New answers tagged road
Right-click on your length field -> statistics -> look at the SUM field
There are many ways to accomplish this task. One of the more straight forward ways is to dissolve your feature class, using the road name as your dissolve field. Each road will now be a single feature, and you can check its length.
EDIT : The default output of line density is in kilometer per square kilometer. So the output of the tool is already what you are looking for (you don't need to divide it again by the size of the circle, this is done automatically). Note that the vector-based approach from @Anggik will be more precise, however you will not have overlapping window analysis.
in my point of view, you should decide your unit area (it could be county boundary or certain grid). after that, do some geoprocessing to divide roads in each unit area. Then you calculate each of roads length in each unit area and divide with the hectarage (or km2).
I think you will have to use something like v.build.polyline. Edit: From the man page: v.build.polyline picks a line and from its start node, walks back as long as exactly one other line of the same type is connected to this node. ...[polylines] sometimes [are] broken into their constituent straight line segments during conversion from one data ...
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