Deficiency-surplus transition function (DeSuTra) in semi-empirical formulas for tumbling of freely falling card
Vladimirs Vorohobovs, Martins Kleinhofs
Quarterly No. 2, 2022 pages 92-98
DOI:
keywords: phenomenology, heuristics, semi-empirical research, tumbling cards, Magnus effect, autorotation, lift force, bifurcation, efficiency reducer, efficiency diminisher, DeSuTra function, singularity
abstract A new phenomenological method for composing analytical formulae to describe dynamic systems using the DeSuTra function as a building block is introduced. Based on heuristic considerations, it is possible to write a correct formula with several unknown coefficients. Next, these coefficients are tuned such a way that the result coincides with the experimental data. To illustrate the viability of such a method, a simple but not trivial aerodynamic system was chosen: the autorotation of a rectangular piece of paper that falls in air. Three correction coefficients (diminishers) were introduced to calculate its rotation frequency. Then a simple expression for the Magnus effect and drag force was used. All the obtained formulae were experimentally proved and the coefficients calculated. The conclusions drawn confirm the usefulness of the presented calculation procedure for the design of composites with chaotically distributed reinforcements.