# Angular velocity

Definition

The change in direction of movement of the nose, center, tail-base point or Head direction line between two consecutive samples, calculated per unit time. Angular velocity is expressed in degrees/second (°/s) and can be either positive or negative (see below).

Calculation

Where:

▪RAVk is the Relative Angular velocity for sample k.

▪RTAk is the Relative Turn Angle for sample k.

▪tk-tk-1 is the time difference between the current and the previous sample.

Angular velocity can be calculated based on body points or the Head direction line:

▪Based on body points, as in the figure above. The angular velocity is calculated from the turn angle of the specified body point (nose, center or tail-base; see below).

▪Based on Head direction. The angular velocity is calculated from the turn angle based on Head direction.

important Note that calculating Angular velocity from Head direction is not the same as calculating it from the nose-point. This is because Turn angle (and therefore Angular velocity) at sample k based on a body point depends on the last three samples k–2, k–1 and k, while Turn angle based on Head direction depends only on the samples k–1 and k.

Range

The minimum and maximum angular velocity depend on the time between two samples. For example, if the sample rate is 25, the maximum attainable turn (+180°, see Turn angle) results in an angular velocity of 180/0.04= 4500°/s.

Absolute vs. Relative Angular velocity

▪Absolute Angular velocity: The rate of change in direction is unsigned. Also known as Turning rate.

▪Relative Angular velocity: The rate of change in direction is signed. Depending on the orientation of the x- and y-axes, a clockwise turn is scored as positive or negative value, a counterclockwise turn is scored with opposite sign (see the relative Turn angle). Turn bias (degrees/s) and circling tendency are synonyms for this variable.

The difference between relative and absolute Angular velocity is best explained by looking at the mean values of the two dependent variables in the following example:

Time | Absolute Ang. vel. | Relative Ang. vel.
0.04 | 10 | -10
0.08 | 45 | 45
0.12 | 35 | -35
Mean | 30 | 0

The mean absolute Angular velocity reflects the amount of turning, whereas the mean relative Angular velocity gives a better indication of the overall direction of turning.

How to specify Angular velocity

1.Click the Add button next to Angular velocity and click the Angular velocity tab. Select Absolute or Relative.

2.Select Head direction angular velocity (body point is ignored) if you want to calculate angular velocity based on head direction.

3.Click the Body points tab. Select the body points for which you want to calculate the velocity. By default, Center-point is selected.

4.Complete the procedure to add the variable. See Calculate statistics: procedure.

Notes

▪If your experiment is set to Only center-point detection or Color marker tracking, the Body points tab is absent. Calculations are based on the center point.

▪If the body point turns more than 180° between one sample and the next, the direction of turning is calculated incorrectly. In the example below, the subject makes a fast counterclockwise turn of 270° between time 2 and 3 (left). The program interprets this as a 90º clockwise turn (right).

As a result, Angular velocity gets a value smaller than expected, and in case of relative Angular velocity a false sign. This kind of error occurs when the sample rate is too low and the subject makes very fast turns. To prevent this kind of error, set the sample rate at such a level that it is practically impossible for the subject to make a turn more than 180° between two subsequent samples.

▪The Head direction line is calculated using the subject’s contour. However, if you swap nose- and tail-base points, or interpolate those two points, the Head direction line is not recalculated using the contour, instead as the prolongation of the segment joining the nose-point and the center-point. Angular velocity is then calculated based on those head direction lines.

Applications

▪The absolute Angular velocity is used to express the amount of turning per unit time. Generally, a high value of this dependent variable is associated with local search, for instance in response to non-volatile semiochemicals (Bell (1991) Searching Behaviour: The Behavioural Ecology of Finding Resources. London: Chapman & Hall).

▪The relative Angular velocity measures the speed of change in direction of movement. The mean of this dependent variable can be used to assess turn bias or circular tendency, the tendency of a subject to turn to a specific direction. Studying this helps detecting peculiarities or abnormalities of behavior (for instance, stereotypic movements, reaction to toxic substances, etc.).