One of the most basic human functions is to navigate from a starting point to a destination, a task that is completed by all humans’ countless times across their lives and throughout human history. Despite the simple premise, estimating the time required to travel on a trail or cross-country on foot is a complicated process owing to the many different factors and circumstances involved. This blog will brieflydiscuss three methods or calculating hiking times; Naismith’s rule with Langmuir’s Decent Correction, Tobler’s Hiking Function, and The Adjusted Tobler's Hiking Function. These methods have been established as ways to estimate human movement between two points using models based on algorithms that are commonly incorporated in Geographic Information Systems.
If you are interested in applying any of these methods to you own analysis please reach out and I would be more than happy to provide additional details on calculating each method in ArcMap and ArcGIS Pro.
Naismith’s rule with Langmuir’s Decent Correction
Naismith was a Scottish Mountaineer and in the 1800’s devised a rule to calculate hiking times for the average male with average fitness on easy expeditions. His rule stated that it would take one hours travel for every three miles (5 kilometers) on the map, with an additional hour for every 2,000 feet (600 metres) of ascent. While this rule is considered to be a fair indication of travel time and is still in use among expeditioners today, it does not take into account travel time on negative terrain. Langmuir, another accomplished mountaineer and outdoorsmen, proposed the following correction: Subtract 10 minutes per 300 meters of descent between 5 and 12 degrees and add 10 minutes per 300 meters when descending slopes greater than 12 degrees.
Tobler’s Hiking Function
Tobler’s Hiking Function estimates speed taking into account the slope and its direction. It states that travel is at 6 kilometers per hour at -5 percent slope, with speed exponentially decreasing as the slope increases. Tobler’s Hiking function calculates hiking speed slightly faster for downhill travel that uphill on the same slope. Tobler’s Hiking function is widely used and is believed to be the most prevalent model used in least-cost path analysis.
Adjusted Tobler's Hiking Function
On a Raster surface the direction of travel across a slope cannot be determined until after the shortest path has been calculated. The Adjusted Tobler’s Hiking Function sets the fastest hiking speed at 6 kilometers per hour at slopes of zero degrees, with the speed decreasing exponentially as the slope increases. The Adjusted Tobler’s Hiking Function calculates speed the same for uphill and downhill travel on the same slope.
Omissions and Assumptions
It is important to stipulate that several omissions and assumptions are included with all of the methods. While these may seem trivial in nature, they have potential to have a dramatic impact on the calculations and it is important that any end consumers of the analysis produced using these models are informed of and understand them. Naismith’s rule with Langmuir’s Decent Correction is calculated off the assumed speed that an average male with average fitness can perform, on easy terrain. It doesn’t accommodate gender or varying fitness, nor does it account for any additional weight that may be carried on the person. Tobler’s Adjusted Hiking Function assumes the same velocity for both ascents and descents when on the same degree of slope. None of the methods account for vegetation, soil types or obstacles that may impede movement. For example, water courses or swaps. No consideration is given to prevailing climatic conditions, nor to the altitude of the path.