, he recalls the first day of his first-term aerodynamics course, in which his professor explained the “boundary layer,” which slides along an airplane much more slowly than the air a few feet away.
“Here, we only teach aerodynamics in the third year. There, you learn the math as you go,” said Martins.
By the end of his undergraduate degree, Martins became interested in learning more about code and aerospace design. He applied to only one university, an action which he now criticizes as that of an “arrogant young man,” and was lucky he got in – it was Stanford. There, he met his future wife, Sandra Lau, an accomplished pianist earning her own doctoral degree. Martins’ studies homed in on optimization and computational fluid dynamics, which remain foundational to his research.
Connecting aerodynamics and structures
Advances in computing made it possible to simulate the performance of an airplane in a way that was true to life, but improving that aircraft one discipline at a time is unlikely to lead to the best design.
“It’s like if you are on a mountain, and you are trying to get to the lowest valley,” said Martins.
That valley is the most efficient design. But it’s not just getting to the valley. There’s a fence in the way. This fence is design constraints – for instance, wings that won’t break off in flight.
If you restrict yourself to moving north-south first – say, optimizing aerodynamics – you walk until you hit the fence. Now, you’re ready to move east-west, optimizing the structure. But west is uphill, and east runs you into the fence. There’s nowhere to go. However, if you could move north-east – changing the aerodynamics and structure at the same time – you could reach a lower point.
“Multidisciplinary design allows you to move along the diagonal,” said Martins.
Moving along the diagonal with high accuracy wasn’t possible, though. That was going to require a kind of mathematical wizardry. Hired in as a junior faculty member at the University of Toronto in 2002, Martins started his own group to develop it.
The main trick was switching from the conventional method of looking at particular points in the landscape of possible aircraft designs to looking at slopes in the landscape. Points are easier to compute than slopes, but the direction of a slope reveals what changes will improve the aircraft design. Ultimately, that speeds up the optimization algorithm.
While others had used slopes for optimization in the past, Martins’ team was first to stitch them together for two different disciplines. They developed an equation that could look at as many variables as they wanted – without each variable adding to the amount of time it would take to run the optimization. The difficulty is calculating the slopes, also known as “sensitivities” because they reveal how sensitive the aircraft’s performance is to changes in each of the variables. This is the problem that Martins and his students spent most of their time trying to solve.
“The key contribution for us was computing these sensitivities really efficiently with many variables,” said Martins. “So we have sensitivities of the drag with respect to hundreds of shape variables, hundreds of structure variables, and other variables.”
Others had already been working on how to do this for aircraft shape alone, or aircraft structure alone, so the main challenge for Martins and his students was making the aerodynamic and structural aspects of the virtual aircraft affect one another.
“If aerodynamic forces would bend the structure of the wing, you need to see that bent shape in the aerodynamic model,” said Martins.
In addition to modifying the equation to include this crosstalk, they also had to keep a lid on the “finicky” aspects of their approach – namely, in methods like this one, small errors tend to have large effects on outcomes. They combed through their code for bugs and speed bottlenecks. The result was the first high-fidelity aircraft optimization program drawing on more than one field – in this case, aerodynamics and structures.
In the midst of establishing the new method, Martins was invited to give his first keynote presentation in Stockholm, Sweden in 2007. There, he met Carlos Cesnik, the Clarence “Kelly” Johnson Professor at U-M, who would later help Martins join the faculty here.
“He impressed me as a bright young researcher,” said Cesnik. “His talk was outlooking and presented a very intriguing perspective of bringing high-fidelity models to multidisciplinary design optimization.”
Making better optimization more accessible
Martins remains grateful to the University of Toronto for his start as a researcher, but Sandra Lau Martins, who grew up in Long Beach, wanted to return to the US. Although the move to Ann Arbor in 2009 didn’t offer California weather, it was “an improvement on almost every axis” for Martins’ family.
Belonging to a U.S. institution gave him access to funding from NASA and the Air Force, as well as a larger pool of collaborators. The move also helped enable Justin Gray (Aero PhD ’18) to join Martin’s group in 2015 – an outcome that neither would have predicted when Martins first moved to U-M.
Gray and Martins were aware of one another since 2008, when Martins co-organized an American Institute of Aeronautics and Astronautics conference in Vancouver, Canada, on multidisciplinary optimization and design. Gray, then a member of NASA’s Open Multidisciplinary Analysis and Optimization (OpenMDAO) group, was attending to learn more about the optimization field.
Gray took the helm of OpenMDAO in 2010 and hired one of Martins’ PhD graduates, John Hwang, in 2014. Gray was interested in using adjoint methods (the technical name for the sensitivity method) in OpenMDAO, but it wasn’t going to be easy. He compares Martins’ optimization programs to complex machines.
“Prof. Martins’ lab has been pioneering a way to make that machine,” said Gray. “However, each time they want to use adjoints on a new kind of problem, they had to build a new machine from scratch. They had the plans and the knowledge from all the previous machines they had built, so this wasn’t that hard for them. But it was hard enough that they didn’t do it very often.”
Martins’ group had taken aircraft optimization to a new level, but progress was slow, and it was tough for others in the field to follow. Also, the optimization “machines” became more difficult to make with each new discipline added to the mix.
“There was a limit to how big even they could go,” said Gray.
In his year with NASA, Hwang helped integrate the multidisciplinary adjoint methods pioneered in Martins’ group into OpenMDAO. Gray wanted to take this further, incorporating more disciplines and bringing in more people whose optimizations could be better served with the adjoint method. So, he joined Martins’ group as a PhD student to make what he called the “Lego set” version of their optimization algorithms.
“You could build a big adjoint machine simply by snapping together a bunch of smaller adjoint machines,” said Gray. “Because the Lego-block-like adjoint machines were totally generic, it meant that they could be distributed to non-expert users – who could use them to build their own complex optimizers without fully understanding what was making each little block work.”
The array of blocks is so broad that, in addition to Martins’ home turf of aerodynamics and structures, OpenMDAO can find ways to improve propulsion, controls, manufacturing and the economics for an airline flying the plane. And it’s not limited to aircraft – it also advises on the designs of spacecraft and wind farms.
Exploring the future of aircraft
Is high fidelity multidisciplinary design changing the way airplanes are made? Not yet. But those familiar with Martins’ work expect that the approach his group demonstrated will influence how the next generation of aircraft are designed.
Hicken, who first met Martins when he was earning his PhD under a different professor at the University of Toronto, described the push and pull with industry. The researchers in multidisciplinary design offer their code for adoption, while the programs used in industry tend to be five or ten years behind.
At the same time, he added, “Industry sees what we do, sees what Quim does, and says, ‘This is great, but wouldn’t it be better if we could do this?’ So then it pushes us to consider even more complicated problems.”
Several avenues for improving airplanes are currently under exploration, including more efficient placement for engines and deciding a dilemma in wing design. More radical changes are percolating in the design of smaller flying machines. Multidisciplinary design optimization can help with all of them.
Gray’s application of interest struck a chord with one of the aerodynamic phenomena that first intrigued Martins: engines that draw in the slower moving “boundary layer” air that runs along the airplane’s fuselage.
This leads to a trimmer design, with engines integrated into the fuselage rather than hanging off the wings, and it also has the potential to be more fuel efficient. Slower-moving air is easier to accelerate, so the engines can use less energy to produce the same amount of thrust.
“We’ve started to reach the limits of what can be done to improve engine performance on its own,” said Gray, “To continue to reduce aircraft fuel burn, a more integrated approach is needed where the engine and airframe work synergistically.”
However, designing an engine and the shape of the airplane so that they work together is a very hard problem. Gray and Martins collaborated on a study showing how optimization can help overcome that difficulty and design a system that maximizes performance. Anil Yildirim, a current PhD student in aerospace engineering and FXB Fellow, is continuing that work.
As for changes to commercial jets rolling out now, Martins is gratified to see Boeing come to the same conclusion about a design feature that his optimization algorithms have suggested over and over again: longer wings are king for fuel efficiency. The alternative is a sort of fin at the end of the wing, known as a winglet.
Longer wings and winglets both reduce drag by spreading out the vortex spinning over the wing. This enables the plane to produce enough lift with less energy. A longer wing slows the vortex by making it longer, and a winglet makes it taller. With no clear advantage for longer wings, most airplane manufacturers go with winglets for the ease of fitting into airport gates. But Martins’ algorithms have a strong preference for longer wings.
Then, in 2018, Boeing launched the 777x featuring wing tips that fold up to fit at gates and flip down for flight.
“I was really excited when I saw that,” said Martins. “Boeing must really think the same thing, because they’re actually paying an additional penalty in weight to increase the span because of the folding tip mechanism.”
As for more futuristic designs, Martins would like to see a commercial airplane with a blended wing body. With the whole airplane generating lift as one flying wing, calculations suggest that the same wingspan can provide a 20 percent improvement in fuel efficiency. But even with advanced design and modeling tools, Martins doesn’t think it likely that Boeing and Airbus will embrace this wild departure from conventional commercial aircraft.
He pointed out that bolder innovation in aircraft is currently at the business jet level, with companies like Aerion aiming to bring back supersonic passenger flight. Also, Uber and others are developing vertical take-off aircraft – a sort of helicopter/airplane hybrid – for short hops within cities.
“Multidisciplinary design optimization has been used to study sonic boom reduction as well as the efficiency of urban air trajectories,” said Martins.
With the improved accessibility through NASA’s OpenMDAO program, we may see this field advance from an area of scientific inquiry to a technology improving the aircraft industry. For now, Martins notes, several companies are taking a good look at it.
Perhaps the chief advantage that high-fidelity tools offer is enabling companies to explore bigger deviations from their older designs, getting beyond the boundaries that data from existing planes can safely predict. If it is less expensive and risky for companies to design the future of aircraft, we may find that the future arrives sooner.