A curved path can oscillate in many different fashions. It can have one light bend or thousands of sharply wavering twists between its beginning and end points. Whatever the nature of the path, however, traversing the direct distance between two points on the path is always shorter than moving between those two points along the curve. The amount of that curve's deviation from the shortest possible path is called its sinuosity. Calculating it requires only that you know the length of the distance between the points along the curve and the distance of the shortest possible path.
Things You'll Need
Measure the distance between the two points along the curved path if you do not already have it. It does not matter if you use American Standard or Metric units. The length of the curved path can be approximated by dividing it into individual line segments that follow the arcing motion of the curves as closely as possible, measuring the lengths of each individual line segment with a ruler, and adding them together (see Reference 2 for an illustration).
Draw a straight line between the two points with the ruler and measure it. Use the same unit of measurement as you did in Step 1.
Divide the distance measured in Step 1 by the distance measured in Step 2 to obtain the sinuosity of the curved path. The larger your result, the more your curved path segment deviates from a straight line between its two points.
Tips & Warnings
- The sinuosity of a straight line is equal to 1, which means that if you got a result of less than 1 in Step 3, your math was incorrect. Be sure to divide the length of the curved path by the length of the straight line, and not the other way around.
- Photo Credit Thomas Northcut/Photodisc/Getty Images
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