Fundamental Diagram of Stairs: Critical Review and Topographical Measurements

In this contribution an overview about the fundamental diagram for stairs is given. First we discuss discrepancies of fundamental diagrams of well-known planning handbooks for pedestrian facilities and evacuation routes like Predtechenskii and Milinskii (Planning for foot traffic flow in buildings. Amerind Publishing, New Delhi, 1978. Translation of: Proekttirovanie Zhdanii s Uchetom Organizatsii Dvizheniya Lyuddskikh Potokov, Stroiizdat Publishers, Moscow, 1969), Nelson HE, Mowrer FW (Emergency movement. In: PJ DiNenno (ed) SFPE handbook of fire protection engineering, 3rd edn., Chap 14. National Fire Protection Association, Quincy, pp 367–380, 2002), Fruin Fruin (Pedestrian planning and design. Elevator World, New York, 1971), and Weidmann (Transporttechnik der Fussgänger. Institut für Verkehrsplanung, Transporttechnik, Strassen- und Eisenbahnbau, ETH Zürich, Tech. Rep. Schriftenreihe des IVT Nr. 90, 1993, zweite, ergänzte Auflage). To proof the correspondence to real measurements, we present published measurements available in literature.In the second part we derive a fundamental diagram for stairs downwards based on precise trajectories. To check whether our experiments performed under laboratory conditions are comparable with characteristics of motion of every day situations, we present a comparison with a field study carried out at the same staircase. Furthermore the contribution shows a method to gain topographical information of density, velocity, and specific flow structures to get a microscopic insight into pedestrian dynamics on stairs. This information could be used to identify effective bottlenecks