org.opentripplanner.routing.util.elevation.ToblersHikingFunction Maven / Gradle / Ivy
/*
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* 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 {@code 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
*
*/
public class ToblersHikingFunction {
/**
* The exponential growth factor in Tobler´s function.
*/
private static final double E = -3.5;
/**
* The slope offset where the maximum speed will occur. The value 0.05 will result in a maximum speed at
* -2.86 degrees (5% downhill).
*/
private static final double A = 0.05;
/** The horizontal speed to maximum speed factor: Vmax = C * Vflat */
private static final double C = 1 / Math.exp(E * A);
private final double walkDistMultiplierMaxLimit;
/**
* @param 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.
*/
public ToblersHikingFunction(double walkDistMultiplierMaxLimit) {
if(walkDistMultiplierMaxLimit < 1.0) {
throw new IllegalArgumentException("The 'walkDistMultiplierMaxLimit' is " + walkDistMultiplierMaxLimit +
", but must be greater then 1.");
}
this.walkDistMultiplierMaxLimit = walkDistMultiplierMaxLimit;
}
/**
* Calculate a walking distance multiplier to account tor the slope penalty.
* @param dx The horizontal walking distance
* @param dh The vertical distance (height)
*/
public double calculateHorizontalWalkingDistanceMultiplier(double dx, double dh) {
double distanceMultiplier = 1.0 / (C * Math.exp(E * Math.abs(dh/dx + A)));
return distanceMultiplier < walkDistMultiplierMaxLimit ? distanceMultiplier : walkDistMultiplierMaxLimit;
}
}