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Transportation Deployment Casebook/2023/U.S. Airliners

== U.S. Airliners Introduction ==

Airliners Technical Characteristics
Airliners are designed to transport people and cargo for commercial purposes. They come in all sizes and types, from small regional jets to large wide-body aircraft capable of carrying hundreds of passengers. The type of engine used to power airliners varies depending on the era and design of the aircraft. Early airliners typically used piston engines, while later models transitioned to jet engines. Today turbofan engines are the preferred choice for modern airliners. Despite changes in engine technology, the basic principles of aerodynamics remain the same, including the use of Bernoulli's principle to create lift by increasing speed to create pressure differences. Technological advances in aircraft design and engineering have led to the development of more efficient and reliable airliners that have revolutionized the way humans travel and conduct business.

Advantages
The same advantage offered by airliners of different eras is that they offer mankind a faster option for domestic and international travel, saving travel time by ship, train and car for the same distance. From the advent of the airliner in 1926 to the airliners that can carry large amounts of cargo, to now can carry more than 800 passengers at a time, regardless of the number of passengers, flying has been the fastest option for travel. The advantage of the modern airliner is that it is one of the safest travel options available today. Advanced technology, rigorous training programs and strict regulations have all contributed to air travel safety. Airliners are also environmentally friendly, producing fewer carbon emissions per passenger mile than other modes of transportation. The latest airliners have been designed with passenger comfort in mind, offering a range of amenities such as in-flight entertainment, food and beverage service and wireless Internet access. These features have made air travel a popular choice for many passengers.

U.S. Airliner Market
In the early days of the U.S. aviation industry, flying machines were used primarily in the U.S. air mail market. The market for airliners was limited due to a lack of infrastructure and technology. The market for airliners in the U.S. really opened up after the use of stock bombers converted to commercial use after World War I. Between 1940 and 1980, airliners became more complex and efficient due to advances in engineering and manufacturing. The growth of the airliners market was accelerated by an increase in the number of passengers carried per aircraft, which led to lower fares, at a time when large companies such as Boeing and Douglas dominated the aviation industry. Today, Boeing's acquisition of Douglas has led the airliners market in the United States and around the world, with the only competitor being France's Airbus.

The growth of the airliner market is slowing down, with the Covid-19 epidemic as a starting point and fewer people choosing to travel internationally. The 5G network era has allowed more people to telecommute to meetings and schools. Airlines are also retiring more high-capacity aircraft, such as the Airbus A380 and Boeing 747. But global demand for passenger aircraft is still on the rise, with 44,500 new aircraft still to be delivered worldwide over the next 20 years, but with a preference for medium capacity aircraft. From the perspective of airliner design making more passengers enjoy better flight comfort will become the main goal of the future airliner market.

Transportation Modes before the Airliner
Before the advent of airliners, long-distance travel was still largely dependent on two modes of transportation: ships, and trains. While transoceanic travel would only rely on ships to travel. The use of trains or ships will be more obvious in the speed limitations, slower travel speed leads to more time spent in traffic. In the early 1900s, the RMS Olympic cruise across the Atlantic Ocean takes nearly 15 days. And at the time U.S. railroad system was in its heyday. From New York to Iowa also consumed at least a day of time to travel by railroads. At the time, cruises and trains were seen as a more affluent way to travel, so they would have been a good choice for travel comfort. From the perspective of travel efficiency, businesspeople and professionals will need a longer time for long-distance travel. The time consumed was unacceptable to the United States in the Gilded Age, and the disparity between the rich and the poor was extremely serious at the time, coupled with the unrestricted expansion of railroads that led to strikes by American labourers and other negative effects on the railroad mode of transportation itself. Therefore, a faster and more convenient mode of transportation needed to be discovered.

Invention of the Airliner
The invention of the "1903 Wright Flyer", the world's first airplane, led to the development of aviation leading to the emergence of airliners. In the early 19th century, the aerodynamic angle of the glider wing design entered the public eye. At that time the main technical barrier is how to generate sustained power for flight. The Russians had tried steam power with poor results. In 1876, when Étienne Lenoir manufactured the first internal combustion engine, successfully laying the theoretical power foundation for aircraft, allowing the Wright brothers to manufacture their four-cylinder engine as an aircraft engine and successful flight marked the official emergence of aviation.

Fifteen years later, in 1918, the United States officially began airmail service with the "Jenny" Curtiss JN-4H biplane, built by the U.S. Army and Navy , and from 1918 to 1926, there were more than 200 airmail pilots, 35 of whom died in airplane accidents. The danger factor of the aircraft was still at a high level until the end of World War I, when a large number of retired American bombers, the De Havilland DH-4, were turned over to the airmail industry. At a time when the bomber was considered a safer, faster and superior aircraft. The DH-4 proved to be a great challenge to the railroad industry by greatly reducing transit times over long distances, and the time-sensitive financial industry increased its support for the airmail industry at a time when the use of mail for check and securities transactions was extremely common. The rapid growth of the airmail industry led to congressional attention and eventually to the "Contract Air Mail Act of 1925" and the "Air Commerce Act". These two acts made it possible for the airmail industry to be privately contracted and ensured that outside investment would be secure. Also for all people and businesses to safely participate in the airline industry, increasing the opportunity for competition and accelerating the growth of the airliner industry. Beginning in 1925, with policy support, aircraft manufacturing began to develop rapidly, with new fairing designs, piston engines, variable pitch propellers, and other new aircraft designs appearing in large numbers. The first airliner, the Boeing 247, was introduced, with an unprecedented speed (290 km/h) and the ability to carry up to 10 passengers and three crew members, and received an order for $3.5 million at the time. It entered service with United Airlines on May 22, 1933. This successfully opened the chapter on passenger aircraft.

Early market for U.S. airliners (1926-1960)
The introduction of the Boeing 247 officially opened up the early market for piston-engine airliners. Before that, many airlines were trying to make a profit by transporting passengers, and all passenger airlines before the Boeing 247 failed due to high operating costs, and the U.S. federal government had to introduce various subsidies to encourage the development of airliners, including the aforementioned "Contract Air Mail Act" and the "Air Commerce Act". In 1930, the "McNary-Watres Act-The Airmail Act" was enacted to allow mail and airliner routes to be combined and to increase the number of routes as judged. This act has greatly stimulated the airline industry, with more routes to choose from giving more people the option to travel by air, and a large number of newly developed routes boosting the demand for passenger aircraft. With the advent of the Boeing 247 in 1933, high-profit returns led to more companies competing for airliners, and the Douglas Aircraft Company seized the opportunity of the crash of the Boeing 247 in Kansas to produce the DC-2. In 1936, it developed an improved version of the DC-3, which could already carry 21 passengers and was responsible for 90 percent of the world's air traffic. From 1936, when the DC-3 appeared, the number of passengers grew from 100,000 per year to 1 million per year. During this time, the "Civil Aeronautics Act" was enacted and the Civil Aeronautics Administration(CAA) of the United States was officially established, and the airliner officially shifted to the passenger-oriented airliner market.

And such growth came to a brief halt two years after the start of the Pacific War, but the war led to rapid growth in aircraft engineering, And once again Boeing developed the Boeing 307 Stratoliner based on the B-17 bomber design. The world's first airliner that could carry 40 people into the stratosphere .The world's first airliner that could carry 40 people into the stratosphere. And from 1942 after the Battle of Midway, the fact that America will win this war has been well-known to Americans. So in 1943, the number of airliners enplaned passengers back to the level of 1941 and continue to grow in increments of 3 million passengers per year, the late addition of larger capacity passenger aircraft such as the Boeing 307 and DC-4 to make from 1952 to 5 million passengers per year to grow, thus opening the passenger aircraft The era of rapid passenger development began.

The early airliner market evolved from the invention of technology to policy changes, and finally to the development of technology. The early U.S. airliner subsidy policies and related programs for airliner transportation were influenced by the use of policies that allowed airliner development to grow.

The Developing U.S. Airliner Market (1960-2000)
The stage of development of U.S. airliners is one of the more complex stages in the history of global aviation, and this chapter will focus on technology and policy, the two fundamental factors that have changed the stage of development of U.S. airliners. In fact, economic, political and environmental factors have all played a role in the developing U.S. airliner market and will not be discussed in this chapter.

Technology
The Second World War led to jet engine technology. Boeing once again derived a jet airliner based on the bomber (B-47). In 1954, the first U.S. jetliner, the Boeing 707, made a test flight and can carry nearly 200 passengers in a single trip. The first flight was made in 1957, and the market for transoceanic flights and long-distance flights was then fully opened. From 1960 to 1970, the Boeing 707 captured most of the market, and from 1970 onward, the Boeing 747 and Boeing 737 were produced, establishing a monopoly for Boeing in the U.S. airliner market. Airliner technology also reached its peak in this period.

Policy
The first change in policy is regarding the safety of airliners. Beginning around the 1950s, aviation development made U.S. airspace very congested, and two airliner crashes in 1956 and 1958 demonstrated that the air traffic controls applied by the Civil Aeronautics Administration (CAA) were outdated. In 1958, Eisenhower signed the "Federal Aviation Act", which eliminated the Civil Aeronautics Administration and created the Federal Aviation Administration (FAA), which re-regulated the safety of the aviation industry and the use of U.S. airspace by both civilian and military aircraft.

The second was the "Airport and Airway Development Act of 1970", which provided funding for airport development by increasing taxes on fuel, airline tickets, and other taxes. This act was created in response to the needs of the aviation industry.

Then came the "Airline Deregulation Legislation Act of 1978", which lowered fares and increased competition among airlines, making air tickets more affordable.

Finally, the "General Aviation Revitalization Act of 1994", reduced the liability of airline manufacturers and provided a boost to the airline manufacturing industry and an opportunity for small airliner manufacturers. It was an act that added more jobs and promoted the growth of the aviation industry.

The created act during this period to address four factors: safety, infrastructure, price and liability. The chronology of the act creation also represents the importance of each factor, first ensuring aircraft safety, second ensuring the number of airports, then increasing consumption, and finally defining the distribution of liability. Compared to the earlier development-oriented policies established in the airliner market, the policies in the development period have more of a role in defining the framework and establishing the boundaries. Allowing the airliner market to be truly planned and scheduled.

The advanced technology and effective policies of this period also increased the number of passenger aircraft passengers per year in the United States from 60 million in 1962 to nearly 700 million in 2000. The data proves that the U.S. has been successful in the development of the aviation industry.

Maturity Phase (2000 - Present)
From 2000 onward, the number of passengers carried by airliners in the U.S. each year has shifted to a stage where the growth rate has gradually been maintained at a flat rate. The factors that have had this effect are the advancement of technology in the world, the changing needs of airline passengers, the occurrence of unforeseen events and the impact on the economy.

From a technological standpoint, airliner technology is no longer geared toward engine upgrades, and speed and timeliness are no longer the only criteria. The French Concorde supersonic aircraft is a good example. Airliner technology has shifted from engineering to passenger design, including (cabin amenities upgrades, passenger capacity improvements, aircraft stability design and aircraft comfort design), and these metrics are more focused on the passengers themselves. Making air travel more comfortable became the main airliner design goal after 2000 while increasing passenger capacity based on comfort. Both Boeing and Airbus, the two global monopolies in the aviation industry, have launched the Airbus A380 and Boeing 737-Max models with more comfort and higher passenger capacity.

And comfort and high passenger capacity design still did not stop the decline in annual airliner passenger volume in the United States, mainly due to unforeseen events from outside the aviation industry that was caused by economic factors. From the beginning of 2000 to the present, three significant declines in annual U.S. passenger airline passenger traffic have occurred. These three time periods correspond to,

 * 1) 9/11 in 2001, when terrorist events compounded passenger aircraft security factors, resulting in a 36.7% drop in passenger volume compared to 2000.
 * 2) The financial crisis in 2007, when the deep dive in the financial markets led to a significant increase in the price of jet fuel and a decrease in travel demand by the American people due to economic reasons.
 * 3) The COVID-19 epidemic in 2020, the mass transmission of viruses will require the American people to stay in quarantine for longer periods of time, eliminating all necessary air travel. 2020 passenger aircraft capacity is down more than 60% from 2019, the same level of passenger traffic as in 1985.

These contingencies have largely prevented the continued growth trend of airliners, but they also suggest that the mode of transportation itself is in the crosshairs of these contingencies and that even without them it is difficult not to be certain that passenger aircraft will reduce the growth trend. The 5G fast network era has arrived, and securities and checks mailed by aircraft since 1926 can be transmitted in seconds using the network. Telecommuting and meetings are no longer difficult or complicated, and the development of VR and AR is facilitating more means of virtual interaction. Meanwhile, Asia's fast-growing high-speed rail system is competing with airliner systems for domestic transportation at a cheaper price, in the same amount of time and with better comfort. Airliner transportation systems are encountering increasing challenges. The only continuing advantage is the short-time transoceanic capability they have, and this may be the only reason passengers will choose any airliners in the future.

Quantitative Analysis-(U.S. Annual Enplaned Airliner Passengers)
By comparing and combining two sets of data from Airlines for America (Data & Statistics/Past A4Annual Reports 1937-2011) and Bureau of Transportation Statistics (2001 - 2022). Historical data on the number of passengers on U.S. airliners per year from 1926 to 2022 was obtained. The entire life cycle (early, development and maturity) of U.S. airliners were statistically analyzed.

Formula
Three-parameter S-curve logistic function was used :

S(t) = Smax/[1+exp(-b(t-ti)]

S(t) = State Measurement (in units of individual passengers on board)，

t = time (in years)，

t 0 = inflection point time (the year in which half of S max is obtained)，

S max = saturation level (maximum annual passenger capacity of U.S. airliner)，

b = the coefficient to be estimated.

Parameters
In order to fit the model as closely as possible (R-squared close to 1), different Smaxparameters were used for the tests, and the final Smax value was determined by narrowing down the range one at a time from a wide range of tests and a number of tests to determine the true Smax boundary.

The final most tested S-Max value is 93606600 numbers of passengers.

Regression Results
Model fit of the predicted data obtained using S_Max=93606600

Regression Statistics for 1926 to 2022
The reason R Square did not exceed 0.9 is because the number of passengers on U.S. airliners in 2020 decreased by 60% compared to 2019, which is a very abnormal figure, so the model fit data was calculated using S_Max=93606600 for the forecast data until 2021.

Regression Statistics for 1926 to 2019
The R square exceeds 0.9 and reaches 0.91, which makes the forecast data before 2020 more consistent with the model.

Results
The raw record data is placed in the provided Google Sheets for each year against the middle vacancy obtained by reviewing the annual A4A Annual Reports keyword analysis.

The following excel reperents the "Actual and projected recorded of annual enplaned U.S. airliner passengers from 1926 to 2022".

Data Visualization
The analysis of the simulated data curves provides good evidence that the overall prediction fit is consistent with the actual data.

Also, the three phases above, early (1926-1960), development (1960-2000), and maturity (2000-2022) all fit the magnitude of change in the predicted curve.

The only difficulty is that it is more challenging to perform a higher-fit analysis on the 97-year data, and the forecast curve obtained in this paper is still only a close approximation to the true forecast curve, which needs to be more subdivided according to the degree of data variation.

BLUE LINE- Predict Enplaned Passengers       GREEN LINE- Actual Enplaned Passengers


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text:
Transportation Deployment Casebook/2023/Manchester Metrolink

= 1.    Qualitative Analysis =

1.1 Manchester Metrolink
Manchester, one of the UK's major cities, has its own long history of transport. The subject of this paper is the life cycle of Manchester's trams. Historically, the city of Manchester had a busy tram system, a history that can be traced from 1902 to 1949. This history includes the replacement of horse-drawn trams by electric trams, and then the rise of buses and private cars to replace trams. [1]

The last tram run ended in 1949, after which the tram disappeared from the city of Manchester. The city of Manchester has since been faced with the problem of transport links that need to be improved. The issue was raised in 1960 and the project was launched in 1982. Finally, in 1992, a 19-mile tram line was opened, linking 26 stations, and replacing two train lines. [3] Locally, they call this tram system Metrolink.

1.1.1 Description of the mode
Metrolink is a tram system in the Manchester area of the UK that uses the basic technical features of a conventional tram. In terms of technology, it consists of routes, fleets, tram platforms, power supplies and depots. [5] The fleet used for the Metrolink system is the Bombardier M5000, a bi-directional tram, which means that the vehicle can travel in both directions. In terms of route design, the track system consists of a double line, allowing two trams to travel above each other in opposite directions. The Metrolink stations are largely converted from old railway stations. Several entrances and exits will be provided on the line. [3] Metrolink's power supply system is supplied by sustainable electricity. This electricity is generated from hydroelectric power. [6] Metrolink's major advantages include:

·       Provides an efficient and reliable urban transport service. Adequate stations to meet passenger demand for fast and frequent transport services.

·       Metrolink system uses sustainable electricity, reducing carbon emissions.

·       Metrolink's extended routes and services allow more areas to be connected, supporting the development and growth of the city.

Metrolink's main market is the residents and visitors of the Manchester area. In addition, the system provides an important transport service to the surrounding area, making it easier for residents to access Manchester city centre.

1.1.2 Previous scenes
As mentioned, much of Metrolink was developed on the old train system. Before the coming of Metrolink, Manchester's urban transport system consisted mainly of buses and trains. Buses do not provide an efficient transport service in times of congestion. Trains, meanwhile, are limited in that they have fixed and inconvenient stopping routes, which does not allow passengers to get off close to the train. Prior to 1977, the main problem in Manchester was the poor connection of the original train system. The council had proposed that the trains be allowed to pass by digging a tunnel, which was abandoned because of the cost. [7] Moreover, as populations and cities grow, the need for fast and convenient transport is increasing. So, the transport market has evolved from congestion, detours, and a single bus-train system to fast, reliable transport services. For the government level, relatively low-budget light rail options and the conversion of old train tracks came into being. Metrolink offered increased speed and carriage space compared to buses, as well as more convenient boarding and alighting stations than trains. In addition, climate change and increased environmental awareness have stimulated interest in more environmentally friendly, low-carbon modes of transport. This had an impact on the later Metrolink electricity consumption system, which was entirely hydroelectric.

1.1.3 Technology of the mode
Metrolink's brings together different types of technical expertise. The design of the system covers electrical systems, track laying technology, signalling technology, timetable systems and fleet design. [8] The trams are supplied with electricity through the contact network, and the high voltage energy is converted into low voltage electricity for the supply of trams. Trams require a suitable track to be laid to ensure the stability and safety on the track. Signalling is required before the tram enters the station, with audible and visual alerts. After accounting for passenger demand and operating speeds, a timetable is required for passengers to check the arrival time of each tram. Prior to the invention of the electric tram, railed transport was provided by railed horse-drawn trams. [9] The horse-drawn tram has taken on the shape of a modern tram. It has a track system, signs, routes, and timetables. The early trams were based on the horse-drawn tram and improved the track system and added an electrical system. With the advancement of electrification and the development of trackless technology, the modern Metrolink has improved its speed, energy efficiency and scientific management methods over the tram systems of the last century.

1.1.4 Market development
The early market niches of Metrolink were due to the fact that Manchester's two main railway stations were built over a long period of time and therefore resulted in poor transport links between the surrounding city and the city centre. And there are no well-defined transport routes in the urban area. Relying on bus alone cannot meet the growing population and urban development. The initial market niche is therefore intra-city commuting and travel demand.

The enhanced functionality is intended to better serve the existing market and is reflected in the upgrading of the existing carriage environment. With the invention and installation of on-board air conditioning, it will provide passengers with a more comfortable ride. There are also more logical seating arrangements, such as the addition of seats for the disabled. In addition, timetables are set according to the flow of people. Add more trams and improve route coverage during the morning and evening peak commute. Functional enhancements play a role in market development to improve passenger satisfaction. By maintaining passenger demand and satisfaction with Metrolink the funds required to keep the company running and upgrading are maintained.

Functional discovery means serving new markets. With the increased demand for tourism and cross-city commerce, Metrolink has added tourist routes and business expansion projects that contribute to the economic and tourist development of the city. "Everyone goes shopping in Manchester now." Ms. Yasin, from the University of Manchester, said. "This is not transport for transport's sake; this is all about how we produce economic growth in Greater Manchester," says from chief executive of Transport for Greater Manchester, Jon Lamonte. [3]

1.1.5 Role of policy
The policy of borrowing from precursor models is that the Rail Study Group, set up in 1984, learns from the experiences of other cities by drawing on their tram models to inform the development of Metrolink. The proposal is based on existing light rail systems in North America and continental Europe. [11] The innovative policy is reflected in the government's early plans to build the Metrolink transport network in phases. Due to the large financial investment of over £1000M required. The government requires the sponsor of the construction plan to pay part of the cost in the early stages. The terms of the contract allowed tenders for each phase to be replaced by new operators and builders. [12] This policy is also a government- embedded policy that has resulted in attracting investment and support from social capital. The first phase of Metrolink was designed, built, and operated by private contractors. During the birthing phase, some elements of the policy may be locked in. For example, the parking and upgrading of trams must comply with the Disability Discrimination Act and the Rail Vehicle Accessibility Regulations.

1.1.6 Growth of the mode
In the growth of Metrolink, the public plays a driving role; the private sector plays a role in maintaining the system. Metrolink has been opened since 1992 as a solution to the problem of public mobility and urban development. Metrolink has been continuously expanded and updated to date, based on the travel needs of passengers and the expectations of government departments to connect the city to the surrounding cities in general. The private sector is involved in the investment of funds, the provision of technical support and construction, and then the operation and maintenance after completion. This is because the impact of the segment-based delivery policy has resulted in each phase of the Metrolink system being operated by a different private sector. This has the advantage that better options and choices are available. This also leads to Metrolink being continually upgraded, which tends to compete between private companies.

One of the main policy issues that arose during the growth and development phase was access to finance for the expansion of the system. The development of Metrolink has been divided into three phases. In 2000, the cost was estimated at £429 million, but by 2002 the cost was estimated at £820 million. The solution was to split the Phase 3 programme into two smaller phases, with the first £520 million investment secured in 2006; and the second funding approval passed in 2008. [12]

Growing environmental concerns have led to an increased emphasis on promoting sustainable transport modes like Metrolink. The government thus introduced various policies to support the development of public transport, such as the creation of transport agencies and the provision of funding for sustainable transport. This is the reason why Metrolink’s electricity consumption is fully hydroelectric now.

Metrolink has been successful in its growth and development phase due to the cooperation between the public and private sectors. The policy environment also plays a key role in the development of the system, with policies supporting the development of sustainable transport modes like Metrolink.

1.1.7 Mature phase of the mode
The maturity phase of development includes the expansion of services, the improvement of service quality and the introduction of new fleets. The expansion of the service includes an increase in the number of passengers, for example, no longer residents of Manchester and the surrounding cities, but also tourists and businesspeople. Improvements in service quality include the provision of caring seats to facilitate travel by the elderly as well as people with disabilities.

As mentioned, the government's financial constraints may have hindered Metrolink's funding flow and expansion plans. The preparation of funds and bids for social funding can take a significant amount of time and often delay addressing the need to upgrade or expand lines in a particular section of the region.

A global health emergency in the maturity phase is COVID-19. Some of the lockdown policies include limiting the number of people and controlling the distance between people, limiting the number of people on each tram. This led to a demand for passengers that was greater than the supply and spawned passenger non-dependence for a short period of time. A shift to more convenient modes of travel.

In terms of opportunities, Metrolink could consider developing industry-specific services. For example, for express services, Metrolink could set up specific express points in each region, where goods are delivered quickly via tram. This has the benefit of reducing the carbon emissions of conventional land transport by car and moving to more sustainable sources of energy. Reducing the time between deliveries, aiming for same-city deliveries that can be completed in less than a day.

= 2.    Quantitative Analysis = The Manchester Metrolink passenger statistics for each year from 1992 to 2021 are available from the UK Government's Transport Statistics for Great Britain. [13] In order to predict the number of passengers from the raw data, the following formula was used.

S(t) = predicated system size in year t

t0 = midpoint (inflection point) year

K = final market size needed to identify

T = year

a = model parameters to be fit

Since the values of a, t0, and K are unknown in the formula, linear regression is used to predict these values.

X = year

Passengers =number of passengers used Metrolink

The data for 2020 and 2021 show a sharp decline because of the presence of COVID-19. So, these two years were removed from the analysis and the following results were obtained

Table 1 Summary of results A life-cycle analysis of Metrolink in Manchester, UK, can be divided into the following four phases based on its historical development:

·       Birthing phase (1992-1999)

The birth phase of the project was marked by the completion of Manchester's Metrolink in 1992. At this stage, Metrolink faces a number of problems, including financial, technical and policy issues. Therefore, the number of passengers has not increased significantly each year.

·       Growth-development phase (2000-2010)

From the year 2000 onwards, Metrolink entered a phase of rapid growth and development. During this phase, Metrolink introduced new routes and services and expanded existing routes while maintaining high patronage.

·       Mature phase (2010-2019)

As it reached maturity, the Metrolink system began to upgrade in line with the policy environment to ensure its ridership was maintained. Existing routes continued to be expanded and some older facilities and vehicles were updated. In addition, Metrolink has actively explored new technologies and services to better meet the changing needs of its customers. Thus, the increase in the number of passengers at this stage is significant.

·       Decline (2019-2021)

After the advent of Covid-19 in 2020, Metrolink entered a phase of decline. Due to various restrictive policy measures, Metrolink's passenger numbers have plummeted. In addition, Metrolink needed to take additional measures to ensure its safety and hygiene standards.

= 3.    Reference = [1] Allen, R., Greaves, P. and Eyre, M. (2018) Lancashire United: The fleet 1900-1981: Buses, trolleybuses, trams, Lancashire United, South Lancs, Bangor Blue. Manchester: Greater Manchester Transport Society, Museum of Transport.

[2] Vickie Scullard. (2019). Manchester Corporation Tramways gallery.

https://www.manchestereveningnews.co.uk/news/nostalgia/gallery/manchester-corporation-tramways-gallery-15670119

[3] Bounds, A., & Wild, J. (2013). Manchester tram system comes of age after 21 years. FT.com.

[4] Museum of Transport Greater Manchester archive. (1992)

https://www.flickr.com/photos/gmts/16678953170

[5] Department of Transport (2022) Light rail and tram statistics, England: Year Ending March 2022, GOV.UK.

https://www.gov.uk/government/statistics/light-rail-and-tram-statistics-england-year-ending-march-2022/light-rail-and-tram-statistics-england-year-ending-march-2022

[6] Adrian, S. (2010) Procurement of hydro-electricity for Metrolink – the greater manchester light rapid transit system., Energy Planning Knowledge Base RSS.

[7] Richard, B. and Martin, D. (2013) INFRA_MANC: Post-war infrastructures of Manchester, Issuu.

[8] Robbins, M. (2000). The Early Years of Electric Traction: Invention, Development, Exploitation. Journal of Transport History, 21(1), 92–101.

https://doi.org/10.7227/TJTH.21.1.6

[9] Schmucki, B. (2012). The Machine in the City: Public Appropriation of the Tramway in Britain and Germany, 1870–1915. Journal of Urban History, 38(6), 1060–1093. https://doi.org/10.1177/0096144211435121

[10] Knowles, R.D. (1996) “Transport impacts of Greater Manchester's Metrolink light rail system,” Journal of Transport Geography, 4(1), pp. 1–14. Available at: https://doi.org/10.1016/0966-6923(95)00034-8.

[11] Ogden, E. and Senior, J.A. (1991) Metrolink: Official Handbook. Glossop: Transport Publishing.

[12] Nimda (2015) Case studies: Metrolink light rail transport, Case Studies: Metrolink Light Rail Transport, Manchester, United Kingdom - BENEFIT Wiki.

http://www.benefit4transport.eu/wiki/index.php?title=Case_Studies%3A_Metrolink_Light_Rail_Transport%2C_Manchester%2C_United_Kingdom

[13] GOV.UK (2022) Passenger journeys on light rail and trams and undergrounds by system: Great Britain - annual from 1983/84


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Cookbook:Algerian Couscous

This recipe is a great option for when you want to mix up your proteins. Made with mutton and chicken, it can easily be adjusted to include lamb and/or merguez.

Ingredients

 * Vegetable oil
 * Mutton
 * Salt
 * Black pepper
 * Turmeric
 * Potatoes
 * Onions
 * Carrots
 * Tomatoes
 * Water
 * Vegetables
 * Harissa
 * Zucchini
 * Instant couscous
 * Butter

Equipment

 * Stovetop
 * Big pot/saucepan
 * Knife
 * Chopping board
 * Whisk

Procedure

 * 1) Salt and pepper the mutton chops.
 * 2) In a big pot, heat the vegetable oil on medium-high heat. Cook the mutton in the oil in batches with the onions until browned—about 2 minutes per side. Transfer the mutton to a big plate.
 * 3) To deglaze the browned parts, add a splash of water to the pot and use a wooden spoon to scrape the bottom. Add the chicken and mutton chops back to the pot, along with turmeric just enough water to cover. Cover the pot and heat until boiling. Simmer for 20 minutes on medium heat.
 * 4) Add carrots, turnips, and potatoes to the pot and stir. Simmer, covered, for 10 minutes or until vegetables begin to soften.
 * 5) Add the tomato paste, and cook for another 10 minutes until the zucchini is soft.
 * 6) Stir in the chickpeas and cover the pan for about 5 minutes.
 * 7) Pour the cooking liquid into a bowl and whisk in the harissa until well combined.
 * 8) In a saucepan, bring some water to a boil. Turn off the heat and whisk in an equal volume of couscous, along with a dash of butter and salt. Cover the pan and leave it standing for 5–10 minutes, or until all the water has been absorbed.
 * 9) Using a fork, fluff the couscous and toss in 1 tablespoon of vegetable oil. Place in a serving bowl.
 * 10) Put some of the cooked vegetables on a dish for serving. Place the chicken and mutton on different plates. Serve everything with the couscous and harissa sauce.

title: Cookbook:Algerian Couscous


text:
Piano Solo Music: An Encyclopedia/Composers born in the 20th century/Ali-Zadeh, Franghiz

Compositions for piano solo by Franghiz Ali-Zadeh

 * Music for Piano, for prepared piano [YouTube]
 * Prelude, for prepared piano [YouTube]


text: Piano Solo Music: An Encyclopedia/Composers born in the 18th century/Bach, Carl Philipp Emanuel


text:
Piano Solo Music: An Encyclopedia/Composers born in the 20th century/Bacri, Nicolas

Compositions for piano solo by Nicolas Bacri

 * Cahier pour Éloi : Quatre pièces pour la jeunesse
 * Diletto classico, op. 100
 * Suite baroque [YouTube] [YouTube] [YouTube] [YouTube] [YouTube]
 * Sonatina classica [YouTube] [YouTube] [YouTube]
 * Arioso barocco e fuga monodica a due voci [YouTube] [YouTube]
 * Esquisses lyriques 1 - 2, op. 103 [YouTube] [YouTube]
 * Esquisses lyriques 1 - 3, op. 144 [YouTube]
 * Fantaisie, op. 134 [YouTube]
 * L'Enfance de l'art 1 - 7, op. 69 [YouTube] [YouTube] [YouTube] [YouTube] [YouTube] [YouTube] [YouTube]
 * Moments musicaux
 * Nocturne, op. 104 [YouTube]
 * Petit prélude [YouTube]
 * Petites variations sur un thème dodécaphonique [YouTube]
 * Prélude no. 6
 * Prélude et fugue, op. 91 [YouTube]
 * Quartes à jouer 1 - 10
 * Saisons : Quatre intermezzi pour piano, op. 123 [YouTube] [YouTube] [YouTube] [YouTube]
 * Sonata corta, op. 68
 * Sonata impetuosa, op. 122 [YouTube]
 * Sonate no. 2, op. 105 [YouTube] [YouTube] [YouTube]
 * Sonatine pour piano
 * Tenebrae - Nocturne pour piano no. 6, op. 139 [YouTube]
 * Valse triste [YouTube]
 * Variations faciles d'après les variations Lucifer


text:
Transportation Deployment Casebook/2023/Germany

630Introduction
Germany's modern history is marked by key periods with changes in its territory and land. Briefly, the German Confederation (1815-1866, with a brief period in 1848-1850 when the German Empire existed) was an alliance of 39 German-speaking sovereign states a result of the Congress of Vienna in 1815. Following this, the German Empire existed as a unified German monarchist state which lasted until the November Revolution in 1918 which resulted in a republic Germany. Following the end of World War II, Germany was divided into East Germany and West Germany until finally being unified in 1990.

This case study on the passenger railways of Germany focuses on the lifecycle of the German railways, from the commencement of what is the modern railway system in Germany from 1835 until the end of the German Empire in 1918.

The Birth of Railways in Germany
The predecessor to the modern railway system in Germany were mining carts used to transport goods from mines. In Ruhr, tracks were also built above ground to enable the movement of coal from the mines to the River Ruhr to be loaded into vessels.

However, with the development of locomotives in England in 1805 and the advent of the Stockton & Darlington Railway in 1825, this helped to shift people away from the construction of canals, which were costly and inefficient. Early German railway lines were adopted based off existing technological developments within the railway industry.

Despite this, in this period the majority of early railways were primarily used to transport coal, rather the passengers. It wasn't until the opening of the Bavarian Ludwig Railway in 1835 that passenger railways began to be constructed.

The Bavarian Ludwig Railway
Based on the English railways, the Bavarian Ludwig Railway was constructed by the Ludwig Railway Company and operated its first trip from Nurnberg to Furth on December 7, 1835. What is perhaps the most important aspect to note is that this railway adopted much of the English railway's features such as track gauge, which meant that future lines also were built to English railway standards. Unfortunately, subsequent rail lines which were built never connected to the Bavarian Ludwig line and it was eventually converted into a tramway.

Early development
While canals were originally the favoured form of transportation infrastructure, by the 1820s there had been a shift towards railways, despite previous views that railways would contribute to increased smoke and fumes and threaten the industries which benefitted from canal building. As Germany transitioned from being a primarily agricultural economy, the German population began realise the benefits of the railway as a way to encourage economic development within their cities and help to bring unity to the various German states through connectivity.

While initially engineering and hardware was brought in from England, the Germans were quick to learn how to build and operate railways. Educational policy reforms resulted in many cities establishing technical and training facilities to allow Germany to be able to meet the demands of rail building within the country in 1850. Consequently, this also resulted in the rise of the steel industry.

Following the Bavarian Ludwig Railway, the Berlin - Potsdam Railway was constructed in what was then Prussia. This line was constructed and opened in two stages - Zehlendorf to Potsdam in September 1838 and Zehlendorf to Berlin the following month. The Duchy of Brunswick State Railway, the first state owned railway in Germany, opened the same year facilitating trips between Brunswick and Wolfenbuttel.

Growth and Expansion
Passenger railway construction began to grow after the 1840s after the creation of the Zollverein. The Zollverein was a group of German states which way in which tariffs and economic polices was managed. This made it especially important to ensure transport infrastructure was aligned within the union. Prior to the establishment of the Zollverein in 1834, the lack of unity between the German states as well as resistance to new technologies hindered the growth of rail in Germany. However, its growing importance helped to further encourage the construction of railways in Germany and railway lines began to be built, with railway lines linking German cities and the German states having responsibility for the railway lines within their jurisdiction. Increased railway construction lead to an increase of economic development for Germany, opening up new markets, creating demand for skilled workers and further helped to benefit the coal and iron industries.

The first railway linking two German cities opened in 1839, connecting Leipzig to Dresden. This was the first of numerous other long distance train routes which were constructed during the growth era, namely:
 * Berlin to Anhalt,1841
 * Berlin to Frankfurt, 1842
 * Cologne to Herbesthal, 1843
 * Cologne to Minden, 1845, and
 * Berlin to Hamburg, 1846.

These long distance railways opened up improvements in travel between larger German cities and contributed to making the German railway system polycentric. Railway hubs began to be form, with Kothen being the first railway hub when the Berlin to Anhalt line connected with the Berlin to Potsdam line at Kothen. Passenger numbers exceeded expectations due to the overall time-savings due to the speed of travelling by train as well as the lower cost of travelling by rail compared the associated costs of walking the same distance.

As the state governments became more open to railway construction, this lead to more railway lines being constructed. Isolated railway lines began to connect to other cities, closing gaps in the network and resulting in a more extensive railway network, with continuous tracks. This was facilitated by the German states realising the importance of being connected by rail and thus being more receptive to signing treaties which would allow for railway lines to be built across German state boundaries. This in turn meant that there were new connections to major towns, capital cities and important trading centres. When the Cologne Minden Railway Company opened a rail bridge in Cologne in 1859, the German network was connected to the French, Belgian, Hungarian and Mediterranean rail networks.

Maturation and decline
New railways constructed in this era were railway lines which provided more direct services between major cities, rather than the circuitous rail links which were constructed previously and connected larger cities via the smaller towns along its alignment. Rail lines were also constructed to more rural towns to provide greater rail accessibility.

Changes in the political landscape, this time the establishment of the German Empire, lead to changes in the direction of the Germany railways. Following the unification of the German states to become the German Empire, there was a move towards having railway system as a state owned entity. Up until now, the various railway lines were built by private companies, or through state-owned companies. This meant that there was a mixture of different types of operators and operating and funding models. This was a result of the different German states each having different approaches to railway building. In particular, the states in southern Germany which built railway lines through their state-owned companies, while Prussia initially preferred private companies to construct their railways. However despite this, by 1871, several German states had started to operate their own railways. This included the Royal Bavarian State Railways, the Grand Duchy of Baden State Railways and the Royal Saxon State Railways. These state-owned railways were known as Landerbahnen. Following the end of World War I and Germany's defeat, the various state-owned railways were officially amalgamated to form the Deutsche Reichsbahn, a national state run railway company. This also lead to the consolidation of rolling stock and locomotives.

With the rising popularity of the automobile, like many railways around the world, the German railway system started to enter a period of decline. Construction rates for new railroads begin to fall and by the 1930s, railway lines which were unprofitable start to be closed. This trend continues until the end of World War II, where new railway technology aids in the revival of railways in Germany.

Today the German passenger railway system is widely successful, with 33 331 kilometres (2015) of railway line and carrying 200.6 billion passengers. Deutsche Bahn operates the majority of Germany's railways, with a variety of service offerings including InterCity Express trains, long distance high speed rail services, and the S-Bahn, its suburban train services.

Technological advances continues to provide opportunities for the reinvention of the German railway network. As high speed trains continues to increase in popularity as an alternative method of travel, Deutsche Bahn and their InterCity and InterCity Express trains offer options for high speed rail services between German cities as well as countries such as the Netherlands, Austria and France.

A Quantitative Analysis of the Lifecycle of German Railways
The lifecycle of the German Railways follows an S-Curve, similar to most other modes of transportation. The lifecycle of transportation follows three phases - a birthing phase, a growth phase and then a maturity and decline phase. Numerically, the lifecycle model can be represented by the following a three-point parameter logistic equation: S(t)=K/(1+e(-b(t-t0)) Where: S(t)= the predicted system size in year, t t = time (years) t0 = inflection point (midpoint) year K = saturation status level, and b = coefficient

Using this equation, as well as data collected of the length of railway track built in Germany from the period of 1835 to 1918, a lifecycle curve was graphed. Linear regression was used to find the value of K. The S-curve shows a comparison of the predicted kilometres of track built to the length of track actually constructed. While at first track length exceeds predictions, it starts to taper off around the midpoint. The S-curve shows the growth of railway track building since its birth, and has a similar inflection point to the actual data. It also heads into decline around 1918 which is consistent to what happened in real life, where the advent of new technologies and the automobile lead to decline in railway construction.

Because transport construction and growth is affected by the economy and economic policies of the time, an analysis of this S-curve is able to show the time period when economic policies were in favour of railway building and when this started to shift.

It should also be noted that the land boundaries of Germany at the time is different to modern day Germany, and the Germany at in 1918. Nevertheless, the data source for this lifecycle analysis has tried to keep the land boundaries consistent.


text: User:Ziv zhang usyd

title: User:Ziv zhang usyd


title: User:Zjw19971030


text:
Transportation Deployment Casebook/2023/China railway

The railway introduction
Nowadays, Chinese railways operate the largest high-speed railway system in the world and use cutting-edge high-speed train technology, such as the CRH series of rolling stock trains, which have a top speed of more than 350 km/h. The majority of China's railway lines are electrified, which increases train efficiency and lowers pollution. On Chinese railways, the electrification rate has surpassed 80%. Chinese railway signal and communication technology has undergone continuous improvement, and cutting-edge digital communication technology has been implemented to enable real-time communication between trains and dispatching command centers, ensuring the efficiency and safety of railway transportation. Chinese rail is superior to other forms of transportation in a number of ways. One of its key advantages is speed, which enables passengers to go between locations swiftly and safely. Further, it has a remarkable safety record and is a dependable and safe method of transportation. When compared to other forms of transportation like the air and road, the rail system can carry a sizable number of passengers while also being ecologically benign and energy efficient. The backbone of China's transportation infrastructure, China is the principal market for Chinese railways. Via the Belt and Road Initiative, a significant infrastructure project intended to link China with other nations in Asia, Africa, and Europe, it also serves worldwide markets. As an illustration, the CRH series of rolling stock trains have used cutting-edge lightweight materials, innovative braking systems, and energy recovery technologies to enhance train safety and energy usage efficiency. To ensure the smooth and safe operation of trains as well as to increase the stability of train operating speed, Chinese railways employ high-precision track technology.

The transportation mode before railway
Before Chinese railways were built, the major forms of transportation in China were waterways, horse-drawn carriages, camels, rickshaws, sedan chairs, bicycles, etc. There were also more basic light rail systems like rickshaw tracks and steam car tracks. These forms of transportation have a number of drawbacks, including sluggish speeds, low carrying capacities, poor safety, short travel distances, and restrictions according to the seasons and the weather. Due to the geography of China, a large amount of goods needed to be transported over long distances, and it was extremely inefficient to rely only on manpower or horse-drawn carts for large volumes of materials such as coal. China's coal fields were very unevenly distributed, especially between the north and the south, which was necessary for the establishment of railroads as a long transport mode of transportation. The need for transportation is rising quickly, and the market has been enhanced and extended as a result of China's fast industrialization and urbanization. People are interested in new transportation technologies and modes in this situation, particularly those that may boost transportation's speed, capacity, and efficiency.

The invention of railway
The Tangxu Railway, suggested by Li Hongzhang and built independently by the Chinese, began in 1876 and was inaugurated in 1888. Prior to being powered by steam, the railway was first pulled by horses and mules. The railway had a total length of 9.7 kilometers and had a rail spacing of 1435 millimeters. Subsequently, in 1909, Zhan Tianyou, a railway engineer, invented the herringbone railway as a solution to the height between Nankou and Badaling. The Chinese completed every step autonomously, including the design and construction.

The development of Chinese railways may be dated to the late 19th and early 20th century, when American and European railway building, and operation technology were adopted. Several various technological specialties, including mechanical engineering, civil engineering, electrical engineering, signal engineering, and communications engineering, were used to introduce train technology in China. The physical infrastructure, such as train tracks, tunnels, bridges, and stations, is designed and constructed by civil engineers. Locomotives and other rolling equipment are designed and constructed by mechanical engineers. Signaling and communication systems were created and constructed by electrical engineers. The routes, timetables, and logistics of the railway were planned by transportation engineers. The fast expansion of China's railways was made possible by the integration of these technological skills. In order to improve passenger transportation between China's main cities, the creation of Personal Dedicated Line started in the 1990s. The railways didn't utilize slab tracks previous to this. Due to its fast operation and high availability potential, slab track systems are drawing more and more interest for PDL architectures. Yet up until 2006, only short-distance tunnels or bridges utilize slab track in China. Just three slab track system types—prefabricated slab systems, integrated systems, and elastically mounted double-block sleeper systems—have been taken into consideration for practical implementation. On the Qinshen railway line, slab rails were used on the lengthy bridge for the first time in 1999. (Between Qinhuangdao and Shenyang). At a length of 404 kilometers, the line was completed and opened in 2003. The first freshly constructed high-speed railway line in China, this is an electrified double-track railway with a top speed of 200 km/h. The Chinese MOR has been transferring Slab track technology and know-how from Germany and Japan since 2005 to hasten PDL development. Two Chinese railway track types, CRTS I and CRTS II, were created as a result of the transfer of four slab track systems with two base forms (prefabricated slab tracks and bi-block sleeper tracks)

Early market development
The early market dates back to the Qing Dynasty before 1911. The first railway in China was built by the British in 1879, and the Chinese government built its own railway in 1881. At the start of the Second Sino-Japanese War between 1937 and 1945, most of the new lines were built in the Japanese-occupied northeast. The ensuing Chinese civil war from 1945 to 1949 led to delays in the construction of new railways and the destruction of many railways. After the founding of New China in 1949, the central government established planning standards for railway construction, emphasizing national integration by expanding the railway system. The first five-year plan was carried out from 1953 to 1957, and railways were mainly built in the northwest and southwest. From 1964 to 1978, more railroads were built in the Northwest and Southwest, areas safe from foreign invasion, known as the "Third Front of Defense". Between 1966 and 1976, due to the slow development of railways in China during the Cultural Revolution, only 8,500 kilometers of new lines were added. The focus of national transportation investment has shifted to the eastern coastal areas, and the development of railways has shifted from building new lines to increasing the capacity of existing lines in the north and east at the commencement of economic reform and open policy, that is, in 1978. In the mid-1980s, due to unbalanced regional development, the railway focused on the expansion and electrification of existing lines in shoreline areas, while the sources of railway funding became more diversified. China's railway network matured after the mid-1990s. The focus of railway development was to build new lines and upgrade existing lines in the western, northeastern, and central regions, thereby reducing regional inequality.

The birthing phase
At birthing phrase, China relied heavily on railways for freight and long-distance transportation. The development of railways is an important core for the formation of China's transportation hubs and economic belts and the development of urban systems. After the defeat in the Sino-Japanese War of 1894-1895, the Qing government ceded land and paid compensation, the invaders took the opportunity to put pressure on it, swayed China's railway rights and interests, and forcibly built them. According to their own needs, they designed and built a batch of railways respectively. The standards were different, and the equipment was messy, which caused the chaos and backwardness of China's railways in the early stage. Therefore, after the founding of New China in 1949, the government formulated policies for the integration of the railway system and standards for railway construction planning. These policies were ingrained in the birthing phrase of the railway and continued to shape China's railway system for decades to come. The policy of making railway development a national strategic priority is still in effect.

In addition to the railways operated by the central government at the time, there was a small network of state-owned local railways linking mines, farms, factories, and forest areas. The central government encourages the construction of these smaller railways, while the national railway system provides technical assistance when smaller railways can stimulate regional economic development.

The growth phase
From a historical perspective, the first "Five-Year Plan" policy's implementation era may have marked the start of China's railways' growth phase. The government placed a major emphasis on the development of the transportation system between 1953 and 1957, and more than 60% of infrastructural development RMB 901.5 million—went towards building railways. The trend chart readily demonstrates the tremendous rise throughout this time. Since then, the government's position has evolved, placing a higher focus on national security while developing railways. National security was increasingly crucial as a result of China cutting off diplomatic ties with the Soviet Union and the United States' involvement in the Vietnam War in the early 1960s.

According to the policy, line growth is mostly centered on "third-line development" areas, which include western mountainous Sichuan, Guizhou, and southern Shanxi provinces, as well as Henan, Hubei, and western Hunan provinces. The central government adopted the strategy of directing the development of the eastern coastal areas in the middle of the 1980s and moved the focus of railway expansion to promote economic growth. As another example, the Sanshui-Maoming railway was jointly constructed by local governments, foreign finance, and loans from international organizations. Hence, policies such as resource development, economic development, and national security play important roles in helping the rapid advancement of China's railways.

The mature phase
The mature stage of China's railways began after the 1990s. This stage is called the "corridor construction stage", and the main purpose is to strengthen the railway corridor. At this stage, the central government adopts a balanced development strategy to narrow regional gaps, focusing on areas with underdeveloped railways such as the west, northeast and central regions. During this process, China's railways developed rapidly, and railway construction opened a new era.

Moreover, since 2000, the Chinese government has vigorously promoted the construction of high-speed railways. The purpose of this initiative is to improve the speed and efficiency of the railway, support economic development and strengthen the connection between regions. In the following decades, China's high-speed rail network developed and expanded rapidly, becoming the largest high-speed rail network in the world. Up to now, China's railways have entered a mature stage, and the railway network has become completer and more efficient. As a result, market competition has become more intense, and aviation and automobiles have become popular modes of transportation. In order to adapt to the market, the railway system also focuses on improving efficiency and improving service quality to give passengers a better experience.

While adapting to the market, it is also limited by the lock-in effect of infrastructure and technology, because a large amount of capital has been invested in existing technology and infrastructure, which has added obstacles to re-innovation and the development of more efficient modes of transportation. Still, Chinese railways can be reinvented and built on new technologies like high-speed rail and maglev trains to become more efficient modes of transportation. At the same time, the innovative technology can also reduce the environmental pollution caused by the use of fuels, reduce energy consumption and emissions, so as to achieve sustainable development of future transportation.

Formula presentation
In order to plot the S-curve, the original data (passenger traffic) of China's railways from 1949 to 2021 were selected. by formula $$St=Smax/[1+exp(-b(t-ti)]$$

$$St$$ stands for passenger traffic

$$t$$ stands for year (1949-2021)

$$ti$$ is the year that $$1/2Smax$$ can achieve,

$$Smax$$ is $$K$$, which represents the saturation level and is the maximum passenger volume.

The setting of the $$K$$ value is to find the maximum value of the actual data and then add 10,000 to finally become 370,000, 380,000, 390,000 and so on.

$$b$$ is the slope,

In order to determine b and c it is also necessary to adopt the formulas，$$Y=bX+c  $$,  $$Y=\ln(passenger/K-passenger)$$, $$X$$ represents year

Through the formula, Calculate the values for each year and compare them. After that, determine K the value (Smax) by comparing the R square to find the largest R square. It can be seen from the data that when is 580000, the R square is the largest.

Interpretation of result
The graph indicates that the S-curve and the real data curve have an appropriate fusion. From around 1949 to 1957, when the People's Republic of China was just established, the main task was to manage the country's railway capital construction, and the curve was relatively stable. Over the ensuing decades, railroad construction grew steadily.

It can be seen from the chart that the trend of the curve is rising slowly, which may be the reason for the slow growth of passenger traffic due to economic downturn and other reasons. After 2003, due to the technological upgrading and innovation of China's railways, railway construction has reached a mature stage, and passenger traffic has also grown rapidly, exceeding the expectations of the S-curve. According to the model, half of Smax will be reached in 2027. Therefore, passenger traffic may continue to grow, but in 2020 and 2021, due to the impact of covid 19, passenger traffic will drop off a cliff, so the S-curve will not fit perfectly. China's traffic continues to grow, so the recession is not demonstrated in the graph.


text:
Transportation Deployment Casebook/2023/Saskatchewan Railway

Introduction
Saskatchewan is a province in western Canada with an estimated population of 1,205,119 as of 2020. Historically, the people here lived mostly by farming. The advent of the railroad promoted the development of agricultural civilization in the region and connected it geographically with the rest of Canada and the United States. In this case, the difficulties involved in developing transportation policies and solutions to those concerns can be examined by focusing on the life cycle of rail traffic.

Technological Characteristics
A wheeled vehicle that transports people and cargo along the track is called a railway, which the locomotive and carriages are guided by the track. Most modern wheels and rails are constructed of metal. There are typically more than two sets of carriages in rail transportation due to the metal wheels typically reduced friction resistance compared to rubber-tired wheels. A steam or diesel engine provides the propulsion when running.

Advantages
The railway is the dominant technology of the modern era also the representation of the development and assurance of modernity.

Transportation and Economy
First, it can move people and cargo more rapidly and cost-effective. According to Withuhn(2019), transportation prices per mile decreased tenfold and transit speeds improved tenfold as rail networks expanded across North America in the 19th century. Two million people were employed by the railways at a period of great prosperity. Additionally, almost all happenings in industry, mining and agriculture depend on the railway system. In the following nearly 100 years, it becomes to a significant national economic index indicator.

Community and Culture
Railway is necessary for both personal and professional travel, the sale of commodities, delivery, and mail. Individuals enjoy the items from the distant place in time and encourages interpersonal contact. Even across countries, regional ties have become deeper. In addition to fostering social connection, the railway also promoted cultural interactions. Lengthy train rides gave rise to new genres of literature and advertising.

Politics
As a symbol of the contemporary world, the significance of railroad is the effective fusion of equipment, labor, buildings, capital, transportation, and decision-making tools.

The shares, the intricate bureaucracy, and the multiple procedures imply that the railway is a driving force behind the development of the transportation system on a political and social level. Moreover, due to its networked nature, urbanization, suburbanization, nation-building, colonial exploitation, and global capitalism are all made possible.

Main Market
As an entity, the railway network has a firm grip on a nation. Revill (2013) claims railways serve as a sort of spatial dictature, and corporate profit-seeking is a form of feudalism with exploitative and coercive characteristics. For instance, the Grange Movement in the US in 1867 provided evidence of the scope and significance of the fight between farmers and the railways and territorial monopoly. Railroad supported in immigration, economy, and market relying on people. It was commonly accepted that Saskatchewan's wheat boom in 1896 depended on the expansion of the railway system.

Piror mode
In Saskatchewan, trails and waterways were the primary modes of transportation prior to the construction of railways. Waterways like the Saskatchewan River and its tributaries was commonly used and transporting via canoes and steamboats.

Trails offered another mode of mobility in Saskatchewan, which usually include native paths, buffalo trails, and explorer trails. Horses and cows were used as “engine” and connected with carts, wagons, and travois, for transporting.

Limitations of prior mode
Nature condition: The weather in Saskatchewan is comparatively extreme(Atlas of Alberta Railways, n.d.). It is situated at high latitudes and close to the middle of the continent, far from the ocean's moist and regulating impact. Therefore, the dry summer may restrict the traffic on waterways, while the cold winter may lead the river to freeze over.

Low carrying capacity: The amount of cargo is limited via ships due to holding space. The wagons and carriages are limited by the size of the road as well as the distance.

Invention of the railway locomotive
With the time and the progress of science and technology, railway locomotive types are divided into 3 classes, including steam, Internal combustion and electric.

Steam
Three essential parts constitute the steam locomotive: the boiler, the engine, and the carriage (G.D. Dempsey C.E & C.E, 2015). Their functions are to produce power, transform the power into traction, and transport freight and people, respectively. The machine is propelled by steam, which is generated inside and frequently receives injections of water and fuel. As water is turned into steam and expands significantly, the process provides usable energy. Thus, the goal in the design is to obtain as much power as possible from as small a machine as possible. The last part - the carriage, including the frame and wheels - provides stable conditions for working and running.

Internal combustion
Internal combustion locomotives are fueled to generate rotational power, which is transmitted to the wheels. The steam engine was unable to generate adequate power as productivity and demand increase. This led to the birth of the internal combustion engine. The benefits of the internal combustion engine, include:

 * High efficiency: refers to the percentage of fuel energy that is transferred to labour performed away from the steering wheel. An internal combustion locomotive achieves 25% efficiency, while a steam engine only achieves 8% (Franco & P. Labryn, 2013).
 * Reduced cost: Because internal combustion engines don't need to pre-heat the machine, they save cost on fuel and labour.
 * No water consumption: In nations with limited water resources, the purchase of water might be an extra expense.
 * The potential for long-distance travel: The power produced by the steam engine limitations make it impossible to travel more than 300 kilometers.

Electric
Electric locomotive, powered by electricity, that travels along a track through a conductor. Electric locomotives profit from the high efficiency with lower energy wasting. Without engines or exhaust pipes, there is less mechanical noise when electric locomotives operating. They produce short-term surge power for quick acceleration, therefore, is suitable for short commute. Moreover, renewable or low-carbon energy sources can powered such as solar and wind.

Market Development
First, technological improvement is a prerequisite for railway growth. Productivity significantly rose since the first industrial revolution. The first steam locomotive was created by Richard Trevithick and it became economically feasible for commercial usage after iterations.

Enhancing regional connectedness is the second. The Champlain St. Lawrence Railway (C&SL), an internal provincial railway, is the first railway in Canada in 1836. At that time, connecting the significant economic hubs on the mainland has been one of the railways' main responsibilities.

The growth of the railways and agriculture were interdependent, as was indicated in the wheat boom. The expansion of railways increased the possibility of transporting products, which fueled the expansion of agriculture.

Birth phase
The Qu'Appelle, Long Lake and Saskatchewan Railway (QLLS), which started operating in 1882, was the first railway in Saskatchewan. The federal government constructed the railway as a component of the Transcontinental line that connects eastern and western Canada (from Regina to Prince Albert with a subline to Fort Carlton). The Canadian Pacific Railway (CPR) finally took over the QLLS in 1885, because of a financial success. The route was extended by CPR and changed from narrow gauge to standard gauge, playing a significant role in the transcontinental rail network. The Canadian Northern Railway Corporation (CNR) was established in 1891 and started constructing railways in western Canada, including Saskatchewan.

The Canadian Parliament enacted the Canadian Pacific Railway Act of 1881 at the time. It served as the legal foundation to construct the Pacific Railway for the CPR because of significant financial and manpower requirements. The Canadian Pacific Railway Act of 1881 stipulated that to assist the building of the railway, the government would provide the CPR a sizable piece of land, financial gifts, and advantageous tax status. Also, the government imposed other requirements including a deadline of building and service. Through this act, a strong support is provided for the construction of national railway, and also promoted the Canadian economy and national unity.

Growth phase
The main line of Grand Trunk Pacific Railway (GTP) was finished in 1910, opening up a second transcontinental railway route through Saskatchewan. After 2 year, the Saskatchewan Grain Growers Association was established by the government to promote improved rail rates and services for farmers. The Saskatoon Municipal Railway, the first urban railway in the province, started running a streetcar system in 1913. Over a tenth of the 2,266 miles of track the CPR constructed between 1923 and 1931 were in Saskatchewan grassland.

Although Parliament had never implemented any legislation that directly impacts tolls, it is essential that freight rates for grain exports from western Canada in the transportation aspect. The reason might be because following the Second World War, the overall reliance on wheat declined as mineral, forestry, and fisheries resources were exploited in Canada. Wheat, the economic backbone of Saskatchewan, was less impacted by rail charges.

Nonetheless, there were still discrepancies and disagreements about railway fees between the CPR, farmers, and the government, as the conflict between the public and private sectors. For instance, the Canadian government imposed Crow's Nest rates on the export of wheat crops to the east. The rising cost of operating the railroad and the new tariffs meant that CPR faced a loss of revenue (Currie, 1967), and farmers would have to pay the freight. Even though Crow's Nest prices were eliminated in 1919, Western farmers asked for the right that reduced train rates and improved service especially in the era of The Great Depression. It was not until 1933 that the federal government established the Canadian Wheat Board.

Mature phase
The railway sector developed throughout the following two to three decades, until 1950s. Railway industry decreased as the industry of cars and trucks rose. In Saskatchewan, railway branches started to disappear practically as soon as the final line was constructed. Both Canadian National Railway (CNR) and Canadian Pacific Railway (CPR) asserted that running several branch lines depending on the grains was a loss-making endeavor. The Robson Commission was established by the federal government, allowing railways to sever all 525 miles (845 km) of expensive branch lines. More than 1,450 miles (2,333 km) of branch lines were abandoned during the following five years, with half of those abandonments taking place in Saskatchewan.

Also, there was a union and job issue. In 1860s, the Railroad Brotherhood was established to represent workers. Strikes in June and December 1883 were caused by the miserable living and working conditions in the mobile camps, low income as well as the intense job demands. Moreover, the greatest strike in Canadian history occurred in 1950 when 130,000 railway employees went on strike against the CPR and CNR.

Re-invent phase
The development of the railway system took a new turn in 1995. To provide rural villages and resource development initiatives with rail connectivity, the Hudson Bay Railway started operating in northern Saskatchewan. The revival of railways has also been seen in the world. Substantial money has been spent on upgrading the rail infrastructure, particularly on building high-speed train lines. The trains are more competitive due to air network high-capacity and road network congestion. In addition, investment in railways becomes a tool to lower carbon dioxide emissions because of rising fuel prices and global warming. The re-invention of railway provide an opportunity for the cities with mature urbanization.

= Quantitative Analysis = According to data provided by Statistics Canada, the railway industry length of track operated at the end of the year, the estimation of a three-parameter logistic function is below.

Formula
Three-parameter S-curve logistic function:

S(t) = Smax/[1+exp(-b(t-ti)]

where,

S(t) = State Measurement (operated length of track in km)，

t = time (in years)，

t 0 = inflection point time (the year in which half of S max is obtained)，

S max = saturation level (maximum operated length of track in km)，

b = the coefficient to be estimated.

Ordinary Least Squares Regression:

Y = bX + c

where,

Y = LN(length/(K-length)),

X=Year.

Calculation and Discussion
Firstly, the maximum value is selected from the data of nearly 200 years, which is 96958 km in 1974. On this basis, we increased to 100000 km as the S max, and increased by 10000 each time for 20 iterations. finally, the y value is calculated. In 20 iterations, the maximum RSQ value and the best model fitting degree are selected. The predicted curve of change is calculated according to this value. The result is shown below:

As can be clearly seen from the chart, the rapid growth of railway in the first two decades of the 20th century. It then took more than half a century for it to mature and gradually decline until 2020. This is a little bit different from the expected curve.

'' The Quantitative Analysis in Canada is due to the lack of data in Saskatchewan, which cannot show the life cycle of railway. However, the existing data also illustrated in the appendix. ''

= Reference =

 * Atlas of Alberta Railways. (n.d.). Atlas of Alberta Railways -- The Canadian Pacific Railway. Railways.library.ualberta.ca. https://railways.library.ualberta.ca/Chapters-7-1/
 * Bruinsma, F., Pels, E., Priemus, H., Rietveld, P., Bert Van Wee, & Springerlink (Online Service. (2008). Railway Development : Impacts on Urban Dynamics. Physica-Verlag Hd.
 * Canada. Dominion Bureau of Statistics. Railway transport. Ottawa.
 * Currie, A. W. (1967). Canadian Transportation Economics. University of Toronto Press.
 * Encyclopedia Of Saskatchewan. (2020). The Encyclopedia of Saskatchewan | Home. Uregina.ca. https://esask.uregina.ca/home.jsp
 * Floca, B. (2013). Locomotive. Atheneum Books For Young Readers.
 * Franco, I., & P. Labryn. (2013). Internal-Combustion Locomotives and Motor Coaches. Springer.
 * G.D. Dempsey C.E, & C.E, C. (2015). The Victorian Steam Locomotive (pp. 1–54). Wharncliffe.
 * Government of Canada, S. C. (2022, February 9). Profile table, Census Profile, 2021 Census of Population - Saskatchewan [Province]. Www12.Statcan.gc.ca. https://www12.statcan.gc.ca/census-recensement/2021/dp-pd/prof/details/page.cfm?DGUIDlist=2021A000247&GENDERlist=1&HEADERlist=0&Lang=E&STATISTIClist=1&SearchText=Saskatchewan
 * Revill, G. (2013). Railway (pp. 8–114). Reaktion Books.
 * Statistics Canada. (2023). Historical statistics of Canada: Section T: Transportation and Communication. Www150.Statcan.gc.ca. https://www150.statcan.gc.ca/n1/pub/11-516-x/sectiont/4147444-eng.htm#1
 * Transport Canada. (2021). Transportation in Canada 2020 - Overview Report.
 * Withuhn, W. L. (2019). American Steam Locomotives. Indiana University Press.

= Appendix = Railway industry length of track operated at the end of the year in Canada. (1835-2020)


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