A design rationale for safer terrain park jumps that limit equivalent fall height

Sports Eng (2015) 18:227–239 DOI 10.1007/s12283-015-0182-6 ORIGINAL ARTICLE A design rationale for safer terrain park jumps that limit equivalent fall height Dean Levy1 • Mont Hubbard1 • James A. McNeil2 • Andrew Swedberg3 Published online: 1 September 2015  The Author(s) 2015. This article is published with open access at Springerlink.com Abstract Ski jump landing surface shapes can be created to cushion jumper landing by specifying a value of equivalent fall height (EFH) but, because the shape is calculated by integrating a differential equation, an infinite number of solutions results from the arbitrary boundary conditions. This paper provides a natural rationale for selection of the least expensive (minimum snow budget) one of these that nevertheless satisfies other design constraints, mainly limited normal acceleration and jerk during approach and landing transitions. Choosing the maximum allowable normal acceleration during the approach transition brings the entire infinite family of landing surfaces as close as possible to the parent slope. Limiting the rate of change of normal acceleration (jerk) decreases the likelihood of loss of balance at takeoff and consequent catastrophic spinal cord injuries on landing. An analogous choice, satisfying limited normal acceleration during the landing transition, selects the single member of the infinite family (providing the desired EFH) that lies closest to the parent slope and is therefore least costly to build. Software in the form of a graphical user interface is described that implements these algorithms and is appropriate for inexperienced users to calculate design details before actual fabrication of landing surfaces at a specific jump site. & Mont Hubbard 1 Department of Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, USA 2 Department of Physics, Colorado School of Mines, Golden, CO 80401, USA 3 US Army Maneuver Support Center of Excellence, Fort Leonard Wood, MO 65473, USA 1 Introduction Aerial tricks are now a popular activity for many skiers and snowboarders, and most ski resorts provide dedicated terrain parks jumps allowing enthusiasts to execute these aerial acrobatics. Unfortunately, this has likely contributed to an increase in injuries. Numerous studies have been made concerning this trauma, including those focusing on serious head and spinal cord injuries (SCIs) [1–6]. According to Jackson et al. [5], snow skiing in 2004 replaced football as the second leading cause of SCIs in the US, and these injuries continue [7–12]. Serious SCIs are permanently debilitating and the associated medical and other costs are exorbitant [13, 14]. Not only is the victim affected for the remainder of his or her life, but often entire families’ lives are upended. Snow parks and affiliates have been reluctant to adopt safer terrain park jump design practices, apparently due both to a questionable risk management strategy and to a lack of understanding of the scientific basis of such design. The current risk management strategy has been to lobby for laws that sharply limit liability, including for negligence, and to require patrons to sign strongly worded waivers thereby placing the burden of safety exclusively on the user. Although owners and operators of terrain parks have been found legally liable for damages from poorly fabricated jumps in the past [15], a more recent court ruling [16] may require a fundamental reassessment of this strategy and the responsibility of resorts for the safety of their patrons. In this case, the Oregon Supreme Court ruled [16] that due to (a) the inequitable nature of the resort-patron relationship in the formation of the liability waiver contract, and (b) the harsh and inequitable result that would occur if the ski area were released from liability for their own 228 negligence, such waivers are procedurally and substantively ‘‘unconscionable’’, respectively, and therefore unenforceable. The court further stated that resorts have a ‘‘duty of care’’ in the creation of snow park jumps because they have ‘‘the expertise and opportunity—indeed the common law duty—to foresee and avoid unreasonable risks of their own creation...’’. Arguments for avoiding engineering design have been based in part on the belief of the National Ski Areas Association that ‘‘standards are impossible’’ due to rider and snow variability in terrain park jumps [17]. To the contrary, research has shown that it is possible to design and build much safer terrain park jumps [18–26] based on controlling equivalent fall height (EFH), a measure of the energy dissipated in the rider impact at landing and one of the two most important contributing factors to both the likelihood and severity of snow park related injuries. Examples of such jumps have been built and experimentally verified to perform as expected [27]. For these reasons it is essential that resorts develop and implement practices that can demonstrate their ‘‘duty of care’’ while decreasing the number of injuries in general and SCIs in particular. An engineering approach to the design and construction of snow park jumps is perhaps the best way to accomplish this. To this end, the F27 Committee on Snow Skiing of the ASTM International is in the process of developing standards for snow park jumps [28]. The design philosophy discussed here is an attempt to support this process. To facilitate implementation of safer jump design, we adopt an engineering optimization rationale for choosing a particular solution among the infinite number of solutions [18, 26]. From the set of EFH-limiting jump landing surfaces, the best is deemed to be the one that minimizes the snow budget (the volume of snow required to build the jump above the parent slope) subject to the physical constraints of the pre-existing parent slope. Snow budget is especially important to terrain park operators because it is a good indicator of total cost in time and resources required to construct a jump. Given a set of designer selected parameters, we show below how choosing to minimize the snow budget selects both the location of the takeoff point and the member of the resulting infinite family of EFHlimited surfaces corresponding to that takeoff point, each of which is closest to the parent slope and thus requires as little extra snow as possible. In some circumstances, such as special events, other criteria such as time in the air may take precedence over snow budget, but as long as the desired criteria can be expressed quantitatively, the basic iterative engineering approach outlined here can be used. The design is constrained by requiring acceptable maximum normal accelerations of the jumper in both the approach-takeoff and landing transitions. As proposed by D. Levy et al. Swedberg [21], the approach-takeoff transition incorporates a classic clothoid shape (used previously in design of roadways and even bobsled-luge tracks [29]). As shown below, the clothoid par (...truncated)