Cited by 62Human Mobility and Location-Based AnalysisData Management and AlgorithmsEvacuation and Crowd Dynamics

The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index; none of the 14 sources its claims cite is checked for support yet.

Measuring and modeling the speed of human navigation

Open access
Irmischer, Ian J., Clarke, Keith C.·2018·Cartography and Geographic Information Science

Abstract

Navigation, the goal-related movement through space and time to reach a destination, is a fundamental human activity. Geographers, physiologists, anthropologists, and psychologists have long been interested in the spatial and temporal aspects of navigation speed. Hikers, search and rescue teams, firefighters, the military, and others navigate on foot, and their success depends on understanding how the dynamics of foot-based navigation affect individual capabilities. This research modeled the speed of movement of humans engaged in navigation in wooded environments with varied terrain. Movement models were developed using spatiotemporal analysis of multiple subjects’ trajectories. Speed estimates were collected via satellite positioning from 200 subjects engaged in foot-based navigation. Trajectory data were merged with land-cover data to analyze human navigation over varying slopes and terrain. Generalizing these characteristics provided a model of navigational speed of movement from an origin to a destination along an unknown route. Tobler’s hiking function and Naismith’s rule were used in an analysis of the trajectory data. The model created from this study was shown to outperform those classic human movement speed estimators by predicting route completion time within 10% accuracy (M = 11.1min, 95% CI [9.8, 12.4] min). These models help explain the human dynamics of navigation.]

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

This paper develops and tests a model of human navigation speed on foot that includes wayfinding cost, using GNSS trajectories from 200 USMA cadets navigating hilly, wooded terrain. The derived model predicts route completion times with 9% MAPE, outperforming Tobler’s hiking function (15%) and Naismith’s rule (20%).

Key findings

  • The fastest on-road navigation speed occurred at 5% downhill slope: 1.11 m/s for males and 1.05 m/s for females, which is 34% slower than Tobler’s estimated fastest on-road hiking speed of 1.67 m/s.
  • The fastest off-road navigation speed was 0.78 m/s for males and 0.70 m/s for females, with the off-road model peaking at −2% slope.
  • Mean average percent error (MAPE) between estimated and actual route completion times was 9% for both male and female groups, compared with 15% for Tobler’s hiking function and 20% for Naismith’s rule. For routes approximately 2 h long, the new model estimated completion times within 10 min, about 50% better than Tobler’s function and 100% better than Naismith’s rule.
  • The authors attribute a 34% difference between Tobler’s maximum speed and the subjects’ average top speed to the cognitive cost of wayfinding.

Methods

  • Data were collected from 200 volunteer USMA cadets during Cadet Basic Training in July and August 2015; the sample was approximately 80.5% male and 19.5% female, ages 17–23, navigating hilly, wooded terrain with map and compass to find seven control points approximately 400 m apart in less than 150 min.
  • Movement was recorded with Qstarz BT-1300ST GNSS receivers at 1-s intervals, later downscaled to 10-s resolution; the analysis produced over 130,000 records of 10-s trajectory segments containing walking speed, slope, and on-road/off-road classification.
  • Terrain was classified as on-road or off-road using road centerlines, 1-m satellite imagery, and a 9-m buffer; slope and speed were computed from GNSS outputs, data were binned by 1% slope between ±100%, and exponential/Gaussian curves were fitted and assessed by MAPE against actual route completion times.

Limitations

  • Stated by the authors: subjects were not under direct observational control at all times, subjects were not navigating alone because a safety partner accompanied them, and GNSS measurement constraints likely lowered model precision due to systematic errors, receiver noise, multipath under tree canopy, and 4–6 m RMS locational error.
  • Stated by the authors: the USMA cadet sample is representative of military personnel, but there are likely large differences in navigation speed for different ethnic groups, cultures, and classes, and other variables such as weather, load, footwear, and temperature would increase variation.
  • Evident from the text: there were four times as many male subjects as females, 95% of observations were at slopes between ±65%, and seven trajectories that began at the start point but did not return were removed from the distance and duration summary, likely due to GNSS battery loss or turning off.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1080/15230406.2017.1292150

Cites

9 of 9 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Verification

Claims the paper makes

0 of 14 cited sources checked · 0 supported · 0 flagged

  • Findingown data
    § AQ8

    For routes approximately 2-h long, the new model accurately estimates completion times within 10 min of the actual time.

    “For routes approximately 2-h long, the new model accurately estimates 470 completion times within 10 min of the actual time.”
    Quote in the paperSubstantial claim
  • Findingnone given
    § Discussion

    Movement speed during on-road navigation was found to follow an exponential relationship over the constrained ranges mentioned above.

    “Movement speed during on-road navigation was found to follow an exponential relationship over the constrained ranges mentioned above.”
    Quote in the paperSubstantial claim
  • Findingreasoning
    § AQ8

    Almost all of the curve derived from Langmuir and Naismith falls above the empirical data collected during this study.

    “Figures 4567show that almost all of the curve derived from Langmuir and Naismith falls above the empirical data collected during this study”
    Quote in the paperSubstantial claim
  • Findingnone given
    § Discussion

    Naismith's rule with Langmuir's additions predict a top speed more than three times as great.

    “Naismith's rule with Langmuir's additions predict a top speed more than 395 three times as great.”
    Quote in the paperNot a substantial claim
  • Findingown data
    § AQ8

    Naismith's rule with Langmuir's corrections underestimates the time it took the subjects to navigate from point to point.

    “Naismith's rule with Langmuir's corrections under-490 estimates the time it took the subjects to navigate from point to point.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim. 26
  • It may state two separate claims as one. 17
  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Findingown data
    § Results

    95% of the observations were taken at slopes between ±65% slope.

    “Additionally, 95 % of the observations were taken at slopes AQ7 between ±65% slope.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Findingown data
    § Results

    Mean time on the course was 141 min (range 88-185 min).

    “Time on the course: Mean: 141 min Range: 88-185 min”
    Quote in the paperNot a substantial claim
  • It may state two separate claims as one.

    Findingown data
    § Results

    Tobler's hiking function yielded a MAPE of 15% and Naismith's rule produced a MAPE of 20%.

    “For comparison, Tobler's hiking function yielded a MAPE of 15% and Naismith's rule produced a MAPE of 20% .”
    Quote in the paperSubstantial claim
  • It may state two separate claims as one.

    Findingown data
    § Discussion

    The speed traveled at this grade during navigation is 1.11 m/s for males and 1.05 m/s for females.

    “The speed traveled at this 390 grade during navigation is 1.11 m/s for males and 1.05 m/s for females.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Findingown data
    § Determination of slope and navigation speed

    The calculations resulted in a data matrix containing over 130,000 records representing 10-s segments of each subject's trajectory.

    “These calculations resulted in a data matrix that contained over 130,000 records representing 10-s segments 305 of each subject's trajectory.”
    Quote in the paperNot a substantial claim
  • It may state two separate claims as one.

    Findingown data
    § Discussion

    This study found a general symmetry for navigation speed based on slope with the fastest movement being slightly downhill.

    “This study 380 found a general symmetry for navigation speed based on slope with the fastest movement being slightly downhill.”
    Quote in the paperSubstantial claim
  • It may state two separate claims as one.

    Findingnone given
    § AQ8

    Tobler's curve underestimates navigation speed for slopes less than -15% and greater than 5%.

    “Tobler's curve underestimates navigation speed for slopes less than -15% and greater than 5% .”
    Quote in the paperNot a substantial claim
  • It may state two separate claims as one.

    Findingown data
    § AQ8

    This is about 50% better than Tobler's function and 100% better than using Naismith's rule.

    “This is about 50% better than Tobler's function and 100% better than using Naismith's rule.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Findingnone given
    § Results

    The data shown in Figures 4-7 take the form of a normal curve.

    “The data shown in Figures 4567take the form of a normal curve.”
    Quote in the paperNot a substantial claim
  • It may state two separate claims as one.

    Findingown data
    § Conclusion

    This exploration of navigation, locomotion, and wayfinding has developed a methodology and framework to define the cognitive cost of navigation, which amounted to 34% of the task time in the West Point data.

    “Finally, this exploration of navigation, locomotion, and wayfinding has developed a methodology and framework to define the cognitive cost of 535 navigation, which amounted to 34% of the task time in the West Point data.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim.

    Findingown data
    § Results

    Visual inspection of the figures indicates that the equations predict the bin means rather successfully.

    “Visual inspection of the figures indicates that the equations predict the bin means rather successfully.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Findingnone given
    § Results

    There were four times as many male subjects as females.

    “There were four times as many male subjects as females.”
    Quote in the paperNot a substantial claim
  • It may state two separate claims as one.

    Findingown data
    § Discussion

    The model shows the fastest off-road navigation speed was 0.78 m/s for males and .70 m/s for females.

    “The model shows the fastest off-road navigation speed was 0.78 m/s for males and .70m/s for females.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim.

    Findingown data
    § Results

    The graphical depiction of the data shows a clear relationship between navigation speed and terrain slope.

    “The graphical depiction of the data above shows a clear relationship between navigation speed and terrain slope.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Findingnone given
    § Conclusion

    The measurement devices and the variance of human behavior cause individual segment estimates to be somewhat erratic.

    “The measurement devices and the variance of human behavior cause individual segment estimates to 530 be somewhat erratic.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation
    § Naismith's rule

    Naismith's rule is still used today to estimate the time required for a given cross-country walk.

    “This rule of thumb has been published many times and is still used today to 105 estimate the time required for a given cross-country walk (Langmuir 1984;Aitken, 1977;Clarke, 2015).”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites Langmuir 1984
    • cites Aitken, 1977

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites Clarke, 2015

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation
    § Tobler's hiking function

    Tobler's hiking function remains commonly used in GIS travel time computations.

    “Despite the equation's 155 simplicity, it remains commonly used in GIS travel time computations (Pingel, 2010;Richards-Rissetto & Landau, 2014;Sherrill, Frakes, & Schupbach, 2010;White & Barber, 2012;White & Surface-Evans, 2012).”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites Pingel, 2010 source
    • cites Richards-Rissetto & Landau, 2014

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites Sherrill, Frakes, & Schupbach, 2010

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • It may state two separate claims as one.

    Study design and conductcitation
    § Discussion

    Because of receiver and multipath error, elevation and distance estimates used in computing speed and slope can be expected to be inaccurate and could overestimate distances.

    “Additionally, because of receiver and multi-450 path error the elevation and distance estimates used in computing speed and slope can be expected to be inaccurate and could overestimate distances (Ranacher, Brunauer, Trutschnig, Van Der Spek, & Reich, 2016).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Ranacher, Brunauer, Trutschnig, Van Der Spek, & Reich, 2016

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Study design and conductreasoning
    § Discussion

    Subjects were not navigating alone.

    “(2) subjects were not navigating alone”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim. The paper may give no reason why it holds.

    Interpretationreasoning
    § Conclusion

    The vastness of the number of segments along a route mitigates these limitations.

    “However, the vastness of the number of segments along a route mitigates these limitations.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Study design and conductnone given
    § Experimental methods

    Subjects were assigned a safety partner instructed to accompany but not assist each subject during completion of the navigational test.

    “The subjects were also assigned a safety partner, 260 another cadet who was instructed to accompany but not assist each subject during completion of the navigational test.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim. It may state two separate claims as one.

    Study design and conductown data
    § Experimental methods

    The Qstarz GNSS positional data were not available to the subjects during navigation and the device was not used to aid navigation.

    “Its positional data were not available to the subjects during navigation.”
    • Also stated in: § Experimental methods · plain
      “however, this device was not used to aid navigation.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation
    § Tobler's hiking function

    Tobler's function shows a maximum hiking speed of approximately 1.67 m/s at a slight downhill slope of 5% (approximately 3°).

    “The function shows a maximum hiking speed of approximately 1.67 m/s.This speed occurs at 165 a slight downhill slope of 5 % (approximately 3° ).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Tobler, 1993

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Interpretationown data
    § Results

    Figures 9 and 11 show more variability than Figures 8 and 10, especially at extreme slopes, due to significantly fewer observations.

    “Figures 9 and 11 show more variability than Figures 8 and 10, especially at extreme slopes, due to significantly 345 fewer observations.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.

    Study design and conductreasoning
    § Discussion

    It is impossible to rule out such interference during the data collection.

    “Fundamentally, it is impossible to rule out such interference during the data collection.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim. It may state two separate claims as one.

    Interpretationreasoning
    § The cost of cognition

    Acts such as map reading, analyzing the terrain, decision-making, assessing one's current position, and determining routes have costs associated with them and can be quantified using this rationale.

    “Acts such as map reading, analyzing the terrain, decision-making, assessing one's current position, and determining routes have costs associated with them and can be quantified using this rationale.”
    Quote in the paperSubstantial claim
  • It may state two separate claims as one.

    Interpretationnone given
    § Conclusion

    This investigation of the speed of human navigation on foot has developed and tested a model of navigation speed.

    “This investigation of the speed of human navigation on foot has developed and tested a model of navigation speed.”
    Quote in the paperSubstantial claim
  • It may state two separate claims as one.

    Interpretationown data
    § AQ8

    Tobler's function overestimates the time taken to navigate, primarily because of his model predicting slower off-road navigation speeds.

    “Tobler's function overestimates the time taken to navigate, primarily because of his model predicting 475 slower off-road navigation speeds, as shown in Figures 6 and 7.”
    Quote in the paperSubstantial claim
  • It may state two separate claims as one.

    Interpretationreasoning
    § The cost of cognition

    There is a 34% difference between Tobler's maximum speed and the average top speed of the subjects in this study, which can be attributed to the cognition involved in wayfinding.

    “There is a 34% difference between Tobler's maximum speed and the average top speed of the subjects in this study, which can be attributed to the 520 cognition involved in wayfinding.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Study design and conductnone given
    § Discussion

    Constraints of the measurement devices likely lowered the precision of the models developed.

    “(3) constraints of the measurement devices likely lowered the precision of 420 the models developed.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.

    Interpretationnone given
    § Results

    Seven trajectories began at the start point but did not return; this is most likely due to a GNSS losing battery power or turning off.

    “*Seven trajectories began at the start point but did not return to the start point.This is most likely due to a GNSS losing battery power or turning off.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Interpretationreasoning
    § AQ8

    This is a contributing factor to the difficulty in tuning the model at the individual data segment resolution.

    “This is a contributing factor to the difficulty in tuning the model at the individual data segment 460 resolution.”
    Quote in the paperNot a substantial claim
  • It may state two separate claims as one.

    Interpretationown data
    § Discussion

    This finding is in agreement with Tobler's equation but in contrast to Naismith's formula and Minetti et al. (2002) which reported a non-symmetric relationship.

    “This finding is in agreement with Tobler's equation but in contrast to Naismith's formula and research conducted by Minetti, Christian 385 Moia, Roi, and Ferretti (2002) which reported a non symmetric relationship.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Minetti, Christian Moia, Roi, and Ferretti (2002) source
  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Study design and conductreasoning
    § Discussion

    The safety monitor could have had effects on subject's speed of navigation or how they moved.

    “The fact that a second cadet was assigned by USMA to travel with each subject as a safety monitor could have had effects on subject's speed of navigation or how they moved.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim. The paper may give no reason why it holds.

    Premisenone given
    § Conclusion

    While models of hiking in the woods exist, none of these models have addressed the cognitive aspect of difficult wayfinding.

    “While models of hiking in the 555 woods exist, none of these models have addressed the cognitive aspect of difficult wayfinding.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.

    Premisenone given
    § Tobler's hiking function

    The variables considered by Naismith and Tobler act as a starting point for further development of human dismounted navigation models.

    “The variables considered by Naismith and Tobler act as a 180 starting point for the further development of human dismounted navigation models.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim.

    Interpretationreasoning
    § The cost of cognition

    This research has developed a framework for defining the cognitive cost of navigation.

    “In addition to development of a model for the speed of navigation, this research has developed a framework 500 for defining the cognitive cost of navigation.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim. The paper may give no reason why it holds.

    Interpretationnone given
    § AQ8

    It is probable that the subjects are stopping to plan movement, select new routes, and make navigation decisions on more level ground.

    “It is probable that the subjects are stopping to plan movement, select new routes, and make navigation decisions on more level ground.”
    Quote in the paperNot a substantial claim
38 of 38
  • The authors state this as an assumption.

    Subjects walking very near (<5 m) the road were most likely walking on the road.

    “It is assumed that subjects walking very near (<5 m ) the road were most likely walking on the road.”
  • The paper relies on this without support.

    USMA cadets tested are representative of military personnel.

    “As USMA cadets, the tested subjects 410 are representative of military personnel.”
  • The authors state this as an assumption.

    Naismith's rule or Tobler's hiking function defines the speed of human locomotion.

    “To calculate the cost of cognition, we assume that Naismith's rule or Tobler's hiking function defines the speed of human locomotion.”
3 of 3

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Existing travel rate functions fail to sufficiently account for the vast diversity of landscape conditions that impede foot travel.

    “Although a number of existing travel rate functions exist, they fail to sufficiently account for the vast diversity of landscape conditions that impede foot travel3–11.”

    From A singular, broadly-applicable model for estimating on- and off-path walking travel rates using airborne lidar data (2024) · cites this paper as [6]

    The Tobler’s hiking function section (p. not available) says existing models use slope and a path-versus-non-path distinction as a starting point. The discussion (AQ8; p. not available) finds that Tobler’s and Naismith’s functions misestimate navigation times in the study setting. This supports a limitation of those functions, but the paper does not establish that they fail to account for the vast diversity of landscape conditions that impede foot travel. (LLM, conf=0.82)

    Experimental — accuracy not yet measured
  • Past work has accommodated off-path environments by lumping the vast diversity of landscape characteristics into a single multiplier or a small number of fixed multipliers specific to broad land cover categories.

    “Past work has accommodated off-path environments by lumping the vast diversity of landscape characteristics into a single multiplier3,6 or a small number of fixed multipliers specific to broad land cover categories7,22.”
  • 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.”
  • The importance of median travel rate as a variable highlights inherent variability between individuals, which is also acknowledged in other studies on navigation speed and pedestrian behaviour.

    “While less important to the model's prediction than the landscape variables, the importance of median travel rate as a variable in our model highlights the inherent variability between individuals, which is also acknowledged in other studies on navigation speed and pedestrian behaviour (Irmischer and Clarke 2018;Prisner and Sui 2023).”
  • Travel time estimates reveal an important degree of variability that would be left unaccounted for if fixed multiplicative terms were used to universally estimate off-path, slope-based travel times.

    “Furthermore, our travel time estimates reveal an important degree of variability that would be left unaccounted for if fixed multiplicative terms were used to universally estimate off-path, slope-based travel times3,6,7.”

Citations

Cites

Flagged first, then by citations

Research works printed but not linked: 6

  1. Aitken, R. 1977. Wilderness areas in Scotland (Ph.D. Dissertation). University of Aberdeen, UK.
  2. Clarke K. C., 2015, Maps and web mapping
  3. Irmischer, I. (2016). Space, time, and energy in dismounted navigation (Ph.D. Dissertation). University of California, Santa Barbara.
  4. Langmuir E., 1969, Mountain leadership: the official handbook of the mountain leadership training boards of great Britain
  5. Naismith W. W., 1892, Scottish Mountaineering Club Journal, 2, 135
  6. Tobler W. R., 1993, Non-isotropic geographic modeling

Cited by

Sorted by citations

Metadata

Authors
Irmischer, I. J., & Clarke, K. C.
Affiliations
  • United States Military Academy (US)
  • Department of Geography, University of California, Santa Barbara, CA, USA
Corresponding author
Irmischer, Ian J.
Venue
Cartography and Geographic Information Science
Published
2017-02-28
Volume
45
Issue
2
Pages
177-186
ISSN
  • 1523-0406 (ISSN-L)
  • 1545-0465
OpenAlex
W2608377476
Cited by
62
References
9
Citations by year
2026: 12 · 2025: 4 · 2024: 10 · 2023: 7 · 2022: 6 · 2021: 12 · 2020: 3 · 2019: 4 · 2018: 2 · 2017: 2
FWCI
2.95
Type
journal article
Language
en
Open access
Locations
  • Cartography and Geographic Information Science (publishedVersion)
  • eScholarship (California Digital Library) (submittedVersion)
Topics
  • Social Sciences › Transportation › Human Mobility and Location-Based Analysis
  • Physical Sciences › Computer Science › Information Systems › Data Management and Algorithms
  • Social Sciences › Safety Research › Evacuation and Crowd Dynamics
Keywords
terrain slope, human movement modeling, GPS tracks, land cover, travel time estimation

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