The trip function of a lift

This paper deals with the mathematical derivation of the continuous trip function of a lift. This derivation applies not only to a lift but also to any mass inert mechanism that starts moving from standstill, runs up to a maximum speed or rated speed, to continue for some time, and then stops again after deceleration at completion of its trip along a predetermined track. The trip function determines the traveled distance and the (total) travel time in a continuous relationship with time, rated speed, maximum acceleration and jerk. All kinematic cases of the trip function, such as a short trip without reaching the rated speed, are treated with elaboration of the corresponding specific equations for the total traveled time, maximum achieved speed, etc. The results of the continuous trip function are compared to the results of the equations given in the literature (CIBSE Guide D Annex A2), which are based on a simplified model of the trip function. The conclusion is that the equations based on the simplified model are sufficient accurate for the calculation of handling capacity, journey times, etc. of lifts.