The arcs are an old design called drunkards trail or snake trail. Couldn't find templates online, but here is the directions on how to do it
http://www.earlywomenmasters.net/qui...ail/index.html
The quilt you reference has piecing in the background of the blocks and makes the roadway by color placement. look at tne weewonderfuls blog at oscars quilt and you can see it better. it also divides the background diagonally, so that each block uses four separates fabrics in the background, then to marching oueces for the arcs. It would be difficult to duplicate without curved piecing. What if you used large half square triangle blocks, joined them, marked the curves on the quilt top, then appliqued the "road" as a large meandering piece of bias? It wouldn't be exactly the same, but you would avoid the curves.