A physical interpretation of the rope simulated by the SONO algorithm is
presented. Properties of the tight polygonal knots delivered by the algorithm
are analyzed. An algorithm for bounding the ropelength of a smooth inscribed
knot is shown. Two ways of calculating the ropelength of tight polygonal knots
are compared. An analytical calculation performed for a model knot shows that
an appropriately weighted average should provide a good estimation of the
minimum ropelength for relatively small numbers of edges.Comment: 27 pages, to appear in "Physical and Numerical Models in Knot Theory
and their Application to the Life Sciences
