The DOI matches its Crossref record; 42 of the 42 references it cites were found in a registry or an index.
Using crowdsourced fitness tracker data to model the relationship between slope and travel rates
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One of the critical factors affecting travel rates while hiking, jogging, or running along a trail is the slope of the underlying terrain. Models for predicting this effect have been used in a wide variety of scientific and applied contexts, including recreation planning, search and rescue, wildland firefighter safety, social network analysis, and recreating historical human movement patterns. Despite their wide use, these models are based on datasets with very small sample sizes that were collected without using instantaneous measures of travel rate and assume symmetrical effects about the slope of maximum travel rate. These models also typically resulted in a single mathematical function, ignoring the significant variability that can occur between a fast and a slow individual, or between walking and running travel rates. In this study we modeled travel rates using a database of GPS tracks from 29,928 individuals representing 421,247 individual hikes, jogs, and runs on trails in and around Salt Lake City, Utah for an entire year between July 1, 2016 and June 30, 2017. Three widely-used probability distribution functions (Laplace, Gauss, and Lorentz) were used to predict travel rates based on terrain slope along segments of trails with uniform slopes. To account for the variability in travel rates between fast and slow movement, a series of travel rate models were generated to predict travel rate percentiles, ranging from the 1st to the 99th, thus providing a flexible basis f…
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The function form of Eq. (1) is a suitable basis for modeling travel rates.
“Based on our previous work5,8,39 and preliminary testing, we identified the function form of Eq. (1) as a suitable basis for modeling.”
From A singular, broadly-applicable model for estimating on- and off-path walking travel rates using airborne lidar data (2024) · cites this paper as [39]
Both [8] and [16] looked solely at the effect of walking slope on speed and did not explore additional variables.
“Finally, although these studies had the benefit of using large sample sizes, they both looked solely at the effect of the walking slope on speed, and did not explore additional variables.”
From Improved prediction of hiking speeds using a data driven approach (2023) · cites this paper as [16]
Recent work [8,16] explored data-driven walking speed modelling, but crowdsourced data collection was not controlled, so the data could not be assumed to consist wholly of walking or hiking tracks.
“This has been explored in recent work [8, 16], however the crowdsourced nature of these studies meant that data collection was not controlled, and thus that the data could not be assumed to consist wholly of walking or hiking tracks.”
From Improved prediction of hiking speeds using a data driven approach (2023) · cites this paper as [16]
In [16], data from hikes, jogs and runs was processed together, resulting in a very wide range of movement speed estimates.
“In [16], data from hikes, jogs and runs was processed together, resulting in a very wide range of movement speed estimates.”
From Improved prediction of hiking speeds using a data driven approach (2023) · cites this paper as [16]
Campbell et al.'s slope-travel rate function was used as the basis of predicting egress in the Escape Route Index.
“Campbell et al. [29]'s slope-travel rate function was used as the basis of predicting egress in the Escape Route Index [24].”
From Modeling wildland firefighter travel rates by terrain slope: results from GPS-tracking of type 1 crew movement (2020) · cites this paper as [29]
Previous pedestrian travel rate functions were not derived from data specific to firefighters and assume no load carriage.
“These functions were not derived from data specific to firefighters, and assume no load carriage.”
From Modeling wildland firefighter travel rates by terrain slope: results from GPS-tracking of type 1 crew movement (2020) · cites this paper as [29]
Type 1 firefighters may hike faster on average than the general population and military cadets.
“Since the moderate function predicts travel rates greater than recent pedestrian models from Campbell et al. [29] and Irmischer and Clarke [35], Type 1 firefighters may hike faster on average than the general population and military cadets.”
From Modeling wildland firefighter travel rates by terrain slope: results from GPS-tracking of type 1 crew movement (2020) · cites this paper as [29]
Campbell et al. [29] found that the Lorentz function form was best at estimating slope-travel rate relationships across a wide range of percentiles.
“They found that the Lorentz function form was best at estimating slope-travel rate relationships across a wide range of percentiles:”
From Modeling wildland firefighter travel rates by terrain slope: results from GPS-tracking of type 1 crew movement (2020) · cites this paper as [29]
By combining the slope-travel rate function defined by Campbell et al. and the land cover-travel rate effects defined by WFDSS, spatially-explicit escape route mapping could become a reality.
“By combining the slope-travel rate function defined by Campbell et al. [11], and the land cover-travel rate effects defined by WFDSS [18], spatially-explicit escape route mapping could become a reality.”
From Escape Route Index: A Spatially-Explicit Measure of Wildland Firefighter Egress Capacity (2019) · cites this paper as Campbell et al. [11]
The Campbell et al. slope-travel rate model represents the most accurate understanding of the relationship between slope and travel rates.
“At present, their resulting model represents the most accurate understanding of the relationship between slope and travel rates, and as such, will be used as the basis of simulating slope impedance in this study.”
From Escape Route Index: A Spatially-Explicit Measure of Wildland Firefighter Egress Capacity (2019) · cites this paper as Campbell et al. [11]
A recent study by Campbell et al. overcame previous limitations, producing an improved slope-travel rate predictive model based on a very large database of GPS tracks harvested from Strava and lidar-derived terrain slope data.
“A recent study by Campbell et al. [11] overcame previous limitations, producing an improved slope-travel rate predictive model based on a very large database of GPS tracks harvested from the widely-used mobile fitness tracking application Strava, and light detection and ranging (lidar)-derived terrain slope data.”
From Escape Route Index: A Spatially-Explicit Measure of Wildland Firefighter Egress Capacity (2019) · cites this paper as Campbell et al. [11]
Travel was restricted to directionally-specific slopes within ±30° to avoid extrapolation of the Campbell et al. travel rate function and to avoid modeling travel up or down very steep slopes.
“For the purpose of this study, to avoid extrapolation of the Campbell et al. [11] travel rate function and to avoid modeling travel up or down very steep slopes, travel was restricted to directionally-specific slopes within ±30 • .”
From Escape Route Index: A Spatially-Explicit Measure of Wildland Firefighter Egress Capacity (2019) · cites this paper as Campbell et al. [11]
Pedestrian movement is highly sensitive to local landscape conditions, and assuming uniform effects across individuals or terrain can lead to prediction errors.
“Recent work highlights that pedestrian movement is highly sensitive to local landscape conditions, and that assuming uniform effects across individuals or terrain can lead to prediction errors (Campbell et al. 2019;Campbell, Cutler, and Dennison 2024).”
From Machine learning estimation of off-trail pedestrian travel rates using LiDAR-derived slope, vegetation, and surface roughness (2026) · cites this paper as Campbell et al. 2019
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Metadata
- Authors
- Campbell, M. J., Dennison, P. E., Butler, B. W., & Page, W. G.
- Affiliations
- Fort Lewis College (US)
- Rocky Mountain Research Station (US)
- Corresponding author
- Campbell, Michael J.
- Venue
- Applied Geography
- Publisher
- Elsevier BV
- Published
- 2019-05
- Volume
- 106
- Pages
- 93-107
- ISSN
- 0143-6228 (ISSN-L)
- OpenAlex
- W2926860153
- Cited by
- 87
- References
- 42
- Citations by year
- 2026: 16 · 2025: 11 · 2024: 17 · 2023: 15 · 2022: 15 · 2021: 4 · 2020: 5 · 2019: 4
- FWCI
- 5.24
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Applied Geography (acceptedVersion)
- Funders
- USDA Forest Service National Fire Plan
- National Wildfire Coordinating Group (15CR11221637105, 18JV11221637153, 18JV11221637154)
- National Science Foundation (DEB-1714972)
- Topics
- Social Sciences › Transportation › Human Mobility and Location-Based Analysis
- Social Sciences › Business, Management and Accounting › Tourism, Leisure and Hospitality Management › Recreation, Leisure, Wilderness Management
- Social Sciences › Safety Research › Evacuation and Crowd Dynamics
- Keywords
- terrain slope, hiking, running, jogging, GPS tracks, Laplace distribution, normal distribution, search and rescue
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