A computational model of the two-for-one twister based on the mathematical model described in an earlier paper by the author is used to explore the effects of air-drag and balloon-limiter frictional drag on yarn tension in the balloon. As is to be expected, it is found that increasing the air drag or the frictional drag increases the yarn tension in both the free and the controlled balloon. However, the interaction between air drag and frictional drag is complex, and an increase in air drag may sometimes he compensated for by a decrease in frictional drag. The physics of free-balloon twister operation predicted by this model are highly non-linear, and concepts and terminology from bifurcation theory are introduced and explained in order to describe the behaviour of the free-balloon solutions concisely. The graph of dimensionless guide-eye tension against storage-cylinder radius exhibits a typical hysteresis bifurcation that unfolds as the air-drag parameter is increased. The effect of the balloon-limiter is to reduce the tension in the balloon and, more importantly, to suppress the multiple-solution region that occurs for some ranges of storage-cylinder radius in free-balloon operation.
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W. B. Fraser (1993) studied this question.
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