Many snowsport resorts now have terrain parks and decades-long epi- demiological evidence correlates terrain park use with injuries. Engi- neering design of jumps could reduce injuries by limiting equivalent fall heights, which are proportional to dissipated landing impact energy. No evidence refutes making terrain park jumps safer in this way. We discuss case studies illustrating that large equivalent fall heights are signi cant factors in traumatic injuries on terrain park jumps. We argue that it is the ethical responsibility of engineers to ensure the safety, health, and welfare of the public when performing and presenting research on snows- port safety. Developing standards and adopting design tools for builders can make jumps safer. To reduce injuries, we introduce an online tool that can evaluate existing jumps as well as design jump pro les with safer equivalent fall heights. 1 Introduction Impacts with xed surfaces can cause injury. Greater velocities, perpendicular to the surfaces, provide greater injury potential due to increased kinetic energy dissipation. Equivalent fall height (EFH) is a conceptually simple and familiar measure of impact danger used in safety standards worldwide, from construc- tion [1] to children's playground equipment [2]. EFHs of terrain park jumps can be calculated from Cartesian coordinates of jump pro les using techniques found in Levy et al. [3]. These coordinates include starting points, takeo ramps, and landing hills, all along jumpers' paths. Limiting energy dissipation in human bodies, hence EFH on jumps, reduces likelihoods of injuries and their severities. EFH should be considered because it is clearly connected to injury risk and can be used to design and construct safer jumps. In fact, safety research [4] tells us that designing forgiving environments (i.e., limiting EFH at all possible landing locations) is more e ective than forcing behavioral change (e.g., requiring the jumper to regulate their speed to ensure a landing only in a small safe region). Societal costs of jump injuries are discussed here with case studies that illustrate dangers if EFH is not limited appropriately. We also critique papers that question EFH relevance, written by authors that regularly provide expert testimony defending the ski industry in personal injury lawsuits. We present a web application that can facilitate jumping injury reduction by calculating EFH on current and future jumps. History Gradual introduction of terrain parks in the 1980's was accompanied by in- creased interest in aerial maneuvers and extreme sports participation. Jumps have proliferated since and are today nearly ubiquitous. Roughly 95% of US ski resorts include terrain parks. Unfortunately, this growth correlates with injuries. Two early longitudinal studies in the 1980's and early 1990's [5, 6] al- ready found signi cant increases in head injuries and concussions. Between 1993 and 1997 head injuries accompanied most skiing and snowboarding deaths [7]. Koehle et al. [8] stated \[S]eventy-seven percent of spinal injuries [9] and 30% of head injuries [10] in snowboarding were a result of jumps." Jackson et al. [11] determined that by 2004 snow skiing replaced football as the second leading cause of serious head and spinal cord injuries in America. These early increasing injury assessments persisted. According to Rus- sell et al. [12], \between 5 and 27% of skiing and snowboarding injuries oc- cur[red] in terrain parks [13, 14, 15, 16, 17, 18]". At the rst Winter Youth Olympic Games over a third of all snowboard half-pipe and slope-style com- petitors were injured [19]. Epidemiological research [20, 21, 22] continues to show that injuries on terrain park jumps are more likely and more severe than on normal slopes. Audet et al. [21] provides evidence that skiing or snowboard- ing in a terrain park is a risk factor for head, neck, back, and other severe injuries. Hosaka et al. [22] concludes that jumping is a main cause for seri- ous spinal injuries, regardless of skill level, and suggests that, because spinal 2 injuries' incidence have not decreased over time, the ski industry should focus on designing fail-safe jump features to minimize risks of serious spinal injuries. Similar jump design suggestions have appeared in peer-reviewed literature for more than a decade [23, 24, 25, 26, 27, 28, 3, 29, 30]. Methods Equivalent Fall Height EFH, a common proxy measure for impact danger in industrial safety standards, is the weight-speci c kinetic energy that must be dissipated on falling impact from height h[31, 23, 32]. Initial potential energy mgh is transformed to kinetic energy available to injure in non-rotating falls. Injury potential can be reduced by controlling impact circumstances, e.g. impact cushioning, and body orien- tation, con guration, and motion; however this energy must still be dissipated. Larger EFHs require more elaborate measures to reduce injury; reducing EFH does not. EFH can be interpreted by the general public. People have an intuitive sense of danger when faced with potential falls from large heights and a strong experiential common sense for relating fall height to likelihood of injury. People sense increasing danger associated with falling from larger heights because injury severity increases with fall height [33]. Ground, second, and third oor falls are about 2.6, 5.1, 8.8 m, respectively [34]. The German Society for Trauma Surgery's threshold for trauma team activation is a fall height of 3 m [35]. The US Occupational Safety and Health Administration requires protection for heights over 1.2 m for general workplace safety [1]. Chalmers et al. [2] argues for 1.5 m maximum fall heights for playground equipment. The Swiss Council for Accident Prevention makes speci c recommendations for EFHs below 1.5 m for terrain park jumps requiring basic skills [36]. Even with no standards in Olympic Nordic ski jumps, typical \equivalent landing height\ [32] is only about 0.5 m. EFHhof objects is formally de ned as h=v2 2g(1) wherevis impact velocity and ggravitational acceleration. Kinetic energy of objects moving at velocity vis transformed from potential energy at height h. Beginning from equation 1 equivalent fall heights hcan be determined for any surface, i.e., sloped landing pro le or shape, after jumping [29]. The result, neglecting air drag, is h=x2 4(xtanTy) cos2Ty sin2  tan12y xtanT tan1dy dx (2) 3 a function only of takeo angle T, impact coordinates ( x;y) relative to takeo , and landing surface slopedy dx, but not takeo speed [29]. To analyze jumps, one measures Cartesian coordinates of landing surfaces along jumpers' ight paths and takeo angles. Slopesdy dxare computed from measured coordinates ( x;y). Positive curvatures (concavity) in takeo ramps tend to cause skiers to rotate rearwards, inverting them in ight, so they might land in more dangerous body orientations [37], although ramp curvature does not in uence EFHs. Software and Online Access We presented the rst version of software for designing ski jumps with a speci ed EFH in Moore et al. [30]. It comprises a general-purpose, extensible, object- oriented software library with tools for 2D skiing simulation. Using this code, a web application was developed for interactive jump design. The web application is designed for a non-technical end-user and operable on any desktop, tablet, or mobile device supporting a web browser. We have extended capabilities of this software in version 1.4.0 (March 25, 2021) to assist work described here. New library features automate calculation of EFH for jump pro les described by a set of Cartesian coordinates. Addi- tionally, a new \analysis" page allows users to upload measured jump pro le coordinates in either a comma separated value or Microsoft Excel spreadsheet le. Jumps are then analyzed and EFHs are displayed graphically for interactive user manipulation and viewing. Figure 1 shows the web application with one of the case study jumps (Salvini v. Ski Lifts Inc.) loaded for analysis and explains its primary features. This software is written in Python and directly depends on popular pack- ages including Cython [38], matplotlib [39], NumPy [40], pandas [41], Plotly & Dash [42], pycvodes [43], SciPy [44], SymPy [45], and xlrd. This software is open source and licensed under the MIT redistribution license. The source code is distributed on PyPi1. Users can submit bug reports, feature requests, code improvements, and additions at the Gitlab repository2. The software li- brary's documentation is hosted via Read the Docs3. Basic examples of using the library are provided in the documentation and this paper's supplementary materials. We have also made the web application available for free use online.4 We do not view the software as the de nitive ski jump design and analysis tool, but rather as a foundation. The tool has been released as open-source so that re nements and modi cations are easy and encouraged. The software was designed to be extensible and modular. New surface shapes such as di erent takeo ramps are easily added by building upon the basic surface object using object-oriented programming principles. Similarly, new skier models can be added that incorporate more complex biomechanical features and actions. We 1https://pypi.org/project/skijumpdesign 2https://gitlab.com/moorepants/skijumpdesign 3https://skijumpdesign.readthedocs.io 4http://www.skijumpdesign.info 4 Figure 1: Screenshot of the ski jump design and analysis web app To use the analysis portion of the app, a user selects \Ski Jump Analysis" from the primary menu [1], uploads a .CSV or .XLS le by dragging it onto the screen [3], inspects the input data for accuracy in the table [4], sets the takeo angle [5], runs the analysis by pressing the \Run Analysis" button [6], views results in an interactive plot [2], and downloads results by pressing the \Download EFH" button [7]. 5 make use of this exibility for the web application and for calculations and visualizations presented in the following section. Results In these case studies of American lawsuits, juries ruled for injured plainti s. Negligent jump design and construction contributed signi cantly to injuries [46, 47]. Simulations below use methods in Levy et al. [3], assuming the same skier mass, frontal area, and drag coecient of 75 kg, 0.34 m2, and 0.821, respectively. Vine v. Bear Valley Ski Company In April 2000, Ms. Vine's lower spine was injured when she landed badly while jumping on skis at Bear Valley in California. The jump shape (Fig. 2) was a common form called a \table-top". Builders intend that jumpers completely clear the table, landing on down-slopes near a \sweet spot". The upper panel of Fig. 2 shows the measured jump surface from accident investigation. Vine landed short of the knuckle, de ned as the end of the table-top. This table-top was not at and horizontal as is typical. Instead it was concave, compounding dangers of short landings. At the 11 m landing horizontal distance measured from takeo , the surface sloped upwards approximately 5. Concave table tops exacerbate detrimental e ects of failing to align landing zone tangents close to jumper ight paths at impact. The lower panel displays EFHs at di erent landing locations. These are greatest just short of the knuckle. At the sweet spot, just past the knuckle, EFH drops precipitously to about 1 m, although landing in this narrow re- gion requires jumpers to control takeo speeds very accurately to within about 1 m s1. Landing at 11 meters, Vine's EFH was instead almost 4 meters, equiv- alent to falling from between one and two stories [34]. She had also rotated backward in ight, landed on her lower spine and was paralyzed. Lower EFH would have decreased risk of injury, due to lower impact forces. Jumps with smaller EFHs can be created at similar costs. The green jump pro le in the upper panel of Fig. 2 shows a possible jump design, see Levy et al. [3], of similar size with similar ight times that ensures constant (small) EFHs of about 1 m. Interestingly, the convex shape of this jump is close to the original concave table-top inverted, showing that convex landing shapes are critically important for limiting EFHs. This alternative jump design would have lowered impact forces for landings at all locations. In 2002, the jury ruled in favor of Ms. Vine, agreeing that Bear Valley was responsible for providing unsafe jumps. Salvini v. Ski Lifts Inc. In 2004, Mr. Salvini attempted a table-top jump on skis in the terrain park of The Summit at Snoqualmie Ski Resort, in Washington state. Salvini over- shot the intended landing location while traveling at typical skiing speeds [48], 6 10 5 05Vertical Position [m]Flight @ 7 m/s Flight @ 10 m/s Flight @ 14 m/s 10 5 0 5 10 15 20 25 Horizontal Position [m]0123456Equivalent Fall Height [m] 3.7 5.4 6.8 8.1 9.3 10.6 11.8 12.3 12.7 13.2 13.7 14.2Figure 2: Bear Valley jump compared to possible safer design Top: Measured landing surface (solid black) and jumper ight paths (intermittent black) from measured 30takeo angle. A 14 m s1takeo speed is used as the design speed [3] for a comparison jump (solid green) shaped to have constant EFH of 1 m. Bottom: EFH for both jumps in corresponding colors at 2 m intervals. Numbers above bars indicate takeo speeds required to land at that location. Intermittent horizontal gray lines indicate increasing relatable fall heights: knee collapse, average 1ststory fall, and average 2ndstory fall. 7 rotated backward during ight and landed on his back, ultimately su ering quadriplegia. The jury sided with Mr. Salvini and he was awarded a judgment of $14M. At his landing location of 30 m the EFH exceeded 10 meters, approximately a 3-story fall. Figure 3 shows the measured jump pro le from the accident investigation. For takeo speeds over 13 m s1, the lower panel shows that the EFH is over 10 m and growing linearly with larger takeo speeds. Severe injury is almost certain in falls this high, especially if landing body orientation loads the spine, as in this case. The upper panel also shows a jump pro le (green) designed to have a 1 m EFH for all speeds below 16 m s1. This pro le requires signi cantly more snow than the measured jump but limits EFH to 1 m. This jump highlights how extreme EFHs can become if jumps are not properly designed. Nobody would voluntarily jump out of three story windows, snow or not, as injuries are clearly likely. Our internal altimeter tells us so, but it is impossible for recreational skiers to evaluate EFHs simply by looking at jumps. These two case studies demonstrate that de cient jump landing shapes have devastating consequences and that engineering analysis and design based on well-established laws of mechanics could be used to design jumps that limit EFHs safely. Designing jumps this way is based on mechanics elucidated cen- turies ago by Isaac Newton and Emilie du Ch^ atelet [49], and fundamental to physics and engineering education. Designing jumps to limit EFHs unquestion- ably reduces injury risk by reducing impact energies and associated forces. Discussion Moral Imperative \Hold paramount the safety, health and welfare of the public" [50], is the rst canon of engineering ethics. Ethics is not a matter of opinion and should not be optional, but rather is the foundation for engineering. The rst canon compels engineers to use their technical expertise to protect snowsport participants from injuries. Reducing EFHs cannot increase likelihoods of injuries. Building well designed, safer jumps is no more laborious than building poorly designed, unsafe jumps. There is no reason not to control EFHs with ethical design algorithms and software. Nonetheless ski industries and their insurance companies are reluctant to adopt and endorse such design methods, choosing instead to invest in litigation defense rather than technologies for constructing safer jumps. They hire engineers to profess doubt on the fundamental physics of EFHs during litigation. Publications cited by the defense in litigation to support these doubts provide little or nothing for the safety, health, and welfare of the public, that engineers should hold paramount. In their book \Merchants of Doubt" [51], Oreskes and Conway have studied this problem more generally. They show that in numerous industries over the last 60 years, scienti c evidence accumulated that commonly accepted indus- 8 15 10 5 05Vertical Position [m]Flight @ 8 m/s Flight @ 15 m/s Flight @ 16 m/s 10 0 10 20 30 40 Horizontal Position [m]051015Equivalent Fall Height [m] 3.6 5.7 7.3 8.4 9.0 9.7 10.3 10.8 11.4 11.9 12.4 12.9 13.6 14.3 15.0 15.7 16.3 16.9 17.6 18.2 18.7 19.3Figure 3: Snoqualmie jump compared to possible safer design Top: Measured landing surface (solid black) and jumper ight paths (intermittent black) for measured 25takeo angle. The 16 m s1takeo speed is used as the design speed for a comparison jump (solid green) with constant EFH of 1 m. Bottom: Equivalent fall height for both jumps in corresponding colors at 2 m intervals. Numbers above bars indicate takeo speed required to land at that location. Intermittent horizontal gray lines indicate increasing relatable fall heights: knee collapse, average 1ststory fall, average 2ndstory fall, and average 3rdstory fall. 9 trial activities were harmful, to individuals and society. However, industries had vested interests in continuing practices that were dangerous to the public, perhaps because operational changes would have led to signi cant, short-term costs and inconvenience. Examples carefully described and analyzed [51] in- clude using DDT, smoking tobacco, producing acid rain from coal- red power plants, causing ozone holes from CFCs, damaging health with second-hand to- bacco smoke, and changing our climate with CO2 emissions. Rather than using the scienti c evidence as a basis for changes in practice, strategic responses of industries have been to \emphasize the controversy among scientists and the need for continued research" [51]. This same strategy is used by some snowsport industries and their defense experts, who disparage EFHs. To sow doubt and counter solid, fundamental, ethical, scienti c concepts of jump designs limiting EFH, defense experts intro- duce confounding factors to cloud and confuse basic issues. Consider as evidence three papers [52, 53, 37] co-authored by well-known ski industry defense experts who have testi ed for snowsport resorts and their insurance companies. We do not fundamentally question their empirical ndings but we do question their interpretation of the ndings, namely their conclusion that greater fall height is not a basic indicator of greater risk of injury. Shealy et al. [52] conducted an experimental study attempting to test the hypothesis that takeo speed is a predictor of the distance from a jump take-o to landing. They reached the mechanically impossible conclusions both that there is \no statistically signi cant relationship between takeo speed and the distance traveled" and that \takeo speed is not a dominant or controlling factor (in how far a jumper travels)" [52]. These conclusions were used to question the soundness of analytical mechanical modeling of jumper ight used in Hubbard [23] and McNeil et al. [26]. Some of these same authors later vouched for terrain park jump safety. Using data held by the National Ski Areas Association (NSAA), Shealy et al. [53] concluded that their \hypothesis that jumping features resulted in an increase risk of injury [was] not . . . substantiated." [53] This is the only study we are aware of with this conclusion. It is dicult to reconcile it with the voluminous contradictory research documenting the unique dangers posed by terrain park jumps in tens of other studies cited both herein and in [23, 24, 26, 27, 28, 3, 29, 30]. Although NSAA releases yearly totals of resort-related fatalities and catastrophic injuries, the raw data on which Shealy et al. [53] was based is not publicly available, thus making these results unveri able. The data was collected from press releases produced by the NSAA [53], which has an inherent con ict of interest, thus potentially introducing confounding bias. In a third experimental study (N=13) speci cally designed \to evaluate in- jury mitigation potential of surfaces limiting EFH" [37], Scher et al. clearly show that body orientation, i.e. falling directly on one's head (in all trials), can cause dangerous cervical spine compression loads [37], even at low fall heights. They report on e ects of EFH but only test heights from 0 :23 m to 1:52 m, sim- ilar to limitations in Shealy et al. [52] by restricting ranges of their independent variables, and ignoring fall heights known to have caused severe injuries regard- 10 less of body orientation. Yet, they insinuate that EFH has no appreciable e ect on injuries. The title, \Terrain Park Jump Design: Would Limiting Equivalent Fall Height Reduce Spinal Injuries?" implies that they appear to believe that falling from greater heights might notcause greater injuries. Why propose such mechanically awed hypotheses? Sowing doubt on EFH as a basic indicator of risk appears to be paramount. Extending the scope of ndings is a common mistake, but one that should not be made by ethical, professional engineers when safety, health, and welfare of the public is at issue. Fundamental laws cannot be disproved by these kinds of jumping experiments. If statistical or experimental results seem in con ict with predictions from classical mechanics, the problems are probably with the statistical or experimental design or their interpretations, but not fundamental laws of mechanics. Defending dangerous practices that lead to injuries helps prolong these practices, which leads to further injuries, clearly contradictory to ethical engineering. Engineering experts defending ski industries and their practices could be complicit in continued societal damage, and in doing harm to the safety, health, and welfare of the public. As Upton Sinclair wrote \it is dicult to get a man to understand something when his salary depends on his not understanding it" [54]. It is not evident that these papers [52, 53, 37] \hold paramount the safety, health and welfare of the public". They are silent on how their ndings can be used to reduce injuries. They obscure a scienti cally fundamental, mechanically irrefutable fact that impacting surfaces at lower normal velocities is safer. They \create the appearance that the claims being promoted were scienti c" [51, page 244]. Fundamental laws have made mechanics a science. Findings that contradict such fundamental laws should be carefully scrutinized and review processes accepting such articles should be questioned. Organizations also merchandise doubt. A decade ago, NSAA argued [55] that, because of rider and snow variability, terrain park jump \standards are essentially impossible." While it is true that the \virtually . . . in nite number of ways that a given feature may be used by an individual . . . varying speed, pop, body movement, takeo stance, angles of approach, the attempting of di erent kinds of maneuvers, landing stance, and the type of equipment used (skis or snowboard) . . . create a wide variety of experiences for the users" [55], none of these in fact preclude EFH analysis and rational engineering design. This was shown clearly in Hubbard and Swedberg [25] which examined quantitatively the e ects of variations in factors actually involved in the mechanics: takeo speed, snow friction, air drag, tail wind, snow melt and jumper pop. These so-called \uncontrollable factors" fell into three groups: (1) those for which there is zero sensitivity, i.e., an uncontrollable factor that makes no di erence in the ability of the designed jump to deliver the designed EFH; (2) those for which fairly large parameter variations cause only insigni cant maximum deviations in EFH, and (3) those for which the factor can be taken into account in the design process itself and its larger e ect on EFH completely eliminated in the unsafe direction. The allegation that design of limited EFH surfaces is prevented by the complex- ity of the problem and by the large number and types of parameter variations 11 away from nominal is false; in fact the allegation is just more merchandised doubt. In snowsport injury cases, testifying for injured plainti s and testifying defending corporations are not ethically equivalent. The former attempts to address problems that cause injuries, holding paramount the public's safety, health, and welfare. The latter attempts to defend practices that might have contributed to the injury, to limit nancial losses of corporations. The idiom \two sides to every question", is not appropriate in science and engineering [51, page 268]. Engineers whose scholarly work ignores engineering's rst canon of ethics in favor of merchandising doubt can diminish the scienti c integrity of engi- neering journals and engineering conferences. Journal editors should recognize submissions primarily intending to cast doubt on good science and engineering for what they are, tools of insurance companies for defending civil suits, and reject these submissions. Papers whose ndings help to perpetuate dangerous practices for the short-term nancial bene t of industry and which apparently do nothing for the safety, health, and welfare of the public, are unethical and do not belong in engineering journals or conference proceedings. What Can Be Done? Absolutely, the most important change will be to incorporate rigorous, rational processes and scienti c principles that consider mechanical impact safety into designing freestyle jumps. At present a large fraction of, if not most, jumps in the USA are created in a formulaic way using two straight lines, a horizontal deck (tabletop) and nearly constant-slope landing region, linked by a curved knuckle. This design philosophy is recommended in the instructions provided by the NSAA [56] and is presumably followed by their members. Although such jumps are simple and thus easy to design, research has shown that jumps with bi- linear geometry have generally poor EFH behavior [24], i.e. that they can have low EFH only in a small region just past the knuckle (called the \sweet spot"). In a recent version of their freestyle terrain park notebook [56], the jump landing area is even termed the \landing plane" because it is envisioned to be planar. There is no reference to any concept such as EFH or similar measure of impact or its e ect on safety because the NSAA's strategy is to put the responsibility for safety fully on the jumper. There is no quantitative consideration of jump impact safety (e.g. from the point of view of EFH) beyond the experience of the designer. The skiing industry continues to resist more scienti cally-based rational approaches to design, in spite of the fact that computer aided design (and even computer-assisted fabrication and maintenance) of snow park jumps (see Figure 4) has been available from snow groomer manufacturers for over 5 years [57]. The 2015 NSAA reference [56] still contained the statement that \Standards are essentially impossible . . . ". Once the jump surface has been designed, the next most important change is to build accurately what was designed. Presently a dominant fraction of jumps are simply fabricated by groomer operators, based on perhaps a few 12 Figure 4: Commercial availability of computer-aided design and computer-controlled fabrication of snow park surfaces began as early as 2016. The right panel shows Prinoth's computer generated 3-D jump land- ing surface with their family of simulated jumper paths, even ones outside the central vertical bisecting plane, with the landing surface colored corresponding to the EFH incurred by the jumper at that landing point. The left panel shows a computer-controlled snow groomer tted with two GNSS receivers that allow real time measurement of their position to an accuracy of about 2 cm, calcula- tion of the yaw and roll of the groomer blade, and precise closed loop control of the snow addition and removal process. Images courtesy of Prinoth, supplier of snow groomers for the winter Olympics in China 2022. measurements of distances and slopes (deck length, takeo angle, landing region angle and length) during the process. But the design concepts are overly simple and do not incorporate or address quantitative indicators of safety such as EFH. The introduction of computer controlled grooming (see Figure 4), similar to computer aided manufacturing (CAM) and machining (CNC), will facilitate construction of more complex designed shapes precisely and accurately to within ten centimeters. These would include the non-trivial constant EFH surfaces provided by our online ski jump design software that limit landing impulses to acceptable levels. Every jumper (and parent of young jumpers) should be able to con rm that a jump is not unsafe before trying it. Appropriate inspection, evaluation, cor- rection, and maintenance of existing jumps, and the design and construction of safer new jumps should be promoted. Postings should be required and include EFHs, the certi ed inspectors name, and when last inspected and maintained. Inspections should be frequent enough to ensure that jumps meet safe design standards, particularly regarding takeo s and starting points to prevent inadver- tent inversions due to take o ramp curvature. Standards need to be developed that limit EFHs in collaboration between industry and research engineers to de- sign, build, inspect, maintain, and post safer jumps. An example of rst steps in this area is a terrain park safety guide by the Swiss Council for Accident Prevention [36]. To complement standards, certi cation programs are needed for jump build- 13 ing, inspection, and maintenance. ASTM, an American organization for a wide variety of consensus standards, provides a historical example of a successful cer- ti cation program. ASTM Committee F27 was created in 1982 for skiing safety and began to develop ski binding standards. Proponents were led by orthopedic surgeons and academic researchers [58]. Industry argued that standards were unattainable because release value measurement was impossible by ski shops, just as industry now makes similar arguments about jumps [56]. Nevertheless certi cations and inspection standards for bindings were developed, which led to fewer lower-extremity equipment-related injuries [58]. Now however no medical professionals and almost no academics remain in F27. E orts to create similar standards for terrain park ski jumps began in F27 more than a decade ago [59], yet no standards have yet resulted with any appearance of increasing safety for the public. The US skiing industry, aided by the NSAA, has been successful in delaying the implementation of standards. In parallel with standards development, assessing and possibly reshaping ex- isting jumps to eliminate dangerous EFHs should be a straightforward route for ski resorts to proactively increase terrain park safety. Accurate enough measure- ments of existing surfaces can occur even with simple tools, e.g. tape measure and digital level, and consume relatively little time and e ort per jump (see supplementary materials for details). Calculation and visualization of EFHs from these measurements can take some time without a computational pro- gram for calculating EFHs from hill pro les. The user-friendly, freely-accessible open-source online web application tool that we have made available for jump designers and builders has almost instantaneous calculation and visualization steps, solving this problem. With this software, jump builders can add safety assessment to their toolbox, even accessing it from a smartphone or tablet on hills. We see no reason that this basic assessment should not be part of every jump construction process. The only ethical decision is to adopt these methods; saving even one person from a life of paralysis, or even death, must be worth the relatively minor inconvenience of shaping jumps using the methods in Levy et al. [3]. Conclusion There are, of course, more factors than jump takeo and landing pro les that contribute to injuries on terrain park jumps. Yet normal impact velocity can be easily controlled with a properly designed and fabricated jump. There is no evidence that decreasing designed EFH increases injuries in falls; injuries can only decrease. Thus we see no reason not to adopt constant low values of EFH for public-use jump designs. Builders of jumps that are not designed as forgiving environments are negligent. Public safety must be held paramount to short-term return-on-investment. The methods implemented in the software illustrated in Section provide a starting point for realizing EFH-conscious designs in terrain parks. We hope to see the design and analysis adopted by commercial grooming equipment man- 14 ufacturers so that safety is made integral to jump design. Our software can grow and evolve through contributions from other researchers to incorporate many other nuances of injury prevention. We also see the methods providing a structure for standards development. And minimally, we see the software as an immediately usable tool for jump fabricators in the eld. Acknowledgements We thank Rado Dukalski for feedback on the web application and Yumiko Hen- neberry, Lyn Taylor, and Andy Ruina for feedback on the manuscript. Declarations MH served as a plainti 's expert witness in the two case studies discussed above and in numerous other similar cases since. CB testi es occasionally on behalf of plainti s in ski and snowboard injury cases. He has collaborated with Shealy and C. D. Mote, Jr., Sher's doctoral advisor, on ski safety research, has participated in ASTM F27 since the 1980s on standards for bindings, boots, and skis, and holds patents on ski and snowboard binding designs intended to reduce injuries. Funding Not applicable Other Declarations Availability of data and material All data is available at https://gitlab. com/moorepants/skijumpdesign andhttps://gitlab.com/mechmotum/ ski-jump-analysis-paper . Code availability The skijumpdesign version 1.4.0 source code is archived at https://doi.org/10.5281/zenodo.4637076 . Additionally, it and the paper's source code is available at https://gitlab.com/moorepants/ skijumpdesign andhttps://gitlab.com/mechmotum/ski-jump-analysis-paper . Author's contributions JM and MH contributed to the study conception and design. Material preparation, data collection and analysis were performed by JM and MH. The rst draft of the manuscript was written by JM, BC, MH, and CB. MH and CB were primarily responsible for drafting the parts on merchandising doubt and ethics, respectively. All authors read and approved the nal manuscript. BC and JM wrote the accompanying software. Ethics approval Not applicable 15 Consent for publication JM, BC, MH, and CB consent for publication.