Map of area around Rivertown
The gravity model derives its name and basic premise from Isaac Newton's law of gravity. Newton's law states that the attractive force between any two bodies is directly related to the masses of the bodies and inversely related to the distance between them.
Reilly (1931) used a gravity model to develop the Law of Retail Gravitation, used to determine the likely number of trips from generator areas (usually residential districts) to attractor areas (e.g., retail districts), using the following formula:
Interaction = Size Generator (G) * Size Attractor (R) * Constant (K) / distance (squared)
("*" means multiply)
In gravity models, the number of trips between two areas is directly related to activities in the area represented by trip generation and attraction and inversely related to the separation between the areas represented as a function of travel time. Therefore, areas with large amounts of activity tend to exchange more trips and areas farther from each other tend to exchange fewer trips.
Using Reilly's formula, population size can be converted into the number of trips generated. Residential areas are usually considered as generating trips, since people leave their homes in the morning and return to them in the evening. The number of trips generated is based on household characteristics, and most commonly includes the number of automobiles and number of people in the household.
Newton's gravity theory states that the force of gravity is inversely proportional to the distance between two bodies. The effect of distance between zones on the amount of travel between zones isn't so neatly defined -- if you were going to go shopping at one of the two identical shopping centers described below, which would you choose?
Shopping Center A--7 miles away/8 minutes by freeway
Shopping Center B--5 miles away/20 minutes by city streets
You'd probably choose shopping center A, because the trip takes less than half as long as a trip to shopping center B, even though B is closer. Friction factors represent the effect that various levels of travel time have on travel between zones. These factors are determined in a model's calibration process.
A more general term than travel time for the separation of zones is "impedance." Impedance can represent travel time, cost, distance, or a combination of factors. Generally, impedance is a weighted sum of various types of times (walking, waiting, riding) and types of cost (fares, operating cost, tolls, parking cost). In the past, travel time was used in the gravity model to measure separation and to develop friction factors. We now have the capability to include other factors, such as tolls and operating cost, in the impedance function, which more accurately represent the separation between zones.
Example:
An example clearly shows the use of the gravity model for planning. Assume the fictional city of Rivertown is divided into various zones. Residential zones A and B generate respectively approximately 1,000 and 2,000 shopping trips each day. Rivertown has three shopping areas, which attract trips to them based on their size (in total sq.ft.). They are C, D, and E, with sizes of 50,000, 100,000 and 150,000 sq. ft. respectively. Assuming there are 40 trips attracted for each 1,000 square feet, this becomes 2,000 trips for Zone C, 4,000 trips for Zone D, and 8,000 trips for Zone E.
The distance between the generators (residential areas) and attractors (shopping areas) is measured in distance (in miles). These distances are shown in the chart below:
Zone A to Zone C 10 miles
Zone A to Zone D 20
Zone A to Zone E 30
Zone B to Zone C 15 miles
Zone B to Zone D 20
Zone B to Zone E 25
Map of area around Rivertown
To calculate the number of trips produced from each residential area to each shopping area, the following formula is used:
T = G * R * K(t) / d-squaredwhere:
T = the number of trips produced in generator zone and attracted to attractor zone
G = the trips produced from generator zone
R = the trips attracted to attractor zone
K(t) = the friction factor constant for interchange (based on travel time between)
d = distance between zones (in miles)
The next step is to enter the friction factors for each zone. These factors are determined from research on origin-destination data, and reflect the area wide effect of travel time on a driver's willingness to drive to various destinations. Obtaining these factors is the principal operation of gravity model calibration. Assume the following as friction factors for this example:
By local streets .025
By freeway .035(Note: These friction factors are not realistic, and used only for purposes of this example.)
Thus, to find the number of trips generated from Zone A and attracted to Zone C, which is driven on local streets:
T(A-C) = GA * RC * K(t) / d-squaredT(A-C) = 1,000 * 2,000 * .025 / 100 = 500 trips per day
As another example, the number of trips generated from Zone B and attracted to Zone C can be found as follows:
T(B-D) = 2,000 * 4,000 * .035 / 225 = 700 trips per day
Suggested other pages... Economic development
