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Predicting energy expenditure with loads while standing or walking very slowly
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The Pandolf et al equation had bias -51 ± 88 W and RMSE 102 W for overall course metabolic rate estimates.
“Pandolf et al 6 -72 ± 463 468 0.29 -51 ± 88 102 0.79”
From Metabolic Costs of Military Load Carriage over Complex Terrain (2018) · cites this paper as [6]
Comparable samples were used in original load carriage studies, including the datasets used to validate the Minetti et al (n = 10), Pandolf et al (n = 6), and Santee et al (n = 16) equations.
“However, it should be noted that comparable samples were used in many of the original load carriage studies 22 including the datasets used to validate the Minetti et al 13 (n = 10), Pandolf et al 6 (n = 6), and Santee et al 8 (n = 16) equations.”
From Metabolic Costs of Military Load Carriage over Complex Terrain (2018) · cites this paper as [6]
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 [11]
Roads and trails tend to promote maximally efficient travel, where available.
“However, given their relative low slope, ground surface stability, and lack of vegetation impedance, roads and trails tend to promote maximally efficient travel, where available [8,10,16,17].”
From Escape Route Index: A Spatially-Explicit Measure of Wildland Firefighter Egress Capacity (2019) · cites this paper as [16]
The validity of existing explanations for the substantial differences in walking economy observed across different surface gradients is largely unknown.
“Finally, the validity of existing explanations for the substantial differences in walking economy observed across different surface gradients (3,8,49,54,56) is largely unknown.”
From Walking economy is predictably determined by speed, grade, and gravitational load. (2017) · cites this paper as [56]
The errors of the ACSM and Pandolf et al. (56) equations corresponded to 15.8 and 13.4%, respectively, of the overall mean measured for validation group subjects across all trials completed.
“56) equations corresponded to 15.8 and 13.4%, respectively, of the overall mean measured for the validation group subjects across all of the trials completed (2.13/13.5 ϭ 15.8 and 1.81/13.5 ϭ 13.4%).”
From Walking economy is predictably determined by speed, grade, and gravitational load. (2017) · cites this paper as [56]
The two predictive equations with greatest conditional breadth, those of Pandolf et al. and the American College of Sports Medicine (ACSM), are the most widely used.
“The two predictive equations with greatest conditional breadth, those of Pandolf et al. (56) and the American College of Sports Medicine (ACSM) (3), are the most widely used.”
From Walking economy is predictably determined by speed, grade, and gravitational load. (2017) · cites this paper as Pandolf et al. [56]
The Pandolf et al. equations tended to underpredict level and declined values while also overpredicting the values obtained on positive grades.
“The Pandolf et al. (56) equations tended to underpredict level and declined values while also overpredicting the values obtained on positive grades.”
From Walking economy is predictably determined by speed, grade, and gravitational load. (2017) · cites this paper as [56]
The overall predictive error for ACSM was larger, as was the zero error baseline vs. the equation of Pandolf et al. (56).
“The overall predictive error for ACSM was larger, as was the zero error baseline vs. the equation of Pandolf et al. (56).”
From Walking economy is predictably determined by speed, grade, and gravitational load. (2017) · cites this paper as Pandolf et al. [56]
For both the ACSM and Pandolf et al. (56) equations, the standard errors of estimate were nearly twice as large and exhibited bias predominantly across grade.
“For both the ACSM and Pandolf et al. (56) equations, the standard errors of estimate were nearly twice as large and exhibited bias predominantly across grade.”
From Walking economy is predictably determined by speed, grade, and gravitational load. (2017) · cites this paper as Pandolf et al. [56]
The Pandolf et al. (56) model equation had slightly better overall performance than the ACSM model equation.
“The greater conditional breadth of the Pandolf et al. (56) model equation resulted in slightly better overall performance (Figs. 4, E and F, 5, E and F, and 6, E and F) vs. the ACSM model equation.”
From Walking economy is predictably determined by speed, grade, and gravitational load. (2017) · cites this paper as Pandolf et al. [56]
The inability of skeletal muscle to convert lost gravitational potential energy into accumulated chemical energy reveals the physiologically unsound foundation of this prevailing approach.
“The inability of skeletal muscle to convert lost gravitational potential energy into accumulated chemical energy reveals the physiologically unsound foundation of this prevailing approach (3,8,17,25,56,78).”
From Walking economy is predictably determined by speed, grade, and gravitational load. (2017) · cites this paper as [56]
The absolute accuracy of the ACSM equation declined marginally vs. the prediction of the unloaded values in part I, whereas that of the Pandolf et al. (56) equation improved marginally by 0.1 ml O2·kg−1·min−1.
“The absolute accuracy of the ACSM equation also declined marginally vs. the prediction of the unloaded values in part I, whereas that of the Pandolf et al. (56) equation improved marginally by 0.1 ml O 2 •kg Ϫ1 •min Ϫ1 .”
From Walking economy is predictably determined by speed, grade, and gravitational load. (2017) · cites this paper as Pandolf et al. [56]
Both the ACSM and Pandolf et al. model equations are amalgams of a series of smaller studies and data sets.
“In contrast, both the ACSM (3); and Pandolf et al. (56) model equations are amalgams of a series of smaller studies and data sets (for ACSM, see Refs 17 and 55; for Pandolf et al, see Refs. 25”
From Walking economy is predictably determined by speed, grade, and gravitational load. (2017) · cites this paper as [56]
Other algorithms constructed to calculate cost through energy expenditure are a better fit for testing the movement of construction timbers.
“However, other algorithms (Pandolf, Givoni & Goldman 1977; Van Leusen 2000) have been constructed to calculate cost through energy expenditure, which we suggest are a better fit for testing the movement of construction timbers.”
From A least cost analysis: correlative modeling of the chaco regional road system (2019) · cites this paper as Pandolf, Givoni & Goldman 1977
Measuring costs through Pandolf function and calculating movement along a roadway corridor offer the best method to model correlative pathways across the unmodified Chaco landscape.
“The above case studies demonstrate that measuring costs through the Pandolf, Givoni & Goldman’s (1977) function and calculating movement along a roadway corridor offer the best method to model correlative pathways across the unmodified Chaco landscape.”
From A least cost analysis: correlative modeling of the chaco regional road system (2019) · cites this paper as Pandolf, Givoni & Goldman 1977
Algorithms that calculate cost through energy expenditure are a better fit than time-based algorithms for testing the movement of construction timbers.
“have been constructed to calculate cost through energy expenditure, which we suggest are a better fit for testing the movement of construction timbers.”
From A least cost analysis: correlative modeling of the chaco regional road system (2019) · cites this paper as Pandolf, Givoni & Goldman 1977
Energy expenditure algorithms are a better fit for testing the movement of construction timbers than time-based algorithms.
“However, other algorithms (Pandolf, Givoni & Goldman 1977; Van Leusen 2000) have been constructed to calculate cost through energy expenditure, which we suggest are a better fit for testing the movement of construction timbers.”
From A least cost analysis: correlative modeling of the chaco regional road system (2019) · cites this paper as Pandolf, Givoni & Goldman 1977
Givoni and Goldman (1971) and Pandolf et al. (1977) developed prediction equations for the metabolic cost of load-carrying while walking on different terrains and slopes.
“Givoni and Goldman (1971) and Pandolf et al. (1977) developed prediction equations for the metabolic cost of load-carrying while walking on different terrains and slopes.”
From Preferred walking speed on rough terrain: is it all about energetics? (2019) · cites this paper as Pandolf et al. (1977)
Both Givoni and Goldman (1971) and Pandolf et al. (1977) utilized a terrain factor η that represents the effect of the surface type on metabolic rate.
“Both of those studies utilized a terrain factor η that represents the effect of the surface type on metabolic rate.”
From Preferred walking speed on rough terrain: is it all about energetics? (2019) · cites this paper as Pandolf et al., 1977
Grid search optimization produced terrain factors of 1.9 and 3.1 for Givoni and Goldman (1971) and Pandolf et al. (1977), respectively.
“This procedure produced terrain factors of 1.9 and 3.1 for Givoni and Goldman (1971) and Pandolf et al. (1977), respectively.”
From Preferred walking speed on rough terrain: is it all about energetics? (2019) · cites this paper as Pandolf et al., 1977
The prediction equation of Givoni and Goldman (1971) had the best match to our rough terrain data (lowest RMSE), although the Pandolf et al. (1977) equation is used more commonly.
“Note that although the Pandolf et al. (1977) equation is used more commonly, the prediction equation of Givoni and Goldman (1971) had the best match to our rough terrain data (lowest RMSE).”
From Preferred walking speed on rough terrain: is it all about energetics? (2019) · cites this paper as Pandolf et al., 1977
The Pandolf equation includes speed, load, and positive-only gradient capabilities.
“The most established is the equation by Pandolf et al. (5) which was originally formulated from several relatively small treadmill and overground walking datasets (6–8) to include speed, load, and positive-only gradient capabilities.”
From Real-world walking economy: can laboratory equations predict field energy expenditure? (2021) · cites this paper as Pandolf et al. [5]
Forecasts of the energy cost of Pandolf's formula were verified by test phases on individuals of different age and sex by varying speed and load carried.
“Forecasts of the energy cost of this formula were able to be verified by several test phases on individuals from different classes of age and sex (Epstein et al. 1987;Pandolf et al. 1976Pandolf et al. , 1977) ) by varying the speed and the load carried.”
From Mobility of paleolithic populations: biomechanical considerations and spatiotemporal modelling (2021) · cites this paper as Pandolf et al. 1977
More complex formulas account for a complex of factors such as human body mass and carried load, terrain factor coefficient, and movement speed, allowing prediction of metabolic costs of movement.
“Более сложные формулы учитывают комплекс факторов, таких как масса тела человека и переносимого им груза, коэффициент фактора местности и скорость пере-движения, позволяя прогнозировать метаболические затраты на передвижение [Pandolf, Givoni, Goldman, 1977].”
From GIS optimal path modeling for analyzing paleolithic settlement systems: methodological issues (2026) · cites this paper as Pandolf, Givoni, Goldman, 1977
Overall energy expenditure is determined by carried load, movement speed, and grade or ground slope, each with readily identifiable effects.
“Overall energy expenditure is also determined by other variables such as carried load, movement speed, and grade or ground slope [3–5], each with readily identifiable effects.”
From Human walking in the real world: interactions between terrain type, gait parameters, and energy expenditure (2021) · cites this paper as [4]
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Metadata
- Authors
- Pandolf, K. B., Givoni, B., & Goldman, R. F.
- Venue
- Journal of Applied Physiology
- Publisher
- American Physiological Society
- Published
- 1977-10-01
- Volume
- 43
- Issue
- 4
- Pages
- 577-581
- ISSN
- 0161-7567 (ISSN-L)
- 8750-7587
- 1522-1601
- OpenAlex
- W2238368310
- Semantic Scholar
- 4e18133fff165f8b4909d53e77fd5d7883cd581d
- Cited by
- 474
- References
- 0
- Citations by year
- 2026: 12 · 2025: 17 · 2024: 19 · 2023: 18 · 2022: 17 · 2021: 32 · 2020: 18 · 2019: 29 · 2018: 27 · 2017: 24 · 2016: 18 · 2015: 24 · 2014: 24 · 2013: 15 · 2012: 21
- FWCI
- 1.26
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Applied Physiology (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Health Sciences › Medicine › Physiology (medical) › Cardiovascular and exercise physiology
- Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Physical Activity and Health
- Health Sciences › Health Professions › Physical Therapy, Sports Therapy and Rehabilitation › Balance, Gait, and Falls Prevention
- Keywords
- energy expenditure estimation, slow walking, physical workload
- MeSH terms
- Body Weight, Energy Metabolism, Physical Exertion, Humans, Locomotion, Male
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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