Simulation of a Helicopter Crash
by Seungjae (Jason) Lee and Chido Mpofu

Below is a simulation representing the helicopter crash near Calabasas, California, on January 26th, 2020. The crash claimed the lives of nine people: Alyssa Altobelli, 14; Keri Altobelli, 46; John Altobelli, 56; Kobe Bryant, 41; Gianna Bryant, 13; Payton Chester, 13; Sarah Chester, 45; Christina Mauser, 38; and the helicopter's pilot, Ara Zobayan, 50. The preliminary N.T.S.B. report indicated that at the time leading to the crash the helicopter was flying through thick fog [3]. Due to the fog, the pilot would not have had a visual reference and would have had to rely mainly on the vestibular system.

Humans rely on various inputs such as the vestibular and visual systems when perceiving self-motion in a moving vehicle such as a helicopter. In the absence of visual input—for example, if a person is in the dark—they rely mainly on the vestibular system. To perceive a change in motion—for example, entering a curve—requires a certain detectable threshold to be reached. As a result, a straight-line path will feel the same as a curved path if the threshold is not reached upon entering the curve. Therefore in the case of the helicopter moving in the fog, if the initial angular acceleration was below the human perceptual threshold, the initiation into the curve would not have been detected by the pilot. Distractions such as noise and vibrations affect the threshold and therefore the ability to detect entry into the curve. Furthermore, the speed at which the turn is initiated can make it difficult to perceive, for example, if the turning was slow.

Once in the turn, the forces on the body are exactly the same as if the helicopter were still flying level. Not only can a human not perceive this difference, the laws of physics show that even the most sensitive device cannot distinguish between these motions. While in this motion, the pilot would feel the same as if the helicopter were flying in a straight path with a visual reference. The feeling is so compelling that some pilots will ignore their instruments thinking that their instruments have a wrong reading when in fact the instruments are correct. Because of this difference in perception and actual motion, the pilot would not have been able to feel that the helicopter was crashing until the helicopter was out of the fog, which was too late.

To explain this phenomenon, the simulation below was created in MATLAB® [4] based on a spatial disorientation model of Holly [1,2]. Both papers provide a model on how motion would be perceived in the absence of a visual reference. The simulation shows how a curved path can feel exactly the same as a straight path. Using this model, a video is shown below of the simulation. The video shows a motion similar to that proposed by the preliminary report of how the helicopter descended until it hit the ground.

Video: Simulation of a curved helicopter trajectory with forces exactly the same as those during straight-and-level flight. Also shown is the straight-and-level flight that a human pilot and passengers would probably be (incorrectly) feeling. The two helicopters are scaled up by a factor of four. At bottom is a further expanded helicopter to show the orientation of the descending helicopter.

References

  1. Jan E. Holly, Baselines for three-dimensional perception of combined linear and angular self-motion with changing rotational axis, Journal of Vestibular Research 10 (2000) 163–178.
  2. Jan E. Holly, Saralin M. Davis, Kelly E. Sullivan, Differences between perception and eye movements during complex motions, Journal of Vestibular Research 21 (2011) 193–208.
  3. “Read the Preliminary N.T.S.B. Report About the Kobe Bryant Helicopter Crash.” The New York Times, February 7, 2020. https://www.nytimes.com/2020/02/07/us/kobe-bryant-ntsb-report.html
  4. MATLAB®, MathWorks, Natick, Massachusetts.