Under Construction Building and calculating turn radii By Mike Price, Entrada/San Juan, Inc. Fog Lines and Tangents Past exercises in this series used speed limits, global turns, and slope to modify transportation network travel times. This exercise addresses the need for modeling tight turns on narrow winding roads when mapping rural, mountainous terrain. Although I challenged my students at Bellingham Technical College to develop a fast, repeatable way to calculate radii for turns on existing mountain roads, we hadn't made any progress until one day last spring. I was driving home from a meeting where radius turns were discussed when my eyes began following the fog line on the right side of my highway travel lane. In Washington state, the fog line helps a driver track the roadway edge during limited visibility. I was fascinated by the way the line would appear straight, then curve, then straighten again. Sometimes, the line would even transition from a curve to the left, to a curve to the right, and back to a left curve again, without straightening. I thought I might be onto something. I realized that if I could map these inflection (or tangent) points through each curve, ArcMap would calculate the length of its connecting chord. I also thought that I could use ArcMap to model and measure the distance from the turn chord to the farthest point away from the line and even calculate the travel distance around the curve. After trying all types of geometric constructions using circles, ellipses, and irregular curves, I discovered a simple formula that required only the chord length and the perpendicular distance from the chord to the maximum curve extent (a line called the Middle Ordinate). I tried this formula on several curves, and it worked. On the Internet, I found the same formula on several engineering sites. I realized that it would be possible to draw and measure these lines in ArcMap and use this simple formula to determine the radii of a number of curves. 50 ArcUser Winter 2010 www.esri.com