The standard potential model

While Reilly’s model uses the ratio of an index of mass to an index of distance (e.g. M ia /dib) to the express the attraction of a place, the potential mode uses the sum of the attraction of individual places express the general notion of accessibility or potential. The standard potential expresion is as the follows.

Pi=∑Mk/dik= M1/di1+M2/di2+…+Mq/diq

where Pi is the potential at location i; Mk is the mass at location k; dik is the distance between i and k.

The potential expresses the total influence (thus attraction) of a place (e.g. location i) as a result of its relationship with other places. It carries the idea that the influence of a location is radiated from the place itself and other, especially nearby places. This is best seen from clusters of stores in close proximity. The clustering of the shops makes each shop more attractive than if one store is all alone and far away from the next store. A larger potential value is the result of either larger masses from the place itslef and the nearby places, and the close distance from places with larger masses. A smaller potential reflect the small masses of places and its locational isolation.

For example, the “BosWash” megalopolis (Fig. 1) at the northeast coast of the United States, stretching from Boston to Washington D.C including New Youk City, Philadelphia, Wilmington, and Baltimore, among others, has a profound impact on political, economic, social, and cultural events in the United States. Each urban center plays its own role in shaping such influences. However, it is the clustering of large urban areas in such proximity which has magnified each city’s impacts. Moving these cities far apart would significantly reduce the role of “BosWash” and each city’s impacts. On the other hand, Chennai (or Madras), the historical city of India, is a large city by itself with 7 million population. However, its southern coastal location causes its relative isolation, reducing its influence in the Indian urban hierarchy (Fig. 2).

Fig. 1 BosWash in U.S. urban system                    Fig. 2 Chennai in Indian urban system

Since potential can be calculated for all places, the potential contour maps can be generated to show spatial pattern of potentials, as shown in Fig. 3 and Fig. 4 which show population potentials of the U.S. and India. While the population potential maps reinforce the population maps, they magnify the clusters of larger centers in proximity and reduce the influence of large places in isolation.

Fig. 3 U.S. population potentials                        Fig. 4 Indian population potentials

Income can be used to create potentials to reflect the market demand while the production to reflect the potentials of supply, as shown in Fig. 5 and Fig. 6.

Fig. 5 U.S. market demand potentials based on income         Fig. 6 U.S. onion supply potentials based on onion production