Test 4: Measurement of the fundamental diagram

PASS

1. Definition

A corridor 1000 m long and 10 m wide carries three measuring areas of 2 m by 2 m at about 450, 500 and 550 m. The middle area is the main one; the other two are controls. The corridor is filled with persons of nearly equal free speed (for example 1.2 to 1.4 m/s) at 0.5, 1, 2, 3, 4, 5 and 6 persons per m². At each area the mean speed over 60 s is determined; the first 10 s may be dropped as a transient. The fundamental diagrams follow from the results, with flow equal to speed times density. In a second step the corridor is narrowed until persons can only walk one behind the other without overtaking, and the diagram is checked again for this line movement.

Source: RiMEA 4.1.1, Test 4, pp. 29-30, Fig. 5 (the English text calls it Figure 4). This is a paraphrase, not the text of the standard.

Reference: RiMEA e.V. (2025). RiMEA: Richtlinie für Mikroskopische Entfluchtungsanalysen / Guideline for Microscopic Evacuation Analysis, version 4.1.1. https://rimea.de/ (Page numbers are the page numbers of the bilingual guideline (n / 56).)

2. Scenario

Top view of the scenario for Test 4

Scenario figure from the executed notebook.

3. What to expect

RiMEA names no values: the speed-density and flow-density diagrams are to be created from the measurements. It notes that empirical data exist for this test (p. 22). RiMEA sets no fixed pass limit (p. 28).

Our criterion: Local density increases with population and walking speed does not increase with density

4. Our result

Status: PASS

Test cases of this row

Case Status Result Run

test_speed_density_relation

PASS

density_speed_flow_by_population (P/m^2, m/s, P/(m s))
3 groups × 3 series × 4 points
Download CSV

Show values

group	point	density [P/m^2]	speed [m/s]	flow [P/(m s)]
control1	1	0.5067	1.198	0.6071
control1	2	0.8179	1.194	0.977
control1	3	1.385	1.189	1.647
control1	4	1.927	1.183	2.28
main	1	0.7975	1.197	0.9548
main	2	1.328	1.196	1.588
main	3	1.996	1.194	2.384
main	4	2.939	1.196	3.514
control2	1	0.7662	1.197	0.9174
control2	2	1.307	1.194	1.56
control2	3	2.091	1.195	2.499
control2	4	3.033	1.197	3.629

n = 6000 · seed 42

test_speed_density_relation: comparison over populations [1000, 2000, 4000, 6000]: density strictly increases; bound: speed rise between consecutive populations <= 0.05 m/s; window 10-60 s, per measuring area

Result figure for Test 4

Result figure from the executed notebook.

5. Our implementation

Deviations from the standard:

The corridor is 200 m long and 10 m wide, one fifth of the specified length. The areas sit at x = 50 m (control) and x = 100 m (main, and a second control beside it), not around 450 to 550 m.
The runs use 1000, 2000, 4000 and 6000 agents, which gives about 0.5, 1, 2 and 3 persons per m². The densities 4, 5 and 6 persons per m² are not run.
The single-file line-movement case is not run.
Agents start spread over the whole corridor and walk to an exit at the downstream end. The corridor is not periodic, so the density in an area is a mean over the 10 to 60 s window and is not held fixed.
The pass rule is the suite’s own: at each area the measured density rises with the agent count, and the mean speed does not rise by more than 0.05 m/s from one density level to the next. Flow is computed as speed times density and is not asserted.

Model: WarpDriverModel

Test function: tests/vv/test_rimea.py::test_speed_density_relation
Scenario file: Rimea-04-fundamental-diagram.zip

6. Our notebook

Test 3: Walking speed down stairs Test 5: Premovement time