Transportation and its influence on cities

Transportation and its Influence on Cities F. L. HASSLER Depurtment qf Trunsportation,

This paper tions: “How and “What there such on the role

Transportation Systems Center, KmdalI MA, USA

Square, Carnhridyr,

presents some theoretical background and empirical findings relevant to the quesdo you characterize technology quantitatively. particularly transportation systems?“. forces give rise to cities? Are there any observed regularities in their growth’? Is concepts focus a thing as an optimum or equilibrium city size?” The underlying transportation plays in urban growth and interaction.

Transportation plays a key role in shaping our cities and their economy. In the United States, the automobile makes possible the logistics of modern urban living, and the truck, plane, train, and barge make possible the intercity commerce that sustains our economy and governs the competition between urban centers. In the work below some evidence of the quantitative effects of transportation on the arrangement and organization of cities is presented. The study stresses cities, nations, for example, and the way these spatial forms and relationships change over time. Such study today is greatly aided by some of the regularities that have been noted in the last century and observed to exhibit some continuity over time. Two major types of regularities are involved, those developed by Stewart, Warntz. and others [l] and those explored by Zipf, Pareto, and others [2,3]. The second class of regularities, called rank-order rule regularities, indicates, for example, that if one orders cities of the United States by population. the largest one is roughly twice the size of the second, 3 times the size of the third and so on. More generally r = (X,/X,)4

(1)

where X, is the maximum value of some characteristic of the members of the set, and X, is the value of the characteristic of the rth member. The first class of regularities deals with the concepts of demographic forces, potentials, and energies. According to these concepts, people interact with one another in much the same way as electric charges, magnets, or gravitational masses. That is, there is a “demographic force ” F,, that varies as the inverse square of the distance, rl 2. separating two groups of people, P, and P2 F,=

-C,-

PIP2

(2)

r12

where C is a constant of proportionality. It is an attractive force at large distances. From this one can derive expressions for the potentials and the energies bound up in the spatial relationships of people. Thus, for example, the population potential at a point i, due to the presence of 259

F. L. Husslrr

260 Pi people

at a point ,i is given by

where ‘ij is the distance separating points i and ,i. At the U.S. Department of Transportation’s Transportation Systems Center (TSC) in Cambridge. several of us have been studying the historical growth of transportation in the United States and its correlation with the national economy and urban development, hoping to show some of the fundamental relationships quantitatively. In one set of studies. [4,5] demographic or population potential was computed based upon state-by-state census data since 1790. Figure 1 shows an east-west profile from New York to San Francisco of population potential, normalized to correct for total national growth, for three different periods. The shape of the curve east of the Rocky Mountains stabilized around 1910. The only change since then reflects a relatively small migration to the far west that continues to the present time. The arrows represent points at the crest of a “population wave” as it spread slowly westward. Figure 2 shows the velocity of the “population wave” as it progressed westward and compares it with estimates of the historical average velocities of intercity passenger and freight during the era of the rise of the railroads. The evident correlation is completely in accord with a physicist’s expectation that the velocity of a migration process will be directly related to the velocity of physical transport. At modern velocities. the “population wave” which began at the birth of our country and reached the Pacific coast in the 1930’s would have had time to make one and one-third trips across the country in the last 45 years. Assuming no new waves of major immigration into the United States, we are led to expect east-west population equilibrium somewhere between the year 2000 and 20.50. The relation of the above to urban affairs has two parts. First, mass migrations are an important source of population for the growth of established urban areas. Second, expansion creates the seed towns that become large urban areas much later. With this in mind, we turn to a second set of studies undertaken at TSC [6-91. (1790) Pop. 8

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Transportation

and its I~jlurncr

on Cities

261

In analyzing urban spatial form, Bussiere and Snickars [lo] have used a theoretical argument maximizing urban “entropy” to show that residential population density is an exponentially decreasing function of distance from the city center p(r) = p. eCk’*

(4)

assuming only that the population is fixed and that the cost of movement within the city is proportional to distance moved. TSC analysts tested the exponential density relationship for 35 of the largest cities in the United States, using detailed 1970 census tract data. [11,12] The fit was excellent with standard deviations in almost all cases less than 3% as shown in Table 1 and in Fig. 3(a-j). Values of p0 and k for each city were derived. See ref. 13 for a discussion of the limitations of this view. An analytical definition of total urban area population, P,, not subject to the vagaries of area1 definition can be derived from (4):

Populations for the largest United States cities obtained from (5) were then arrayed versus rank-order in the normal way and are plotted in Fig. 4. The form of (1) that best fits the data for large United States cities has an exponent q = 1.23, and the agreement with the general rank-order rule form is good. Related data is found in the Statistical Abstract of the United States on the distribution of urban places (cities and towns) by size for each census year from 1790. The distribution can be derived theoretically from the rank-order rule, and a plot of the log of the number of urban areas with a population P against the log of P will give a straight line with the same slope, q. Figures 5(a-f) provide examples of this type of plot for several different periods. One feature of the rank-order rule and the related distribution function for city size has to do with human “preference” for cities of a given size. If q > 1 the probability

262

St. Pctersbur& LA SF Detroit New York Chicago Miami Seattle St. Louis Boston I I Providence 12 Dallas 13 Cbeland 14 Philadelphia 15 Atlanta I6 San .lose 17 Pittsburgh IX Minn. St. Paul I9 K.C. 20 Houston 21 D.C. 22 Cinc. 23 Phoenix 24 San Diego 25 Buffalo 26 Dayton 27 Port 2X Baltimore 29 Louisville 30 Indianapolis 3 I Milwaukee 32 Denver 33 Columbus 34 San Antonio 35 New Orleans I. 2 3 4 5 6 7 8 9 IO

0.0861 & 0.0046 0.09X0 * 0.0008 0.135 5 O.OIOi 0.113 * 0.0013 0.143* 0.00I I 0. I54 * 0.0028 0.167 + 0.0026 0.167 * 0.0010 0. I 74 * 0.00 I4 0. I7Y * 0.002x 0. I79 + 0.0065 0.180 * 0.0024 0.19 I * 0.0039 0. I92 _t 0.0020 0. I97 * 0.001 I 0.204 * 0.0040 0.206 _t 0.0027 0.2 IO + 0.007x 0.2 IO + 0.0035 0.2 I3 * 0.0041 0.216 f 0.0073 0.224 f 0.00’4 0.231 * 0.0029 0.247 + 0.0043 0.265 f 0.0024 0.277 ) 0.0048 0.277 * 0.0015 0.284 & 0.0073 0.28X f 0.0018 0.297 f 0.0045 0299 f 0.0042 0.30’) f 0.006X 0.320 f 0.0054 0.369 ) 0.0065 0.406 + 0.0030

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of finding a person in a large city is less than that of finding him in a small city (i.e. humans “prefer” smaller cities). Conversely. if L/ < 1 people “prefer” large cities. If q = 1.0 people have no “preference”. Cities world-wide have been observed to exhibit rank-order exponents in the range 0.97 5 y I 1.40. mostly at the high end of the range. From examination of plots like those in Fig. 5, it appears that y was very close to 1.0 in the United States until quite recently. In fact. the distribution function form for 1970 (Fig. 5f) is entirely consistent with the rank-order form in Fig. 3, for the large city end of the spectrum. A departure of the data from the linear “Zipf law” or rank-order rule fit, seems to have begun around the early 1900s at about the same time that the national population potential stabilized east of the Rockies. A fall off in the generation rate of “seed” towns coupled with the impact of mechanization of farm labor, would explain the observed data. Since we are observing an increasing slope of the curve at the large city end of the scale. in recent times there is weak evidence that Americans increasingly are “preferring” life in towns of the size 10,000 to 100.000 people.

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F. L. Hassler

Fig. 4.

In physics, the specific forms of the distribution function of a set of things arise from the details of the interactions of the members of the set, and the conservation laws of number, momentum, and energy. One area of current research at TSC involves the attempt to derive the distribution function for urban areas by analogous reasoning. We are investigating at this point whether the recent trends in the distribution function

Lrl( POP) Fig. 5(a).

Tramportation

and its Influence

269

on Cities

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will continue until the shape resembles a Maxwell-Bol~man equilibrium ~stribution function. Qualitatively, the impact would be to strengthen the weak “preference” somewhat. In a second aspect of research in the second set of studies, [IS] the demographic force thesis was employed to compute demographic self-potentials and self-energies for urban areas, using the observed exponential residential density relationships. Self-potential (at the city core) is given approximately by the expression

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Both I/, and E, exhibit rank-order behavior although rank-orders for P,, V,,, and E, differ. From this we concluded that pO and k must be correlated. Buss&e [ 131 has shown for selected European and Canadian cities that this is indeed the case, and the consequence is a steadily declining central population density and a gradual dispersion of the exponential form. This is in qualitative agreement with observations of

Trunsportation

and its Influence

271

OH Cities

Fig. 5(f).

United States cities, and with the expectation that automobile technology (and transit technology before that) has made possible a more dispersed life style. Attempts to date to show quantitatively that such an effect is due to a dependence of k in (4) on velocities of physical transport have given trends in the right direction but of insufficient magnitude [9], and work has been hampered by a lack of available United States urban time series data. We suspect we must construct similar models of commercial/industrial density behavior and then develop a two-specie, time-dependent growth model to account for the observed behavior, and work is underway in that direction. Throughout the second set of studies, concepts from the first set were used and so it was natural to attempt some union. If the concept of demographic energy is to be taken literally, it represents the energy involved in “human interaction”. It was felt that this quantity, if literally valid, would correlate directly with energy consumption in the society. Further, if the outputs of the societal activities were correctly evaluated relative to one another, it was felt that “constant dollar” GNP would be a second valid measure of the energy involved in “human interaction”. Energy consumption was analyzed and compared to the sum of urban and interstate demographic energies. The relationship is (BTUs)

= C.

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272

F. L. Hassler

Transportation

and its Injluence

,273

on Cities

the macroeconomy. Clearly this quantity has not changed much in 100 years. (By comparison, the ratio of energy consumed to labor hours worked in the economy is a measure of mechanical advantage in the economy and accounts for more than 80% of the labor productivity gains in the last century.) If we extrapolate these curves as indicated we obtain very close agreement with the current long-range forecasts of U.S. GNP (DRI Control Long IO/75 estimate) and energy consumption (Ford Foundation’s Energy Policy, [14] 1974 Historical Growth Energy Forecast). Figure 6(b) presents the demographic energy plot and an extrapolation based upon census population projections (also indicated). The shaded band of the demographic energy plot indicates the urban self-energy contribution estimated for all United States cities. It is evident that increasing urbanization in the United States is reflected in the increased urban contribution to the total demographic energy. 1000

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In the Ford Foundation study of U.S. Energy Futures, two alternatives to the historical growth scenario were developed. One called the Technical Fix Scenario results in energy consumption growth as indicated in Fig. 6(c). Such a forecast is consistent with the historical relationship of demographic energy and energy consumption. If mechanical efficiency remains relatively unchanged then GNP will continue to correlate directly with energy and demographic energy. The third Ford Foundation Energy Future, called Zero Energy Growth, flattens out 20% below the technical fix level. Should such a future occur without offsetting gains in mechanical efficiency, significant impacts on per capita GNP gains and urbanization would be felt. In particular, smaller cities and towns would have to grow at the expense of larger ones in order to preserve the rough equivalence of demographic energy with physical energy consumption and economic value generated. How hard is it to make mechanical efficiency gains? Research at TSC in Automotive Energy Efficiency [ 151 may give you some feel for this. The automobile consumes about 55”/) of the energy spent in all forms of transportation in the United States which, in turn. is about 25’;/, of all energy consumed in the United States. Figure 7 provides estimates of the increase in fuel efficiency judged technically feasible for various technological alternatives. Such gains are impressive and are considered easier to capture than most opportunities for conservation in other areas of the economy. To convert the conservation potential of automotive technology into a reality will require a large degree of cooperation between labor and management. between competing manufacturers, between industry and the government. and between the industry and the consuming public. If successful, an increase of IO”;, in total national mechanical efficiency is possible. SUMMARY We have attempted to show that the development of intercity transportation technology increased the speed of propagation of demographic forces that give rise to the generation and growth of urban areas. Within cities, the impact of transportation costs with distance gives rise to an exponentially declining residential density from the city

Transportation

and its Influencr

on Cities

275

center. It is probable, but not yet demonstrated completely, that the development of urban transportation technology has been the causal force in dispersing the compact urban form. The evidence implicitly shows in the rank-order behavior of cities shows of people for cities and towns in the range of the emergence of a weak “preference” 10,000 to 100,000 inhabitants. Such evidence is physically consistent with a damping out of large regional migrations and the emergence of more cooperative interactions between urban entities. Macroproperties of our society such as GNP and energy consumption correlate remarkably with the macroproperty of demographic energy. Increasingly severe constraints on future energy availability are consistent with the reduced rate of growth of demographic energy inherent in the reduced population growth, the reduction in magnitude of regional migrations and the “flight” from the larger urban areas. Increased cooperation of the elements of society necessary to capture the potential benefits of technology such as improvement in automotive fuel efficiency may offset some of the attendant losses in economic growth, but it may be realistic to forecast futures where economic growth rates are less than currently assumed. REFERENCES See, for example, J. Q. Stewart: The Development of Social Physics. American Journal of Physics (May. 1950). Press (1941). 2. G. K. Zipf, Natiorrul Unity aud Disunity, Principia qf Least Effort (Hafner, 1965). 3. G. K. Zipf, Humun Behavior and the Principal Migratiorl Velocities and Correlation with Trunsport Velocities in thr U.S. from 1970 to 4. SS-200-IJ3-18, Present. F. L. Hassler (Jan., 1976). 5. SS-200-U3-19, East-West Migratiorl in the U.S. 179ObI970. F. L. Hassler (Feb., 1976). 1. Orr thr Size of Cities, F. L. Hassler (Oct., 1975). 6. WP-200-U3-1 7. WP-200-U3-12, Theoretical Comiderution of the Distrihutiorz Functions for City Size, F. L. Hassler (Oct., 1975). 8. WP-200-U3-13, Macro Properties of Urban Artmm-1970 Statistics, F. L. Hassler and D. Kahn (Nov., 1975). 9. SS-200-U3-17. Macro Properties of Urban Areas (2)~Sornr Dynamic Models, F. L. Hassler (Jan., 1976). 10. Bussiere. R. and Snickars, F.. Derivation of the Negative Exponential Model by an Entropy Maximixing Method. Encironment and Planning. 2. 295 -301 (1970). 11. DOT-TSC-OST-75-45.1. Urban Data Book, L. Bronitsky, M. Costello. C. Haaland and S. Schiff (1975) Final Report. 12. DOT-TSC-OST-75-45.11. Urban Data Book, L. Bronitsky, M. Costello, C. Haaland and S. Schiff (Nov., 1975). 13. Static and Dynamic Characteristics of the Negative Exponential Model of Urban Population Distributions. R. Bussiere, p. 38 of Patterns and Processes in L’rharz and Regional Systems, edited by A. G. Wilson (Pion Ltd.. 1972). 14. A Time to Choose, America’s Energy Future (Energy Policy Project of the Ford Foundation, 1974). Task Force on Motor Vehicle Goals Beyond 1980 (to be published). 15. Report of Interagency I.