This text was initially printed by Quanta Journal.
Within the fall of 2014, Andrew Wilson took a front-row seat in Ken Ono’s number-theory class at Emory College, in Atlanta. Wilson was not solely double-majoring in utilized math and physics; he was additionally a walk-on member of Emory’s swim staff. Ono took an curiosity in Wilson’s ambitions. “We thought that, collectively, perhaps we may use our curiosity in arithmetic to assist him enhance as a swimmer,” Ono says.
Ono, who usually research summary patterns in numbers and particular capabilities referred to as “modular kinds,” started amassing and analyzing acceleration information from Wilson and different Emory swimmers to establish and quantify their weaknesses. “It obtained to the purpose the place I may simply see what an athlete was doing with out truly watching them swim,” he says.
Inside two years, Wilson had received nationwide collegiate championships; he would go on to earn a gold medal on the 2021 Tokyo Olympics. By then, Ono was on the College of Virginia, the place he labored alongside Todd DeSorbo—the pinnacle coach for each UVA swimming and the U.S. Olympic ladies’s swim staff. Ono will be part of the Olympic-team employees in Paris later this summer season as a technical guide. “I really feel like we’re all on this collectively, making an attempt to make one thing new,” he says.
Jordana Cepelewicz of Quanta spoke with Ono about how he has used arithmetic to assist swimmers make it to the Olympic stage. The interview has been condensed and edited for readability.
Jordana Cepelewicz: So how profitable has your program been?
Ken Ono: The outcomes converse for themselves. A bunch of our individuals went to the Olympics in 2021. At the newest World Championships, each feminine American gold medalist in particular person occasions was a UVA athlete. Kate Douglass confirmed up right here at UVA a number of years in the past, swimming the 200-meter breaststroke in two minutes and 30 seconds. Now she’s the American report holder, with a time of two minutes, 19.30 seconds. She simply broke the U.S. Olympic trials’ all-time report, and he or she’s a favourite to win the Olympics this yr.
5 UVA athletes, together with Kate, simply turned U.S. Olympians—one-fourth of the U.S. ladies’s staff! Gretchen Walsh received the 100-meter butterfly, setting the world report. Paige Madden obtained second within the 400-meter freestyle, proper after Katie Ledecky; Paige is now a two-time Olympian.
Cepelewicz: What was your preliminary purpose?
Ono: Should you take the swimming out of it, we have now Newton’s legal guidelines of movement. These are the equations that we work with. We wished to fastidiously perceive the implications of Newton’s legal guidelines utilized to swimmers within the pool. How can we measure acceleration, deceleration, and drag? These have been the primary questions that we needed to reply within the growth of our instruments.
Cepelewicz: How did you get began?
Ono: It started innocently sufficient—with Saran Wrap and accelerometers designed for shark monitoring that I purchased from marine-technology outfits. We didn’t know what we have been doing. I wanted to lock these accelerometers to swimmers. So I obtained Saran Wrap and wrapped these sensors round their waists tremendous tight. Some swimmers have been simply too highly effective, so the sensors by no means stayed contained in the Saran Wrap. So now I’ve these belts that my spouse made which have a bit of pocket for the sensors.
Cepelewicz: It took time to get this experimental setup to work.
Ono: It was laborious to even get the info. Our protocols for waterproofing have been humorous. They regarded like Boy Scout directions: “Wrap the accelerometer in tissue paper, burrito type.” And we found that a few of our sensors may fail. They have been very delicate to mild. So we needed to trend little plastic UV covers to guard them.
It wasn’t that way back that we have been that beginner. We’ve come a great distance since then.
Cepelewicz: What sort of information do you gather?
Ono: I report swims with high-definition video, and with accelerometers and power paddles. I’ve additionally assembled a really giant battery of assessments that look nothing like swimming. I check how athletes swim after they take their kicks at totally different tempos. I check how versatile they’re, how drained they get after sure duties. I need to get sense of what their capabilities will likely be.
Throughout these swims and assessments, I measure the power that’s generated in three-dimensional area by the athlete’s legs, by undulation on the hips, and by their fingers. Excessive-definition video typically captures solely 24 screenshots per second. Every sensor provides me 512 power vectors per second. They will reveal stuff you’ll by no means see within the video.
Cepelewicz: Like what?
Ono: One refined factor that we picked up on very simply—and also you wouldn’t see it together with your eyes—is how an athlete may change the execution of their kicks three strokes away from the wall, inflicting them to lose time.
That’s only one instance. Utilizing our information, we carry out a really cautious and severe evaluation of every particular person swimmer. We get a breakdown of the swim. My first assessments search for the place you’re decelerating for no good motive. Some athletes actually wrestle with their transitions, coming into and popping out of a wall. Or they could have to right their head placement in a streamline, an underwater glide the place they’re not truly swimming. On the Olympic and World Championship stage, the place races may come all the way down to hundredths of a second, these items matter.
As soon as we wipe out these sources of deceleration, then we take a look at what limbs are doing in movement. As you fatigue, how is your stroke falling aside? Are you maximizing the proportion of power you generate in order that your physique swims in the proper course?
Cepelewicz: How do you extract this data out of your information?
Ono: A few of it is so simple as linear algebra. When an athlete takes a stroke, they’re producing power that may be pointed downward, upward, to the proper or to the left, or within the course of the swim. We use linear-algebra methods to calculate the proportion in every of these instructions.
Would you consider that we’ve by no means measured anybody who was greater than 60 % environment friendly within the 4 strokes —freestyle, breaststroke, butterfly, and backstroke? It’s mainly unimaginable. In April, we had Paige Madden put on power sensors, and we modeled the trail of her hand as she took a stroke and recovered. We computed that within the first lap of her swim, 59.1 % of the power her proper hand generated was propelling her within the course she wished to go. That’s superior.
However by Lap 8, solely 42.1 % was propelling her ahead. Not solely was she getting extra drained, however her execution was beginning to collapse. So utilizing simply these insights from linear algebra, we gave her some cues about how you can swim the race in a different way. And the following day, on Lap 8, she was near 50 %. One month later, she swam her private finest.
Our paddles don’t allow you to lie. We don’t allow you to idiot yourselves.
Cepelewicz: And this math works the identical for all 4 strokes?
Ono: I’ve by no means been in a position to get our power sensors to work for breaststroke. There’s an excessive amount of occurring. I get information, however I can’t make heads or tails out of it.
Cepelewicz: Why is breaststroke tougher to cope with?
Ono: I want I may let you know. I imply, in breaststroke, your fingers are doing rather more by way of in-sweep, out-sweep. That’s a tough drawback. However I don’t know.
Cepelewicz: You additionally use your information to make predictions and develop race methods, proper?
Ono: That’s proper. We are able to use all our information to construct a “digital twin” of an athlete. Digital twins are mathematical fashions of difficult programs and processes, such because the unfold of COVID or the migration of populations of animals—issues that modify over time.
Besides, in my case, it truly is a digital twin. It seems like an EKG, going tch, tch, tch, and it’s developed primarily based on the info I’ve captured about an athlete’s actions. I can mannequin how they’ll race beneath totally different situations. Over the past seven or eight years, I’ve collected hundreds of swims from greater than 100 high athletes. So I can race your digital twin in opposition to the database, make changes, and assemble the optimum formulation it’s best to use to your race—what number of kicks do you are taking off the dive; the place do you place your fingers coming right into a flip; what number of breaths do you are taking, and in what sample? It’s curated per athlete, per inch. We are able to say: Should you swim utilizing this formulation, you’re going to do the 100-yard backstroke in beneath 48 seconds.
These simulated races between digital twins may present a competitor two or three ft forward of you at a selected time limit—however I don’t need you to fret about that, since you’ll see that in Leg 3, they’re going to decelerate, and also you’ll catch up.
Should you watch footage of NCAA races, you’ll in all probability get a way that the UVA athletes appear to have this additional swagger, like they can not lose. And there’s after all reality to that, as a result of they’re profitable on a regular basis. However one of many surprising advantages of our work is, of their thoughts, they assume, If I swim that formulation, I win the race.
Cepelewicz: What challenges have you ever needed to overcome whereas doing these analyses?
Ono: There are a number of. For instance, the query of orientation in three-dimensional area is important. Your physique is consistently in movement. So how can we resolve when the power is definitely going within the course of the swim? It’s not that simple. We needed to guarantee that we have been basing our analyses on the proper orientations.
Accelerometer information could be very noisy. Accelerometers are very delicate. So a few of the arithmetic that’s deeply theoretical entails the way you easy the info to dampen out the noise. I have to know when a peak is significant. I’ve to have the ability to take a look at a stream of accelerometer information and say: That is the place you’re respiratory to the proper, however you lifted your head up a bit of an excessive amount of, or that is how a lot power you generated within the prompt you moved off the wall, earlier than you began decelerating. I want that stage of sensitivity. I have to have faith that the numbers I get imply what I feel they imply.
Determining the proper methodology to easy out this noisy information was in all probability probably the most refined sort of arithmetic that we needed to do, and that’s very secret.
Cepelewicz: What have you ever taken away from this expertise?
Ono: We haven’t found or invented any new math. We’re not doing rocket science right here. What I feel this proves is that the eye to element that comes from pondering analytically has benefit. I need to discover the stuff nobody else has, and use Newton’s legal guidelines, along with experimentation and a few linear algebra, to assist craft the very best performances for the athletes we work with.
There are nonetheless coaches that don’t take us severely. However that’s not my job. My job is to assist these athletes enhance as swimmers, and to assist get as a lot of them on the Olympic staff as we will.
I’m a pure mathematician by coaching. That may be slightly lonely. So that is maybe the one time in my life the place my coaching as a mathematical scientist appears to matter to a big group of individuals. It has been a dream trip.
