A new analysis of the helicopter crash that killed basketball star Kobe Bryant illuminates a counterintuitive truth about how we perceive the physical experience of flight. The simulation created by two Colby students shows that the gravitational force of two very different trajectories—the intended flight path and the errant one—can be indistinguishable.

The helicopter carrying Bryant, his daughter, and seven others was flying in foggy conditions when it crashed near Calabasas, Calif., on the morning of Jan. 26, 2020. About 40 minutes into the flight, the pilot told air traffic controllers he was climbing to 4,000 feet, according to a preliminary report from the National Transportation Safety Board. But seconds later, the helicopter veered left and began to descend before colliding with the hillside.

Wouldn’t any experienced pilot have felt the helicopter’s descent and corrected course? The answer is no, and the recently released simulation explains why. Researchers Seungjae “Jason” Lee ’20 and Chido Mpofu ’20, with oversight from Professor of Mathematics Jan Holly, determined that a downward, curving trajectory like that of Bryant’s helicopter could exert physical force identical to a straight, level path.

News reports about the crash have alluded to pilot disorientation as the probable cause. “This work by Jason and Chido demonstrates how ‘disorientation’ does not mean ‘confusion,'” Holly said. “This case was almost certainly a simple but dangerous misinterpretation of forces on the body.”

Holly’s research focuses on this kind of disconnect, known as spatial disorientation. Most of us have experienced it at one time or another: You might look outside the window during a flight and realize by looking at the ground that the plane is tilted at an angle you didn’t expect.

Seungjae “Jason” Lee ’20, left, and Chido Mpofu ’20, with oversight from Professor of Mathematics Jan Holly, determined that a downward, curving trajectory like that of Kobe Bryant’s helicopter could exert physical force identical to a straight, level path, preventing a pilot flying without visual cues from knowing that the aircraft could crash.

The risks of pilot spatial disorientation in flight are well known, but the Colby students’ simulation highlights how certain trajectories can be particularly dangerous. Lee and Mpofu researched existing reports about the crash to determine information about altitude, speed, turn radius, and other flight details. They then fed this data into an existing mathematical model Holly created. The goal: to see how the helicopter’s tragic course might compare gravitationally to a straight and even one.

“I was surprised by how well the model fit with the actual accident,” Lee said. “Since the pilot did not have vision due to fog, our model does strongly support that spatial disorientation affected [him].”

Many models built to predict spatial disorientation will include known physiological effects, accounting for how humans tend to misinterpret certain motions. But Lee and Mpofu’s simulation excluded the physiological factor, analyzing solely according to the laws of physics. While the results do not perfectly map the helicopter’s actual path, the simulated crash trajectory’s gravitational force on the body proved to be exactly the same as that of a straight-ahead course.

“A ‘perfect’ pilot would not be able to feel the difference between the descending flight and level flight,” Holly said. “Not even the most sensitive force- and torque-sensing apparatus can tell the difference.”

Of course, pilots can also consult aircraft instruments to judge what is happening during a flight. But the trip in question was operating under visual flight rules, meaning the pilot was relying on sight rather than instrumentation. Sometimes even instruments cannot convince a spatially disoriented pilot that something is amiss, a fact Holly has observed in transcripts from other flights: “The feeling is so compelling that a pilot will actually think their instruments are broken.”

A simulation that shows two helicopters taking very different flight paths while the physiological effects on the pilots remain indistinguishable.

“I say, ‘With this math you’re using, you can model this.’ It gives a really concrete example of how undergraduate students can do cutting-edge work.” —Jan Holly, professor of mathematics

Researchers try to understand spatial disorientation partly by conducting experiments in which subjects are spun on a large centrifuge in the dark. In these experiments, people display certain physiological “blind spots” regarding movement. If you are in a chair without the ability to see around you, for example, and the chair begins to move along a circular path at a constant speed, at first you will be able to sense that you are rotating. Within seconds, however, you’ll think you’ve slowed down, and within a minute, you won’t realize you’re moving at all.

“Even if the person’s rotating really fast, they still won’t say they feel like they’re rotating,” Holly said. “They’ll say, did someone turn on the air conditioner?”

This happens so reliably that spatial disorientation models can predict it. But the models have their own blind spots: Predictions go awry, for example, if a subject is propelled in a half-circle and then stopped. In this scenario, people will report feeling as though they are moving in an S-shaped motion; but most models predict they will feel as though they are facing outward, positioned sideways through the curve.

“So far, none of the models is accurate in certain situations,” Holly said, “which means that we don’t really understand how the brain is working.”

That is what spatial disorientation research really aims to demystify: How the brain works. The implications are important not just for everyday flight but also space missions, where zero gravity makes the task of predicting human perceptions of motion even trickier. The research could also help in diagnosing inner ear disorders by comparing the data from a symptomatic person’s brain with a normal one.

While studying with Holly, Lee and Mpofu were focused on refining existing models to better predict physiological responses. When the crash happened, the professor saw an opportunity to demonstrate in real-world terms how easy it is to misread one’s motion. At her suggestion, Lee and Mpofu switched gears, using her model to produce the crash simulation. Both students expressed that the project led to a realization that what they had been studying in experiments was affecting people outside research labs.

“I really started seeing the importance of mathematical modeling and thinking through different scenarios of what’s going on around you [in the real world],” said Mpofu of working on the simulation. “The skills I learned from this project, I’m going to carry with me.”

Their results illustrate a point that Holly often makes to her students: That this kind of analysis isn’t solely the purview of top scientists.

“I say, ‘With this math you’re using, you can model this,'” Holly said. “It gives a really concrete example of how undergraduate students can do cutting-edge work.”