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I am newb to QGIS and don't know if the following is possible.

I have a hill, most of which is given over to rectangular pasture fields. I hypothesize that the longwards alignment of the majority of the fields is parallel to the slope but would like to prove this. I already have a DEM from which I have generated slope, hillshade and contours over which I can overlay colour mapping.

Any ideas how I can use QGIS to prove my hypothesis?

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If I understand you correctly, I think you might solve it by extracting the aspect of the DEM, and then using the zonal statistics plugin to get the mean aspect of each pasture, and compare the aspect to the shape of the respective polygon. You could connect the mean aspect value with an arrow symbol in each polygon as a visual aid.

http://docs.qgis.org/2.2/en/docs/user_manual/plugins/plugins_zonal_statistics.html

You could also break up the polygons into several pieces as well to get a more detailed view.

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