Geometric Method for Solving the Rope Path Curve for Cabin Deceleration in Cable Car Station

In the article “New Technological Approach to Cable Car Boarding”, the authors attempted to correctly design the curve geometrically along which the rope moves through the station during the deceleration of cabins with attaching platforms in a central position, primarily intended for mass public transport. Since the suspension continuously connects the cabin and the rope during cabin deceleration, the rope moves at a constant speed along a special curve that enables the cabin to stop in the central position. This curve is symmetric with respect to the longitudinal axis of the station. However, the authors found that in the previous article presenting this cable car system, an error was made in the geometric design of the rope path curve, which the original authors were not aware of at the time. They determined that, in the presented example, a suspension length of 8 m was too short for the combination of rope speed of 5 m/s (cable car speed) and cabin deceleration of 0.5 m/s2. This article revisits this geometric problem in greater detail. The study shows that not every combination of rope speed, suspension length, and cabin deceleration in the central position functions correctly. First, the boundary conditions and spatial constraints of the rope path curve were defined. Based on the upper bound and lower bound rope path lengths, the optimal or correct shape of the rope path curve was determined geometrically. The study concludes that for a given combination of rope speed (cable car speed) and cabin deceleration, only one suspension length is suitable. In the case of a rope speed of 5 m/s and cabin deceleration of 0.5 m/s2, the correct suspension length is 16.85 m. The authors also found that the result depends on the time interval used in constructing the curve.