this method is the classical method for calculating the density.

Method C: Illustration of the measurement area

The density \(\langle \rho \rangle_{\Delta x}\) is defined as the number of pedestrians divided by the area of the measurement section:

\[\langle \rho \rangle_{\Delta x}=\frac{N}{b_\text{cor}\cdot\Delta x}.\]

The spatial mean velocity is the average of the instantaneous velocities \(v_i(t)\) for all pedestrians in the measurement area at time \(t\):

\[\langle v \rangle_{\Delta x}=\frac{1}{N}\sum_{i=1}^{N}{v_i(t)}.\]