Analysis of transitions between different ringing schemes of the church bell

• We present a different ringing schemes of church bell.
• The transition between ringing schemes is possible either by change of propulsion or by modification of yoke.
• The presented idea can be used in theoretical analysis and to develop mounting layouts for new bells.

In this paper we investigate dynamics of church bells, characterize their most common working regimes and investigate how to obtain them. To simulate the behavior of the yoke-bell-clapper system we use experimentally validated hybrid dynamical model developed basing on the detailed measurements of the biggest bell in the Cathedral Basilica of St Stanislaus Kostka, Lodz, Poland. We introduce two parameters that describes the yoke design and the propulsion mechanism and analyze their influence on the systems' dynamics. We develop two-parameter diagrams that allow to asses conditions that ensures proper and smooth operation of the bell. Similar charts can be calculated for any existing or non-existing bell and used when designing its mounting and propulsion. Moreover, we propose simple and universal launching procedure that allows to decrease the time that is needed to reach given attractor. Presented results are robust and indicate methods to increase the chance that the instrument will operate properly and reliably regardless of changes in working conditions.