Using open maps for urban search and rescue.

If I understand right you would need a map and when you click a place it should draw all the possible places a person could have walked to, in a limited time.

I think nothing like that exists, but could be done.

This is a similar idea but with public transport. You move the slider in the bottom, and see how far you can get with public transport in a given time. It doesn't work with all cities. It uses OSM data of public transport.

There is a number of ways you can do this. There is an in-built grid division in the way map tiles are served up. I think it's rather elegant and simple to make use of this. For example a tile with coordinates 130994,87124 can be opened in the browser at this URL: http://tile.openstreetmap.org/18/130994/87124.png

The '18' in this URL is the zoom level.

CloudMade do a diddy 64x64px version of tiles following the same coordinate scheme.

You should take a look at the QualityStreetMap tool, which uses tile coordinates, and has a selecting interface. In fact it has an open tagging scheme which you could perhaps just use directly for tracking your searches. Job done! However you'd probably want to look at installing it on your own server.

Another tool which does interesting grid things is MapOSMatic. Grid lines drawn on the PDF output maps.

Yet another option is to look at the FOSS Viking package. I know it runs on Linux & Windows.

While ostensibly designed for view GPS tracks, it works really well for simply looking at maps and creating your own routes. The default installation allows maps from several different OSM tile servers (the things that take the data and make pictures out of it), along with some other sources including areal photography.

Viking also allows you to overlay additional information on the maps, including creating grids. The grids are just drawn as lines (no reference numbers).