# Introduction of streetcar system

'Streetcar' (also called 'street railway' or 'trolley') is a means of local public transit which use vehicles that run on rails (RPR Consulting, n.d.). It used to be the mainstream public transit mode in over one hundred cities of North America in the early-20th century. Streetcars can be either designed to run in a shared lane with other traffic, or they can be designed to have dedicated right-of-way. Early streetcars were usually horse-drawn, then electric-driven had gradually become the common source of power.

## Main advantages

With the completion of electrification and the gradual maturity of streetcar technology, the advantages of the system have gradually become significant. One of its biggest advantages is its ability to provide relatively convenient, comfortable, reliable, fast-speed and high-capacity public transport services (James, 2019).
In terms of convenience, the train needs to run on the track, so the operating route is fixed. Since many streetcar systems did not set fixed stations during the earliest operation, a passenger could ride on a streetcar anywhere there was a track (Eppinga, 2015).
In addition, as the streetcars run on the track, compared to the horse-drawn car, the electric-driven streetcars can run more smoothly, providing a more comfortable ride experience for passengers.
Regarding the capacity and speed, electrified vehicles obviously have faster driving speeds and higher capacity than horse-drawn carts. Because of these advantages, the streetcar system at the time was considered the most advanced and fashionable mode of travel in the US. Streetcar was blooming since the 1880s (Stromberg, 2015).

## Main market

Due to the above-mentioned advantages, the streetcar system was dominating the public transport market in most of the main cities in the US. Its market expansion is highly coordinated with the urban sprawl of the metropolis. Large quantity of citizens began to move from the crowded city centre to the suburbs and took a streetcar to the downtown for commuting, or to a market centre for shopping (Bell, 2017). This is also very similar to the current market characteristic of a modern rail transit system.

# Before the age of streetcar

Before the birth of the streetcar, most of the cities in the US were walking cities (Smithsonian Institution, 2017). The scope of activities, such as working or shopping, was usually limited within the walking distance of the residents. Equipped with abundant infrastructure, residents would live as close as possible to a city centre. The inconvenience of long-distance travelling limited the development of the city, and the city centres became over-crowded and unsuitable for living (Bell, 2017).
There were some attempts to use horse-drawn or mule-drawn carriages to provide public transport services in the 1800s, before the electrification of streetcar system (Geels, 2005). Other types of motive power tried in the early US includes steam dummies and cable cars. Although the carriages ran on a track, such kinds of dynamics cannot meet the demand for a high-speed, mass-capacity public transport service (Siemens, n.d.). In addition, the illness of the animals would also affect the stability of the system.

# The intervention of the mode

The invention of the streetcar system comprised the technological expertise of electricity and rail transit. Ever since 1835, there were efforts for applying electric traction for railroad (Locomotive, n.d.). In 1879, Siemens and Halske presented an electric-driven locomotive at an exhibition in Berlin, which marked the first successful application of electric traction (Siemens, n.d.). Two years after the exhibition, Siemens built the world’s first electric railroad in Berlin with a total length of 2.5 kilometres.
Efficiency of transport was redefined by electric locomotives. Even in the modern era, there is no other type that can match the low operating costs and high tractive efforts provided by electric locomotives (Electric Locomotives (USA), n.d.).

# Lifecycle of streetcars in Arizona (1887-1948)

Streetcar services in Arizona was mainly distributed in Phoenix. The operation of Phoenix streetcar system began in 1887, and terminated in 1948 (Eppinga, 2015).

## Early market development (1887-1895)

The Phoenix streetcar system was the first public transit system in the state of Arizona. 1887 was the birth year of Phoenix streetcar (City of Phoenix, n.d.). Moses Hazeltine Sherman was the operator of the streetcar. At that time, he was an outstanding member of the community and an investor in real-estate. A business franchise was granted to him by the city, and in order to seek a breakthrough in his business, he developed the streetcar system.
At the beginning, the streetcars in Phoenix were horse-drawn or mule-drawn. It was not until 1893 that the first electric-driven streetcar in Phoenix was put into operation. By 1895, animal-drawn streetcars were all eliminated, the Phoenix streetcar system had completed its electrification process (The Phoenix Trolley Museum, 2014). By that year, the total length of track was 10 miles.
During the early market development, no fixed stops were designed, and passengers could get on and off the streetcar anywhere there were tracks. Therefore, more residents along the route could experience the convenience of the service. As expected, the boundary of Phoenix was expanded, and Sherman’s business was boosted.

## The growing phase (1896-1920)

The length of track of Phoenix streetcar grew from 10 miles in 1896 to 32.5 miles in 1920.
Although the total mileage tripled in these years, the market growth was not smooth. In 1910, a fire accident destroyed the car barn and some of the streetcars. In 1913, employees of the railway company went on a strike. Many residents participated in the strike and boycotted the streetcar operation. Sherman’s company began to decline, and revenue of the streetcar system ran short. The company faced the problem of high maintenance cost.

## The mature and decline phase (1921-1948)

Since the early 1920s, patronage stats began to decline. The system was under deficit. Unable to afford the operating expenses, in 1925, Sherman sold the company to the City of Phoenix at a price of $20,000. Since then, the operation of the streetcar had changed from private to public. Soon in 1927, a bond of $750,000 was invested for the renewal of the system (The Phoenix Trolley Museum, 2014).
However, the rapid development of automobiles started changing the way people travel. The streetcar system cannot match for the convenience of the automobile, and because of the complain of the noise, streetcars were gradually replaced by the diesel buses. The Great Depression from 1930 to 1932 accelerated the decline of streetcar. The tracks were gradually removed. In 1948, the streetcar services were ended in Phoenix.

## The reborn of rail transit in Arizona

In the modern era, the traffic congestion in metropolis caused by automobiles calls for the return of mass-capacity public transit systems. The operation of Valley Metro, a modern light rail system, marked the new era of rail transit in Arizona (Valley Metro, 2017). Now it is the 14th busiest light rail system in the US.

# Quantitative Analysis

'McGraw Electric Railway Manual – the red book of American street railway investment' provided the track mileage data of all the streetcar systems in the US between 1894 and 1920. Table 1 shows the length of tracks of each streetcar system in Arizona in that period:
Table 1: Length of tracks (miles) in Arizona
| Year | Miles of track | Miles of track | Miles of track | Miles of track | Miles of track | Miles of track | Total |
| Year | BISBEE | DOUGLAS | PHOENIX | TUCSON | PRESCOTT | WARREN | Total |
| 1894 | | | 10 | | | | 10 |
| 1897 | | | 10 | | | | 10 |
| 1898 | | | 10 | | | | 10 |
| 1899 | | | 10 | | | | 10 |
| 1900 | | | 10 | | | | 10 |
| 1901 | | | 10.5 | 2.5 | | | 13 |
| 1902 | | | 11 | 2.5 | | | 13.5 |
| 1903 | | | 11 | 5 | | | 16 |
| 1904 | | 3 | 11 | 5.5 | | | 19.5 |
| 1905 | | 4 | 12 | 5.5 | | | 21.5 |
| 1906 | | 4 | 14 | 5.5 | | | 23.5 |
| 1907 | 5 | 9 | 14 | 5.5 | | | 33.5 |
| 1908 | 8 | 10 | 14 | 5.5 | | | 37.5 |
| 1909 | 8 | 10 | 14 | 5 | | | 37 |
| 1910 | 8 | 10 | 16 | 5 | 2.5 | | 41.5 |
| 1911 | 10 | 10 | 30 | 5 | 2.5 | | 57.5 |
| 1912 | 10 | 10 | 30 | 5 | | | 55 |
| 1913 | 10 | 10 | 27 | 5 | | | 52 |
| 1914 | 8 | 10 | 30 | 5 | 2.5 | | 55.5 |
| 1917 | | 10 | 32.5 | 5 | | 6.7 | 54.2 |
| 1918 | | 10 | 32.5 | 5 | | 6.7 | 54.2 |
| 1919 | | 10 | 32.5 | 5 | | 6.7 | 54.2 |
| 1920 | | 10 | 32.5 | 5 | | 6.7 | 54.2 |

## The S-curve regression model

In this quantitative analysis, S-curves (status vs time) is used to analyse the lifecycle of the streetcar system in Arizona. A three-parameter logistic function will be estimated:
$S(t)={\frac {K}{1+e^{-}b(t-t_{0})}}$
where:
$S(t)$ is the status measure (i.e. miles of track),
$t$ is time (in years),
$t_{0}$ is the inflection time (year in which ${\frac {1}{2}}K$ is achieved),
$K$ is saturation status level,
$b$ is a coefficient,
$K$ and $b$ are to be estimated.
Due to the quality of the analysis, the length of track in each system in Arizona are aggregated to get the sum value of the miles of tracks in the state in each year. First, the saturation status is estimated as 80 miles. According to the test, the highest R square is acquired when $K$ is set to 80, meaning that the model has the best goodness of fit, as is illustrated in Figure 1:
Next, the regression analysis is applied. The result of the regression is as follows:
Table 2: Regression statistics
Regression Statistics :
| Multiple R | 0.950555275 |
| R Square | 0.903555331 |
| Adjusted R Square | 0.899171483 |
| Standard Error | 0.355415504 |
| Observations | 24 |
Table 3: Regression Results
| Variable | Description | Value |
| $K$ | Saturation Status Level | 80 |
| $b$ | Coefficient | 0.150465541 |
| $t_{0}$ | Inflection time | 1911 |

## Interpretation

The R square of the model is 0.9036, meaning that the model has an excellent goodness of fit, 90.36% of the value of miles of track in the state can be explained by the corresponding year.
The P-value of the independent variable (i.e., year) is less than 0.01, meaning that the years as the independent variable in this model are statistically significant in predicting the miles of tracks in that corresponding year.
From the regression model, it is predicted that the mileage of the streetcar system in Arizona would maintain its growth trend before reaching 80 miles, the saturation status level. 1911 would be the inflection year, where the miles of track would reach 40 miles. Subsequently, the growth rate would slow down. This is in line with the actual growth trend.

# References

Bell, R. (2017). How Cities Are Embracing Streetcars Once Again. https://www.metro-magazine.com/10002970/how-cities-are-embracing-streetcars-once-again
City of Phoenix. (n.d.). History of Public Transit in Phoenix. Retrieved 22 March 2021, from https://www.phoenix.gov:443/publictransit/about/history-of-public-transit-in-phoenix
Electric Locomotives (USA): Trains, Manufacturers, History. (n.d.). American-Rails.Com. Retrieved 23 March 2021, from https://www.american-rails.com/electric.html
Eppinga, J. (2015). Phoenix's First Light Rail System. Arizona Capitol Times. https://azcapitoltimes.com/news/2015/01/30/phoenixs-first-light-rail-system/
James, O. (2019). We miss streetcars' frequent and reliable service, not streetcars themselves. Mobility Lab. https://mobilitylab.org/2019/04/17/we-miss-streetcars-frequent-and-reliable-service-not-streetcars-themselves/
Locomotive. (n.d.). Encyclopedia Britannica. Retrieved 23 March 2021, from https://www.britannica.com/technology/locomotive-vehicle
RPR Consulting. (n.d.). USA Streetcar Systems. Retrieved 23 March 2021, from http://www.railwaypreservation.com/vintagetrolley/vintagetrolley.htm
Siemens. (n.d.). On track – Siemens presents the world's first electric railway [Newton_company-content]. Siemens. Retrieved 23 March 2021, from https://new.siemens.com/global/en/company/about/history/stories/on-track.html
Smithsonian Institution. (2017). A Streetcar City. National Museum of American History. https://americanhistory.si.edu/america-on-the-move/streetcar-city
Stromberg, J. (2015). The real story behind the demise of America's once-mighty streetcars. Vox. https://www.vox.com/2015/5/7/8562007/streetcar-history-demise
The Phoenix Trolley Museum. (2014). A Brief History Of Public Transportation in Metro Phoenix. https://web.archive.org/web/20140829025756/http://phoenixtrolley.com/history/history-of-transit/
Valley Metro. (2017). About Valley Metro. Valley Metro. https://www.valleymetro.org/about/overview