velocity_track {QuAnTeTrack} | R Documentation |
Calculate velocities and relative stride lengths for tracks
Description
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
|
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 |
method |
A character vector specifying the method to calculate velocities for each track. Method |
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.
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).
Logo
Author(s)
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
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.
See Also
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)
# 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)
# 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)