Photo Credit: Gus Ruelas
Joseph Erwin’s latest engineering project started as an inside joke.
The USC Viterbi School of Engineering alumnus has been playing the trombone since middle school. His friends would often play a silly game where they would find the most inefficient way possible to play a song using the trombone’s slide, unnecessarily extending both the distance the slide moved and the effort needed to move it. In other words: Erwin and friends turned an easy song to play into an impossible one.
“It just looks crazy because your slide is flying all over the place,” said Erwin, who earned his master’s degree in operations research engineering in 2023.
This craziness is only possible because of what’s called “alternate positions,” Erwin explained. In normal trombone playing, musicians default to moving the slide as close as possible to “first position,” or the base note of the instrument. Using alternate positions is a way to try and make trombone playing easier or more manageable for a player. This “alternate positions” system is a more advanced skill, and while there are various methods to use them, no one had come up with a way to do so efficiently.
Of course, that was until Erwin’s new paper, “Optimizing trombone slide positions: a network-based shortest paths approach to musical expression,” which was published in the December 2025 issue of the SIAM Undergraduate Research Online (SIURO) academic journal.
Erwin, who’s also an alumnus of the USC Trojan Marching Band, began his work by developing an algorithm to test these alternate positions for optimal paths. In doing so, he found ways to avoid fatigue and reduce physical effort while playing the instrument.
“It’s similar to how your phone finds the pathway [on] Google Maps. Using the same algorithm, you’re just kind of trying to find a way through every route,” Erwin said.
Erwin tested many different types of alternate position methods to help optimize this trombone playing — such as “shortest path,” which minimizes the distance the slide travels, and “impulse minimization,” which tries to reduce large and difficult slide changes.
When it came time to pick the song for Erwin to test his algorithm on, it was an easy decision.
“Fight On” — the 103-year-old USC fight song.
“It’s one of the main songs we play in the band.” Erwin said. “I’ve had some of my friends review that as well, and I’ve played it myself. You can come up with a pretty optimal sequence, and it’s definitely not the one that we used in the band. That’s just based on tradition. There’s a certain visual style that you want to have when you’re in the band, and it’s not the optimal one.”
While this study focused exclusively on the trombone, Erwin could see how this optimization work might transfer to other instruments as well.
“I know that string players do have to sync up their bow movement. My freshman year roommate pointed out that [this study] might have some utility there, just trying to find more optimal string fingerings and bow movements,” Erwin said.
In addition to his previous studies in USC’s Daniel J. Epstein Department of Industrial & Systems Engineering and his current work as a technical analyst at the RAND Corporation, Erwin was also a teaching assistant at the marching band from 2022 to 2023. He hopes that his work in studying alternate positions can help trombone players of all levels, even for those who haven’t learned what alternate positions are yet.
“The things that we play in the band are pretty technical and everyone comes into the band with a very different level of capability. Some people come in not knowing how to play trombone. So, they may not even think that there’s a better way to do it,” Erwin said. “I was always trying to encourage people to find these little shortcuts.”
Published on January 29th, 2026
Last updated on January 29th, 2026