How Robust is Equivalent Fall Height for Predicting Injury Severity in Snow Jumps?

Example snow jump with a constant equivalent fall height landing surface.


Equivalent fall height has been proposed as an important measure to minimize in the design of safer ski and snowboard jumps [Hubbard2009]. The equivalent fall height is a proxy measure for the impact velocity of a human against a surface. It provides better context for a layperson to perceive the associated danger, i.e. people have a strong experiential sense of the danger associated with falling from a given height. Jumps can be designed with a specified equivalent fall height by simulating a particle model of a jumper [Levy2015]. These models seem simplistic but they are a useful because both the equivalent fall height is such a dominant corollary to injury and it's predictive power is robust to many other factors that can cause injury in a jump landing [Hubbard2012]. Nevertheless, there are naysayers to the idea that jumps should be designed with a small equivalent fall height. One objection is that the particle models do not capture enough of reality to be useful, see [Shealy2010] & [Scher2015]. The goal of this project would be to extend the particle model to one or more rigid bodies which can have angular rotation and tangential forces due to friction on the landing surface are considered. Here are some questions that could possibly be answered:

  • Is equivalent fall height a robust measure of injury severity with respect to a rotating jumper? Or is a different measure necessary?
  • How dangerous is the force to the skier in terms of the tangential and normal components?
  • For what angular rotation and surface friction conditions is or isn't equivalent fall height a dominant cause of impact forces?
  • How much curvature can safely be permitted in the takeoff ramp shape to prevent large tangential impact forces?
  • Are there simple measures or criteria like the equivalent fall height for the particle model that can be used for jump design that considers the rotational affects of the jumper?
  • Are there any reasons that equivalent fall height should not be lowered in jump designs with respect to rotating impacts?

Possible Approach

  • Literature review on foundational topics: human body collisions, ski jumping, measures of injury severity in falls & collisions, etc.
  • Develop a simple rigid body model and show that it simulates reasonable free-rotating ski jump flight. See [Hubbard1989] for one such model.
  • Exercise the simulation to find impact velocities and/or forces for differing initial conditions and landing surfaces.
  • Expand the skijumpdesign library and web application [Moore2018] with any validated findings.

Required Skills

  • 2D rigid body dynamics and impact
  • Simulation of rigid body dynamics
  • Visualisation with Python based tools
  • Web application (basic HTML/CSS and Dash)


[Hubbard1989]M. Hubbard, R. L. Hibbard, M. R. Yeadon, and A. Komor, "A Multisegment Dynamic Model of Ski Jumping," Journal of Applied Biomechanics, vol. 5, no. 2, pp. 258–274, May 1989, doi: 10.1123/ijsb.5.2.258.
[Hubbard2009]M. Hubbard, "Safer Ski Jump Landing Surface Design Limits Normal Impact Velocity," Journal of ASTM International, vol. 6, no. 1, p. 10, 2009, doi: 10.1520/STP47480S.
[Shealy2010]J. Shealy, I. Scher, L. Stepan, and E. Harley, "Jumper Kinematics on Terrain Park Jumps: Relationship between Takeoff Speed and Distance Traveled," Journal of ASTM International, vol. 7, no. 10, p. 10, Nov. 2010, doi: 10.1520/JAI102885.
[Hubbard2012]M. Hubbard and A. D. Swedberg, "Design of Terrain Park Jump Landing Surfaces for Constant Equivalent Fall Height Is Robust to ‘Uncontrollable’ Factors," in Skiing Trauma and Safety: 19th Volume, R. J. Johnson, J. E. Shealy, R. M. Greenwald, and I. S. Scher, Eds. 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959: ASTM International, 2012, pp. 75–94.
[Levy2015]D. Levy, M. Hubbard, J. A. McNeil, and A. Swedberg, "A design rationale for safer terrain park jumps that limit equivalent fall height," Sports Engineering, vol. 18, no. 4, pp. 227–239, Dec. 2015, doi: 10.1007/s12283-015-0182-6.
[Scher2015]I. Scher, J. Shealy, L. Stepan, R. Thomas, and R. Hoover, "Terrain Park Jump Design: Would Limiting Equivalent Fall Height Reduce Spine Injuries?," in Skiing Trauma and Safety: 20th Volume, R. J. Johnson, J. E. Shealy, and R. M. Greenwald, Eds. 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959: ASTM International, 2015, pp. 72–90.
[Moore2018]J. K. Moore and M. Hubbard, “skijumpdesign: A Ski Jump Design Tool for Specified Equivalent Fall Height,” The Journal of Open Source Software, vol. 3, no. 28, p. 818, Aug. 2018, doi: 10.21105/joss.00818.

See Also

How to Apply

Send an email to with the title of the project in the subject line. Include an approximately half-page motivation letter explaining why you want to work in the Bicycle Lab on this project along with your current resume or C.V.