ESTIMATING HIKING TIME ALONG A SEGMENT - TOBLER


The simplest way to calculate travel time over your route segments, is to make an assumption about walking speed, e.g. a constant 3 miles per hour. However, this client wanted to account for slope a la Tobler's hiking function, since this is substantially hilly terrain and a constant walking speed is not necessarily realistic.

This process requires 3D data, containing elevation. If your data is only 2D, get a DEM and load up ArcGIS and produce 3D data, aka LINESTRING Z. Don't worry, I'll wait...

And now it's fairly easy:

-- Supplement each trail segment with a length. The example here transforms the geometry to
-- a State Plane SRS with feet as units.
ALTER TABLE trails ADD COLUMN length_feet float;
UPDATE trails SET length_feet = ST_LENGTH(ST_TRANSFORM(the_geom,3734));

-- Now the Tobler calculation. We fetch the elevation of the first and last
-- vertices of the linestring, divide by length, and that's the slope.
-- Remember, we split our segments into 100-foot lengths so this is mostly accurate.
-- If you keep yours as mile-long trails your accuracy may vary.
-- The 0.911344 converts from Tobler's own units (kilometers per hour)
-- to our preferred units (feet per second, to match the length in feet)
ALTER TABLE routing_trails ADD COLUMN tobler_fps FLOAT;
UPDATE routing_trails SET tobler_fps =
0.911344 * 6 * EXP(
-3.5 * ABS(
    (
      ST_Z(ST_StartPoint(ST_TRANSFORM(the_geom,3734)))
      -
      ST_Z(ST_EndPoint(ST_TRANSFORM(the_geom,3734)))
    )/length )
);

-- Now that each segment has its speed in feet per second and its length in feet,
-- the duration in seconds is simple. In our case, we calculate for three different
-- travel modes and we assume that bicyclists are being safe and only doing 3X as fast as walking.
UPDATE routing_trails SET duration_hike = length_feet / tobler_fps;
UPDATE routing_trails SET duration_bike = duration_hike * 0.33;
UPDATE routing_trails SET duration_horse = duration_hike * 0.66;

Discussion

I don't really know how accurate Tobler's function is, nor the degree to which it makes a difference in the accuracy of route duration estimates. Still, our original approach is to presume 3 miles per hour (4.4 feet per second) on foot, 3X that for bicycles, and 1.5X that for equestrian. Taking the slope into account may miss a lot of factors, but it can't be any worse!