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I have a shapefile of polygons, and wish to calculate the maximum length (parallel to flow) and width (perpendicular to flow) - both straight lines. I calculated the mean aspect (i.e. flow direction) using DEM pixels for each polygon. The image below shows what I'm attempting (mw = width, ml = length).

Example

Any ideas on where to start? I've found the 'Bearing Distance to Line' tool, which could potentially help to draw polylines for each polygon but am unsure regarding this and the rest.

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    In your picture, the maximum length isn't a straight line, yet the maximum width is. Is your intention to find the maximum length in a straight line, or following the flow direction? – Adam Jan 9 '17 at 0:15
  • @Adam Sorry, poor choice of image. I have calculated a mean aspect (straight line) and the maximum length needs to be a straight line parallel to this. Cheers – Darren J Jan 9 '17 at 8:18
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Have a look at this answer to Calculating maximum distance within polygon in x-direction (east-west direction) in PostGIS?

While the question pertains to PostGIS, the answer provided by whuber describes how to achieve your objective, and includes some R code as an example.

You could try implementing these procedures in ArcGIS Desktop using ArcPy.

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