Displaying distance using thiessen polygons

Question

Good Morning,

I am new to ArcMap and have been trying to work through a problem-

I would like to display the relationship between points based on distance, speed travelled and time.

So-  If I have one location that requires 6 minutes to start and travels at 125 knots and two others require 12 minutes to get started and travel 132 knots, how does that affect coverage?  I am trying to adjust the thiessen polygon to account for these costs rather than just display the exact midpoint of the three related points. In theory the one polygon should be a slightly different size/push than the other two?

Any help would be GREAT!

1 knot = 1 nautical mile per hour = 6076 feet per hour

curtvprice · Answer

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]

Dist_analysis.jpg