Calculate velocities and relative stride lengths for tracks

velocity_track() calculates the velocities and relative stride lengths 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() 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.

Logo

References

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

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.

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
#> 
#>