GEOMETRIC TRENDS IN THE EVOLUTION OF A SMALL LOG-SPIRAL EMBAYMENT ON THE ILLINOIS SHORE OF LAKE-MICHIGAN

The evolution of a small log-spital embayment was monitored during nine months of 1989 on the Illinois shore of Lake Michigan adjacent to the slate-owned North Point Marina at Winthorp Harbor. Maximum shoreline recession during the monitoring was 61 m. A graphical method was used to locate the log spiral center, and regression analysis, identified the best fit logarithmic spiral curve for each of the ten mapped planforms. Geometric characteristics that progressively decreased during the evolution were the spiral angle (alpha) and the radius (r(o)) from the log spiral center to the origin. Geometric characteristics that progressively increased were the rotation angle (theta) over which the planform matched a logarithmic-spiral curve, and the spiral radius (r) at the maximum rotation angle. This study demonstrates that: (1) a graphical means is an efficient way to determine the center of a log-spiral bay; and (2) a dynamic equilibrium exists during the log-spiral evolution with the planform showing excellent agreement to a logarithmic spiral curve from the earliest bay development through the expansion landward and down coast.