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7 Infrastructures for Movement Past and Future CESARE MARCHETTI Not snow, nor rain, nor heat, nor night keeps them from accomplishing their appointed courses with all speed. Herodotus, Histories Man is a territorial animal; the book of history could well be considered a string of squabbles (by turns glorious or miserable but mostly bloody) over territorial dominance. The instinct of a territorial animal is to expand its territory as far as possible.Yet curiously, ancient empires never became larger than an area allowing 15-day mail service from the capital. Beyond that distance, acquisitions tended to become unstable and to split away, indicating perhaps a lunar cycle in man's submission and trust. If the greed of the king required more territory, he had to develop an appropriate infrastructure to speed the messenger service. The Persian empire is a textbook example of such development; and what Herodotus said about the King of Persia's messengers, U.S. postal workers have adopted as a credo. When Marco Polo explored China, he witnessed many marvels, but apparently nothing struck him more than the efficient Chinese mail and messenger system and the infrastructure that supported it. Ancient civi- lizations did not transport much in terms of mass, even by sea, but the transportation of men and information always received the best available technology and some extraordinary engineering efforts. This emphasis on transporting people and information is not a cultural imprint of Euroasiatic origin; the Amerindian civilizations found the same solution to the same problem. In the technological context of a neolithic culture, the Incan roads and bridges appear to be just as extraordinary an engineering and organizational feat. Their most important function was to speed messages carried by runners, who traveled up to 300 km a day 146

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INFRASTRUCTURES FOR MOVEMENT 147 using a sophisticated relay system. The stimulus to set the high-speed system in motion may usually have been royal letters, but important missions were undertaken by high-ranking officials or missi dominici, indicating a limited substitutability between the transportation of pure information and that of people. Such behaviors and relationships, so deeply ingrained in the animal nature of man (the "beast"), are here forever, naturally, and can provide a solid basis for a model of the long-term development of transportation systems. The work of Zahavi (1981) embodies mathematically the drives of the territorial animal. We could say that every man is a territorial animal and that, as such, he will try to maximize the extent of the territory he uses. Zahavi found that the constraints to this activity are time (a little more than one hour per day is dedicated to extramural movement) and energy, indexed here by money (15 percent of disposable income is dedicated to transportation expenses). Within these constraints, time and money are allocated to different means of locomotion to maximize range. This conceptual scheme permits us to draw a general, long-term con- clusion: what the system wants is low-cost speed (low cost is obviously contextual). Nowadays, most of humanity walks, giving a personal ter- ritory not far different from that of a village (about 10 square kilometers Ekm211. In Western countries, most moving people own a car, the mean speed of which is an order of magnitude greater than walking-about 50 km per hour (h). The resulting territory is then 100 times larger (1,000 km21. Interestingly, this mean speed has remained unchanged during the last 50 years, suggesting the existence of a homeostatic mechanism. The mean speed of air transport is about an order of magnitude larger than that of a car-about 500 km/in. Thus, the jet set has a territory that is 100 times larger than that of the car set. The final objective is obviously to have the world as one's territory, and with the world's growing pop- ulation, more and more sites are becoming valuable visiting points. To belong to a city, one must have easy access to its services. Ancient cities, be they Rome or Peking, did not become larger than a radius that could be transited by walking or riding on public transportation for one hour, and some spot checks indicate that the same is true today. This means that extremely large cities, which are now coalescing here and there, need first of all a fast transportation network. The figures in this chapter give some quantitative glimpses of the spread of trans- portation systems at the world level and some quantitative hints about the future. In his delightful collection of offbeat statistics, Zipf (1972) reported on the hierarchical structure of city sizes. Cities can be considered informational machines; as such, they are served well by a hierarchical

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148 CESARE MARClIE~ITI information system. But if people can move across a set of cities within the one-hour time limit using air shuttles, some high-level functions can then be split between the cities and synthesized through personal movement, just as if such people were living in different quarters of the same city. In other words, corridors such as the Bosnywash corridor in the eastern United States and the Shinkansen corridor in Japan ac- tually operate as single cities- at least at the level of hierarchical in- formation processing-but it is information bound to flesh, like that of . . . . . . t he masse aom~nZc'. Over the past two decades the magnetic levitation (or Maglev) train for the next Shinkansen line has made mixed progress. Indeed, the only thing that has remained constant during these years is the required one-hour transit time between its terminals, Tokyo and Osaka. The obvious impli cation is that the 70 million people who have gravitated to that strip of land have the aspiration and potential to become part of a single city. In the hierarchical information scheme, size is a prerequisite for power. In other words, the Shinkansen corridor, with its 70 million people, may become the hierarchical capital of the world, a position London held for more than a century. A transportation analyst looking forward in time at the development of networks sees intense interaction among settlements on a grand scale. But how grand? As is shown later in this chapter, the context of air trans- portation calls for an airplane capable of operating at speeds as great as Mach 8, a development that will reduce the transit time between any two locations with suitable landing facilities to about one hour. The "grand scale" will then be the world. The world is imploding into larger and larger settlements, which makes such a global intercity air transport system logical. Over the long term (which is probably not all that long, considering the time necessary to realize such huge and complex networks and the exponential speed at which people implode into cities), transportation must be conceived of in terms of cities. But what will such cities look like? Doxiadis and Papaioannou (1974) in their seminal book on Ecumenopolis, give some guidelines on the shape cities (i.e., the "super" city) will take; basically a chicken-wire system of large mesh with blobs and smears here and there. In such a system, vacuum-tunnel Maglev trains would be perfect for the job of transporting people, accelerating at 8 Gs for half the trip and decelerating the other half. From my earlier analysis ( 1983), the Maglev system should begin operations about the year 2000. Thus, the Shin- kansen experiment will give us a solid context for our thinking about the future.

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INFRASTRUCTURES FOR MOVEMENT 149 METHODOLOGY Most of the analysis undertaken here uses a version of Darwinian ideas incorporated into Lotka's (1956) equations of competition between species in ecological niches. At the first level the analogy is formal, but the fit is excellent. At the second level, biological systems and social systems are information systems. The analogy may be substantial at this level. A second aspect of the methodology is that it is just phenomenological. Thus, only facts are examined, and they are organized using the model. Explanations are not usually given, but the reader is always free to anolv his or her own to the facts described. The methodology looks for invariants in sets of measurements. These invariants can be constants- for example, the human mortality for au- tomobile accidents or the energy input-output ratio in energetically close agricultures or they can be functional relationships, that is, quantitative rules or "laws." In this second area the models derived from a Darwinian concept of the working system proved to be of widest application. In these models the time dynamics is reduced to a competition between subsystems. Much has been written about these models, which have been applied extensively in genetics and ecology. A schematic treatment is reported in the appendix to this chapter. The examples of competition between subsystems can be reduced to three cases (or models). ~ 1 ~ Case 1: The Malthusian Population This population represents a single species growing in a niche of limited resources. This is the case of self-competition-that is, competition among individuals for resources. The classic biological example is a colony of bacteria growing in a bottle of broth. When a population cannot be enum- erated, as in the case of bacteria, the growth phenomena follow the same rule-for example, the growth of a sunflower is measured by its height and the growth of a road network is measured by its length. This case is modeled using logistic equations. Because of the many constraints that must be satisfied, it is easy to use this case improperly. For this reason many failures (in the area of human population growth, see Pearl, 1924, for example) occur when it is applied. The Malthusian population case is mapped using three-parameter lo- gistics. The parameters are not normally known externally; they are de- termined by the best fit method. Socioeconomic examples are the growth of the registered car population in Italy after World War II (Figure 7-1) and the growth of the telegraph system in the United States (Figure 7-21.

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150 CESARE MARCHEITI Fraction (fl 10' 10 1o-l 10-2 -90% -50% -10% l 1% ~1 1 J1 970 Fit = 22 yr 1 1 1 1950 1960 1970 1980 1990 2000 Year FIGURE 7-1 Car registrations following World War II in Italy. Saturation point = 20 million cars. In Figure 7-1 the logistic equation for car registration is linearized, using the Fisher and Pry (1970) transform, logged - {).This presentation fa- cilitates graphic handling of these data and the comparison of sets of curves in the same graph. The saturation point, not visible in the graph, is given numerically, as is the time constant (At), which is the time required to go from 10 to 90 percent of the saturation level. Case 2: One-to-One Competition In this case a new species is introduced into a niche previously occupied by another species. Haldane (1924) applied this case to biology when studying the penetration of a mutant, and Fisher and Pry (1970) applied it in a number of examples of market substitution. The treatment of case 2 is much easier than that of case 1, especially if one is interested in the ratios of population numbers or market fractions of the competitors. Case 2 is treated with two-parameter logistics. Because one species filled the niche at time zero, the sum of the individuals gives the size of the niche. An example of this case is the substitution of cars for horses

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INFRASTRUCTURES FOR MOVEMENT lo1 10 : 10-1 lo-2 151 / 190j~ At= 54yr 1 900 Year 1 950 FIGURE 7-2 Miles of wire in the Western Union telegraph system in the United States. Saturation point = 2.3 million mi. for personal transportation in the United States. The sum of horses and cars is the actual level of personal transportation. This is an example of simple substitution. Over about 20 years most of the personal transpor- tation in the United States shifted from horse to car (see chapter 81. The substitution is not easily explained, however, because cost and speed were roughly the same. Case 3: Multiple Competition This case is a generalization of case 2 in which new species are intro- duced sequentially into the same niche; a few thus are present at any given time in a phase-in or phase-out configuration. Case 3, which was originally developed by Marchetti and Nakicenovic (1979), is treated with a mixture of interacting logistics and transition functions. Multiple competition is in fact the rule in the real world, and the preceding cases can be considered simplifications of this general case when perturbations from other species are considered small. By deter- mining niche shares or market shares of competitors, one can construct the life cycle of each competitor, introducing only two parameters in the equations. The parameters may change over time, but they change inter- actively so that no external information is needed. An example of this case is the competition among primary energies for world markets (Figure

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152 1o2 101 10 10-1 10-2 _ , 0.30 Oily 1850 1900 1950 Year FIGURE 7-3 Primary energy substitution worldwide. CESARE MAR CHETTI on o.so 0.70 c o 0.50 0.10 0.01 2000 2050 7-31. In Figure 7-3, the coordinates are those of a Fisher-Pry transform. The great stability of the dynamics of the substitution for such a long time results from the fact that price elasticity and shadow prices always have the correct values. Nakicenovic (1987) shows the same analysis for the competition of transport infrastructures in the United States. This methodology was originally used for diagnostics that is, to have a compact, consistent description of what happened. With the accumu- lation of analyzed cases, however, it became clear that actual systems are extremely stable in time although subject to variable levels of noise. That is, the subjacent equations are followed for decades and centuries, which led to the use of the diagnostics in a forecasting mode. Many precautions were taken to ensure that booby traps common to such predictions were avoided. It was then concluded that forecasting within a period corre- sponding to about 50 percent of the time constant of any particular sub- system is safe. AIR TRANSPORT This section briefly surveys the dynamics of air transport worldwide to show these models at work. The kind of object studied is immaterial, provided that the appropriate indicators of its definition are identified. Efficient indicators for air transport can be either ton-kilometers per year (ton-km/year) or passenger kilometers per year (pass-km/year), if

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INFRASTRUCTURES FOR MOVEMENT 153 this subset activity is analyzed. For individual airplanes the preferred indicator is ton-kilometers per hour, the "flux" of payload. As shown in Figure 7-4, air transport since World War II can be mapped with the utmost precision. The saturation point of 200 billion ton-km/year was calculated by best fitting. It is remarkable that the increases in the price of jet fuel in 1974 and 1979 had no effect on the performance of the system. Such homeostatic behavior is characteristic of these large systems. When an external condition changes, the system rearranges itself internally to hold its trajectory. The air transport system is a huge "clockwork" system made up of smaller and smaller interlocking wheels. If a general Darwinian view holds for the similarity in behavior of subsystems at different hierarchical levels, the smaller wheels will also fit in the same mathematical pattern. For example, Lufthansa Airlines, which accounts for only a few percent of world air traffic, fits perfectly (Figures 7-5, 7-6, and 7-71. Figure 7-6 (ton-kilometers per year) is similar to Figure 7-5 (passenger-kilometers per year) except that it includes cargo. Passengers are by definition cal- culated at 80 kilograms each. In both figures' Lufthansa appears to be on a saturation course, a situation rarely perceived as such inside companies Fraction (I) 2 1o1 l 10 1o-l - 99% 90/0 - 50% - 10% tar ,,~B707 10-2 by' I ' ' ' ' it a,' i' B747 ' At = 32 yr 1950 1960 1970 1980 Year 1990 2000 2010 FIGURE 7-4 Air traffic (billion ton-kilometers per year) in the Western world. Saturation point = 200 billion ton-kmJyr.

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154 .. .. . CESARE AIARCHE7TI Fraction (f) 2 10 l ;~ 10 10-1 10-2 - 99% - 90% - 50% - 10% 1 /^ ~ 90%~ / I' / 1 974 ~ `^ At=21yr i/ ;; ~7 . . , 1 ~. . . 1960 1970 Year 1980 1 990 FIGURE 7-5 Lufthansa Airlines: billions of passenger-kilometers per year. Sat- uration point = 25 billion pass-km yr. themselves. Often a decline in growth rate is interpreted as overcautious- ness in management and investment, and ends in excessive capitalization and debts. Figure 7-7 shows equipment, following the rules of the game, for both quantity and quality. When the management of a company does not perceive the externality of the rules, overinvestment will result that is, the company will exceed in a nontransitory way its intrinsic saturation level of about 100 airplanes. Incidentally (transitory) mistakes appeared when the first batch of B-747s was purchased. It is practical to measure the tools for operating an air transport system- that is, airplanes in terms of their function. Airplanes can be classified according to their flux (how many ton-kilometers per hour they can trans- port). Thus, an airplane is again a very small wheel in the air transport system, quantified homogeneously. Figure 7-8 plots successful long-range passenger aircraft introduced during the last 40 years, using the dates of their first commercial appearance. This figure condenses the description of some of the deep mechanisms that connect airplane performance and air traffic. The thin dashed line represents world air traffic, expressed in passenger-kilometers per hour; the upper line represents the evolution of first-level airplane capacity, also expressed in passenger-kilometers per

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INFRASTRUCTURES FOR MOVEMENT 155 hour. The two lines are parallel, indicating that when first-level airplanes were introduced, their flux was a constant fraction of the traffic's flux. Because machines grow horizontally with traffic, forecasting traffic per- mits forecasting the performance of successful airplanes, usually a soul- wearing decision for airframe makers. In this context an essential feature for the success of the Concorde was lacking: it was too small by a factor of almost three. About 4,000 airplanes have been in service with commercial air com- panies (basically, the members of the International Air Transport Asso- ciation) over the last 30 years, despite an approximately 50-fold increase in traffic. Presumably, 4,000 airplanes is the minimum number needed to satisfy the time and space configuration of travel demand. (The number of oil tankers in service is about the same.) According to the forecasting power of the equations, air traffic will Fraction (I) 1o2 1o1 10 10-1 10-2 r 99% _ 90% - 50% - 10% 1% /: 1950 1960 1970 83% -/ 1 976 a,~ 1' ..' i' fit= 23yr 94%~ , I I ~ 1980 1 990 Year FIGURE 7-6 Lufthansa Airlines: billions of ton-kilometers per year. Saturation point = 5 billion ton-km yr.

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156 102 1o1 10 -1 10 10-2 CESARE A1ARCHE~I Fraction (f) - 90% - 50% - 10% 1% / (100) 1963 ad - fit = 28 yr - .~ .~7 ~ __ B747 fit - 32 yr 5' 1950 1960 1970 Year 1980 1990 FIGURE 7-7 Lufthansa Airlines, planes in service. Saturation point = 100 planes. increase by about 25-30 percent during the next 15 years. Thus, using the rules observed here, a stretched B-747 (Jumbo 1000) may well satisfy this demand. Airports need only plan then for an increase in throughput and pulse intensity. Engine designers should not be too preoccupied either, because lighter materials, better aerodynamics, and increased engine ef- ficiency (requiring less fuel on board) will take care of the extra payload without the need for major engineering breakthroughs. The situation appears more lively, however, if we zoom ahead in time. The general idea is that more income will lead to using a larger share of the traveling hour for faster (and more expensive) transport modes. An analysis of the intercity passenger-kilometers of different systems in the United States (see Figure 8-15 in Nakicenovic, this volume), reveals airways' increasing market share in intercity travel, with a possible in

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164 lol 10 lo-l lo-2 CESARE MARCHETTI f 1 853 J lo/ At= 56yr / 1800 1850 1900 Year FIGURE 7- 1 6 Railway systems for 40 countries worldwide, plotted by dates when system construction began. good target for Keynesian tactics (i.e., more public works) to counter the effects of the current recession. MOVING ENERGY Energy products are the largest single item moved around on the earth's surface, and they occupy a dominant position in the world's bulk trade and internal transport. This section describes a product life cycle for each of the primary energy sources coal, crude oil, natural gas, and nuclear power that have a commercial (long-distance) impact. The section is intended to show where we are going in terms of energy, to indicate the potential quantities involved, and to suggest some appropriate technolo- g~es. This analysis is based on the Darwinian competition for market shares among the primary energy sources: wood, coal, crude oil, natural gas, and "X," or a source yet to come (called fusion here). This competition has been stable over the past 150 years, with three energy crises and their related price increases, wars, and depressions having little effect on the mechanism.

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INFRASTRUCTURES FOR MOVEMENT 1o2 1o1 > 10 1 -2 ~ 10 165 I (I) '(UK) (NL) ~ ~E) I ~I I ~ 1982 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 Year )1 10 10-1 ~ (EEC_9) 197/ i' ,' f ~ t=24yr 10-2 ~ ' ' ' ' ' ' 1948 1950 1955 1960 1965 1970 1975 1980 1985 Year FIGURE 7-17 Construction of motorways in Europe. B: Belgium; EEC-g: Eu- ropean Economic Community; F: France; ERG: Federal Republic of Germany; I: Italy; NL: the Netherlands; and UK: United Kingdom.

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166 103 - - a) ~10 _ o ._ - 3 C) < ~10 _ o 0.1 CESARE MAR CHE=I Asymptote ~ 300 1 O9t 200 109t Actual , / Integrated coal demand Forecast / / Total energy demand Annual Demand 1 800 1 900 Year 2000 FIGURE 7-18 World coal consumption (in billions of tons). 2100 Because absolute quantities are needed and the life cycle is measured in terms of market shares, it was necessary to assume that a mean world energy consumption growth of 2.3 percent (which has been the case during the last 200 years) is acceptable for the next 150 years. If the world population then doubles every 70 years (it now doubles every 30 years), world per capita energy consumption in 2150 will equal the present level in the United States. Coal Coal reached its maximum market share penetration in the 1920s, and it has been losing ground ever since. Because of the expanding total energy market, however, the absolute quantity of coal consumption continued to grow; it has now reached its maximum level (this has occurred during the last few years). Consequently, the global infrastructure for coal will shrink although its geographical distribution will inevitably change. Despite this phase-out, the amounts that will be used cumulatively are still impressive: about 100 billion tons against the 200 billion tons already extracted (Figure 7-184. Approximately 3 billion tons of coal are processed each year. The straight line in Figure 7-18 represents total energy demand worldwide as interpolated and extrapolated from historical data, adopting

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INFRASTRUCTURES FOR MOVEMENT 167 the historical mean rate of growth of 2.3 percent per year. The actual coal demand curve approaches total energy demand in the 1920s when the main source of primary energy was coal, as shown by the market pene- tration curve (coal then covered about 80 percent of the market). This total energy demand does not contain the Kondratief oscillation; thus, it may be locally incorrect. The upper curve gives the cumulative amount of coal consumed. Most of this coal is now used in making electricity and, at a much lower level, steel. In developed countries, nuclear energy appears to be the inevitable competitor for the base load production of electricity, and steel comes increasingly from recycling through the use of electric steel pro- cesses. Thus, the geographical distribution of coal use will presumably move toward developing countries, which are also more willing to accept the pollution burden. A special case is China, which is now almost com- pletely dependent on coal and is ready to use 10 times as much. Use of the same analytical methods to look at the development of the electrical system and at the share of coal-generated electricity (to see if absolute quantities match) would probably reveal that there will be too much coal. This situation opens the way to molten-iron coal burning, a process in which electricity and synthetic gas are produced at the same time. Molten-iron coal burning is a process in which coal is dissolved in iron to remove impurities, including sulfur, before injecting oxygen in the iron bath to burn the carbon. The resulting product, 1400C gas, is then used to produce electricity and subsequently to synthesize methanol (methanol is formed from carbon monoxide and hydrogen). Because the coal is burned at the mine, long-distance exportation of electricity and methanol would occur, thereby avoiding local pollution as well as train traffic pollution. This process, which is being studied at the Nuclear Research Center in Julich, Federal Republic of Germany (Hafele et al., 1986), has been christened "zero emissions." It is a configuration and process that may well lie within the constraints and skills of developed countries. Oil Oil, the so-called lifeline of Western countries, has been selling at about the same level for the past few years. According to the product life-cycle analysis (see Figure 7-3), the use of oil has just peaked in terms of market shares, and it is now peaking in terms of absolute quantities. Because the share is falling sharply, the expansion of energy markets will compensate for the fall for only another 20 years (Figure 7-191. Apparently, however, there will be no growth after the market share peaks, as there has been

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168 In o 103 o - o - E In - o 10 1 0.1 C,ESARE MARCHETTI Forecast Actual , / . Hated oil demand 1 total energy demand/ / - - , 400 1 09 tons Annual oil demand 1 900 Year 2000 FIGURE 7-19 World oil consumption (in billions of tons). 2100 for coal. The infrastructure for oil therefore has no reason to grow globally, although its geographic distribution may change considerably during the next 100 years, before the market share finally falls to 1 percent. Because the size of oil tankers is closely linked to the amount of oil traded overseas and because more accurate exploration reveals oil deposits closer to the final consumers, a continuous decrease in the tonnage of tankers can be expected, a trend that is already occurring. Thus, neither port facilities for megatankers nor megaterminals will be necessary. Because the demand for coal and nuclear energy will cut into the demand for heavy oils and because progress in oil refining has made upgrading relatively easy, all of the oil on the market will probably be used to produce transportation fuels. (Natural gas may provide substantial help in refining operations by improving the hydrogen content of the feed, but this should not influence the infrastructure for gas.) Although oil appears to coast and slow down on what it achieved, the amount of oil still to be extracted is impressive, about 300 billion tons against the lOO billion already extracted. (Estimates about resources are always dated, but this 300-billion-ton es- timate appears reasonable for the time span considered here.) As it is for coal, the demand for oil can be dynamic in the spatial sense, but it is basically business as usual. Almost 4 billion tons of oil are

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INFRASTRUCTURES FOR MOVElIENT 169 processed per year, a mass roughly equivalent to that of coal. Its market share did not go as high as that of coal, however, because its introduction into the market was a bit "late" in historical terms. Natural Gas If coal and oil sound much like the railways more of the same, but running down the most interesting prospect seems to be natural gas, at least within our life span. The product life cycle of gas displays nothing unusual (Figure 7-201. Because its next competitor (nuclear energy) was introduced a good 70 years later, however, natural gas has had time to gain a large market share, which will reach a maximum like coal, 70 percent around the year 2040. Above all, natural gas is facing a larger and larger energy market. Quantities of natural gas will then increase by an order of magnitude over . . present quantities. This expansion will be realized by the development of networks in such countries as Brazil and India. The largest pipelines will also increase their capacities proportionally. This means that gas pipelines must be developed to carry 10 times as much gas as the present 58-inch (in.) pipe, the largest in use. Because the amount of gas transported grows almost in proportion to the cubic power of the diameter of a pipeline (if subsonic), a doubling of pipeline size to 120 in. can be expected. And because economic distance Jo' 10 10 ~ Fraction (f) - 90% - 50% - 1 0% ~ / Actual Forecast it\/ ,~ '1~' 1900 1950 2000 2050 2100 2150 Year FIGURE 7-20 Product life cycle of natural gas, worldwide.

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170 CESARE MARCHED grows linearly with the diameter of a pipeline, these trunk lines can be expected to carry gas 5,000-6,000 km from the source. Obviously, the implications of such developments will be political as well as infrastruc- tural. No attempt is made here to unveil what will happen in the liquefied natural gas (LNG) area after 1995. It is possible that new cooling methods will make LNG more appealing and that large LNG tankers will develop in response to volume trading. This kind of analysis is probably possible using Darwinian methodology. As for past and future extraction, natural gas production is just in its initial stage. The cumulative amount extracted to date is only a negligible share (about 2 percent) of the cumulative total: about one trillion cubic meters or, in equivalent energy, about six times that of oil. Nuclear Energy As shown in Figure 7-20, nuclear energy is projected to succeed natural gas as the world's primary energy source in the latter half of the twenty- first century. The real breakthrough in the use of nuclear energy will come when electricity grids are saturated sometime during the next 10 years in France and during the next 30 years in most of the Western world (see Figure 7-124. At that point, nuclear energy must incorporate an energy vector that is flexible, transportable, and storable presumably, hydrogen. Because hydrogen travels well (much like natural gas), the primary energy generators (nuclear plants) can be located far from consumer areas, ending the uneasy cohabitation of today. In addition, they can be extremely large ( 100 times the size of current plants), making the system again reasonable. A new continental pipeline network suitable for hydrogen may then be installed during the next Kondratief cycle (1995-2050), instituting the first round of a stable energy infrastructure. Each continent will have a few generation points, presumably located on its shores, that are capable of producing hydrogen in the terawatt range. Like those for the Maglev trains, the signs of such a development should appear in the next 10-20 years. CONCLUSION This tour d' horizon set out to elucidate problems in the deployment of transportation infrastructures and to identify techniques that might generate consistent descriptions and forecasts. At the level described here, changes generally occur slowly, even when technological progress appears hectic, because social absorption is slow. Thus, choices must be long-sighted and well timed, and this is not easy.

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INFRASTRUCTURES FOR MOVEMENT 171 Great breakthroughs are usually controlled by context. Context and its links with innovation can be deepened beyond the cursory analysis pre- sented here, perhaps just through sheer research effort. The most en- couraging discovery made in undertaking the analysis was the extreme dynamic stability of the transportation system and subsystems at all hier- archical levels. REFERENCES Debecker, A., and T. Modis (Digital Equipment Corp., Geneva, Switzerland). 1986. Determination of the uncertainties in S-curve logistic fits. Paper submitted to the Sixth International Symposium on Forecasting, Paris, June 15-18, 1986. Doxiadis, C. A., and J. C. Papaioannou. 1974. Ecumenopolis: The Inevitable City of the Future. Athens: Athens Center of Ekistics. Fisher, J. C., and R. H. Pry. 1970. A Simple Substitution Model of Technological Change. 70-C-215. Schenectady, N.Y.: General Electric Company; see also Technological Fore- casting and Social Change 3:75-88, 1971. Hafele, W., H. garnet, S. Messner, M. Strubegger, and J. Anderer. 1986. Novel integrated energy systems: The case of zero emissions. In Sustainable Development of the Bio- sphere, W. C. Clark and R. E. Munn, eds. Cambridge, England: Cambridge University Press. Haldane, J. B. S. 1924. The mathematical theory of natural and artificial selection. Trans- actions, Cambridge Philosophical Society 23:19-41. Kondratief, N. D. 1926. Die langen Wellen der Konjunktur. Archiv fur Sozialwissenschaft und Sozialpolitik 56:573-609. Lotka, A. J. 1956. Elements of Mathematical Biology. New York: Dover. Marchetti, C., and N. Nakicenovic. 1979. The Dynamics of Energy Systems and the Logistic Substitution Model. RR-79-13. Laxenburg, Austria: International Institute for Applied Systems Analysis. Marchetti, C. 1983. On a Fifty Years Pulsation in Human Affairs: Analysis of Some Physical Indicators. PP-83-5. Laxenburg, Austria: International Institute for Applied Systems Analysis. Mensch, G. 1975. Das technologische Patt. Frankfurt, FRG: Umschau Verlag. English translation: Mensch, G. 1979. Stalemate in Technology. Cambridge, Mass.: Ballinger. Montroll, E. W., and N. S. Goel. 1971. On the Volterra and other nonlinear models of interacting populations. Reviews of Modern Physics 43(2):231. Nakicenovic, N. 1979. Software Package for the Logistic Substitution Model. RR-79-12. Laxenburg, Austria: International Institute for Applied Systems Analysis. Nakicenovic, N. 1984. Growth to Limits, Long Waves and the Dynamics of Technology. Ph.D. dissertation. University of Vienna. Nakicenovic, N. 1987. Transportation and Energy Systems in the US. WP-87-01. Lax- enburg, Austria: International Institute for Applied Systems Analysis. Nukem. 1984. Nukem Market Report on the Nuclear Fuel Cycle. p. 18. NUKEM GesmbH, Hanau, Federal Republic of Germany. Pearl, R. 1924. Studies in Human Biology. Baltimore, Md.: Williams & Wilkins. Peschel, M., and W. Mende. 1983. Leben wir in einer Volterra Welt? Berlin: Akademie Verlag. Verhulst, P. F. 1845. Nouveaux M6moires de l'Academie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique 18:1-38.

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172 C'ESARE MARCHET1I Zahavi, Y. 1981. The UMOT-Urban Interactions. DOT-RSPA-DPB 10/7. Washington, D.C.: U.S. Department of Transportation. Zipf, G. K. 1972. Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology. New York: Hafner. (Facsimile of 1949 edition.) APPENDIX The Darwinian behavior of population is described in general in sim- plified form by the famous Volterra-Lotka equations: - iNi - AijNiNj, d! 1=! where Ni is the number of individuals of species i. (The properties of the solutions to these equations have been described by Montroll and Goel, 1971, and in the recent treatise by Peschel and Mende, 1983.) The quan- tities a, A, and A are parameters for which a physical interpretation is possible; Hi is the rate of growth of population i in the absence of predation, and Hi is the cross section of interaction between population i and popu- lation j. Special Cases: The Malthusian Case A physically intuitive example of this case is a population of bacteria growing in a bottle of broth (Verhulst, 18451. The bacteria act as machinery to transform chemicals present in the broth into bacteria. The rate of this transformation (other things, e.g., temperature, being equal) is propor- tional to the number of bacteria (the transforming machinery) and the concentration of the transformable chemicals. All transformable chemicals will ultimately be transformed into bacterial bodies. Thus, to use homogeneous units, one can measure broth chemicals in terms of bacterial bodies. N(t) is therefore the number of bacteria at time t, and N is the amount of transformable chemicals at time 0, before multiplication starts. The Verhulst equation can then be written as: = aN (N-N), dt whose solution is (1) N 1 + e (at + b) (2) where b is an integration constant, sometimes written as to; a is a constant

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INFRASTRUCTURES FOR MOVEMENT 173 that is independent of the size of the population. Thus, there is no proximity feedback. If we divide both sides of equation 2 by N. extract the expo- nential term, and then take the logarithm of both sides, we obtain log 1 f f-at + b, where N f-= N N is often called the niche, and the growth of a population is given as the fraction of the niche it fills. Obviously, this analysis has been done with the assumption there are no competitors. A single species grows to match resources (N) in a Malthusian fashion. One-to-One Competition Case This case was originally treated by Haldane (1924) and reported by Lotka (19561. It deals with the simple case of genetic competition from a mutant; that is, a new variety (1) has a reproductive advantage, k, over the old variety (21. This means that at every generation the ratio of the number of individuals in the two varieties will be changed by 1/~1-k). If n is the number of generations starting from n = 0, then Ro <1 - k)n N _ _ , N2 where att= 0. N: If k is small, as it usually is in biology (typically 10-3), then N. Ro = N2 e-kn (3) (4) We are now back to equation 2, except for the very favorable fact that we have an initial condition (Ro) instead of a final condition (N). This means that in relative terms the evolution of the system is not sensitive to the size of the niche, an extremely useful property for forecasting.

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174 CESARE MARCHE~ITI Multiple Competition Case The concept underlying the package developed for multiple competition (Nakicenovic, 1979) is the reduction of multiple competition to a set of double competitions by bunching competitors. The treatment is not gen- eral. In fact, oscillatory behavior, a characteristic of the solutions of the Volterra-Lotka equations, does not appear. In the hundreds of actual cases in which this concept was applied, the fits obtained were excellent, and the objects studied did not oscillate. Derivation of the equation parameters is usually undertaken by least- squares fitting on the Fisher-Pry transform that is, log f/~1-f). This may require further investigation, however, because visual fitting by ex- perts results in parameter values that are more efficient for forecasting. An analysis of the effect of noise in the data on calculation of the size of the niche in Malthusian growth has been carried out by Debecker and Modis (1986).