Friction of Distance

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Friction of distance is the idea that movement over space requires effort, resulting in an undesirable loss of resources, typically called a cost or impedance, that is directly proportional to the distance between a source and destination. This impedance is analogous to friction in physics (which results in a loss of energy during movement), hence the name. Friction of distance is one of the fundamental concepts of geography, because agents (people, animals, institutions) will tend to want to minimize this cost in their spatial activities, leading to consequential choices about the locations of routes, sources, and destinations. In turn, several analytical tools in Geographic information systems implement the concept of friction of distance and the consequent cost-minimizing goals.

For example, say a family is deciding which grocery store to patronize. All else being equal, they will likely choose the one that is more conveniently located, with a minimal travel time. In the aggregate, thousands of these decisions will impact the revenue of the various stores. The family will find a preferred route between their home and the store, likely the one with the shortest travel time, and use that route regularly. In the aggregate, thousands of these decisions will impact the traffic patterns over the city's streets. Consequently, store owners will use their knowledge of this tendency when locating new stores, by finding sites that have a minimal distance to a large population. City planners will use their knowledge of this tendency when planning improvements to the city's street system by identifying the locations of major destinations (business parks, shopping centers) and sources (residential neighborhoods) and planning optimal routes between them.[1]

Types of Impedance

Depending on the type of movement occurring, the resulting impedance can take a number of forms, such as:

  • Distance (often a fallback when other cost measures are not available)
  • Travel time
  • Travel energy expenditure (e.g., calories for pedestrians, vehicle fuel consumption)
  • Cost of constructing new pathways, such as roads or utility lines
  • Impacts of construction and/or usage of a pathway on the natural and human environment (e.g., pollution, habitat loss, disruption of neighborhoods)


Friction of Distance impacts a wide variety of natural and human activities, and is thus the basis of a number of geographic problems implemented as GIS tools.

Route Optimization

Many activities require agents to find the minimum-cost route between a source and destination. In fact, the case could be made that this is the single most commonly used analytical GIS task, because it is used daily by millions of people on web maps and smartphones. This task is implemented in two very different kinds of tools in GIS, as the nature of the solution space requires different algorithms. Network Analysis tools assume that the routes must follow a pre-existing linear network, such as a street system or a utility infrastructure. Conversely, Cost Distance Analysis tools are used when travel can occur anywhere over two-dimensional continuous space (e.g., wildlife migration or identifying corridors for future road construction).

Location Analysis

When one is tasked with determining the best location to build a new facility, such as a store, fire station, or park, a common criterion is to find a site that is maximally convenient to potential patrons (and thus will have maximum patronage). As with routing, location analysis has two classes of tools, depending on the solution space. Location-allocation algorithms are used for networks (i.e., assuming that people have to drive to a store), while clustering algorithms such as Lloyd's K-means are used for continuous space.

Spatial interaction and distance decay

Individual movement actions can be aggregated in many ways. One way is to summarize the volume of movement (in either direction) between any two locations, a concept known as spatial interaction. The Friction of distance means that all else being equal, short-distance movements will be preferred over long-distance movements, so the volume of interaction between two locations will be inversely proportional to the distance between them. In fact, geographers have found that in most situations, interaction volume is inversely proportional to the square of the distance between them. This tendency and its implementation in analytical models is commonly known as Distance decay, the Inverse-square law, or Gravity models (due to its mathematical similarity to force interactions in physics such as gravity, magnetism, and light).[2] Distance decay modeling is used in a wide variety of applications, from international trade to wildlife habitat.

Spatial Autocorrelation

One result of spatial interaction is that the more two places interact over a period of time, the more similar they eventually become in various characteristics. This effect occurs at scales from atomic (e.g., interacting molecules transferring energy leading to similar temperatures) to regional (e.g., historic standardization of national languages through inter-city interactions) to global (e.g., the spread of American culture via mass media and the Internet). Based on the principle of Friction of distance and the consequent Distance Decay effect, the likelihood of similarity is inversely proportional to distance. As Waldo R. Tobler stated in his First law of geography, "All things are related, but near things are more related than far things."[3] This tendency can be modeled statistically as Spatial autocorrelation, which states that the value of a spatially-dependent variable (a field) at a location, f(x,y) is positively correlated to the value of the same variable at a nearby location, say f(x+k, y), and that the smaller k is, the stronger the correlation. Spatial autocorrelation is the foundation of many field-based GIS techniques, such as Geostatistics, Interpolation, and Isarithmic mapping.

Technology and the "death of Geography"

Because so many geographic processes and patterns depend on Friction of Distance, one would expect that changes to the strength of impedance will have long-lasting effects on these processes and patterns. This has happened in profound ways over time. Most importantly, the continued development of transportation technology over the past 200 years has vastly decreased the financial and time costs of moving longer distances, and telecommunications technology has effectively eliminated any distance-based costs of moving information around the world.

These two changes have led to a general reduction in the friction of distance in many aspects of geography, leading in turn to increased interaction over much longer distances, and thus higher spatial autocorrelation in many cultural and economic characteristics of the population; basically, globalization. This has led some to claim that geography is no longer relevant.

While geography may have become irrelevant in some aspects of life in which it was once crucial (especially anything related to the spread of information), the friction of distance and thus geography is still very relevant in other aspects. For example, any task that requires individual travel, such as people patronizing parks, schools, and restaurants, will be very dependent on distance for the foreseeable future.


  2. de Smith, Michael, Paul Longley, Michael Goodchild (2016) Distance Decay Models Geospatial Analysis, 5th Edition
  3. Tobler W., (1970) "A computer movie simulating urban growth in the Detroit region". Economic Geography, 46(2): 234-240.