# Turn angle

Definition

The change in direction of the nose, center, tail-base point or Head direction line between two consecutive samples.

Calculation

You can calculate Turn angle in two ways, based on body points or the Head direction line.

Based on body points

Turn angle is calculated as the difference between two subsequent values for Heading of the specified body point:

▪DHeading = Headingk - Headingk-1

▪If DHeading < -180°, then Relative Turn angle = DHeading +360°.

▪If DHeading ³ +180°, then Relative Turn angle = DHeading -360°.

▪Else Relative Turn angle = DHeading.

In the example below, there is a turn to the right (clockwise) at sample k. The heading HEk-1 is positive, while HEk is negative. As a result, the difference HEk - HEk-1 is negative. For the default axis orientation shown in the figure below, a clockwise turn corresponds to a negative Turn angle. A counter-clockwise turn corresponds to a positive Turn angle.

Based on Head direction

Turn angle is calculated as the difference between two subsequent values for Head direction (see the figure below, left). This value is independent of the position of the body points:

▪DHead direction = Head directionk - Head directionk-1

▪If DHead direction < -180° then relative Turn angle = DHead direction +360°.

▪If DHead direction ³ +180° then relative Turn angle = DHead direction -360°.

▪Else relative Turn angle = DHead direction.

The Turn angle based on head direction depends only on the samples k–1 and k, while the Turn angle based on a body point depends on the last three samples (k–2, k–1 and k. See the example below.

note The Head direction line is calculated using the subject’s contour. 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. Turn angle is then calculated based on those head direction lines.

Absolute vs. Relative Turn angles

▪Absolute Turn angle: The difference in direction is unsigned. Absolute Turn angle ranges from 0° to +180°.

▪Relative Turn angle: The difference in direction is signed. With a default axis orientation, a clockwise turn is signed negative, and a counterclockwise is signed positive. Therefore, the Relative turn angle ranges from -180° to +180°. Relative angles help you distinguish between clockwise turns and counterclockwise turns.

Absolute and Relative turn angles result in different averages. Consider for example two angles, -10° and +40°. The average relative turn angle is (-10°+40°)/2 = 15°. The average absolute turn angle is (10+40)/2 = 25°.

tip Use the picture below to know the sign of a turn. With the default axis orientation, a clockwise (right) turn means a negative turn angle. A counter-clockwise t (left) turn means a positive angle.

Whenever you use a coordinate system other the default one, rotate the image to know the sign of the turn. For example, a right turn on a coordinate system with the x-axis flipped gets a positive value:

How to specify Turn angle

1.Click the Add button next to Turn angle and click the Turn angle tab. Select Absolute or Relative.

2.Select Head direction turn angle (body point is ignored) if you want to calculate turn angle based on the Head direction line.

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

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

This tab is not available if you choose the option in step 2.

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

Below: Relative and absolute turn angle based on the change in direction of the Head direction line. Top: dependent variables visualized in Integrated visualization (Analysis > Results > Integrated Visualization). First chart: Relative turn angle, showing positive and negative values for left and right turns of the head, respectively. Second chart: Absolute turn angle. Bottom: dependent variables when exported in the raw data file (Analysis > Export > Raw Data).

Relative Turn angle and axis orientation

Relative Turn angle depends on the orientation of the x- and y- axes in the Arena Settings used for that trial. By default, the x-axis is horizontal and pointing to the right. A clockwise turn is scored as a negative value, and a counterclockwise is scored as a positive value. However, if the x-axis is pointing to the left, a clockwise turn is scored as a positive value, and a counterclockwise turn is scored as a negative value.

Below: The sign of the Relative Turn angle (RTA) depends on the orientation of the x- and y-axes. The example illustrates the effect of four different axis orientations on a clockwise turn. The sign inside the circles indicates the sign of Heading (HE) values. When the difference HEk - HEk-1 is larger than +180° or smaller than -180° (examples on the right), the rules described in Heading apply.

If the axes are swapped, the reference line is now vertical. the Relative Turn angle is calculated relative to the vertical axis. Compare the following figure with the example at the top-left corner of the figure above.

Notes

▪The mean, standard deviation and variance are calculated with linear statistics.

▪Turn angle is calculated in a way different from that in EthoVision 3. This is because Turn angle is based on Heading, which is set consistent with Head direction.

▪Turn angle is very sensitive to small, random movements of the body points. When the animal sits still, Turn angle can get very high, unrealistic values. To remove such small movements from your data, Smooth the Tracks, then run analysis.

▪Turn angle should not be confused with turn bias or turning rate. These are actually synonyms for the dependent variables Relative Angular velocity and Absolute Angular velocity, respectively.

Application

Assessing turn angles can be helpful for detecting stereotypic movements. In this case, consecutive turn angles tend to have large values (for example, in circling behavior of rodents), or show repeating patterns (for example, rocking or waving). For better quantification of biases in the left/right direction, first filter the data with the Minimal Distance Moved method, to ignore points where the animal does not move significantly.

Cumulative Turn angles are used to calculate rotations. See Rotation