org.opentripplanner.routing.util.elevation

Class ToblersHikingFunction

java.lang.Object

org.opentripplanner.routing.util.elevation.ToblersHikingFunction

public class ToblersHikingFunction
extends Object

Tobler's hiking function is an exponential function determining the hiking speed, taking into account the slope angle. It was formulated by Waldo Tobler. This function was estimated from empirical data of Eduard Imhof. [ Wikipedia ]

 Walking speed(W):

     W = 6 m/s * Exp(-3.5 * Abs(dh/dx + 0.05))
 

The 6 m/s is the Maximum speed achieved. This happens at angle 2.86 degrees or -5% downhill. In OTP we want to apply this as a multiplier to the horizontal walking distance. This is done for all walkable edges in the graph. To find the walkingtime for an edge we use the horizontal walking speed. Therefore:

 Given:
   Vflat : Speed at 0 degrees - flat
   Vmax  : Maximum speed (6 m/s)

   Vmax = C * Vflat

 Then:
               1
   C = ------------------  = 1.19
        EXP(-3.5 * 0.05)
 And:

   dx = Vflat *  t
   W = C * Vflat * EXP(-3.5 * ABS(dh/dx + 0.05))

 The Horizontal walking distance multiplier(F) then becomes:

                      1
   F = -----------------------------------
        C * EXP(-3.5 * ABS(dh/dx + 0.05))

 Examples:

   Angle  | Slope % | Horizontal walking distance multiplier
   -------+---------------------------------------
    19,3  |   35 %  |  3,41
    16,7  |   30 %  |  2,86
    14,0  |   25 %  |  2,40
    11,3  |   20 %  |  2,02
     8,5  |   15 %  |  1,69
     5,7  |   10 %  |  1,42
     2,9  |    5 %  |  1,19
     0,0  |    0 %  |  1,00
    −2,9  |   −5 %  |  0,84
    −5,7  |  −10 %  |  1,00
    −8,5  |  −15 %  |  1,19
   −11,3  |  −20 %  |  1,42
   −14,0  |  −25 %  |  1,69
   −16,7  |  −30 %  |  2,02
   −19,3  |  −35 %  |  2,40
   −21,8  |  −40 %  |  2,86
   −24,2  |  −45 %  |  3,41
 

Constructor Summary

Constructors

Constructor and Description
ToblersHikingFunction(double walkDistMultiplierMaxLimit)

Method Summary

Modifier and Type	Method and Description
double	calculateHorizontalWalkingDistanceMultiplier(double dx, double dh) Calculate a walking distance multiplier to account tor the slope penalty.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ToblersHikingFunction

public ToblersHikingFunction(double walkDistMultiplierMaxLimit)

Parameters:

walkDistMultiplierMaxLimit - this property is used to set a maximum limit for the horizontal walking distance multiplier. Must be > 1.0. See the table in the class documentation for finding reasonable values for this constant.

Method Detail

calculateHorizontalWalkingDistanceMultiplier

public double calculateHorizontalWalkingDistanceMultiplier(double dx,
                                                           double dh)

Calculate a walking distance multiplier to account tor the slope penalty.

Parameters:

dx - The horizontal walking distance

dh - The vertical distance (height)