Not exactly basic ArcMap (!)... this is pretty full-bore spatial analysis. Fortunately, Raster Calculator or arcpy map algebra is great for this kind of thing.First things first, you want to be using a projection that reasonably preserves distance and direction over your study area. UTM is a nice simple choice if your study area is less than 1000 km wide.Seems to me the easiest approach would be develop some sort of time of travel surface for each vessel using Spatial Analyst, and then do raster analysis of the surfaces. For example a surface of time of travel to each cell from a point would be:time = distance / speed If you used the Euclidean distance tool to get the distance, divided by speed to get time, and added your startup time, you'd have a raster where each cell has the time required to get there from the vessel location. Do this analysis for your study area extent for all three vessels, and you'll have three time of travel rasters.Here's a Map Algebra expression for that:
env.extent = "studyarea"
starttime = 6 / 60. # hours to start
speed = 125 * 1852 # meters per hour - assuming your map coordinates are meters
t1rast = startime + EucDistance("vessel1") / speed # hr + m / (m/hr) = time of travel to cell in hours
At that point you can do more analysis, for example, use the Cell Statistics tool to create a minimum time raster with a hours value for each cell in your study area. This doesn't tell you which one - just what the shortest time of travel is. This is where it gets even more fun - you can find which vessel was the nearest (minimum time) with a Map Algebra expression like this:
Con(min_time_rast == t1ras, 1, Con(min_time_rast == t2ras, 2))
Note these Spatial Analyst tools can be used through their tool interface, from the Python window, ModelBuilder, or the Raster Calculator tool. These are exactly the same tools, just accessed differently.[ATTACH=CONFIG]27273[/ATTACH]
