Derivation of a universal elevator round trip time formula under incoming traffic

Abstract

The design of vertical transportation systems still heavily relies on the calculation of the round trip time (τ). The round trip time (τ) is defined as the average time taken by an elevator to complete a full trip around a building. There are currently two methods for calculating the round trip time: the conventional analytical calculation method and the Monte Carlo simulation method. The conventional analytical method is based on calculating the expected number of stops and the expected highest reversal floor and then substituting the values in the main formula for the round trip time. This method makes some assumptions as to the existence of some special conditions (such as equal floor heights and a single entrance). Where these assumptions are not true in a building, this invalidates the use of the analytical formula the use of which will lead to errors in the result. The conventional analytical equation can be further developed to cover some of the special conditions in the building, but they do not cover all these special conditions and also do not cover combinations of these special conditions. The simplest round trip time equation makes the following assumptions: equal floor heights, a single entrance, equal floor populations and that the rated speed is attained in one floor jump. The case of unequal floor populations can be accounted for by amending the values of the probable number of stops and the highest reversal by using the formulae for the unequal floor population case. The work presented in this piece of work identifies the most important four special conditions (out a total of nine conditions) that are assumed in the classical round trip time analytical equation. It then develops analytical formulae for calculating the round trip time equation for any of the four special conditions or any combination of these conditions under incoming traffic conditions. A numerical example is given and verified using Monte Carlo simulation. Practical application: This piece of work presents new equations that allow the designer to evaluate the value of the round trip time. The equations can deal with special cases such as top speed not attained in one floor journey, multiple entrances, unequal floor heights and unequal floor populations. Once the value of the round trip time is obtained, the elevator system can be designed, providing the required number of elevators, their speed and capacity.