# Heading

Definition

The direction of movement of the nose, center or tail-base point of the current sample relative to a line parallel to the x-axis in the coordinate system. 'Compass heading' and 'compass angle' are synonyms for Heading. See also Heading to point

Calculation

Heading is calculated in three steps:

1.The smallest angle a is found between the reference line and the vector connecting the samples k–1 and k.

The figure below shows the relationship between the angle a formed by the segment joining samples k-1 and k, the horizontal line parallel to the x-axis, and the dependent variable Heading (HE). Four cases are illustrated, corresponding to the possible directions an animal’s body point can be moving relative to the x-axis. Here, it is assumed the x-axis is horizontal and pointing to the right, and the y-axis is pointing upward.

2.The value of a is calculated according to the formula:

Where:

▪DMk is the distance moved at sample k.

▪Xk and Xk-1 the x-coordinates of the center, nose or tail-base point at sample k and k–1, respectively.

Because the way a is defined, it can only range from 0° to 90°.

3.How to convert a to Heading depends on the direction of movement between samples k–1 and k. The relation between Heading and a is determined by the following rules (see step 1 above).

- If DX > 0 and DY ³ 0, then Heading = a.

- If DX ³ 0 and DY < 0, then Heading = - a.

- If DX < 0 and DY £ 0, then Heading = -(180 - a).

- If DX £ 0 and DY > 0, then Heading = 180 - a.

Where DX = Xk - Xk-1 and DY = Yk - Yk-1.

Range

Heading ranges from -180° to +180°.

How to specify Heading

1.Click the Add button next to Heading.

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

Notes

▪If your experiment is set to Center-point, nose-point and tail-base detection, click the Body points tab and select the body points for which you want to calculate heading.

▪The mean, standard deviation and variance are calculated with circular statistics. See Statistics available.

▪Heading is calculated relative to the orientation of the x-axis you have chosen in the Arena Settings used for that trial. By default, the x-axis is horizontal and pointing to the right. If the x-axis is not horizontal or is pointing to another direction, Heading is calculated based on that axis direction.

Application

Heading is used in studies of spatial orientation. For example, you can use it to determine the direction of flight of a moth relative to the direction of the air flow in a wind tunnel. In a Morris water maze test, you can use this variable to measure initial heading of the path after releasing the animal in the basin.