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Calculate velocities and relative stride lengths for tracks

Source: R/velocity_track.R
velocity_track.Rd

velocity_track() calculates the relative stride lengths and velocities for each step in a series of tracks, based on the step length, height at the hip, and gravity acceleration.

Usage

velocity_track(data, H, G = NULL, method = NULL)

Arguments

data

A track R object, which is a list consisting of two elements:

  • Trajectories: A list of interpolated trajectories, where each trajectory is a series of midpoints between consecutive footprints.

  • Footprints: A list of data frames containing footprint coordinates, metadata (e.g., image reference, ID), and a marker indicating whether the footprint is actual or inferred.

H

A numeric vector representing the height at the hip (in meters) for each track maker. The length of this vector should match the number of tracks in the data.

G

Gravity acceleration (in meters per second squared). Default is 9.8.

method

A character vector specifying the method to calculate velocities for each track. Method "A" follows the approach from Alexander (1976), while method "B" is based on Ruiz & Torices (2013). If NULL, method "A" will be used for all tracks.

Value

A track velocity R object consisting of a list of lists, where each sublist contains the computed parameters for a corresponding track. The parameters included are:

  • Step_velocities: A vector of velocities for each step in the track (in meters per second).

  • Mean_velocity: The mean velocity across all steps in the track (in meters per second).

  • Standard_deviation_velocity: The standard deviation of velocities across all steps in the track (in meters per second).

  • Maximum_velocity: The maximum velocity among all steps in the track (in meters per second).

  • Minimum_velocity: The minimum velocity among all steps in the track (in meters per second).

  • Step_relative_stride: A vector of relative stride lengths for each step in the track (dimensionless).

  • Mean_relative_stride: The mean relative stride length across all steps in the track (dimensionless).

  • Standard_deviation_relative_stride: The standard deviation of relative stride lengths across all steps in the track (dimensionless).

  • Maximum_relative_stride: The maximum relative stride length among all steps in the track (dimensionless).

  • Minimum_relative_stride: The minimum relative stride length among all steps in the track (dimensionless).

Details

The velocity_track() estimates speed from stride length using classical formulas.

As shown by Prescott et al. (2025), such estimates may be misleading— particularly when tracks are produced on unconsolidated substrates, where actual speeds can be substantially lower than calculated. Moreover, equal stride lengths may correspond to different velocities, and conversely, different stride lengths can sometimes reflect similar velocities, depending on gait and substrate conditions. These values should therefore be treated with caution, both in this function and in subsequent functions that incorporate velocity estimates. By contrast, when trackways are formed on firmer or semi-consolidated surfaces, the formulas are more reliable and can provide useful estimates. Use is best regarded as comparative or historical unless the substrate context supports more confident interpretation.

#' The velocity_track() function calculates velocities using two methods:

Method A: Based on Alexander (1976), with the formula: $$v = 0.25 \cdot \sqrt{G} \cdot S^{1.67} \cdot H^{-1.17}$$

  • v: Velocity of the track-maker (in meters per second).

  • G: Acceleration due to gravity (in meters per second squared), typically \(9.81\ \text{m/s}^2\).

  • S: Stride length, which is the distance between consecutive footprints (in meters).

  • H: Height at the hip of the track-maker (in meters).

  • The coefficients \(0.25\), \(1.67\), and \(-1.17\) are derived from empirical studies. These coefficients adjust the formula to account for different animal sizes and gaits.

This method applies to a wide range of terrestrial vertebrates and is used to estimate velocity across different gaits.

Method B: Based on Ruiz & Torices (2013), with the formula: $$v = 0.226 \cdot \sqrt{G} \cdot S^{1.67} \cdot H^{-1.17}$$

  • v: Velocity of the track-maker (in meters per second).

  • G: Acceleration due to gravity (in meters per second squared), typically \(9.81\ \text{m/s}^2\).

  • S: Stride length (in meters).

  • H: Height at the hip of the track-maker (in meters).

  • The oefficient \(0.226\) in method B is a refinement based on updated data for bipedal locomotion.

Based on Thulborn & Wade (1984), it is possible to identify the gaits of track-makers on the basis of relative stride length, as follows:

  • Walk: \(A/H < 2.0\); locomotor performance equivalent to walking in mammals.

  • Trot: \(2.0 \leq A/H \leq 2.9\); locomotor performance equivalent to trotting or racking in mammals.

  • Run: \(A/H > 2.9\); locomotor performance equivalent to cantering, galloping, or sprinting in mammals.

References

Alexander, R. M. (1976). Estimates of speeds of dinosaurs. Nature, 261(5556), 129-130.

Prescott, T. L., Griffin, B. W., Demuth, O. E., Gatesy, S. M., Lallensack, J. N., & Falkingham, P. L. (2025). Speed from fossil trackways: calculations not validated by extant birds on compliant substrates. Biology Letters, 21(6), 20250191.

Ruiz, J., & Torices, A. (2013). Humans running at stadiums and beaches and the accuracy of speed estimations from fossil trackways. Ichnos, 20(1), 31-35.

Thulborn, R. A., & Wade, M. (1984). Dinosaur trackways in the Winton Formation (mid-Cretaceous) of Queensland. Memoirs of the Queensland Museum, 21(2), 413-517.

See also

tps_to_track

Author

Humberto G. Ferrón

humberto.ferron@uv.es

Macroevolution and Functional Morphology Research Group (www.macrofun.es)

Cavanilles Institute of Biodiversity and Evolutionary Biology

Calle Catedrático José Beltrán Martínez, nº 2

46980 Paterna - Valencia - Spain

Phone: +34 (9635) 44477

Examples

# Example 1: Calculate velocities for the MountTom dataset using default settings.
# H_mounttom contains hip heights for each track in the MountTom dataset.
# The function will use the default method "A" for all tracks.
# Hip heights are inferred as four times the footprint length, following Alexander's approach.
H_mounttom <- c(
  1.380, 1.404, 1.320, 1.736, 1.364, 1.432, 1.508, 1.768, 1.600,
  1.848, 1.532, 1.532, 0.760, 1.532, 1.688, 1.620, 0.636, 1.784, 1.676, 1.872,
  1.648, 1.760, 1.612
)
velocity_track(MountTom, H = H_mounttom)
#> $Track_01
#> $Track_01$Step_velocities
#> [1] 1.917671 1.699122 1.724574 1.690528 1.646310 1.521394 1.326607 1.634729
#> 
#> $Track_01$Mean_velocity
#> [1] 1.645117
#> 
#> $Track_01$Standard_deviation_velocity
#> [1] 0.17006
#> 
#> $Track_01$Maximum_velocity
#> [1] 1.917671
#> 
#> $Track_01$Minimum_velocity
#> [1] 1.326607
#> 
#> $Track_01$Step_relative_stride
#> [1] 1.553054 1.444507 1.457425 1.440128 1.417452 1.352034 1.245544 1.411473
#> 
#> $Track_01$Mean_relative_stride
#> [1] 1.415202
#> 
#> $Track_01$Standard_deviation_relative_stride
#> [1] 0.08868808
#> 
#> $Track_01$Maximum_relative_stride
#> [1] 1.553054
#> 
#> $Track_01$Minimum_relative_stride
#> [1] 1.245544
#> 
#> 
#> $Track_02
#> $Track_02$Step_velocities
#> [1] 1.446657 1.678316 1.833994 1.901630 2.320863 1.891043 1.662219 1.903494
#> 
#> $Track_02$Mean_velocity
#> [1] 1.829777
#> 
#> $Track_02$Standard_deviation_velocity
#> [1] 0.2544829
#> 
#> $Track_02$Maximum_velocity
#> [1] 2.320863
#> 
#> $Track_02$Minimum_velocity
#> [1] 1.446657
#> 
#> $Track_02$Step_relative_stride
#> [1] 1.305107 1.426506 1.504327 1.537305 1.732091 1.532175 1.418298 1.538208
#> 
#> $Track_02$Mean_relative_stride
#> [1] 1.499252
#> 
#> $Track_02$Standard_deviation_relative_stride
#> [1] 0.1241122
#> 
#> $Track_02$Maximum_relative_stride
#> [1] 1.732091
#> 
#> $Track_02$Minimum_relative_stride
#> [1] 1.305107
#> 
#> 
#> $Track_03
#> $Track_03$Step_velocities
#> [1] 2.434079 2.860861 3.171859 2.291902
#> 
#> $Track_03$Mean_velocity
#> [1] 2.689676
#> 
#> $Track_03$Standard_deviation_velocity
#> [1] 0.4022265
#> 
#> $Track_03$Maximum_velocity
#> [1] 3.171859
#> 
#> $Track_03$Minimum_velocity
#> [1] 2.291902
#> 
#> $Track_03$Step_relative_stride
#> [1] 1.815427 1.999825 2.127300 1.751165
#> 
#> $Track_03$Mean_relative_stride
#> [1] 1.923429
#> 
#> $Track_03$Standard_deviation_relative_stride
#> [1] 0.1719874
#> 
#> $Track_03$Maximum_relative_stride
#> [1] 2.1273
#> 
#> $Track_03$Minimum_relative_stride
#> [1] 1.751165
#> 
#> 
#> $Track_04
#> $Track_04$Step_velocities
#> [1] 1.830533 1.623483 1.409200 1.532089
#> 
#> $Track_04$Mean_velocity
#> [1] 1.598826
#> 
#> $Track_04$Standard_deviation_velocity
#> [1] 0.1776776
#> 
#> $Track_04$Maximum_velocity
#> [1] 1.830533
#> 
#> $Track_04$Minimum_velocity
#> [1] 1.4092
#> 
#> $Track_04$Step_relative_stride
#> [1] 1.410104 1.312308 1.205659 1.267558
#> 
#> $Track_04$Mean_relative_stride
#> [1] 1.298907
#> 
#> $Track_04$Standard_deviation_relative_stride
#> [1] 0.08606683
#> 
#> $Track_04$Maximum_relative_stride
#> [1] 1.410104
#> 
#> $Track_04$Minimum_relative_stride
#> [1] 1.205659
#> 
#> 
#> $Track_05
#> $Track_05$Step_velocities
#> [1] 2.175188
#> 
#> $Track_05$Mean_velocity
#> [1] 2.175188
#> 
#> $Track_05$Standard_deviation_velocity
#> [1] NA
#> 
#> $Track_05$Maximum_velocity
#> [1] 2.175188
#> 
#> $Track_05$Minimum_velocity
#> [1] 2.175188
#> 
#> $Track_05$Step_relative_stride
#> [1] 1.680626
#> 
#> $Track_05$Mean_relative_stride
#> [1] 1.680626
#> 
#> $Track_05$Standard_deviation_relative_stride
#> [1] NA
#> 
#> $Track_05$Maximum_relative_stride
#> [1] 1.680626
#> 
#> $Track_05$Minimum_relative_stride
#> [1] 1.680626
#> 
#> 
#> $Track_06
#> $Track_06$Step_velocities
#> [1] 1.868553 1.995720
#> 
#> $Track_06$Mean_velocity
#> [1] 1.932136
#> 
#> $Track_06$Standard_deviation_velocity
#> [1] 0.08992089
#> 
#> $Track_06$Maximum_velocity
#> [1] 1.99572
#> 
#> $Track_06$Minimum_velocity
#> [1] 1.868553
#> 
#> $Track_06$Step_relative_stride
#> [1] 1.512270 1.573083
#> 
#> $Track_06$Mean_relative_stride
#> [1] 1.542676
#> 
#> $Track_06$Standard_deviation_relative_stride
#> [1] 0.04300131
#> 
#> $Track_06$Maximum_relative_stride
#> [1] 1.573083
#> 
#> $Track_06$Minimum_relative_stride
#> [1] 1.51227
#> 
#> 
#> $Track_07
#> $Track_07$Step_velocities
#> [1] 1.1580528 0.8799351 1.1565610 1.5947244 1.6218920 1.3654251
#> 
#> $Track_07$Mean_velocity
#> [1] 1.296098
#> 
#> $Track_07$Standard_deviation_velocity
#> [1] 0.2869998
#> 
#> $Track_07$Maximum_velocity
#> [1] 1.621892
#> 
#> $Track_07$Minimum_velocity
#> [1] 0.8799351
#> 
#> $Track_07$Step_relative_stride
#> [1] 1.1181185 0.9485583 1.1172557 1.3542404 1.3680084 1.2340304
#> 
#> $Track_07$Mean_relative_stride
#> [1] 1.190035
#> 
#> $Track_07$Standard_deviation_relative_stride
#> [1] 0.1608436
#> 
#> $Track_07$Maximum_relative_stride
#> [1] 1.368008
#> 
#> $Track_07$Minimum_relative_stride
#> [1] 0.9485583
#> 
#> 
#> $Track_08
#> $Track_08$Step_velocities
#> [1] 1.840475 1.822117 1.615424 1.429871 1.893798
#> 
#> $Track_08$Mean_velocity
#> [1] 1.720337
#> 
#> $Track_08$Standard_deviation_velocity
#> [1] 0.1938159
#> 
#> $Track_08$Maximum_velocity
#> [1] 1.893798
#> 
#> $Track_08$Minimum_velocity
#> [1] 1.429871
#> 
#> $Track_08$Step_relative_stride
#> [1] 1.406970 1.398550 1.301268 1.209585 1.431239
#> 
#> $Track_08$Mean_relative_stride
#> [1] 1.349522
#> 
#> $Track_08$Standard_deviation_relative_stride
#> [1] 0.09259133
#> 
#> $Track_08$Maximum_relative_stride
#> [1] 1.431239
#> 
#> $Track_08$Minimum_relative_stride
#> [1] 1.209585
#> 
#> 
#> $Track_09
#> $Track_09$Step_velocities
#> [1] 2.836024 2.628135 2.426088 1.824772
#> 
#> $Track_09$Mean_velocity
#> [1] 2.428755
#> 
#> $Track_09$Standard_deviation_velocity
#> [1] 0.4360513
#> 
#> $Track_09$Maximum_velocity
#> [1] 2.836024
#> 
#> $Track_09$Minimum_velocity
#> [1] 1.824772
#> 
#> $Track_09$Step_relative_stride
#> [1] 1.878065 1.794374 1.710448 1.442246
#> 
#> $Track_09$Mean_relative_stride
#> [1] 1.706283
#> 
#> $Track_09$Standard_deviation_relative_stride
#> [1] 0.188858
#> 
#> $Track_09$Maximum_relative_stride
#> [1] 1.878065
#> 
#> $Track_09$Minimum_relative_stride
#> [1] 1.442246
#> 
#> 
#> $Track_10
#> $Track_10$Step_velocities
#> [1] 1.531647
#> 
#> $Track_10$Mean_velocity
#> [1] 1.531647
#> 
#> $Track_10$Standard_deviation_velocity
#> [1] NA
#> 
#> $Track_10$Maximum_velocity
#> [1] 1.531647
#> 
#> $Track_10$Minimum_velocity
#> [1] 1.531647
#> 
#> $Track_10$Step_relative_stride
#> [1] 1.243837
#> 
#> $Track_10$Mean_relative_stride
#> [1] 1.243837
#> 
#> $Track_10$Standard_deviation_relative_stride
#> [1] NA
#> 
#> $Track_10$Maximum_relative_stride
#> [1] 1.243837
#> 
#> $Track_10$Minimum_relative_stride
#> [1] 1.243837
#> 
#> 
#> $Track_11
#> $Track_11$Step_velocities
#> [1] 2.076045
#> 
#> $Track_11$Mean_velocity
#> [1] 2.076045
#> 
#> $Track_11$Standard_deviation_velocity
#> [1] NA
#> 
#> $Track_11$Maximum_velocity
#> [1] 2.076045
#> 
#> $Track_11$Minimum_velocity
#> [1] 2.076045
#> 
#> $Track_11$Step_relative_stride
#> [1] 1.578469
#> 
#> $Track_11$Mean_relative_stride
#> [1] 1.578469
#> 
#> $Track_11$Standard_deviation_relative_stride
#> [1] NA
#> 
#> $Track_11$Maximum_relative_stride
#> [1] 1.578469
#> 
#> $Track_11$Minimum_relative_stride
#> [1] 1.578469
#> 
#> 
#> $Track_12
#> $Track_12$Step_velocities
#> [1] 2.055415
#> 
#> $Track_12$Mean_velocity
#> [1] 2.055415
#> 
#> $Track_12$Standard_deviation_velocity
#> [1] NA
#> 
#> $Track_12$Maximum_velocity
#> [1] 2.055415
#> 
#> $Track_12$Minimum_velocity
#> [1] 2.055415
#> 
#> $Track_12$Step_relative_stride
#> [1] 1.569058
#> 
#> $Track_12$Mean_relative_stride
#> [1] 1.569058
#> 
#> $Track_12$Standard_deviation_relative_stride
#> [1] NA
#> 
#> $Track_12$Maximum_relative_stride
#> [1] 1.569058
#> 
#> $Track_12$Minimum_relative_stride
#> [1] 1.569058
#> 
#> 
#> $Track_13
#> $Track_13$Step_velocities
#> [1] 1.0479855 0.9131596 0.7996623 0.9715874
#> 
#> $Track_13$Mean_velocity
#> [1] 0.9330987
#> 
#> $Track_13$Standard_deviation_velocity
#> [1] 0.1046951
#> 
#> $Track_13$Maximum_velocity
#> [1] 1.047985
#> 
#> $Track_13$Minimum_velocity
#> [1] 0.7996623
#> 
#> $Track_13$Step_relative_stride
#> [1] 1.293046 1.190695 1.099729 1.235746
#> 
#> $Track_13$Mean_relative_stride
#> [1] 1.204804
#> 
#> $Track_13$Standard_deviation_relative_stride
#> [1] 0.08161704
#> 
#> $Track_13$Maximum_relative_stride
#> [1] 1.293046
#> 
#> $Track_13$Minimum_relative_stride
#> [1] 1.099729
#> 
#> 
#> $Track_14
#> $Track_14$Step_velocities
#> [1] 1.642322 1.384645
#> 
#> $Track_14$Mean_velocity
#> [1] 1.513483
#> 
#> $Track_14$Standard_deviation_velocity
#> [1] 0.1822052
#> 
#> $Track_14$Maximum_velocity
#> [1] 1.642322
#> 
#> $Track_14$Minimum_velocity
#> [1] 1.384645
#> 
#> $Track_14$Step_relative_stride
#> [1] 1.371800 1.238534
#> 
#> $Track_14$Mean_relative_stride
#> [1] 1.305167
#> 
#> $Track_14$Standard_deviation_relative_stride
#> [1] 0.09423395
#> 
#> $Track_14$Maximum_relative_stride
#> [1] 1.3718
#> 
#> $Track_14$Minimum_relative_stride
#> [1] 1.238534
#> 
#> 
#> $Track_15
#> $Track_15$Step_velocities
#> [1] 1.481571 1.819262 1.714949 1.727258
#> 
#> $Track_15$Mean_velocity
#> [1] 1.68576
#> 
#> $Track_15$Standard_deviation_velocity
#> [1] 0.1438632
#> 
#> $Track_15$Maximum_velocity
#> [1] 1.819262
#> 
#> $Track_15$Minimum_velocity
#> [1] 1.481571
#> 
#> $Track_15$Step_relative_stride
#> [1] 1.252836 1.416743 1.367525 1.373394
#> 
#> $Track_15$Mean_relative_stride
#> [1] 1.352624
#> 
#> $Track_15$Standard_deviation_relative_stride
#> [1] 0.0700531
#> 
#> $Track_15$Maximum_relative_stride
#> [1] 1.416743
#> 
#> $Track_15$Minimum_relative_stride
#> [1] 1.252836
#> 
#> 
#> $Track_16
#> $Track_16$Step_velocities
#> [1] 1.204506 1.319338 1.530753 1.656302 1.486676 1.558870 1.438280
#> 
#> $Track_16$Mean_velocity
#> [1] 1.456389
#> 
#> $Track_16$Standard_deviation_velocity
#> [1] 0.1524638
#> 
#> $Track_16$Maximum_velocity
#> [1] 1.656302
#> 
#> $Track_16$Minimum_velocity
#> [1] 1.204506
#> 
#> $Track_16$Step_relative_stride
#> [1] 1.120470 1.183262 1.293401 1.355917 1.270970 1.307575 1.246030
#> 
#> $Track_16$Mean_relative_stride
#> [1] 1.253947
#> 
#> $Track_16$Standard_deviation_relative_stride
#> [1] 0.07957735
#> 
#> $Track_16$Maximum_relative_stride
#> [1] 1.355917
#> 
#> $Track_16$Minimum_relative_stride
#> [1] 1.12047
#> 
#> 
#> $Track_17
#> $Track_17$Step_velocities
#> [1] 0.5915414
#> 
#> $Track_17$Mean_velocity
#> [1] 0.5915414
#> 
#> $Track_17$Standard_deviation_velocity
#> [1] NA
#> 
#> $Track_17$Maximum_velocity
#> [1] 0.5915414
#> 
#> $Track_17$Minimum_velocity
#> [1] 0.5915414
#> 
#> $Track_17$Step_relative_stride
#> [1] 0.9683894
#> 
#> $Track_17$Mean_relative_stride
#> [1] 0.9683894
#> 
#> $Track_17$Standard_deviation_relative_stride
#> [1] NA
#> 
#> $Track_17$Maximum_relative_stride
#> [1] 0.9683894
#> 
#> $Track_17$Minimum_relative_stride
#> [1] 0.9683894
#> 
#> 
#> $Track_18
#> $Track_18$Step_velocities
#> [1] 1.855606 1.676314 1.873988 1.404891
#> 
#> $Track_18$Mean_velocity
#> [1] 1.7027
#> 
#> $Track_18$Standard_deviation_velocity
#> [1] 0.2176438
#> 
#> $Track_18$Maximum_velocity
#> [1] 1.873988
#> 
#> $Track_18$Minimum_velocity
#> [1] 1.404891
#> 
#> $Track_18$Step_relative_stride
#> [1] 1.410077 1.326836 1.418425 1.193662
#> 
#> $Track_18$Mean_relative_stride
#> [1] 1.33725
#> 
#> $Track_18$Standard_deviation_relative_stride
#> [1] 0.1042735
#> 
#> $Track_18$Maximum_relative_stride
#> [1] 1.418425
#> 
#> $Track_18$Minimum_relative_stride
#> [1] 1.193662
#> 
#> 
#> $Track_19
#> $Track_19$Step_velocities
#> [1] 2.650903
#> 
#> $Track_19$Mean_velocity
#> [1] 2.650903
#> 
#> $Track_19$Standard_deviation_velocity
#> [1] NA
#> 
#> $Track_19$Maximum_velocity
#> [1] 2.650903
#> 
#> $Track_19$Minimum_velocity
#> [1] 2.650903
#> 
#> $Track_19$Step_relative_stride
#> [1] 1.778779
#> 
#> $Track_19$Mean_relative_stride
#> [1] 1.778779
#> 
#> $Track_19$Standard_deviation_relative_stride
#> [1] NA
#> 
#> $Track_19$Maximum_relative_stride
#> [1] 1.778779
#> 
#> $Track_19$Minimum_relative_stride
#> [1] 1.778779
#> 
#> 
#> $Track_20
#> $Track_20$Step_velocities
#> [1] 1.631206 1.396409
#> 
#> $Track_20$Mean_velocity
#> [1] 1.513807
#> 
#> $Track_20$Standard_deviation_velocity
#> [1] 0.1660266
#> 
#> $Track_20$Maximum_velocity
#> [1] 1.631206
#> 
#> $Track_20$Minimum_velocity
#> [1] 1.396409
#> 
#> $Track_20$Step_relative_stride
#> [1] 1.286657 1.172319
#> 
#> $Track_20$Mean_relative_stride
#> [1] 1.229488
#> 
#> $Track_20$Standard_deviation_relative_stride
#> [1] 0.08084897
#> 
#> $Track_20$Maximum_relative_stride
#> [1] 1.286657
#> 
#> $Track_20$Minimum_relative_stride
#> [1] 1.172319
#> 
#> 
#> $Track_21
#> $Track_21$Step_velocities
#> [1] 1.719009 1.860508
#> 
#> $Track_21$Mean_velocity
#> [1] 1.789759
#> 
#> $Track_21$Standard_deviation_velocity
#> [1] 0.1000548
#> 
#> $Track_21$Maximum_velocity
#> [1] 1.860508
#> 
#> $Track_21$Minimum_velocity
#> [1] 1.719009
#> 
#> $Track_21$Step_relative_stride
#> [1] 1.379331 1.446237
#> 
#> $Track_21$Mean_relative_stride
#> [1] 1.412784
#> 
#> $Track_21$Standard_deviation_relative_stride
#> [1] 0.04730944
#> 
#> $Track_21$Maximum_relative_stride
#> [1] 1.446237
#> 
#> $Track_21$Minimum_relative_stride
#> [1] 1.379331
#> 
#> 
#> $Track_22
#> $Track_22$Step_velocities
#> [1] 0.917559 1.250737
#> 
#> $Track_22$Mean_velocity
#> [1] 1.084148
#> 
#> $Track_22$Standard_deviation_velocity
#> [1] 0.2355923
#> 
#> $Track_22$Maximum_velocity
#> [1] 1.250737
#> 
#> $Track_22$Minimum_velocity
#> [1] 0.917559
#> 
#> $Track_22$Step_relative_stride
#> [1] 0.9286649 1.1179364
#> 
#> $Track_22$Mean_relative_stride
#> [1] 1.023301
#> 
#> $Track_22$Standard_deviation_relative_stride
#> [1] 0.1338351
#> 
#> $Track_22$Maximum_relative_stride
#> [1] 1.117936
#> 
#> $Track_22$Minimum_relative_stride
#> [1] 0.9286649
#> 
#> 
#> $Track_23
#> $Track_23$Step_velocities
#> [1] 3.753784
#> 
#> $Track_23$Mean_velocity
#> [1] 3.753784
#> 
#> $Track_23$Standard_deviation_velocity
#> [1] NA
#> 
#> $Track_23$Maximum_velocity
#> [1] 3.753784
#> 
#> $Track_23$Minimum_velocity
#> [1] 3.753784
#> 
#> $Track_23$Step_relative_stride
#> [1] 2.216404
#> 
#> $Track_23$Mean_relative_stride
#> [1] 2.216404
#> 
#> $Track_23$Standard_deviation_relative_stride
#> [1] NA
#> 
#> $Track_23$Maximum_relative_stride
#> [1] 2.216404
#> 
#> $Track_23$Minimum_relative_stride
#> [1] 2.216404
#> 
#> 

# Example 2: Calculate velocities for the PaluxyRiver dataset using default settings.
# H_paluxyriver contains hip heights for each track in the PaluxyRiver dataset.
# The function will use the default method "A" for all tracks.
# Hip heights are inferred as four times the footprint length, following Alexander's approach.
H_paluxyriver <- c(3.472, 2.200)
velocity_track(PaluxyRiver, H = H_paluxyriver)
#> $Track_1
#> $Track_1$Step_velocities
#>  [1] 0.2884087 0.2667234 0.2246319 0.2038125 0.2297207 0.2673225 0.2495612
#>  [8] 0.2303131 0.2352243 0.1496251 0.1616271 0.2372131 0.2426553 0.2254857
#> [15] 0.2041018 0.2211659 0.2609607 0.2515620 0.3030204 0.2519311 0.2015630
#> [22] 0.1627231 0.2052861 0.2788176 0.2525451 0.2455988 0.2475302 0.3025814
#> 
#> $Track_1$Mean_velocity
#> [1] 0.2357754
#> 
#> $Track_1$Standard_deviation_velocity
#> [1] 0.03865919
#> 
#> $Track_1$Maximum_velocity
#> [1] 0.3030204
#> 
#> $Track_1$Minimum_velocity
#> [1] 0.1496251
#> 
#> $Track_1$Step_relative_stride
#>  [1] 0.3789154 0.3615884 0.3262496 0.3077913 0.3306554 0.3620745 0.3474711
#>  [8] 0.3311657 0.3353764 0.2557886 0.2678840 0.3370715 0.3416810 0.3269916
#> [15] 0.3080528 0.3232259 0.3568899 0.3491365 0.3902964 0.3494432 0.3057525
#> [22] 0.2689704 0.3091219 0.3713188 0.3499529 0.3441569 0.3457750 0.3899578
#> 
#> $Track_1$Mean_relative_stride
#> [1] 0.3347413
#> 
#> $Track_1$Standard_deviation_relative_stride
#> [1] 0.03373255
#> 
#> $Track_1$Maximum_relative_stride
#> [1] 0.3902964
#> 
#> $Track_1$Minimum_relative_stride
#> [1] 0.2557886
#> 
#> 
#> $Track_2
#> $Track_2$Step_velocities
#>  [1] 0.4217631 0.4424676 0.5313636 0.5147757 0.5386046 0.5371984 0.4793255
#>  [8] 0.3964918 0.3818617 0.4191057 0.4207669 0.3792643 0.5615777 0.7805553
#> [15] 0.5455458 0.3713092 0.3961137 0.4110622 0.5113603 0.5568550 0.6203647
#> [22] 0.6723679 0.7106800
#> 
#> $Track_2$Mean_velocity
#> [1] 0.5043818
#> 
#> $Track_2$Standard_deviation_velocity
#> [1] 0.11228
#> 
#> $Track_2$Maximum_velocity
#> [1] 0.7805553
#> 
#> $Track_2$Minimum_velocity
#> [1] 0.3713092
#> 
#> $Track_2$Step_relative_stride
#>  [1] 0.5453924 0.5612701 0.6263007 0.6145187 0.6313974 0.6304098 0.5888162
#>  [8] 0.5255821 0.5138819 0.5433321 0.5446207 0.5117860 0.6473884 0.7884788
#> [15] 0.6362574 0.5053306 0.5252820 0.5370638 0.6120740 0.6441228 0.6871563
#> [22] 0.7210902 0.7454200
#> 
#> $Track_2$Mean_relative_stride
#> [1] 0.6037814
#> 
#> $Track_2$Standard_deviation_relative_stride
#> [1] 0.0789691
#> 
#> $Track_2$Maximum_relative_stride
#> [1] 0.7884788
#> 
#> $Track_2$Minimum_relative_stride
#> [1] 0.5053306
#> 
#> 

# Example 3: Calculate velocities for the PaluxyRiver dataset using different methods
# for velocity calculation. Method "A" is used for sauropods, which is more
# appropriate for quadrupedal dinosaurs. Method "B" is used for theropods, which
# is more appropriate for bipedal dinosaurs. Hip heights are inferred as four times
# the footprint length, following Alexander's approach.
H_paluxyriver <- c(3.472, 2.200)
Method_paluxyriver <- c("A", "B")
velocity_track(PaluxyRiver, H = H_paluxyriver, method = Method_paluxyriver)
#> $Track_1
#> $Track_1$Step_velocities
#>  [1] 0.2884087 0.2667234 0.2246319 0.2038125 0.2297207 0.2673225 0.2495612
#>  [8] 0.2303131 0.2352243 0.1496251 0.1616271 0.2372131 0.2426553 0.2254857
#> [15] 0.2041018 0.2211659 0.2609607 0.2515620 0.3030204 0.2519311 0.2015630
#> [22] 0.1627231 0.2052861 0.2788176 0.2525451 0.2455988 0.2475302 0.3025814
#> 
#> $Track_1$Mean_velocity
#> [1] 0.2357754
#> 
#> $Track_1$Standard_deviation_velocity
#> [1] 0.03865919
#> 
#> $Track_1$Maximum_velocity
#> [1] 0.3030204
#> 
#> $Track_1$Minimum_velocity
#> [1] 0.1496251
#> 
#> $Track_1$Step_relative_stride
#>  [1] 0.3789154 0.3615884 0.3262496 0.3077913 0.3306554 0.3620745 0.3474711
#>  [8] 0.3311657 0.3353764 0.2557886 0.2678840 0.3370715 0.3416810 0.3269916
#> [15] 0.3080528 0.3232259 0.3568899 0.3491365 0.3902964 0.3494432 0.3057525
#> [22] 0.2689704 0.3091219 0.3713188 0.3499529 0.3441569 0.3457750 0.3899578
#> 
#> $Track_1$Mean_relative_stride
#> [1] 0.3347413
#> 
#> $Track_1$Standard_deviation_relative_stride
#> [1] 0.03373255
#> 
#> $Track_1$Maximum_relative_stride
#> [1] 0.3902964
#> 
#> $Track_1$Minimum_relative_stride
#> [1] 0.2557886
#> 
#> 
#> $Track_2
#> $Track_2$Step_velocities
#>  [1] 0.3812738 0.3999907 0.4803527 0.4653572 0.4868985 0.4856273 0.4333103
#>  [8] 0.3584286 0.3452030 0.3788715 0.3803733 0.3428550 0.5076662 0.7056220
#> [15] 0.4931734 0.3356635 0.3580868 0.3716003 0.4622697 0.5033969 0.5608097
#> [22] 0.6078206 0.6424547
#> 
#> $Track_2$Mean_velocity
#> [1] 0.4559611
#> 
#> $Track_2$Standard_deviation_velocity
#> [1] 0.1015011
#> 
#> $Track_2$Maximum_velocity
#> [1] 0.705622
#> 
#> $Track_2$Minimum_velocity
#> [1] 0.3356635
#> 
#> $Track_2$Step_relative_stride
#>  [1] 0.5453924 0.5612701 0.6263007 0.6145187 0.6313974 0.6304098 0.5888162
#>  [8] 0.5255821 0.5138819 0.5433321 0.5446207 0.5117860 0.6473884 0.7884788
#> [15] 0.6362574 0.5053306 0.5252820 0.5370638 0.6120740 0.6441228 0.6871563
#> [22] 0.7210902 0.7454200
#> 
#> $Track_2$Mean_relative_stride
#> [1] 0.6037814
#> 
#> $Track_2$Standard_deviation_relative_stride
#> [1] 0.0789691
#> 
#> $Track_2$Maximum_relative_stride
#> [1] 0.7884788
#> 
#> $Track_2$Minimum_relative_stride
#> [1] 0.5053306
#> 
#>