1. Chapter 5 Principles of Spatial Interaction
Introduction
The Interaction Matrix
The Bases for Spatial Interaction
Transportation Networks
Flows on Networks
Transport Impacts on Economic Activities

2. The Interaction Matrix
Direction of flow?
Connectivity Matrix
Measures of connectivity
Ratio: actual/potential links
In this example:
10 links of 20 potential:
Ratio = .5 O B O D O A O C O E

3. Flow Matrices Example Fig. 5.2 (p. 78) Also our i/o table
Why are patterns of flow organized as they are around:
Flows originating at particular places
Flows terminating at particular places
The routing structure used to move from origin to destination

4. The Bases of Spatial Interaction
Ullman’s three-part framework:
Complementarity (place utility; alternative scales in Figure 5.3)
Transferability (cost re: distance)
Intervening Opportunities (competing sources of supplies)
Ullman’s Research on railroad flows,
passenger flows, for data in the 1950’s,
and railroad flows for 1929.

5. Ullman’s Famous Railroad Map

6. Wheeler & Mitchelson’s Research on Information Flows
P (1) Information genesis, (2) hierarchy of control, and (3) distance independence
Information genesis – determined by center corporate control points, not by a market that demands the information
Hierarchy of control – size mediates volume
Distance has little impact the volume of information flow
Used to explain realignment of U.S. urban hierarchy

7. City Systems and Relations With Surrounding Territory
Functional areas versus uniform regions:
the umland concept
Figure 5.4 – distance decay in interaction
Spreading of commuter fields: Figure 5.6
The formalization of this concept by the BEA – The system of BEA Economic Areas
(The dead idea of the Concorde on page 83: Illustrates how forecasts of technology are risky)

8. Transport Networks
Influence of physical and political geography on their configuration

9. Another Boundary Impact on Transport Networks
See also Figure 5.8 in text

10. Taafee/Morrill/Gould Model of Transport Development
Figure 5.9 in text
A development sequence similar to the Vance model
Weak initial linkages
Penetration of remote territory
Development of more complex transport routes
Development of highly interconnected systems

11. The Location of Transport Routes & Networks
From the isotropic plain to “real” landscapes: water bodies & river corridors, hills, mountains, swamps, oceans & the poles
Seattle - impact of glaciation: water, hills
The underlying principle of complementarity
Cost components: fixed & variable
Configuration into networks

12. The Location of Transport Routes & Networks
From the isotropic plain to “real” landscapes: water bodies & river corridors, hills, mountains, swamps, oceans & the poles
Seattle - impact of glaciation: water, hills
The underlying principle of complementarity
Cost components: fixed & variable
Configuration into networks

13. Fixed & Variable (Operating) Costs

14. Network Options Least Cost to Use Least Cost to Build Hybrid B A A A B
Maximum
Connectivity
High Travel
Costs AC, BD
Benefit-Cost Evaluation of Network Choice:
- Benefits: relative travel cost (savings), interaction
- Costs: investment, operations

15. Evaluating Networks for Maximum Net Benefits5 4 
Cost = 10
Revenue = 15
Net Benefit = 5
Cost = 12, R = 18
Net Benefit = 6
Cost = 14, R = 25
Net Benefit 11
Cost = 19, R = 29
Net Benefit = 10 10  
(a)  3 7   
(b)      
(c)    
(d)   

16. Impact of Multiple Transport Modes on Routes
Land
Costs: Land = $2/ton-mile
Sea = $1/ton mile
XAY = 10*$1+10*$2 = $30
XCY = 15*$1+6*$2 = $27
XBY = 12*$1 +7*$2 = $26 X  15
Water 10 12  A  B  C
Land 7 6 10  Y

17. Other Impacts on Network Structure
Construction costs of given mode in different types of environments
Impact of borders - political boundaries -
Impact of politics (transcontinental RR; current battle over RTA line)
Impact of technology - mail flows; telephone calls (flat long distance rates), the WEB, “The End of Geography?”

18. Factors Influencing Transport Rates
1. Grouping freight rates into zones
2. Variations due to commodity characteristics
(a) Differences in cost of service related to:
(1) Loading characteristics
(2) Size of shipment
(3) Perishability and risk of damage
(b) Elasticity of Demand for Transportation
3. Variations due to traffic characteristics
(a) intermodal competition
(b) traffic density
(c) direction of haul pp

19. Desire Lines – Impact of Distance on Interaction

20. The Gravity Model: “Social Physics”
Iij = k * PiPj
Dijb
where I is interaction between place i and j,
p(i) and p(j) are populations of places I and j, k is an empirically derived constant,
and D(i,j) is the distance between i and j, raised to an empirically derived constant, b.
Stewart, Ravenstein, Ullman

21. Example of Gravity Model: Visitors to Olympic National Park

22. Olympic National Park, Continued

23. Olympic National Park, Cont.

24. Transport Impact on Development
Punt here, to take up this topic later (Janelle)
Key point: transport (and communications) improvements have reshaped the geography of production
Janelle’s argument
The long-run reduction in the cost of the friction of space