From defense systems to space exploration — and potential ultrafast travel on Earth — hypersonic technologies have several applications. However, there are a number of open challenges in flying at over five times the speed of sound.
This summer, a William & Mary program focused on how to solve some of these problems, involving W&M, University of Virginia and James Madison University undergraduates alongside high school students from around the Tidewater region.
“HyperStats: Statistical Training for Interdisciplinary Hypersonics” is an eight-week summer program, led by W&M Assistant Professor Greg Hunt, allowing students to enhance their statistical and data science skills and apply them to aerospace engineering projects. Funded by the U.S. Department of Defense, the program wrapped up its first edition earlier this month, with funding already secured for next summer. Data is one of the central initiatives of Vision 2026, W&M’s strategic plan.
“The idea is to train students for the future,”
said Hunt.
Despite not having an engineering school, William & Mary offers majors and educational experiences that support graduate education in several engineering fields. An example is the engineering-oriented curriculum track combining applied science and physics elements.
According to the most recent data from the National Science Foundation, William & Mary is a top feeder for science and engineering doctorates across the country — the second among all high-research universities in the U.S. — producing a high number of graduates who eventually earn a Ph.D. in the field.
“In some of these fields, like aerospace engineering, statistical and data science skills are ever more important to solve real-world problems,” said Hunt, who teaches in the mathematics department.
A key component of HyperStats was a tour of NASA Langley’s facilities, which gave students the opportunity to learn more about Hyper-X, a past NASA program that culminated with the flight of a jet-powered aircraft reaching almost 10 times the speed of sound.
Those interested in the next iteration of the HyperStats program can save this link, where more information will become available in the next few months. The next round of applications will open in November 2023.
“This project has been an outgrowth of previous collaborations with those at NASA on research of which I have been a part,” said Hunt. The HyperStats experience was not a first for him: Alongside Chancellor Professor of Mathematics Rex Kincaid, he had already worked with students on aerospace problems with support from the Virginia Space Grant Consortium.
Hypersonic speeds, hypersonic problems
Hypersonic vehicles fly at Mach 5 — five times the speed of sound — and above, which is over six times the speed of a typical commercial aircraft.
When vehicles travel so fast, the air friction creates extreme heat that needs to be managed; also, these high-speed engines only have a few milliseconds to mix and burn fuel and air, which causes challenges in the combustion process.
The students worked in pairs on real research problems, such as quantifying the uncertainty of a thermal protection system, understanding high-speed fluid dynamics of these high-speed engines under non-ideal flow conditions, and optimizing the design of the inlet of an engine.
For former “space kid” Nick Reeder ’24, a data science and mathematics student, working on space-related issues through the HyperStats program was a “dream come true.”
The ultimate aim of his project was performing uncertainty quantification, a challenging task requiring enormous amount of computing power. He worked on understanding how the design of these vehicles propagates into uncertainty in how the vehicles behave in practice.
As Reeder mentioned, aerospace agencies and companies perform this task using wind tunnels, which are large tube-shape facilities in which air is blown around an object to simulate flight conditions; and supercomputers running complex simulations that are time-consuming and require vast computing power.
What he and his partner did was develop a surrogate. “Basically, you get a little bit of data, train a machine learning model, and then you use the predicted data to do the rest of the analysis,” he said.
A lot of variables are involved in hypersonic flight, which takes place in extreme conditions. The surrogate helped identify safe temperature ranges; as Reeder put it, their work helped predict what the prediction should be.
“We were able to build a pretty accurate model on the surrogate we were using,” said Reeder. “It was a smaller simulator or a toy simulator, effectively, to prove that the methods work.”
Students also took part in weekly meetings where they had the opportunity to present their work and be exposed to novel research happening in the mathematics department.
“I had never been to a math symposium or presentations before, so it was exciting just hearing people talk about the things that they are passionate about,” said Reeder.
Hunt said he involved high school students as a way to show them different opportunities before their commitment to a specific field.
“As a statistician, data scientist and educator, I have found that bringing in students to work on cutting-edge problems in aerospace is a great way to expose students to the power of statistical ideas by working on consequential problems,” said Hunt.
Antonella Di Marzio, Senior Research Writer