How Fractal Complexity Distorts Distance and Elevation Gain in Trail and Mountain Running
The Case for Course Measurement Standardisation
DOI:
https://doi.org/10.51224/SRXIV.481Keywords:
Course measurement, Trail Running, Mountain Running, Race classification, GPS accuracyAbstract
Research Question:
Trail and mountain running (TMR) is a rapidly growing and increasingly professionalized sport. However, the absence of a common standard for measuring race courses creates inconsistencies in distance and elevation gain metrics. This study investigates how fractal complexity affects these measurements at varying GPS resolutions and emphasizes the need for standardized course measurement protocols in TMR.
Research Methods:
GPX files from 34 UTMB World Series race courses, including final events in Chamonix, were analysed. Horizontal distance, elevation gain, km-effort, and fractal complexity were computed at varying GPS spatial resolutions (0.2–100 m). Elevation data were refined using a 20-cm Digital Elevation Model (DEM) to minimize errors. Courses were systematically resampled and compared to assess the effects of spatial resolution on race measurements and classifications.
Results and Findings:
The findings reveal that a decrease a in the spatial resolution of GPS measurements leads to significant reductions in measured horizontal and vertical distances, with discrepancies of up to 10%. These inconsistencies affect race course classifications, athlete benchmarking, and performance comparisons across different events.
Implications:
This study highlights the importance of standardising GPS spatial resolution to improve the accuracy and consistency of trail and mountain running race measurements. Adopting a 1-metre resolution would enhance the reliability of distance, elevation gain, and km-effort calculations, ensuring fairer race classifications and comparability across events. The proposed methodology can also benefit other sports and disciplines that rely on precise course measurements, such as cycling, hiking, and skiing, by reducing discrepancies caused by varying measurement protocols.
Metrics
References
Mandelbrot, B. (1967). How long is the coast of Britain? Statistical self-similarity and fractional dimension. science, 156(3775), 636-638.
Lam, N. S. N., & Quattrochi, D. A. (1992). On the issues of scale, resolution, and fractal analysis in the mapping sciences. The Professional Geographer, 44(1), 88-98.
Mandelbrot, B. B. (1998). Is nature fractal?. Science, 279(5352), 783-783.
Li, X. (2014). Using complexity measures of movement for automatically detecting movement types of unknown GPS trajectories. Am. J. Geogr. Inf. Syst, 3(2), 63-74.
Skinner, B. (2020). The fractal dimension of the Appalachian Trail. arXiv preprint arXiv:2011.03332.
World Athletics in cooperation with AIMS. (2023). The measurement of road race courses: Road running & race walking (Revised edition). World Athletics.
Corbitt, T., Barry, J., Merchantville, N. J., Bright, B., Campbell, R., Roxbury, W., ... & Neck, G. (1964). Measuring Road Running Courses. Ted Corbitt.
Vallan, A., & Realpe, L. R. (2022). Length measurement of road race courses: Experimental comparison of GPS trackers (Master’s thesis, Politecnico di Torino, Master Degree in Biomedical Engineering).
Georgopoulos, A., Papageorgaki, I., Tapinaki, S., & Ioannidis, C. (2012). Measuring the classic marathon course. International journal of heritage in the digital era, 1(1), 125-144.
Gløersen, Ø., Kocbach, J., & Gilgien, M. (2018). Tracking performance in endurance racing sports: evaluation of the accuracy offered by three commercial GNSS receivers aimed at the sports market. Frontiers in physiology, 9, 1425.
Rampinini, E., Alberti, G., Fiorenza, M., Riggio, M., Sassi, R., Borges, T. O., & Coutts, A. J. (2015). Accuracy of GPS devices for measuring high-intensity running in field-based team sports. International journal of sports medicine, 36(01), 49-53.
Campbell, M. J., Dennison, P. E., & Thompson, M. P. (2022). Predicting the variability in pedestrian travel rates and times using crowdsourced GPS data. Computers, Environment and Urban Systems, 97, 101866.
de Smet, D., Verleysen, M., Francaux, M., & Baijot, L. (2018). Long-distance running routes’ flat equivalent distances from race results and elevation profiles. In 6th International Congress on Sport Sciences Research and Technology Support (Vol. 1, pp. 56-62).
Sánchez, R., & Villena, M. (2020). Comparative evaluation of wearable devices for measuring elevation gain in mountain physical activities. Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, 234(4), 312-319.
Sanchez, R., Egli, P., Besomi, M., & Truffello, R. (2024, July). Assessing the impact of Digital Elevation Model resolution on Elevation Gain Estimations in Trail Running. In 2024 International Conference on Electrical, Computer and Energy Technologies (ICECET (pp. 1-5). IEEE.
Scarf, P. (2007). Route choice in mountain navigation, Naismith's rule, and the equivalence of distance and climb. Journal of Sports Sciences, 25(6), 719-726.
Prisner, E., & Sui, P. (2023). Hiking-time formulas: a review. Cartography and Geographic Information Science, 50(4), 421-432.
Kay, A. (2012). Pace and critical gradient for hill runners: an analysis of race records. Journal of Quantitative Analysis in Sports, 8(4).
Emig, T., & Peltonen, J. (2020). Human running performance from real-world big data. Nature communications, 11(1), 4936.
Campbell, M. J., Dennison, P. E., Butler, B. W., & Page, W. G. (2019). Using crowdsourced fitness tracker data to model the relationship between slope and travel rates. Applied geography, 106, 93-107.
UTMB World (n.d.). UTMB World Series Events. Retrieved November 18, 2024, from https://utmb.world/
Chan, G., Hall, P., & Poskitt, D. S. (1995). Periodogram-based estimators of fractal properties. The Annals of Statistics, 1684-1711.
NASA Shuttle Radar Topography Mission (SRTM)(2013). Shuttle Radar Topography Mission (SRTM) Global. Distributed by OpenTopography.
Robusto, C. C. (1957). The cosine-haversine formula. The American Mathematical Monthly, 64(1), 38-40.
Menaspà, P., Impellizzeri, F. M., Haakonssen, E. C., Martin, D. T., & Abbiss, C. R. (2014). Consistency of commercial devices for measuring elevation gain. International Journal of Sports Physiology and Performance, 9(5), 884-886.
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Copyright (c) 2024 Raimundo Sanchez, Pascal Egli, Kilian Jornet, Michael Duggan, Manuela Besomi (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
