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8 Dynamics and Replacement of U.S. Transport Infrastructures NEBOJSA NAKICENOVIC This chapter uses several indicative examples to assess the time needed to build new and replace old transport infrastructures and energy transport systems. As the examples will show, both the growth and senescence of transport infrastructures evolve as regular processes, which are describable by S-shaped logistic curves. Not all growth and senescence phenomena can be described by simple logistic functions, however. Sometimes more complex patterns are observed, which are often described by envelopes that can be decomposed into a number of S-shaped growth or senescence phases. Two typical cases are (1) successive growth pulses with inter- vening saturation and a period of change, and (2) simultaneous substitution of m-ore than two competing technologies. In the first case, successive S- shaped pulses usually represent successive improvements in perfor- mance for example, aircraft speed records in which the first pulse is associated with the old technology, the piston engine, and the second with the new technology, the jet engine. In the second case, simultaneous substitution of competing technologies is usually described by increasing market shares of new technologies and decreasing market shares of old technologies. This chapter will demonstrate that the evolution of transport infrastructure can be described both by the performance or productivity of competing technologies and by their market share (see also chapter 71. For both of the cases just mentioned, it will be shown that the devel- opment of transport networks is subject to regular patterns of change, which can in principle be used for forecasting future trends. Most of the examples are taken from the United States because it is one of the few 175
176 NEBOJSA NAKICENOVIC countries to have well-documented experience of most of the technological changes that have occurred over the last 200 years. Because most of these changes subsequently diffused throughout the world, the examples also indicate the dynamics of these processes elsewhere. In this chapter, the use of the term infrastructure is rather narrow, referring only to transportation and energy grids and networks, and other components of these two systems. These systems are interesting because they have played a crucial role in the economic and technological devel- opment process, are very capital intensive, and, in general, have long lifetimes. Analysis of the historical development of these two systems will include a quantitative description of performance improvement, the gen- eral evolution of a particular infrastructure, and the replacement of old technologies and infrastructures by new ones in terms of their relative market shares. The term performance is used as a multidimensional con- cept (i.e. as a vector rather than a scalar indicator), and, where appropriate, the size of an infrastructure is measured as a function of time. The first section of this chapter describes the evolution of transport systems and their related infrastructures. The analysis starts, somewhat unconventionally, with the youngest technologies, aircraft and airways, and ends with the oldest transport networks, canals and waterways. The second section describes the evolution of energy consumption and pipe- lines as an example of dedicated transport infrastructures; The appendix briefly describes the methods and statistical tests used for this analysis. TRANSPORTATION Aircraft Aircraft are the most successful of today's advanced modes of trans- portation. Other concepts of rapid transport such as high-speed trains have shown limited success, but they are not used as universally as aircraft. In fact, the rapid expansion of air travel during recent decades has its roots in the developments achieved in aerodynamics and other sciences many decades ago and especially in the engineering achievements made between the two world wars. The DC-3 airliner is often given as the example of the first "modern" passenger transport because in many ways its use denotes the beginning of the aircraft age. The use of aircraft for transportation has increased ever since, and their performance has improved by about two orders of magnitude (about a hundred times). Figure 8-1 shows the increase in air transport worldwide measured in billions of passenger-kilometers per year (pass-km/year). It includes all carrier operations, including those of the planned economies.
U.S. TRANSPORT INFRASTRUCTURES 1 800 1 600 1400 1200 - _ - y a.' 1 000 - cn Q) u, (A cow ~800 o 600 400 l i/ At= 29yr 1940 1950 1960 1970 1980 1990 2000 Year FIGURE 8-1 Air transport worldwide, all operations. 177 The logistic function has been fitted to the actual data, and it indicates that the inflection point in the growth of air carrier operations occurred about 10 years ago (around 1977~. Thus, after a period of rapid exponential growth, less than one doubling is left until the estimated saturation level is achieved after the year 2000. The growth rate has been declining for about 10 years. If the projection here is correct, it will continue to do so until the total volume of all operations levels off after the year 2000 at about a 40 percent higher level than that experienced at present. Figure 8-2 shows the same data and fitted logistic curve transformed as X/(K -X), where x denotes the actual volume of all operations in a given year (from Figure 8-1, given in millions of passenger-kilometers per hour [pass-km/in]) and K iS the estimated saturation level. The data and the estimated logistic trend line are plotted in Figure 8-2 as fractional
178 1n2 ~ Year FIGURE 8-2 World air transport, logistic plot. NEBOJSA NAKICENOVIC ~ - / / (K=200) ~ iB747 /\B707 ~ t = 29yr ~-B377 1 1 '1 1 1 1 1 1 1 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 - 0.99 - - - _ _ 0.90 _ _ _ _ 0.70 0 IL 0.30 0.10 0.01 shares of the saturation level,f = X/K, which simplifies the transformation to/1 - A. Transformed in this way, the data appear to be on a straight line, which is the estimated logistic function.] Perhaps the most interesting result is that it took about 30 years for world air transport to reach the inflection point (about half of the estimated saturation levelly and that within two decades the saturation level will be reached. This raises a crucial question: What will happen after such a saturation? Can we expect another growth pulse, a decline, or the insta- bility of changing periods of growth and decline? Most likely a new period of growth associated with new technologies will follow the projected saturation. To understand the implications of a possible saturation in world air transport operations and future developments, one must look at the trans- port system in general, comparing aviation with other modes of transport, and analyze the various components of the air transport system itself. Aircraft, airports, and ground services are the most important components of the air transport infrastructure. The commercial aviation infrastructure differs, however, from the infrastructures of other competing transport systems such as roads or railways in that airports are not continuously connected physically as are pipelines, roads, and railroad stations.
U.S. TRANSPORTINFRASTRUCTURES 179 The global fleet of commercial aircraft and how it developed can be described in a number of ways. An obvious descriptor of the fleet is the number of aircraft in operation worldwide. This number increased from about 3,000 in the l950s to almost 10,000 in the 1980s. During the same time, however, the performance or carrying capacity and speed of aircraft increased by about two orders of magnitude. Thus, the size of the fleet is not the most important descriptor, because much of the traffic is allocated to the most productive aircraft operating among the large hub airports while other aircraft constitute the feeder and distribution system for des- tinations with a lower traffic volume. The analogy between air transport systems and electrical grids or road systems is very close: large aircraft correspond to high-voltage transmission lines or primary roads. Figure 8-3 shows the improvement over time of one important perfor- mance indicator for commercial passenger aircraft: carrying capacity and speed (often called productivity) measured in passenger-kilometers per hour. Each point on the graph indicates the performance of a given aircraft when used in commercial operations for the first time. For example, the :, - 1o-1 // ( K= 1200} B747/, / / TU-144 B707 / . DCA130O 1011 DC-8' ·. Concorde TU-114~ ~ B527 DC 7 ·CV880 DC-7C- .;Caravelle L649,4 / DC-4/ · ·. CV340 DC-3 ~ / ~/ ·:/ 1o-3- / i/ 1 1 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 At = 30.8 yr Lag = 9 yr Year / / _ 0.99 _ 0.90 _ 0.70 . - 0.10 0.01 . _ 0.001 0.50 O 0.30 ce 11 FIGURE 8-3 Passenger aircraft performance. Source of data: Angelucci and Ma- tricardi (1977), Grey (1969~.
180 NEBOJSA NAKICENOVIC DC-3 was introduced in 1935 with a performance of about 7,400 pass- km/h (21 passengers at 350 km/h); the B-747 was introduced in 1969 with a performance of about 50O,000 pass-km/in (500 passengers at 1,000 km/ hi. The largest planned B-747s can carry almost 700 passengers. They are therefore about a hundred times as productive as the DC-3 50 years ago. The upper curve in Figure 8-3 represents a kind of performance fea- sibility frontier for passenger aircraft because the performance of all other commercial air transports at the time they were introduced was either on or below the curve. Long-range aircraft on the performance feasibility curve were commercially successful; all other planes, whether they were successful or not, are below the curve. Thus, at any given time there appears to be only one appropriate (best) productivity specification for long-range passenger planes. Because the more recent jet transports all fly at about the same speed, the appropriate design for a new long-range transport should allow for a capacity of more than 700 passengers. Ac- cording to the estimated curve, the asymptotic capacity for the largest aircraft is about 1,200 passengers at subsonic speed (1.2 million pass-km/ h or 10 billion pass-krn/yr). This implies that the next pulse in aircraft performance, if it occurs, would take place after the saturation phase. It would start at about 1.2 million pass-km/in and grow to much higher levels by at least one if not two orders of magnitude. Thus, after the year 2000, long-range aircraft might be larger and faster. Another interesting feature of Figure 8-3 is that the productivity of all passenger aircraft is confined to a rather narrow band between the performance feasibility curve and a "parallel" logistic curve with a lag of about nine years. This logistic curve represents the growth of world air transport from Figure 8-2. It took about 30 years for the performance of the most productive aircraft to increase from about 1 percent of the estimated asymptotic performance to about half that performance (for example, the DC-3 represents the 1 percent achievement level and the B-747 roughly the 50 percent mark). In many ways the achievement of the 50 percent level represents a struc- tural change in the development of the entire passenger aircraft industry and airlines. With S-shaped growth (that is, a logistic curve) the growth process is exponential until the inflection point or the 50 percent level is achieved. Thus, at the beginning, the productivity of aircraft is doubled many times within periods of only a few years. Once the inflection point is reached, however, only one doubling is left until the saturation level is reached. In Figure 8-3, for example, this development phase occurred in 1969 with the introduction of the B-747. Because the B-747 can, in principle, be stretched by about a factor of two, it could remain the largest
U.S. TRANSPORTINFRASTRUCTURES 181 long-range aircraft over the next two decades. Thereafter, a new growth phase with either larger or faster long-range aircraft is conceivable; the more distant future may possibly see both. Before the inflection point, stretching does not help for more than a few years, given the rather frequent doublings in productivity. Conse- quently, new solutions are necessary. The necessity for new solutions also means that having a model that performs poorly on the market can be a crucial but nevertheless reversible mistake, provided the manufacturer is able to launch a new, improved performance model after a few years. After the inflection point, however, this strategy is no longer possible because those aircraft that are successful can be stretched to meet market demand through the saturation phase. Thus, in the late 1960s the introduction of new, long-range aircraft suddenly became riskier because it was no longer possible to launch a new model after a few years. The B-747, for example, had the appropriate productivity, whereas two other competitors, the DC- 10 and L- 101 1, were too small. The introduction of a 700- to 800-passenger aircraft in the near future would be risky because a stretched B-747 can do the same job; the introduction of a smaller long-range aircraft would probably fail because it would fall short of the primary market requirements. The only routes open to smaller, longer range transport such as the MD11 or Airbus 340 are those for which the B-747 is too large. In the long run, most of the long-range traffic will be between large hubs and will be less in the form of direct traffic between smaller airports. The market niche for long-range aircraft with fewer than 500 passengers will therefore be very limited. A feasible alternative might be to redesign the MD11 and the Airbus 340 as wide-body, shorter range transports suitable for frequent cycles. The design of a cruise supersonic aircraft able to carry 300 to 400 passengers, or a hypersonic transport able to handle 200 to 300 passengers, may therefore be a better strategy for the first years of the next century. To some extent, these principles also explain why the Concorde cannot be a commercial success: with a capacity of 100 passengers, it is 150 passengers short of being a serious competitor for the B-747. How probable is the development of a large cruise supersonic or hy- personic transport? S-pulses do not occur alone but usually in pairs. Thus, at saturation, structural change will occur, leading to a new growth pulse (probably S-shaped) and in turn to new productivity requirements and therefore to supersonic or hypersonic transport. The alternative is that air transport will saturate pe~anently over the next few decades, and the wide-bodied families of subsonic transports will actually constitute the
182 1ol 10° 10 1_ 10 - 2 NEBOJSA NAKICENOVIC 1o2 ·/ :, - Jets Pistons (hp.) Max Thrust (kg)~ ( ~ = 3800) ( K = 29,000) - ~- 1936 / ~k. . ~ -~9 = · ~ . . 1966 ·/ I/ 30 yr-/ i hit= 30yr . , , , , , , , 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Year . - 0-99 0.90 - y 0.70 ~ - 0.50 0 0.30 0.10 - 0.01 FIGURE 8-4 Performance of aircraft engines. Source of data: Angelucci and Ma~icardi (1977), Grey (19691. asymptotic technology achievement. This alternative is unlikely, however, because air transport may become the dominant mode of passenger (long- distance) travel in the next century. Figure 8-4 shows the improvement in the performance of civil aircraft engines since the beginning of aviation. The first piston engine visible on the plot is the French Antoinette engine, rated at 50 horsepower (hp.) in 1906, and the last is the American Wright Turbo Compound, rated at 3,400 hp in 1950. These engines represent an improvement in power of almost two orders of magnitude over 44 years and about 90 percent of the estimated saturation level for piston engines (about 3,800 hp.). A parallel development in the maximal thrust of jet engines follows with a lag of about 30 years, starting in 1944 with the German Junkers Juno 004 (rated at 900 kg) and ending with the American Pratt and Whitney JT9D in the early 1980s with 90 percent of the estimated thrust saturation level at about 29,000 kg. Both pulses in the improvement of aircraft engines are characterized by a time constant (fit) equal to about 30 years. The midpoints (inflection points) of the two pulses, which occurred in 1936 and 1967, respectively, coincided with the introduction of the DC-3 and
U.S. TRANSPORTINFRASTRUCTURES 183 the B-747. In fact, the Pratt and Whitney Twin Wasp, introduced in 1930, became the power plant for the DC-3. This engine also served as the basis for subsequent and more powerful derivatives such as the Wasp Major introduced in 1945 toward the end of the aircraft piston engine era. Thus, certain parallels are evident in the dynamics of passenger aircraft development beyond the obvious similarity in the time constant (/\t = 30 years). Those engines introduced slightly before the inflection point, such as the Twin Wasp, are "stretched" by doubling the cylinder rows to increase the power. In the Wright Turbo Compound, representing the last refinement in aircraft piston engines, turbocharging was used to derive shaft power. Otherwise, the engine was a direct derivative of the Wright Cyclone series introduced in the early 1930s with Cyclone 9 (which orig- inally powered the DC-24. The time constant for the development of passenger aircraft is therefore about 30 years. Thirty years after the standard industry design emerged during the 1930s, the B-747, the first wide-body jet to enter service, became one of the most significant improvements in commercial transport, and its productivity represents half of the estimated industry saturation level that may be approached toward the end of this century. Thus, within a period of 60 years the life cycle will be completed: from standardization and subsequent rapid growth characterized by numerous improvements through the inflection point, when the emphasis changes to competition characterized by cost reductions and rationalization. These characteristics of the industry, including steady improvement in performance, are well illustrated by the development of the B-747 family. The emergence of a new aircraft engine at the beginning of a new phase of growth is very likely toward the end of the century after the projected saturation has been reached. Furthermore, the characteristics of the long- range aircraft in this hypothetical growth pulse are implicit in this analysis. The saturation in the thrust of turbojet and turbofan engines indicates that a new generation of engines will emerge over the next few decades, a generation having much higher thrust ratings and growth potential. The only realistic candidates are the ramjet or scram engines with efficient off-design flight engine characteristics, or perhaps the HOTOL-type air- breathing rocket engines. Thus, a new pulse in the improvements of aircraft engines will most likely be associated with some variant of the variable- cycle air-breathing engine with a high Mach number and perhaps even ballistic flight potential. This trend would single out methane as the fuel of choice between Mach 3.5 and Mach 6, with a small overlap of hydrogen starting at Mach 5. Thus, cryogenic methane-powered cruise supersonic aircraft may become the mode of transport with the highest productivity after the year 2000.
184 NEBOJSA NAKICENOVIC The Automobile At the beginning of this century, few proponents of the automobile envisaged that its use would spread as rapidly as it did throughout the world. As a commercial and recreational vehicle the motor car offered many advantages over other modes of transportation? especially animal- drawn vehicles. Perhaps the most important advantage was the possibility of increasing the radius of business and leisure transport. At first the railroads were not challenged by the automobile. Rather, railroads helped the spread of the automobile by offering efficient long- distance transport that combined well with the use of motor vehicles for local urban and rural road transport. Within a few decades, however, the automobile had become an important form of transport for both local and long-distance passenger travel in the United States. Since the 1930s the total mileage traveled by motor vehicles in general has been divided almost equally between rural and urban travel. The automobile had a relatively late start in the United States in relation to European countries (for example, France, Germany, and the United Kingdom). According to the records, four motor vehicles were in use in the United States in 1894. This was followed, however, with an impressive expansion of the automobile fleet: 16 vehicles in 1896; 90 in 1897; 8,000 in 1900; almost 500,000 10 years later; and more than 1 million after another 2 years. Thus, the United States quickly surpassed the European countries both in production and in the number of vehicles in use. Figure 8-5 shows the rapid increase in the number of cars used in the United States. The automobile fleet is characterized by two distinct secular trends, with an inflection in the 1930s followed by less rapid growth rates. Because the two secular trends of the curve appear to be roughly linear on the logarithmic scale in Figure 8-5, the automobile fleet evolved through two exponential pulses. Thus, in this example the growth of the automobile fleet did not follow a simple, single S-shaped growth pulse. The working hypothesis in this case is that the two trends indicate two different phases of the dissemination of motor vehicles in the United States. The first characterizes the substitution of motor vehicles for horse-drawn road vehicles, and the second the actual growth of road transport after animal-drawn vehicles essentially disappeared from American roads (see Nakicenovic, 19861. Only after the completion of this substitution process did the automobile emerge as an important competitor of the railroads for the long-distance movement of people and goods and perhaps as a com- petitor of urban transportation modes such as the tram, subway, or local train. Thus, the first expansion phase was more rapid because it represents a "market takeover" or expansion in a special niche; the second represents
U.S. TRANSPORTINFRASTRUCTURES 105 _% cn ° 4 _' in .~ o 3 a) 10 Q 1o2 1o1 1 850 ~, /' Cars - Horses _~: - - 185 - / 1 900 1950 2000 Year FIGURE 8-5 Number of road horses and mules and automobiles in the United States. the actual growth of the road vehicle fleets and their associated infra- structures. The lack of historical records of the exact number of horse-drawn vehicles in the United States soon after the introduction of the automobile in 1895 makes it difficult to describe accurately the assumed substitution of the motor car for the horse during the first, more rapid expansion phase of the motor vehicle fleets. The number of draft animals (road horses and mules) and automobiles given in Figure 8-5 therefore are a rough ap- proximation of this substitution process. Horse and saddle were sometimes used as a "road vehicle," but often more than one horse was used to pull buggies and wagons. City omnibuses used about 15 horses in a single day, and a stagecoach probably used even more because the horses were replaced at each station. Figure 8-5 therefore may exaggerate the number of horse-drawn vehicles if the number of draft animals is used as a proxy for the number of vehicles actually in use. On the other hand, farm work animals are not included in Figure 8-5, although certainly they were also used for transport, especially in rural areas. Although estimates of nonfarm horses and mules are not very accurate and are unevenly spaced in time, Figure 8-6 indicates that the automobile replaced horse- and mule-drawn road vehicles during a relatively short period and that the substitution process proceeded along a logistic path.3
186 NEBOJSA NAKICENOVIC 1o2 r / o.ss 101 L \ idogc | Horses\ //e rs o ~ 10° ~\~ 0 50 / I, t\t~12yr1 030 10-] / \\ - 0.10 1900 1910 1920 1930 Year FIGURE 8-6 Substitution of cars for horses, United States. Motor vehicles achieved a 1 percent share of total road vehicles shortly after 1900 and a 50 percent share in 1916. A complete takeover occurred in 1930 when there were 0.3 million road horses and mules and 23 million cars, an increase from only 2 million cars 10 years earlier. Thus, the inflection point in the growth of the automobile fleet from Figure 8-5 actually coincides with the end of the replacement of animal-drawn road vehicles by motor cars and explains the apparent "saturation" in the growth of motor vehicles observed by many analysts during the late 1920s and early 1930s. This perceived saturation marks the beginning of a new phase in the motorization of America, with growth rates comparable to those of the expansion of horse-drawn vehicles before the automobile age. Seen from this perspective, the growth in the number of all road vehicles is a continuous process from 1870 to the present. Figure 8-7 shows the secular increase of all road vehicles, horse-drawn and motor-powered, as a logistic growth process with an apparent saturation level of about 350 million vehicles after the year 2030 and a At equal to about 100 years. Because the growth of road transport in general and the substitution of automobiles for horse-drawn carriages and wagons overlap in time, to- gether they produce two growth trends in the automobile fleet with an inflection point in the 1930s marking the structural change in the com- position of the road vehicle fleets. The growth of all road vehicles results in one single logistic trend, however. Thus, like aircraft, road vehicles constitute a kind of distributed infrastructure that expands in time as one connected system.
U.S. TRANSPORTINFRASTRUCTURES 187 Both air and road transport systems require, in fact, elaborate and sophisticated infrastructure. Perhaps the most obvious examples are air- ports and supporting ground systems for aircraft, and roads and service infrastructures for road vehicles. Airports and railroads were obviously constructed to provide the infrastructure for aircraft and trains, but it is not so clear whether the automobile caused the need for good roads or the construction of good roads caused the development of the automobile industry (this argument was debated in the 1930s; see, for example, Ep- stein, 19281. Either way, the expansion of road vehicle fleets is paralleled by growth in the mileage of surfaced roads, although the total mileage of all roads increased very slowly from 3.16 million miles (ml) in 1921 to 3.85 million mi in 1981. The total length of all roads, which has remained almost unchanged over the past 60 years, is one of many indicators that do not portray logistic growth trends. It is possible, however, that the mileage of all roads increased during earlier times (during the colonial period, for example) and was saturated 100 years ago or even earlier. Figure 8-8 shows the total road mileage in the United States and the mileage of urban streets (formerly defined as municipal streets), rural roads, and all urban and rural surfaced roads (bituminous penetration, asphalt, concrete, wood, stone, and other). This figure shows that the growth of surfaced roads paralleled that of all road vehicle fleets while the total mileage of all roads remained almost unchanged. The expansion of surfaced roads preceded the expansion of motor vehicles, however. In 1o2 104 10° 10-' . _ 10-2 1850 1 900 At =1 OOyr 1 950 Year FIGURE 8-7 All road vehicles in use in the United States. o.ss o.so y x 11 0.70 ~ o . 0.30 _ 0.10 0.01 2000
188 104 ce ._ 3 O 10 to to ; 1o2 1900 1910 1920 1930 1940 1950 1960 Year FIGURE 8-8 Mileage of all roads in the United States. NEBOJSA NAKICENOVIC Total Rural Surfaced Urban 1970 1980 1990 2000 1905, 8 percent of all roads were surfaced, but fewer than 80,000 motor vehicles were in use compared with about 3.3 million road horses and mules (in addition to the 22 million draft animals used for farming). Thus, the early surfaced roads were developed for horses and not automobiles, but motor vehicles quickly expanded into the growing infrastructure. Figure 8-9 shows the substitution of surfaced roads for unsurfaced roads, a process that lasted about 73 years (At). The first rapid-growth phase of motor vehicle fleets occurred therefore while less than half of American roads were suitable for their use. The substitution process shown in Figure 8-9 does not reflect the vigorous road construction effort after the depres- sion years in the United States. Rather, it indicates a lack of such effort during the 1910s and 1920s because the actual expansion of surfaced road mileage was somewhat below the long-term trend during these two dec- ades. A similar underexpansion occurred during the early 1970s, but the deviation from the trend appears to have been compensated for during the last few years. This behavior is reassuring because it confirms the obser- vation that adequate infrastructure is a prerequisite for the expansion of transport systems. Figure 8-10 shows the increase in surfaced road mileage as a logistic growth process with a saturation level of about 3.5 million mi (almost reached with 3.4 million mi today). This process parallels the substitution process of surfaced roads for unsurfaced roads shown in Figure 8-9. The dashed logistic function represents the growth in the number of all road vehicles from Figure 8-7. Thus, surfaced roads, as an important infra- structure for road transport, appear to be in the saturation phase today; the automobile fleet, on the other hand, is still growing and should reach its saturation phase in about 50 years.
U.S. TRANSPORTINFRASTRUCTURES 1o2 1o1 10° 10 ~ Unsurfaced surfaced 189 0.99 c o 0.70 0.50 ~ 0.10 L I I I At = 73 yr ~j 1 o-2 0.01 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Year F~GuRE 8-9 Substitution of surfaced roads for unsurfaced roads in the United States. 1o2 1o1 10° 10-1 0.99 1 f - - - - - . ~ /&t=50 yr 0.90 0.70 =, o . _ 0.10 10-2 , ~1 1 1 1 1 1 1 1 0.01 1900 1910 1920 1930 1940 1950 1960 1 970 1980 1990 2000 Year F~GuRE 8-10 Mileage of surfaced roads in the United States. The dashed line shows the growth in the number of all road vehicles, from Figure 8-7.
190 NEBOJSA NAKICENOVIC Railroads Although air transport and the automobile are still expanding modes of passenger travel, railroads are now in the postsaturation development phase, and their position in intercity passenger traffic in the United States is being eroded. A symbol of this decay is the discontinuation of trans- continental railway service in the United States. The first railroads of significant length were introduced more than 150 years ago; widespread air travel, on the other hand, is only about 50 years old, and the first automobile dates from about 100 years ago. Although railroads were developed largely in Europe, they, like the automobile, had their most dramatic growth in the United States. By 1840, more than 10 years after the first commercial lines went into service, the United States had almost 4,500 km of railroad track compared with Europe's 3,000 km (Taylor, 19621. The Baltimore and Ohio Railroad, probably the first commercial railroad in the United States, was chartered in 1829; 2 years later, it had 13 mi of track in operation. Many projects soon followed. In 1833 the Charleston and Hamburg Railroad along the Savannah River route, with 126 mi of track, was the longest railroad in the world under single management. By 1835 three Boston railroads were in operation one to Lowell, one to Worcester, and the third to Providence. To some extent the early railway lines were feeder lines for canal and waterway transport systems in much the same way that the early com- mercial motor vehicles were feeders for railways. Tramways (early, ded- icated tracks with animal-drawn or steam trains) in the Pennsylvania coalfields augmented canal traffic, and some of the first railroads connecting to the Erie Canal originally served as its branch lines. The early railroads, in fact, were not allowed to compete with the Erie Canal, but they were largely independent transport agents and proved to be sturdy competitors of the older canals. For example, the Boston and Worcester Railway was a competitor of the Blackstone Canal, and when the Providence and Worcester Railroad was completed, it put this canal out of business. The Baltimore and Ohio Railroad took business away from the Chesapeake and Ohio Canal, and the Charleston and Hamburg Railroad was designed to, and did to some extent, divert traffic from the lower Savannah River. Beginning in the 1830s railroads expanded rapidly in the United States for almost 100 years. Figure 8-11 shows the increase in operated mileage of the first and other main tracks in the United States since 1835. The mileage increased as a single logistic pulse reaching saturation in 1929 with a l\t equal to 54 years. It declined logistically thereafter with a At equal to about 118 years. The actual length of operated main track
U.S. TRANSPORTINFRASTRUCTURES 1o2 1ol 10° 10-1 10-2 191 0.99 ,4: At=54yr/| At= 11Rvr 0.90 0.70 1l 0.50 O - c' 0.30 List 0.10 _ ;01 1850 1900 1950 2000 Year FIGURE 8-11 Growth pulse in main rail track operated in the United States. infrastructure increased from about 4,500 km (less than 3,000 mi) in 1840 to more than 480,000 km (about 300,000 mi) in 1929 about two orders of magnitude in 90 years. By comparison, the decline was a rather slow process: by the 1980s the length of main track actually in operation had decreased by about one-third to some 320,000 km (about 200,000 ml). Thus, the decline phase (about 50 years up to the present) appears to be slower than the growth phase, probably because older technologies and infrastructures can be put to new uses after they saturate. By doing so, they may avoid complete displacement by new competitors. For example, sailing ships, wood fires, and horseback riding have all become favorite leisure time and sporting activities even though they were replaced by new technologies long ago. In this way, railways may be put to new uses perhaps for local passenger and tourist traffic similar to ocean cruises despite their insignificance as a mode of intercity passenger travel. Some canals are already serving such a purpose even though they have not been a profitable means of passenger transportation since the heyday of railroads. Both canals and railroads still offer, however, efficient transportation for low-value goods (per unit weight). Many technological improvements were introduced in the United States during the first decades of the railroad expansion, including the shift in basic construction materials of rails from wood to larger shares of iron and later steel. Iron rails were a significant improvement because they made the use of heavier locomotives and loads possible, thereby increasing
192 1o2 10 1 0 10-1 10-2 NEBOJSA NAKICENOVIC nns ~ / ' ,<~-~030 0.01 1930 1940 1350 1960 1970 Year FIGURE 8-12 Substitution of diesel for steam locomotives in the United States. the efficiency of rail transport. At the same time the energy sources also changed. The draft animals used in the first tramways were replaced by steam locomotives fired by wood, which remained the principal fuel of railroads until about 1870 (Schurr and Netschert, 19601. Wood was then replaced by coal, and later steam locomotives in general were replaced by diesel locomotives. Figure 8-12 shows the substitution of diesel for steam locomotives. The first diesel locomotive was introduced in 1925 when the total number of locomotives peaked at about 69,000, a few years before the length of main track in operation reached its maximum and started to decline. A few electric locomotives were introduced earlier, but they never gained importance in the United States and remained less than 2 percent of the total locomotive fleet. The replacement of steam by diesel loco- motives was a swift process that lasted slightly longer than 20 years (the substitution of automobiles for horses lasted less than 30 years). In 1938 diesel locomotives represented a 1 percent share of all locomotives and by the 1960s more than a 99 percent share. Thus, although the substitution of diesel for steam locomotives was a fast technological change, the continuous increase in performance of the railroad transport system was characterized by longer secular trends. Since the first generation of designs at the beginning of the last century, the traction of locomotives has increased through improvements in energy conversion and a subsequent increase in horsepower, and through in
U.S. TRANSPORTINFRASTRUCTURES 193 creased weight (possible only because of improvements in tracks and materials). The absolute peak in the total installed horsepower of all locomotives was achieved in 1929 with more than 100 million hp for approximately 60,000 (mostly steam) locomotives. This peak coincided with the maximal length of main tracks also achieved in 1929. Other indicators of the railroad system in the United States show that the 1920s represented the culmination of railways. For example, the num- ber of passenger train cars in service peaked in 1924 at more than 57,000; the number of freight train cars in service peaked in 1925 at more than 2.4 million. The number of passengers carried (more than 1.2 billion) and passenger-miles (more than 47 billion) also peaked during the same decade (19201. All of these indicators declined subsequently by between 30 and 40 percent of the maximal values reached during the 1920s. A certain parallel in the development of automobiles and railroads can be detected. In a superficial way, both systems imitated the design of the transport modes they were competing with and eventually replaced. The first motor vehicles were literally horseless carriages; they were almost identical except for the difference in the prime mover. In the same way, early railroad passenger cars were similar to stagecoaches in both design and appearance. Nevertheless, both new transportation technologies rep- resented radical improvements and changes with respect to their prede cessors. More fundamentally, the expansion of main track was only slightly faster than the expansion of surfaced roads in the United States. Both growth processes are characterized by a At equal to about 50 years, but the inflection points of the two growth pulses are separated by 56 years the main tracks reached half the saturation level in 1890 whereas surfaced roads reached that point in 1948. Thus, the growth of these two infra- structures is characterized by a time constant of about 50 years, but the decline of railroad infrastructure appears to have been a much slower process. Another fundamental similarity in the evolution of the two transportation systems is that while the railroads were saturating, the automobile industry consolidated and introduced important changes that generated subsequent growth. Railways reached their saturation point during the 1920s, the same decade in which the substitution of automobiles for horses was completed. Other fundamental innovations, such as mass production and closed car bodies, were also introduced in the rapidly expanding auto- motive industry during this period. It is useful therefore to distinguish two different aspects of the evolution of the two transport infrastructures. Although the growth of main tracks and surfaced roads lasted about 50 years, the technological changes and
194 NEBOJSA NAKICENOVIC substitution of new equipment for old equipment is a much faster process of about 10 to 20 years at the level of locomotive or automotive fleets. These processes continue even after the saturation phase is reached, as the substitution of diesel for steam locomotives indicated. Thus, tech- nological changes are important in both growing and declining industries. In growing industries, new technologies are introduced through new ad- ditions and replacement, and in the declining industries, new technologies are introduced exclusively through partial replacement of old technologies. Canals The similarity in the evolution of rail and road transport systems is perhaps indicative of an invariance in the development pattern of transport systems and their underlying infrastructures. A serious problem arises, however, when comparing these two transportation modes with those that do not depend exclusively on the rigid, man-made links between them. Airways and waterways, for example, rely less on man-made links between nodes because they use the natural environment (air, rivers, and coastal waters). Nevertheless, they require an elaborate infrastructure such as airports, harbors, and canals. Thus, it is difficult to compare the total length of the implicit air and waterway routes and the total length of main railroad tracks or surfaced roads. For both air and waterway routes, how- ever, there are abstract measurements that would, in principle, correspond to the length of the grid: the network of certified route carriers or federal airways in air transport and the total length of continental waterways and canals. Unfortunately, the annual increase in the actual operated mileage length of all air carrier routes and the mileage of used continental water- ways and canals is not very accurately documented in historical records. Thus, only sparse accounts and probably inaccurate estimates must be used in this analysis. The first decades of the nineteenth century in the United States marked the beginning of large roads, canals, tramways, and later railway con- struction projects. During the so-called turnpike era (1800-1830), several of the roads designed for travel between larger towns or to the West across the mountains were completed. Turnpikes, however, were already being abandoned during the 1 820s because of a lack of financial success (Taylor, 1962~. During the same period, canal construction was viewed as a more effective means of internal transportation to complement coastal merchant transport while the construction of turnpikes declined. The "canal era" lasted until the railways became the main mode of long-distance transport a few decades later. From this point of view, the 1830s were turbulent
U.S. TRANSPORT INFRASTRUCTURES 195 years: many turnpikes were abandoned, canal construction was reaching its peak, and some early railway projects were already completed. Thus, since the 1 830s at least three different transport modes have to some extent provided complementary services, but they were also competing directly in many market segments. In contrast to turnpikes and railways, canals connected the various natural links of the inland waterway system and did not represent a transport infrastructure in themselves. They can be com- pared to bridges and tunnels that connect road or rail transport networks. Canals made the inland waterways into an integrated transport system by connecting the lakes in the north with the rivers in the southeast and midwest. The great waterway across the United States never materialized, however. The first canals were built during the 1780s. When completed in 1793, the Richmond Falls Canal was the first canal to exceed 7 mi in length. From then on the pace of canal construction accelerated: by 1800 the total length of canals exceeded 50 mi, and by 1825 more than 1,000 mi were in operation. Rapid construction continued for another 20 years or so, reaching 3,600 mi in 1850 and leveling off at about4,000 mi 20 years later. Thereafter the canal business was so seriously eroded by competition from the railroads that many important canals were decommissioned. Subsequently, the length of all canals in use began to decline. In the United States the rise and fall of operated canals paralleled the growth and decline of the main railway tracks but was displaced in time by about 50 years. In both cases the growth in mileage of the operated infrastructure increased rapidly, but after saturation the decline was far less rapid. Figure 8-13 shows the increase in the length of canals in the United States as a logistic growth pulse with a saturation level of about 4,000 mi after the 1860s. The inflection point, or the maximum rate of growth, was reached in 1832, and the At is equal to about 30 years. Thus, canals have a time constant comparable to that of airways but shorter than that of railways and roads. A possible explanation is that both canals and airways represent only one important component of the respective actual transport infrastructure, which for the former includes all waterways in addition to some man-made canals, and for the latter a large infrastructure of supporting systems such as airports and traffic control. On the other hand, railroads and surfaced roads in themselves constitute a large con- nected infrastructure that is essentially built for a specific purpose. Con- sequently, it takes longer to construct large infrastructures such as roads and tracks than the selected links (canals or, more abstractly, air corridors) and nodes (airports and harbors) needed to expand a new transport system such as water- or airways into an already available natural environment.
96 1o2 1o1 1no . _ 10-1 ~0.10 1 0-2 1 ~/1 1 1 1 1 1 1 0.01 1780 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 ,~ At = 30 yr NEBOJSA NAKICENOVIC 0.99 0.90 Y x 11 0.70 0.50 is, it Year FIGURE 8-13 Length of canals in the United States. Transport Infrastructure The difference in the time constants of air and inland water transport systems, on the one hand, and rail and road transport, on the other, indicates that at least at this level of comparison transport systems having more extensive infrastructures may take longer to expand and possibly longer to complete the whole life cycle from growth to saturation and later senescence. To assess whether the time constants are really different, Figure 8-14 shows the substitution of the four transport systems during the last 180 years in the United States in terms of the operated mileage of the competing infrastructures: canals, main railway tracks, surfaced roads, and federal airway route miles. From this perspective the substi- tution of the four systems over time appears as a regular process.4 Several invariant features are inherent to this substitution process. At any given time, at least three important transport infrastructures are com- peting for shares of the total route length of all transport modes. The longest transport infrastructure is always longer than at least half the total length. Consequently, the second and third longest transport infrastructures are equal to less than half of the total length. This symmetry and the dominating role of the longest infrastructure have been complemented by another regular feature during the last 180 years. The time constant (~\~) increases from less than 50 years for the growth of railway track shares to almost 90 years for surfaced roads and more than 130 years for airway
U.S. TRANSPORTINFRASTRUCTURES log 1o1 10° 10-1 10-2 1800 1850 1900 Canal \ ~Railways\ i Hi\ ORoads ~ 9: 1950 2000 2050 Year FIGURE 8-14 Substitution of transport infrastructures in the United States. 197 0.99 0.90 0.70 0.50 ,' Cal 0.30 LO 0.10 0.01 routes as shares of total length. Thus, the time constant increased by about 40 years for successive infrastructures. The distance between the saturation periods (time of maximal market shares) of railway tracks and surfaced roads is about 100 years. This result may appear to contradict the earlier observation that the total length of railway tracks and surfaced roads took longer to construct than water and airway routes. In fact, the timetable associated with the sub- stitution dynamics of infrastructure lengths is surprisingly consistent in relation to the duration of growth pulses of the four transport modes during the past 180 years. The apparent inconsistency results from the different ways of measuring the growth rates and life cycles of the respective infrastructures. In the case of market shares the increase in a particular transport infrastructure is analyzed in terms of the length of all networks. Thus, even the rapid growth rate of airway route mileage is translated into a comparatively long time constant because at the same time the total length of all transport networks is also growing rapidly. As a result of these rapid growth rates, the share of surfaced roads has been declining since the 1970s whereas the total length of surfaced roads is still growing toward the saturation level (see Figure 8-10~. Thus, the total length of a transport infrastructure (in this case, canals, railroads, and surfaced roads) can still be growing even decades away from ultimate saturation and final senescence while the shares of its length
198 NEBOJSA NAKICENOVIC 1o2 _ : 1o1 10° 1o-l Railwavs ~ ~ Bus ~ 0.99 _ Cars ~,,DD I' - 0.90 0.70 c 0.50 ·°~ 0.30 i= 0.10 1 ''it '- ~1 ~1 1 1 1 1 1 -2 0.01 1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 Year FIGURE 8-15 Intercity passenger traffic substitution in the United States. in that of all transport infrastructures are declining. The saturation and decline of market shares therefore precede saturation in absolute growth in an increasing market, meaning that the eventual saturation of any com- peting technology can be anticipated in the substitution dynamics in a growing market. Although the substitution of younger for older modes of transport is a regular process when measured in total mileage of the four transport infrastructures, it is nevertheless only a proxy for the real dynamics of transportation systems, which should be measured in some common per- formance unit. Because transport systems provide a whole range of ser- vices, such a common descriptor is difficult to define. Two obvious choices of a common unit are ton- or person-kilometers per year. These units do not, however, distinguish between freight and passenger transport or be- tween short and long distances. Thus, there is no obvious shortcut, and it appears necessary to analyze both passenger and freight separately for both short and long distances (for example, intra- and intercity travel). Fortunately, the available historical data make it possible to reconstruct the dynamics of these substitution processes for at least some countries. For example, Figure 8-15 shows the substitution of different transpor- tation modes in intercity (long-distance) passenger travel in the United States since 1950. By excluding urban and metropolitan transport (because explicit statistics are generally lacking), the competition for intercity pas- senger traffic is reduced to four significant transport modes: railways, buses, cars, and airways. The shares of each transport mode are calculated
U.S. TRANSPORTINFRASTRUCTURES 199 in passenger-miles traveled in a given year. According to this analysis the automobile is still the main choice for most Americans and will remain so into the next century in spite of the market share increases of air travel. The losers are railways and buses. The substitution dynamics indicate that during the next decade the share of airways in intercity travel will increase to almost 40 percent, the share of automobiles will decrease to a little more than 60 percent, and the shares of railways and buses will be virtually eliminated. Unfortunately, Figure 8-15 does not indicate the full drama of this replacement process because data are not available for the period before 1950. Nevertheless, the substitution process is consistent with the mileage substitution of the respective transportation infrastructures from Figure 8- 14. For example, the share of main railway tracks falls to less than 1 percent by the end of the century, and the share of railways in intercity travel phases out even earlier, during the 1970s. During the same decade the shares of both automobiles in intercity travel and surfaced road mileage in total length of the transport infrastructure are saturating. In both cases the shares of airways are increasing and are expected to reach a position of dominance (with control of more than half the "market") during the first decades of the next century. This result suggests that a new growth pulse in commercial aviation may be due in about two decades. Cruise supersonic and possibly air-breathing hypersonic transports might be the only technologies likely to provide the growth potential to be achieved in the next expansion phase of passenger travel. Obviously, the above description of these complex systems is incom- plete. Certainly, there are other illuminating ways of describing the dy- namics of these systems. The intriguing aspect of the logistic description of the development of transportation systems is that the systems appear to be interwoven with regular features and a pattern of substitution dy- namics over a period of about two centuries. To show that this is not a feature unique to the evolution of transportation systems, the next section of this chapter describes a similar regularity in the evolution of energy systems. Furthermore, future developments in transport infrastructures are related to likely changes in the energy system, especially with respect to energy transport and propulsion for prime movers. PRIMARY ENERGY Energy Consumption At the beginning of the nineteenth century fuelwood, agricultural wastes, and mechanical wind and water power supplied most of the inanimate energy in addition to animal and human muscle power. This poor energy
200 NEBOJSA NAKICENOVIC 104 103 1o2 - a) 101 10° 10 l _ 1 A, / C~ ~ tear (mechanical) / 10-2~ 00 1850 Year Total ~ ~Nat. gas ~ ~ Won - (electric) I NUC1°ar 1 950 FIGURE 8-16 Primary energy consumption in the United States. menu (by present standards), however, represented a sophisticated energy system compared to earlier practices. In the nineteenth century a consid- erable infrastructure of roads (turnpikes) and canals was in place for timber and later coal transport. Mining, manufacture, and irrigation were also usually associated with elaborate systems of dams and waterwheels. Thus, in the early industrial development phase, energy use depended on the transport system, and energy was one of the more important components of goods transported on canals, waterways, turnpikes, and roads. Fuelwood represented most of the primary energy inputs. Figure 8-16 shows the U.S. annual consumption of fuelwood, fossil energy, mechan- ical water power, and hydroelectric power since 1800. Data are plotted on a logarithmic scale and show the exponential growth phases in con- sumption by piecewise linear secular trends. In the United States, the consumption of fuelwood, once the most important source of energy, has declined since the beginning of the cen- tury, although it is still used widely, especially in the developing countries. With the expansion of railroads and the steel industry and the application of steam in general, the use of coal increased exponentially until the l910s, and it has oscillated ever since. Since their introduction in the 1870s, oil and natural gas have been consumed at even more rapid growth rates. In fact, oil and natural gas curves have the same shape and almost identical
U.S. TRANSPORTINFRASTRUCIURES 1o2 101 10° 10-1 _ 10-2 it, 1 1800 At< \ ,>/fNuclear 1850 1900 1950 2000 Year FIGURE 8-17 Primary energy substitution, United States. 201 0.99 0.90 ~ 0.70 O 0.50 ` LL 0.30 0.10 0.01 growth rates; they are just shifted in time by about 10-15 years. The increased use of oil and natural gas paralleled the growth of the petro- chemical and electrical industries and the expanded use of internal com- bustion and electric prime movers. Because nuclear energy is still in its early phase of development, the steep growth of the last decade may not indicate its future role. Indeed, during the past few years the growth of nuclear energy in the United States and worldwide has declined to more moderate rates. Energy Substitution Although for almost two centuries energy consumption did not draw equally from all sources and the use of all energy sources did not increase equally, primary energy consumption (including fuelwood) increased ex- ponentially at an average growth rate of about 3 percent per year. The decline of older energy sources was more than compensated for by the rapid growth of the new sources. Figure 8-17 shows primary energy substitution in the United States.5 Mechanical water power (mostly hydro and some windmills) and hy- droelectric power are not observable in the figure because of their small contribution to the total energy supply; they barely exceeded the 1 percent level during short periods and were otherwise under that critical level. Thus, before the 1820s fuelwood fulfilled virtually all energy needs in the United States. Coal entered the competition in 1817 at the 1 percent level,
202 NEBOJSA NAKICENOVIC and up to the 1880s it was essentially a two-technology market whatever gains coal made were translated into losses for fuelwood. Wood remained, nevertheless, an important construction material and source of heat and power well into the last decades of the nineteenth century, enough so that the steam age began in an economy based on wood. The first steamboats and locomotives were fired with wood, which remained the principal fuel used by railroads until about 1870 (Schurr and Netschert, 19601. The iron industry was another large wood consumer. Around 1850 more than half of all the iron produced was still smelted with charcoal. The total amount consumed by manufacturing and trans- portation was small, however, when compared with the huge quantities used by households. By 1880, the industrial use of wood had declined, so that domestic use accounted for more than 96 percent of the fuelwood consumed (Schurr and Netschert, 19609. At the same time, coal already supplied almost half of all energy needs, most of it used by emerging industries. In 1880 coal supplied almost 90 percent of the fuel used for smelting iron. The iron was used in turn for construction projects, including larger railroad infrastructures, which by that time used coal as the fuel of choice. Thus, in this respect the end of the last century marks the beginning of industrial development in the United States. Crude oil and natural gas were first used in the United States at the beginning of the nineteenth century, and both held a 1 percent market share during the 1880s. From then on the use of crude oil expanded, and by 1950 the consumption of crude oil surpassed that of coal. Even as late as the 1920s, however, the consumption of crude oil was not much larger than that of fuelwood. The use of natural gas surpassed the use of coal nine years later. In comparing this period with earlier periods, it is re- markable that the structure of energy consumption changed more during the period of oil dominance than ever before. The 1950s, when crude oil became the dominant source of energy, represent the beginning of more intense competition among various energy sources, both in the United States and throughout the world. Over the 150-year period (1800-1950), the energy source that dominated the energy supply also contributed more than half of all primary energy consumption; from 1800 to 1880 this source was fuelwood, and from 1880 to 1950, coal. This is similar to the dominance at any given time of one transport infrastructure over all others with more than half of all mileage. This was observed in the substitution of canals, railway tracks, surfaced roads, and airways (see Figure 8-14~. During the 1970s crude oil was close to achiev- ing a 50 percent share, but before actually surpassing this mark it began to decline. Thus, during the last three decades, three important sources
U.S. TRANSPORT INFRASTRUCTURES 203 of energy shared the market without a single source having a pronounced dominance. This is contrary to the pattern observed during earlier periods and the substitution of transport infrastructures. Figure 8-17 shows that natural gas will dominate the energy picture after the 1980s although crude oil will continue to maintain about a 30 percent market share at the end of the century. The future potential com- petitors of natural gas, such as nuclear or solar energy, have not yet captured enough market shares to allow definitive estimation of their future penetration rates. The starting point for market penetration of nuclear energy was the 1960s, when nuclear power acquired slightly less than a 1 percent share of primary energy. Allowing for further cancellations of already ordered power plants and the possible decommissioning of those in operation and under construction, nuclear energy could at most double its current market share to about 4 percent by the year 2000. This assumed penetration rate is used for the projection in Figure 8-17, which indicates that more than half of all the primary energy consumed during the first decades of the next century will be natural gas. This result illustrates that not only will the natural gas bubble be absorbed in a few years, but methane technologies will also develop in the future, creating new growth sectors. One of the important sectors for gas in the more distant future may, in fact, be aviation. This result is unexpected given the numerous energy debates of the last 10-15 years, but it is perhaps reassuring that we may not have to rely on nuclear or alternative energy sources for another 50 years or so after all. The future that emerges would require fewer radical changes, but the challenges of developing new technologies and improving the performance of already employed technologies would remain. Despite the current dif- ficulties in expanding the use of natural gas in a time of worldwide economic slowdown and low crude oil prices, this scenario paints a dif- ferent picture in the long run. So that readers can better understand how methane might emerge as the dominant energy source of the future, a brief analysis of the evolution of energy transport infrastructures follows. Crude Oil and Natural Gas Transport In contrast to crude oil, which is traded globally, and natural gas, which is transported over continental distances, fuelwood was primarily con- sumed locally, close to the source of timber. Some fuelwood was trans- ported over longer distances, mostly by river flotation, and distributed by waterways or roads. Coal, on the other hand, is a more concentrated form of energy than fuelwood (coal has a higher heat content per unit weight), and coal mines are a more concentrated source than forests. Coal was
204 NEBOJSA NAKICENOVIC 1o2 1 0 I 10° 10 1o-2 0.99 ID ,D: ~~ Z ~ ~ /\t=59.2yr 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 Year 0.90 i_ - x 0.70 ~ 0.50 .o 0.30 LL 0.10 0.01 FIGURE 8-18 Pipeline length for crude oil and petroleum products in the United States. generally transported over longer distances than fuelwood, usually (na- tionwide) by barges, trains, or "trucks" (horse wagons). In the extreme case modest amounts were transported overseas. Thus, the shift from a wood to a coal economy was accompanied by an expansion of energy transport over longer distances and an increasing number of transport modes. The widespread use of crude oil led to use of yet another transport mode pipelines. Indeed, pipelines are becoming an important freight transport mode, with market shares in total ton-kilometers per year com- parable to those of train and truck transport. They are also comparable to railways in total length of the infrastructure or grid: the 200,000 mi of main railroad track in the United States are slightly shorter than the 230,000 mi of crude oil pipelines. Thus, although the total length of the rail and oil pipeline grids is equivalent, the two infrastructures differ in that since the 1920s the railroad system has been declining while oil pipelines have been expanding. Figure 8-18 shows the rapid increase in pipeline length for crude oil and petroleum products in the United States. Expansion of the oil pipeline grid parallels the increase in crude oil shares of total primary energy consumption. Oil held a 1 percent share during the 1880s when the rapid increase in oil pipeline mileage began and followed exponential trends until the 1930s (the inflection point oc- curred in 19371. As if by coincidence, coal, oil's largest competitor, gained a maximal share of primary energy during the same decade. Thus, by
U.S. TRANSPORTINFRASTRUCTURES 205 1937 about half of the current length of the oil pipeline network was already in place, and the growth rates declined slowly. During the 1980s the length of the pipeline network should reach the asymptotic level at about the same time that the crude oil shares of total primary energy saturate. The time constant (/\t) for the expansion of oil pipelines, 59 years, is close to that of the expansion of rail tracks and surfaced roads (about 54 and 59 years, respectively). In the analysis of the expansion of oil pipe- lines, however, numerical instability was encountered in the values of the estimated parameters with respect to different estimation algorithms used in the analysis. In particular, the result reported in Figure 8-18 is based on an estimated saturation level, K, of 238,800 mi with a At equal to 59.2 years; yet an alternative estimation algorithm (used to test the stability of estimated parameters with respect to changes in the assumptions about the weighing of the observations) gave different estimates 246,500 mi and 78.7 years, respectively. In all other examples the variation in the param- eter values was within the estimated uncertainty ranges, as shown in the appendix. Only in the case of oil pipelines was the value for At outside this range. Although crude oil is still the most important energy source, in primary energy consumption it is slowly being replaced by natural gas. In fact, the share of natural gas associated with oil is decreasing in total natural gas production. Thus, greater shares of natural gas transport and end use are based on gas, not oil, technologies (Grubler and Nakicenovic, 19871. This substitution process is also reflected in the increase in natural gas transport and distribution pipelines when compared to the increase in oil pipelines (Figure 8-181. According to Schurr and Netschert (1960), the earliest recorded com- mercial use of natural gas in America was in 1821 (coal then supplied just 1 percent of primary energy and fuelwood and draft animals the rest) when it was used as lighting fuel in Fredonia, New York. Natural gas continued to be used sporadically throughout the nineteenth century. The first pipeline was constructed from Murrysville to Pittsburgh, Pennsyl- vania, in 1883 after the discovery of a large well in 1878. Despite such pioneering projects by the emerging oil and gas industry, methane was considered a waste product. By 1878 both crude oil and natural gas held more than a 1 percent share of primary energy con- sumption, but at that time most of the natural gas was consumed in the vicinity of the oil fields. The natural gas pipeline network began to expand rapidly during the 1890s, or about 20 years after the oil pipelines began to expand. Figure 8-19 shows that this 20-year shift in time persists through most of the
206 1o2 101 10° 10-1 D' At = 60 mi NEBOJSA NAKICENOVIC _ 0.99 / 0.90 _ x 11 _ 0.70 _ 0.50 .o _ 0~30 ILK 0.10 -2 1 ~ 1 1 1 1 1 1 ~1 1 0.01 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Year FIGURE 8-19 Natural gas pipeline length in the United States. growth cycle of the natural gas transport system and distribution infra- structure. The inflection point occurred in 1965, or almost 30 years after the inflection point in the growth of oil pipelines. Because the time constant for natural gas pipelines is about 60 years, and therefore longer but still comparable to that of oil pipelines (59 years), saturation should also occur more than 20 years later, during the 2020s. Again, this is symmetrical to the relationship between the growth phases of oil pipelines and oil's pen- etration of primary energy. The growth pulse started when oil achieved a 1 percent share of primary energy, inflection occurred when oil became the second largest energy source (by passing fuelwood), and saturation of pipeline length was synchronous with the saturation of market shares. Exactly the same pattern can be observed during the growth pulse of natural gas pipelines by comparing Figures 8-17 and 8-19. Growth started toward the end of the last century when natural gas achieved a 1 percent share of primary energy, the inflection point occurred in 1965 when natural gas became the second largest energy source (by passing coal), and sat- uration of both natural gas market shares and length of pipeline should be achieved during the 2020s. A large difference between the growth pulses of oil and natural gas pipelines is the length of the respective transport and distribution networks. As shown in Figure 8-18 the saturation level for oil pipeline length is estimated at about 240,000 mi (about the current length of railroad tracks), while the asymptotic level for the length of natural gas pipelines is esti
U.S. TRANSPORTINFRASTRUCTURES 207 mated at more than 1.3 million mi (more than five times higher). Natural gas is now transported almost exclusively through the pipeline grid. Oil and petroleum products, however, are also shipped by tanker, train, and truck, and for some military uses, even by aircraft. Aside from small quantities of liquefied natural gas and liquid natural gas products, most natural gas reaches the consumer either in a gaseous form or as electricity. The pipeline network for natural gas transport and distribution is therefore much longer than that for crude oil and petroleum products. This, of course, poses the question of whether natural gas will continue to be transported almost exclusively by pipelines in the future, especially if its projected use expands as dramatically as illustrated in Figure 8-17. For liquid natural gas products particularly, it is likely that other transport modes will also be used, conceivably even aircraft. From a technical point of view there are no obstacles to using this transport mode for energy. The question is whether it would be economical and competitive to do so. This question cannot be resolved here, but in the past, similar solutions were found to meet the ever-increasing need to transport more energy over longer distances. Development of a faster means of transport over larger areas and the use of denser and cleaner energy forms were the technological measures taken then to improve the performance of these systems. One could therefore expect further improvements in the near future, which can be fulfilled by a stronger reliance on natural gas and aircraft until better solutions and completely new systems are devised during the next century. Over the next four to five decades, improved versions of the current energy and transport systems and infrastructures must be relied on because the results of this analysis indicate that the time constants involved in installing new infrastructures are about 50 years. CONCLUSIONS The examples analyzed here have shown that the growth and senescence of transport infrastructures can be described as a regular process with logistic secular trends. The time constants (/\t) of these growth processes are clustered around 50 years, with a range of between 30 and 59 years. Considering the poor quality of the historical data on the growth of trans- port infrastructures, it is remarkable that four network or grid transport systems-railway tracks, surfaced roads, and oil and natural gas pipe- lines-cluster even more densely between 54 and 59 years. The time constants for canals and performance improvements in aircraft transport are shorter, about 30 years. For canals and railway tracks, senescence lasts much longer than the growth process. The total length of canals, and
208 IVEBOJSA NAKICENOVIC of railways some 50 years later, declined with a much longer time constant, almost 150 years. Thus, canals are still in use despite a century-long decline. This perhaps explains the long time constants in the substitution of infrastructures. Although the growth in the length of all network or grid transportation infrastructures was a very fast process from about 4,000 mi for canals to about 4 million mi for railways, roads, and airways (a growth of three orders of magnitude in about 150 years) the substitution of transport infrastructures (see Figure 8-14) lasted longer than the actual growth pulses for the four individual infrastructures. The time constant (At) of the substitution process increased from 50 years for railway shares to almost 90 years for surfaced roads and more than 130 years for airways, compared with a time constant of 30 years for the growth pulse of canals and about 50 years for railways and roads. These figures illustrate the permanence of infrastructures and their sites. The decline of infrastructure is a slow process. New infrastructures replace the older ones more through rapid growth of the whole transport system than through physical destruc- tion or replacement of older infrastructures. Despite the remarkable regularity of these growth and substitution pro- cesses the variation in the parameter values of different estimation algo- rithms was outside the uncertainty range for the growth of oil pipelines. Thus, growth processes that follow the simplest possible pattern a single S-shaped path can be difficult to measure even when they are almost complete because the saturation levels are a priori unknown and have to be estimated from the data. Technological substitution processes are in- herently more complex because market shares of all important (competing) technologies have to be measured. Yet in part because of this higher degree of complexity, they are more stable front the statistical point of view. The most sensitive parameter of the logistic function, the asymptotic saturation level K, iS a priori known in this case. By definition, it can never exceed 100 percent of a given market. A more consistent analysis of the evolution of transport systems and their infrastructures would require comparison of the performance and services provided by the different modes over long periods. It was not possible, however, to reconstruct such an indicator for the overall transport system. Yet Figure 8-15, which shows intercity passenger travel during the last 37 years, is a good proxy for such a comparison. The substitution of the four major modes of long-distance travel in the United States is a regular process that singles out aircraft as the transport mode with the highest growth potential. The dynamics and general implications of this substitution process are that this result is consistent with the time constants
U.S. TRANSPORTINFRASTRUCTURES observed for the growth pulses and substitution of the four transport modes- canals, railways, roads, and airways. 209 The primary energy substitution dynamics (from Figure 8-17) indicate that technological substitution can be characterized by regular time con- stants, provided the historical data are accurate enough for the analysis. This is possible to some extent for primary energy consumption because different energy sources can be measured in common (physical, energy) units and because their use is relatively well documented. Furthermore, the technological changes in the energy system (i.e., the shift from older to newer energy sources) are also reflected in a parallel evolution of the energy transport infrastructures. For example, both fuelwood and coal were transported largely by canals and railroads in the same way as most other goods. Crude oil and natural gas, however, are transported by ded- icated pipeline infrastructures. The evolution of these energy transport infrastructures, then, parallels changes in the energy system, but at the same time their growth patterns are no different from those of other transport infrastructures. A general conclusion is that technological changes, such as the substi- tution of road vehicles or locomotives, last a few decades; changes in the transport system and evolution of infrastructures, on the other hand, are longer processes with time constants of between three and seven decades. Thus, the transport infrastructures themselves will not change drastically during the rest of the century, but concurrent technological changes in vehicles, aircraft, and the necessary equipment will improve both the performance and quality of the transport services provided by the current system. More specifically, road vehicles will remain the dominant form of long- distance transport during the next 20 years, but the importance of airways will increase in time. Both transport and energy systems must, however, meet more stringent economic and environmental requirements over longer distances and in a shorter time. In the United States, these systems appear to be still in the expansion phase as no signs of saturation were detected in the analysis. Rather, it was observed that older, still dominant tech- nologies are slowly being displaced by newer competitors, which in prin- ciple offer substantial growth potential. The next generation of aircraft and natural gas technologies represents evolutionary rather than revolutionary technologies that could meet the more stringent requirements through improvements in current designs and practices over the next two decades. New solutions must be developed during this period for later decades, however. In particular, the perfor- mance of transport aircraft is estimated to saturate (in the current growth
210 NEBOJSA NAKICENOVIC pulse) at about 1.2 million pass-km/in, which is attainable with current aircraft technology and some improvements. Thereafter, in a new, hy- pothetical growth pulse, aircraft would have to exceed this level, requiring either large subsonic liners, accommodating perhaps a few thousand pas- sengers, or supersonic cruise or air-breathing hypersonic transport with a more "modest" capacity of a few hundred passengers. The first alternative appears unlikely because it would require very powerful turbofan engines, and their rating appears to be saturating along with the aircraft performance (see Figure 8-41. Exceeding the saturation level would also require pro- cessing large numbers of passengers at terminals over short intervals, thereby creating new peak load management problems for air controllers, airports, and many service systems. Thus, a new engine (perhaps turbofan/ ramjet or ram/scram) could power a supersonic/hypersonic aircraft of the next century with a performance of a few thousand passenger-kilometers per hour. The natural gas economy will provide the necessary liquid methane or other endothermic hydrocarbon fuel, and later cryogenic hy- drogen. APPENDIX Estimation Methods for the Logistic Growth Function This analysis of the development of transport infrastructures and systems was based on the hypothesis that technological growth and substitution processes can be described by the logistic function. In the simplest case the logistic growth function describes the technological life cycle from the early development phase through the rapid growth and expansion phase to the eventual saturation phase. Similarly, this function is used in biology to describe growth such as that of organisms and populations in constrained environments. Here the logistic growth curve is used to analyze the expansion of air travel, aircraft productivity, and the length of surfaced roads, railway tracks, canals, and oil and gas pipelines. This was the simplest case of technology (or infrastructure) growth because in all these examples one single logistic curve described the whole technological life cycle. Unfor- tunately, although this is the simplest class of examples when compared with the more complex pattern of technological substitution, the statistical problems of estimating the parameters of the logistic function from the empirical data were sometimes substantial, especially in those cases in which the ultimate saturation level has not been reached. In brief, the problem is to estimate the three parameters of the logistic function
U.S. TRANSPORT INFRASTRUCTURES 211 () 1 +exp(-~t-~) (1) where t is the independent variable usually representing some unit of time, and a, is, and K are the unknown parameters. Alternatively, the logistic growth curve can be expressed as a linear function of time by moving the (usually) unknown parameter K to the left side of the equation and taking logarithms of both sides: in ~ (r) ~ ~ = cat + (2, This is a convenient form for showing the logistic growth process on semilogarithmic paper because the historical data indicate a linear secular trend (assuming that K can be estimated from the data or that it is a priori known). The three parameters are interpreted as follows in terms of the under- lying growth process: ~ denotes the rate of growth; ~ is the location parameter (it shifts the function in time, but it does not affect the function's shape); and ~ is the asymptote that bounds the function and therefore specifies the level at which the growth process saturates (as t tends to infinity, x(t) approaches K). Thus, all three parameters have clear physical interpretations, although the values of ~ and ~ are not necessarily clear intuitively. The logistic function is a symmetrical S-shaped growth function, with an inflection point, to, at which the growth rate reaches a maximum, x~to) -CX K/4. Symmetry implies that the value of the function is half the asymptote at the point of inflection, ditto) = K/2. Thus, the location parameter of the function can be defined as the point of inflection, to = -Q/c~, or, alternatively, as the time when 50 percent of the saturation level K is reached. The growth rate of the function can be defined alter- natively as the length of the time interval needed to grow from 10 to 90 percent of the saturation level a. The length of this interval is At = (ln 81~/~. This second set of parameters K, /\t, and to also specifies the logistic growth curve (in the same way that K, CX, and ~ do), but these alternative parameters have, in addition, clear intuitive interpreta- tions. A nonlinear least-squares regression method was used to estimate the three unknown parameters of the logistic function from the empirical observations. Alternative estimation algorithms were then used to test the sensitivity of the estimated parameter values to different assumptions about the errors and weighing of observations.6 The estimation methods used in the analysis are reported in Grubler et al. (19871. The values of the estimated parameters for the logistic growth processes, =
312 NEBOJSA IVAKICENOVIC as well as the correlation coefficient R2 and uncertainty ranges for the parameters, are given in Table 8-1. Estimation of the uncertainty ranges is based on a Monte Carlo simulation approach by Debecker and Modis (1986) for the three-parameter logistic function. A total of 33,693 different S-curves were generated and subsequently fitted by the logistic function providing values for K, At, and to, with known and varying distributions of statistical fluctuations. Debecker and Modis concluded that the value of the estimated asymptote K is the most sensitive (it varies the most), depending on the amount and accuracy of the data available. Their results indicated that as a rule of thumb the uncertainty of parameter K will be less than 20 percent within a 95 percent confidence level, provided that at least half of the data are available (at least up to the point of inflection) and that they are at least 10 percent accurate. A more comprehensive treatment of uncertainty ranges and estimation methods is given in Grubler et al. (19871. In all cases, except Figure 8-18, the values of the estimated parameters were within the specified uncertainty ranges. Even alternative algorithms used to estimate the parameters provided values within the specified ranges. The Technological Substitution Models and Parameter Estimates In general, the examples of technological substitution are inherently more complex than the determination of single logistic growth pulses. From a statistical point of view, however, the estimation of substitution processes is much simpler. By setting K = 1, a three-parameter logistic function x~t) can be normalized by setting fats = X(t)/K. For given values of K, it then reduces to a function with two unknown parameters. In the examples of technological substitution, this known asymptote specifies the size of the "market" in which old technologies are replaced by new ones. In the simplest case, there are only two technologies. The market shares are fate for the new technology and 1 - fats for the old technology (Fisher and Pry, 19711. Thus, only the values of to and At must be determined from the observations. Fisher and Pry used the two-parameter logistic function to describe a large number of technological substitution processes. They assumed that once substitution of the new for the old had progressed as far as a few percent, it would proceed to completion along a logistic substitution curve fats At ~ = at + ~ (3) Ordinary least squares were used to estimate parameters At and to in
213 o ._ C) . ~ Cal ._ o so an en a' An: Cal Cal U) a a ~0 1 y y ._ ~4 .= 00 ~ ~ 00 ~ - O of ~ AN ~ ~ Cal ~ cry ~ cut ~ as . . . . . . . . . . . . . O O O O O O O O O O O O O t~ ,~ _ ~ ~ ~ 00 0 - ~ ~ ~ ~ C~ ~ C~ ~ ~ 0 ~ ~ ~ ~o cr~ ~ c~ ~ a~ ~ ~ oo 0 oo o~ ~_______4~____ 00 00 0 ~ ~ ~ ~ ~ 00 \0 . . . . . . . . . . O O ~ O O ~ - ~ ~ O +1 +~ +1 +1 +~ tl t~ tl +I tl _~ ~ oo ~ . . o -_ _ Z +1 +1 O O oo ~ ~D ~ ~ O oo cr c~ r~ ~ . . . . . . . . . . . . . 0 0 0 ~ ~ ~ 00 ~ r~ oo a~ oo O ~N _ 1 ~ U~ U~ ~ o ~ . . . . . . ~ o ~ ~ o ~ a~ - ~\ ~ - t- tl tl +1 +1 +I tl oo ~ - ~ a~ . ~_ . ~_ . . _ o ~ oo ~ oo _ _ st ~ C: - t l z - Z t l ~ ~ o oo oo ~ ~ C~ oo ~ oo . . . . . . . . . . . oo o oo ~ C~ ~ C~ oo ~o oo oo ', oo _ - o ~ oo ~ ~ ~ ~ ~ o ~ ~ ~ _ - , oo ~'t - CN ;^ =: ~ ~ ~ ~ ~ ~.> o o o ~ ~ o o o ~o ~ o _ _ _ =( _, _ _ _ `_ ~ ~ ~ _ o - ~ ~ oo oo - ~ ~ ~ d" ~ - _ _ _ _ _ _ 1 1 1 1 1 1 ~ 1 1 1 1 1 1 oo oo oo X ao oo oo oo oo oo oo oo oo .= . ~ .= .° o o Ct Ct ~ ·_ - ;> - oo ._._ C~ s~ C~Ct C~U: ._ ~ ~ . _ C =4 · - 3 ~ ~: Co4 .C .° C~ e~ - O ~ ~ U - ;> C)
214 NEBOJSA lVAKICElVOVIC all cases in which one old technology is replaced by a new. Table 8-2 gives the estimated parameter values, the estimation period, and the cor- relation coefficients for the three examples given in this chapter. In dealing with more than two competing technologies, a generalized version of the Fisher-Pry model was used because logistic substitution cannot be preserved in all phases of the substitution process. Every given technology undergoes three distinct substitution phases: growth, satura- tion, and decline. The growth phase is similar to the Fisher-Pry substi- tution, but it usually ends before complete market takeover is reached. It is followed by the saturation phase, which is not logistic but which en- compasses the slowing of growth and the beginning of decline. After the saturation phase of a technology, its market share declines logistically (for example, see the path of railway and road substitution in Figure 8-14 and coal substitution in Figure 8-171. It is assumed that only one technology saturates the market at any given time, that declining technologies fade away steadily at logistic rates "uninfluenced" by competition from new technologies, and that new technologies enter the market and grow at logistic rates. The current saturating technology is then left with the residual market share and is forced to follow a nonlogistic path that curves from growth to decline and connects its period of logistic growth to its subsequent period of logistic decline. After the current saturating technology has reached a logistic rate of decline, the next oldest technology enters its saturation phase, and the process is repeated until all technologies but the most recent are in decline. For example, n competing technologies are ordered chronologically according to their appearance in the market, technology 1 being the oldest and technology n the youngest (i.e., i = 1, 2, . . ., n). Thus, all technologies with indices k, where k < j, will saturate before the tech- nology with index j, and technologies 1, where I > j, will saturate after technology j. The historical time series is denoted by aft), where the indices i = 1, 2, . . ., n represent the competing technologies and t the time points (year, month, etc.) of the historical period for which data are available. The fractional market shares of competing technologies, fi (t), are obtained by normalizing the sum of the absolute shares to one: x;(t) jets (4) By applying the linear transform of the logistic function to the fractional market shares,
215 l o ._ ~_ C~ ._ U: ._ C~ o <i o ._ o ._ Ct ._ U) P~ o 3 o . Ct ._ C~ oo ~ .= crx cr.~ ~ c ~ c~ ~ 0 cr. ~ ~ cr oo ~ C~ cr~ cr~ ~ ~ o~ .. .. . . . . . o oo oo o o o o o oo oo_ _ _ _ C~C~ _ __ __ _ . .. .. . _ _~ ~_ _ 111 U ~ ~ o V~ oo oo ~ oo oo ~ ~ cr . .. . . . . o oo o o o o _ _ ~ o- ~ ~ ~ ~ ~ _ ~ ~o oo oo oo oo oo oo ~ o~ ooo oo oo X ___~__ ~____ ~ o ~ ~ C ~o~ ~ ~ o . . . .. .. . . . . ,,,(<, _ ~ o C~ u~ oo ~ ~ ~ ~ a~ 1 - 1 - 1 ~ c~ ~ r ~0 0 0 0 0 0 ~ 0 0 u~ O u~ _ _oo oo u~ ~O ~ ~ oo 00 00 0 00 0 a ~ ~ oo ~ a ~ c~ · _ c ~c~ oo ____ __ ____ __~_ ____ 31 1111 O OO O C~ ~ ~ ~ C ~ ~ ce ~ C~ ~ ON a~ ~ ~oo oo oo C;- ~ ~N V~ ~00 00 00 00 ____ __ ____ __~_ ____ u: ~ ~ ~ _ ~ ~ ~ ~ ~ ~ ~ _ ~ ~ o~ ~ ~- ~ o' v ~ ~: <= ~ m ~ ~ ~ ~ ~ o z O O O O O -` _ _ _ _ _ C, ~ =\ _ _ _ _ 00 o0 00 00 00 00 ~ ~ . ~ O ~ ·= O ~ ~ C,) o~ ~ . ~ . 0 g CtS Ct .s G ~ ~ G Ct 3 Ct .= oc 11
216 NEBOJSA l!lAKICENOVIC (I) l [ f (') ] (s) a transformed time series with piecewise linear secular trends can be obtained. In fact, only three distinct possibilities exist: a decreasing or an increasing linear trend or a phase of linear increase that is connected by a nonlinear saturation phase to a phase of linear decline. The oldest tech- nology (i = 1) always displays a declining linear trend, and the youngest technology (i = n) an increasing linear trend (see Figure 8-17). These linear trends can be estimated, including the increasing linear trends of technologies that enter the saturation phase during the historical period. Ordinary least squares were used to estimate the linear trends for each competing technology. Table 8-2 gave the estimated parameter values for the three multiple substitution processes used here, as well as the esti- mation period (historical time interval for which the parameters were estimated) and the correlation coefficient. Parameter values were not given for cars in Figure 8-15 because they have been saturating during the entire historical period. Consequently, their substitution path is specified by the model. Each estimated linear equation with estimated parameters At and to can be transported into a logistic function with coefficients ~ and ¢: 1 + exp(-ait- Pi) (6) where f(t) is now the estimated fractional market shares of technology i. Because such a logistic function does not capture the saturation phases and represents only growing or declining logistic trends, n Ifi(t) i=1 may exceed 1 for some value of t, although it must be equal to 1 for all t. Thus, the n- 1 estimated logistic equations were left in their original form (6) that is, as specified by coefficients Hi and Pi and one of the n equations was defined as a residual 1 Aft) = 1 ~j 1 + exp (-cxit-Qi) (7) that is, as the difference between 1 and the sum of the n- 1 estimated market shares f(t). The latter equation represents the oldest still growing technology, j, such that of ' 0 where off_ ~ < 0 and j > 1. The selected technology cannot, however, be the oldest technology (i.e., j ~ 1), be- cause the oldest technology is replaced by the newer technologies and,
U.S. TRANSPORT INFRASTRUCTURES 217 consequently, its market shares decline logistically from the start (i.e., ox < 01. Thus, initially, there are n- 1 technologies denoted by indices i ~ j that follow logistic substitution paths, and one technology, j, that reflects the residual of the market that is, the complement of the sum of other technologies and 1. Based on the point in time, tj, at which technology j is defined as a residual, application of the linear transform of the logistic function to the market shares of technology j, defined above, produces a nonlinear function that can be written in the form of equation (59. This function has a negative curvature. It increases, then passes through a maximum at which technology j has its greatest market penetration, and finally decreases. After the slope becomes negative the curvature dimin- ishes for a time, indicating thatfj~t) is approaching the logistic form. But then, unless technology j is shifted into its period of logistic decline, the curvature will begin to increase as newer technologies acquire larger mar- ket shares. Phenomenological evidence from a number of substitutions suggests that the end of the saturation phase should be identified with the point at which the curvature of yet), relative to its slope, reaches its minimum value. This criterion is taken as the final constraint in this generalization of the substitution model, and from it the coefficients for the jth technology in its logistic decline are determined. Thus, the point in time at which the rate of decrease of yet) approximates a constant is determined. From this point on, the rate of change is set equal to this constant, thereby defining a new logistic function. This point of constant slope is approximated by requiring that the relative change of slope is minimal, y (t) .~( ~ = minimum (8) for tj ' t < te' yet) < 0, and yet) < 0. If this condition is satisfied (the point in time at which this occurs is tj~ ~ > tj), the new coefficients for technology j can be determined as ~j=yj~tj+l, and (9) A = yj~tj+~)-yj~tj+~)tj+~. (10) After time point tj, technology j + 1 enters its residual phase. The process is then repeated until either the last technology n enters the sat- uration phase or the end of the time interval (te) is encountered. These expressions, which have been developed in algorithmic form, determine the temporal relationships between competing technologies.
218 NEBOJSA A7AKICENOVIC | PENE (fj(t), c;, Bj, iYo, no) | t, -1901 +iyo+no | t: - 1900 + iyo J I t:-t+1 1 i , NO ~ ~ YES <~ t > tr ~) Y | f`(t)-1/(1+exp( ~;'t-§j)) | NO /: YES fj(t) $~: ~t)] 2 _ y "(t) ~ y (t) aj ~ y'(t) ,Bj ~ y(t) - y'(t) · t _ \/ ~ (t)~1 - :: f`(t) L: l°g [fj(t)/(1 - fj(t))] FIGURE 8-20 Flowchart of the logistic substitution algorithm. Figure 8-20 is a flowchart of the algorithm that describes the logistic substitution process. A more detailed description of this procedure and the software package for the generalized logistic substitution model is given in Nakicenovic (1979, 1984~.
U.S. TRANSPORTINFRASTRUCTURES 219 NOTES 1. One general finding of a large number of studies is that many growth processes follow characteristic S-shaped curves. A logistic function is one of the most widely applied S-shaped growth curves and is denoted by X/(K - X) = exp(cxt + Q), where t is the independent variable usually representing some unit of time; a, if, and K are constants; x is the actual level of growth achieved; and K - X iS the amount of growth still to be achieved before the (usually unknown) saturation level K is reached. Taking logarithms of both sides results in the left-hand side of the equation being expressed as a linear function of time so that the secular trend of a logistic growth process appears as a straight line when plotted in this way. Substituting f = X/K in the equation expresses the growth process in terms of fractional share f of the asymptotic level K reached- that is, the equation becomes[(1 - f) = exp(at + B). 2. This period of elapsed time we call At, and we define it as the time elapsed between the achievement of 1 and 50 percent of the saturation level K (in this example At = 30.0 yr). Given the symmetry of the logistic function the same time is required for the increase from 50 to 99 percent of the saturation level. An alternative definition of At is the time elapsed between the achievement of the 10 and 90 percent level. This definition of At differs slightly from its first definition, but for all practical applications both definitions can be used interchangeably. 3. A large number of studies have found that the substitution of a new technology for an old one, expressed in fractional terms, follows characteristic S-shaped curves. Fisher and Pry (1971) formulated a simple but powerful model of technological substitution by postulating that the replacement of an old technology by a new one proceeds along the logistic growth curvef/(1 -f) = exp(cxt + p) where t is the independent variable usually representing some unit of time, ~ and ~ are constants, f is the fractional market share of the new competitor, and 1 - f is that of the old one. 4. The fractional shares (f) are not plotted directly but as the linear transformation of the logistic curve that is, p( 1 - f ) (in this more general cases if is the fractional market share taken by a given energy and (1 - f) is the sum of the market shares of all other competing transport infrastructures). This form of presentation reveals the logistic sub- stitution path to be an almost linear secular trend with small annual perturbations. Thus, the presence of some linear trends in Figure 8-14 indicates where the fractional substi- tution of transport infrastructures follows a logistic curve. In dealing with more than two competing technologies, the Fisher-Pry model must be generalized because in such cases logistic substitution cannot be preserved in all phases of the substitution process. Every competitor undergoes three distinct substitution phases: growth, saturation, and decline. This process is illustrated by the substitution path of railway tracks, which curves through a maximum from increasing to declining market shares (see Figure 8-14). In the model of the substitution process, it is assumed that only one competitor is in the saturation phase at any given time, that declining technologies fade away steadily at logistic rates, and that new competitors enter the market and grow at logistic rates. As a result the saturating technology is left with the residual market shares (i.e., the difference between one and the sum of fractional market shares of all other competitors) and is forced to follow a nonlogistic path that joins its period of growth to its subsequent period of decline. After the current saturating com- petitor has reached a logistic rate of decline, the next oldest competitor enters its saturation phase, and the process is repeated until all but the most recent competitor are in decline. A more comprehensive description of the model and assumptions is given in Nakicenovic (1979).
220 NEBOJSA NAKICENOVIC 5. As in Figure 8-14, the fractional shares f are not plotted directly but as the linear transformation of the logistic curve that is, f/(1 - f ) (as the ratio of the market share taken by a given energy source over the sum of the market shares of all other competing energy sources). The form of presentation in Figure 8-17 reveals the logistic substitution path as an almost linear secular trend with small annual perturbations. Thus, the presence of some linear trends in Figure 8-17 indicates where the fractional substitution of energy sources follows a logistic curve. 6. In this particular application the difference was in the assumptions about weighing of the observations in the estimation procedure for example, whether unit- or data- dependent weights are used. BIBLIOGRAPHY Angelucci, E., and P. Matricardi. 1977. Practical Guide to World Airplanes, vols. 1-4. Milan: Mondatori (in Italian). Debecker, A., and T. Modis (Digital Equipment Corporation, 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. Epstein, R. C. 1928. The Automobile Industry, Its Economic and Commercial Develop- ment. Chicago: A. W. Shaw Co. Fisher, J. C., and R. H. Pry. 1971. A simple substitution model of technological change. Technological Forecasting and Social Change 3:75-88. Grey, C. G., ed. 1969. Jane's All the World's Aircraft. London: David and Charles Publishers. Grubler, A., and N. Nakicenovic. 1987. The Dynamic Evolution of Methane Technologies. WP-87-2. Laxenburg? Austria: International Institute for Applied Systems Analysis. Grubler, A., N. Nakicenovic, and M. Posch. 1987. Algorithms and Software Package for Estimating S-shaped curves. Laxenburg, Austria: International Institute for Applied Sys- tems Analysis. Marchetti, C. 1979. Energy systems the broader context. Technological Forecasting and Social Change 14:191-203. Marchetti, C. 1983. The automobile in a system context, the past 80 years and the next 20 years. Technological Forecasting and Social Change 23:3-23. Marchetti, C. 1986. Fifty-year pulsation in human affairs, analysis of some physical in- dicators. Futures (June):376-388. 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. Martino, J. P. 1983. Technological Forecasting for Decision Making;. 2d ed. New York: North-Holland. 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. 1986. The automobile road to technological change, diffusion of the automobile as a process of technological substitution. Technological Forecasting and Social Change 29:309-340. Reynolds, R., and A. Pierson. 1942. Fuel Wood Used in the United States, 1630-1930. U.S. Department of Agriculture, Forest Service Circular No. 641.
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