# Transportation Deployment Casebook/2018/The Growth of the Automobile - The United States from 1900-1995
## Qualitative
### The Mode of Automobiles

The automobile is a technology that has spread all across the world and it can be said with fair certainty that the world would not be the same place without them. Automobiles can be seen in nearly every city in the world and are such a common part of life that there are currently 1,282,270,000 vehicles in the world as of 2015 , approximately one vehicle per six people living on the planet, and these numbers are only expected to grow. An automobile is defined as a four wheeled vehicle that is powered by an internal engine , and they can be used for a wide variety of purposes that mainly include the transportation of people and goods.

#### Technological Characteristics

The main piece of technology that an automobile requires is an engine that is powerful enough to move the vehicle. In modern times, this is typically achieved by using an internal combustion engine that runs by burning a fuel – typically petrol and diesel – to provide the energy required for movement. However, in the early stages of development of the automobile there were other alternatives, one of these being the steam engine which has also been proposed in modern times as a more environmentally friendly alternative to these combustion engines in times as recent as the 1970’s. The other main engine type is the electric engine, which formed a significant part of the market in the early developmental stages of the automobile until it was pushed out by the ultimately more successful combustion motors. However, electric powered automobiles are becoming more popular in modern times as society becomes more attuned to environmental issues.
The other significant technology allowing the function and use of the automobile is not found on the automobile itself, but rather is the roads that these vehicles drive on. Roads had been around for millennia prior to the invention of any automobile, however properly functioning roads of a high quality were, and remain, necessary to the function of automobiles. This was especially true of the early automobiles. With these new heavier vehicles roads had to be strong and tough enough to withstand these increased loads without damage , as if roads weren’t of a high enough quality then they would be damaged and so become unusable for future travelers, severely restricting the capabilities of these new automobiles. In 1906 the Stanley Rocket automobile first exceeded contemporary rail speed records, achieving a speed of 127.66mph. The fact that these vehicles were also able to travel at higher speeds than the previously existing transport technologies meant that roads also needed to be smooth to ensure traveler comfort; with limited suspension in early automobiles, uncomfortable travel would likely have resulted in the collapse of the industry.
These are merely two examples of technologies that were required for the automobile to take off, many more exist that are both components of the automobile itself and a part of its surroundings. These technologies could be both hard and soft as well.

#### Advantages of the Automobile

The automobile provided a considerable advantage over other modes of transport that already existed. One was the combination of the ease of use and the range of this technology. Automobiles could travel further than a horse or cart without stopping and also did not require any rest between ‘recharges’ as did using animals for transport. This meant that they could be used for a wide range of applications. Automobiles were also remarkably convenient, giving them an advantage over similarly powered technologies such as trains as they could be used at any time to go anywhere, pending the availability of a road. This made them very convenient to use and would have contributed greatly to their popularity. Another advantage is that they were relatively powerful, meaning that they could be used to transport loads that similarly sized transport modes could not . They were also very easy to use, making them particularly popular with women of the time who did not have to handle a powerful team of horses, such as in a carriage or cart, and this was especially true of the early electrically powered automobiles .

#### Initial Markets

The initial market for automobiles was the wealthy, those who could afford an expensive new technology, and especially those who already used carts and carriages on a regular basis, meaning that many of the early models were designed off contemporary carriage models . This is as these individuals had the most to benefit from this technology, as it would have allowed them to travel more efficiently than previously and so improve their lives. As they became more widely available and affordable, especially through the advent of mass production of automobiles, the market began to expand to include all members of society who valued being able to travel at their own convenience.

### Before the Automobile

Horse drawn vehicles were the most popular means of short distance point to point transport prior to the invention and deployment of the automobile. There were hundreds of variations that existed, including, but by no means limited to: buggies, carts, carriages, omnibuses, cabs, flies, and wagonettes. These would have been found throughout all cities around the world and in most rural areas as these were the simplest and easiest forms of transport that were local and easy to use. However, the fact that these methods were both hard to use and hard to maintain meant that an alternative to horse drawn technology was needed to continue the improvement of transport throughout the world.
Horses themselves were also still used. Beyond merely being ridden from one location to another as a form of personal transport, they were crucial in other forms too. They were the power behind all horse drawn vehicles as well as some of the early trains, although by the time of the automobile they had typically been replaced by steam engines. Horses were also used for agricultural purposes in this time, although steam powered machines were beginning to be used to a far greater extent than previously. The main disadvantage of horses was that they were not as powerful and could not travel for as long as automobile; the addition of their defecation on roads also added an unpleasant aspect to busy and crowded streets. An alternative was needed.
Rail was the main mode in the mid to late 19th century to travel and transport freight across large land distances, and still remains an important technology today. However, rail requires significant amounts of infrastructure to be in place before it can be used, and as such this means that rail is not a convenient form of transport. Although good for long land distances, it was not good for travelling to more isolated locations without rail infrastructure. Also, the increased demand for personalised transport meant that trains could only serve a limited purpose due to their restrictions on servicing and destinations, meaning that other transport modes needed to be used in tandem with trains in order to create an effective and efficient trip.
Ships were the other main form of transport in the late 19th and early 20th centuries, however they had a very different role to most of the other forms of transport at that time. They were used mainly for freight over short distances, but also for any kind of travel over very long distances where trains were not convenient. For example, all cross-ocean travel was done via large ships, however this is clearly not applicable to automobiles and so provided little competition or interaction with the majority of the automobile industry.
In this time, an evolving new market was developing. A new, rising class of middle class white collar workers were emerging to form a new market for a new transportation technology . The automobile was developed in a market dominated by horse drawn vehicles, however people had begun to imagine of the great distances that they could travel in a day rather that the regular travel requirements they might have . As a result, the market for the automobile was growing.

### The Invention of the Automobile

The invention of the automobile is a contested topic, as many individual inventors came up with a range of designs, often independently, however the German Karl Benz is one of those who is most often attributed to making a significant contribution to the development of the automobile. In 1885 he invented the first gasoline powered vehicle ; a three wheeled automobile that was powered by an internal combustion engine. However, this was by no means the first, and certainly not the last, model of the automobile that was made in the early stages of development, as individuals kept on creating and improving on automobiles up until modern times. By the early 19th century, certain trends were appearing in most automobiles that was due to the beginning of the standardisation of the technology.
The automobile drew from many other technologies of the time, as well as those that were around earlier. Perhaps the most significant of these was the bicycle, the development of which laid the foundations for the invention of the automobile. This was as bicycles also used technologies such as pneumatic tyres and ball bearings while also giving the skills required to manufacture automobiles to many mechanics and engineers, many of whom learnt the basis of their trade through working on bicycles. The development of the road system was also largely down to riding groups, literally paving the way for the automobile. The other main technology that was crucial in the development of the automobile was the horse drawn cart, as this formed the main principle behind the design and concept of an automobile. In fact, many of the early models of automobile were designed off contemporary horse drawn vehicles .
The main early changes that happened with automobile design was the means of providing power. The very first designs often included steam, however these were considered dangerous and were also less powerful than other alternatives, and so were quickly phased out. The competition between electric and internal combustion motors however was fierce during the first decades of the automobile. Both had their advantages and disadvantages over each other, but the internal combustion engine won over as it was more powerful and could be more easily refueled than the batteries of its electric competitors.

### The Early Market

The initial market for automobiles was the direct replacement of the old market of those seeking to buy and use horse drawn vehicles. This is as these people were the ones with both the capital required to make an investment into this new technology, but also those who had the need for this technology. The other main use for these new automobiles was as taxis. As the technology was initially quite expensive it did not make sense for most people to purchase one for themselves, and so taxi services, usually utilising electric powered automobiles, sprang up to service the needs of the population at large.
This initial market did expand, and this was largely down to the work of Henry Ford and the creation of the first mass produced cars, the Ford Model T. This meant that automobiles became widely available for the first time and as such this led to an expansion in the market. No longer were automobiles a luxury for the rich, they had become a necessity for the working class citizen. By the mid 1910’s, the automobile had grown from a market of the rich to a market of the many.

### The Role of Policy

The main policies that were placed on the automobile were initially identical to those that were placed on horse drawn vehicles, as automobiles were still very much an emerging technology that was not yet widespread they did not need extensive regulation, especially since the earliest models could travel at a maximum speed similar to those of a horse. Essentially, the only restrictions placed on automobiles during those early years of development were the dimensions of the streets they would be run on.
With the development of automobiles came greater regulation, and this was due to a variety of factors, the main one being the speed at which they could travel. The fact that automobiles began to travel at relatively high speeds meant that the danger of both driving them and being around one had significantly increased. As such, in 1901 Connecticut introduced the first speed limit, restricting drivers to 12mph within their cities and 15mph on rural roads. These laws were later followed by other states and other countries in the world as it was identified that these automobiles could be potentially very dangerous. Further safety laws followed, evolving until finally reaching the modern levels of safety laws we have today.

### The Growth of the Automobile

The growth of the automobile industry can be attributed to a number of factors that came from a range of spheres of influence. One of these was the crucial role that the private sector played, particularly in the continued innovation it displayed in regards to the automobile. Individuals and corporations continued to develop new automobiles that became more powerful, more efficient, and easier to operate, increasing the ease at which individual consumers were able to purchase these new models. An improvement in design naturally led to demand, and so continual improvements in the design of automobiles continued to grow the industry.
Perhaps the most influential private group responsible for the growth of the automobile industry was the company Ford, led at the time by its founder Henry Ford. Ford is the individual who first mass produced automobiles, which was an extremely significant step in the growth phase of the automobiles life. This is as by mass production of these vehicles, the cost of purchasing an individual automobile was significantly reduced. This in turn meant that they became significantly more affordable and so resulted in an increase of demand. This fluctuation was made especially clear when Ford had to stop taking orders for new vehicles for nine weeks so that his company could catch up on the backlog of orders that had accumulated. By introducing the concept of mass production to automobiles, Henry Ford significantly accelerated the growth of the automobile industry.
One of the other ways in which the growth of automobiles was ensured was through the amalgamation of the many automobile manufacturing companies that existed in the early stages of the technology. In 1904 there were 241 automobile manufacturers in the U.S. most producing only a few vehicles each, which dwindled to 44 about a decade later. The merge of many of these companies, and collapse of others, allowed for greater efficiency in the production of automobiles and so contributed to the growth of the industry.
The role of patents did not play an overly significant role in the development of the automobile, however patents were applied for and granted. One of the most notable of these was granted to George Seldon in the U.S. for the design of his internal combustion engine for use in a four wheeled car. This was only granted in 1895 however, and many other versions of the combustion engine had been invented and so this patent did not have a significant affect in limiting innovation. However, his patent was contested by Ford and four other manufacturers in 1911 where they deemed that the patent ruled only over a certain type of engine, allowing the extensive use of any other kind of engine free of royalty charges. Fords comments in this case included: "It is perfectly safe to say that George Selden has never advanced the automobile industry in a single particular...and it would perhaps be further advanced than it is now if he had never been born." Suggesting that this patent did in some way restrict the growth of the automobile industry, but mainly due to the fact that the owner of the patent did little to continue to develop the technology.
The other aspect of improving the market for the automobile was the continued development of road systems. As roads continued to be improved throughout the world for a variety of reasons, the use of automobiles was extended as they were able to reach new locations in quicker times. This meant that the demand for automobiles increased, further fuelling the growth of the automobile.

### Continued Development

As the automobile enters the mature phase of the market, there is one change that is being made that is more significant than any other: the gradual switch from combustion engines to electric engines. This change has been initiated by the greater awareness of the effect of the release of harmful emissions from combustion engines and the continued harm that that is doing to the environment. This change is being made as people understand that these electric motors release less harmful emissions than combustion engines, and so are gradually being phased in as the main propulsion technology in motor vehicles. This technology is still a long way from being completely developed and fully introduced, however it is well on its way. The main aspect of the automobile industry that is involved in continued development is the racing industry, where competing teams always seek advantages over other competitors. This leads to continuous development of vehicles and their components in order to make them more powerful, lighter, faster, and safer. Many of these design improvements are then passed down to the commercial industry to be put in place in standard consumer vehicles.
However, the current market is very much locked into the current conditions and restraints of the automobile. The highway and road systems of most parts of the developed world are completed, and so the accessibility that the automobile provides is very rarely being extended. Many of the laws regarding the regulation of automobiles, such as speed limits, have been in place for extensive periods of time in order to improve safety, and so continual development in areas such as the speed of vehicles will have very little impact in a commercial sense, as these improvements are not as desirable for consumers as they once were.

## Quantitative Analysis

In order to determine how widespread the use of automobiles is in the world, it was decided that the focus should be on the number of vehicles owned, as this gives a good indication of the number of people or households who use them and so an indication of their popularity. To focus on this, data used in this analysis involves the number of automobiles registered in the United States.

### Acquisition of Data Values

The study into the number of automobiles in the United States was conducted using data from the United States Department of Transport, obtained from the Federal Highway Administration (FHWA). The FHWA’s role is to administrate the construction and maintenance of the Federal Highway system in the U.S. as well as conduct research in regards to this system in order to provide assistance to local and state agencies as they seek to maintain stretches of their own roads.
The data for this analysis was sourced from the State Motor Vehicle Registrations by Year (1900-1995), and is taken in this study to be a representative figure of the number of automobiles in the United States during each of those years. This data is represented in the plot below.

### Derivation of the Equations

The analysis for the data that was gathered in this study was intended to fit a model that is dictated by the following equation:
S(t)= K/(1+ e^(-b(t- t_0 ) ) )
This three parameter logistic function uses the following parameters:
* S(t) is the number of vehicles in the U.S.
* t is time (years)
* t0 is the inflection time (year in which 1/2 K is achieved),
* K is saturation status level,
* b is a coefficient.
Where K and b are estimated using curve fitting techniques.
The exact values of K and b were determined by transforming the model equation into the form of the below equation;
y=bx+c
Where the values in this equation are derived from the original model equation as:
* y = ln⁡(S(t)/(K-S(t) ))
* b = b
* x = t
* c = bt_0
In order to determine the values of these parameters, first a range of K values were estimated. These K values were then used along with the existing values of S(t) from the data set with the aim of achieving a value of y = 0. This y value would arise when ln(1) = 0, which occurs when the predicted number of the model matches the actual number that the data has measured for the value of S(t). This means that ideally the K value would return a value of y = 0 for each data point.
The accuracy of these estimations of K were determined using the r squared value for these lines, a measure of the accuracy of a set of data in its correlation to another set. An r squared value of 1.0 is desired as this implies a perfect correlation, however this value is rarely achieved and so a number close to this is acceptable.
Once the optimal K value has been determined, the values for b and c can be determined. The b value can be found by a simple gradient check of the line generated with the specific K value, as this is physical representation of this value within the data. C can be found by first finding the intercept of the data with the y axis of the plotted data, and then by dividing this value by the now known b value, t0 can be found.
To determine each of these values, an excel spreadsheet was used along with the correlating functions for each of the tasks.

### Results of the Model

From the analysis, the following parameters were determined:
| Parameter | Value |
| b | 0.0815 |
| t nought | 1971 |
| K | 180,000,000 |
These were finalised with an r squared value of
r^2= 0.871
This value of r squared was chosen as it was the highest out of all the generated data sets, meaning that it corresponds to the model with the greatest accuracy.
The final values that were projected by the model are displayed in the table below:
| YEAR | TOTAL NUMBER OF AUTOMOBILES | PROJECTED NUMBER |
| 1900 | 8,000 | 550,677 |
| 1901 | 14,800 | 597,281 |
| 1902 | 23,000 | 647,816 |
| 1903 | 32,920 | 702,609 |
| 1904 | 54,590 | 762,018 |
| 1905 | 77,400 | 826,426 |
| 1906 | 105,900 | 896,251 |
| 1907 | 140,300 | 971,944 |
| 1908 | 194,400 | 1,053,991 |
| 1909 | 305,950 | 1,142,921 |
| 1910 | 458,377 | 1,239,302 |
| 1911 | 618,727 | 1,343,749 |
| 1912 | 901,596 | 1,456,928 |
| 1913 | 1,190,393 | 1,579,554 |
| 1914 | 1,664,003 | 1,712,404 |
| 1915 | 2,332,426 | 1,856,310 |
| 1916 | 3,367,889 | 2,012,173 |
| 1917 | 4,727,468 | 2,180,963 |
| 1918 | 5,554,952 | 2,363,723 |
| 1919 | 6,679,133 | 2,561,578 |
| 1920 | 8,131,522 | 2,775,736 |
| 1921 | 9,212,158 | 3,007,495 |
| 1922 | 10,704,076 | 3,258,248 |
| 1923 | 13,253,019 | 3,529,491 |
| 1924 | 15,436,102 | 3,822,827 |
| 1925 | 17,481,001 | 4,139,969 |
| 1926 | 19,267,967 | 4,482,753 |
| 1927 | 20,193,333 | 4,853,135 |
| 1928 | 21,362,240 | 5,253,203 |
| 1929 | 23,120,897 | 5,685,181 |
| 1930 | 23,034,753 | 6,151,430 |
| 1931 | 22,396,253 | 6,654,458 |
| 1932 | 20,901,401 | 7,196,917 |
| 1933 | 20,657,257 | 7,781,611 |
| 1934 | 21,544,727 | 8,411,495 |
| 1935 | 22,567,827 | 9,089,674 |
| 1936 | 24,182,662 | 9,819,402 |
| 1937 | 25,467,229 | 10,604,079 |
| 1938 | 25,250,477 | 11,447,242 |
| 1939 | 26,226,371 | 12,352,559 |
| 1940 | 27,465,826 | 13,323,814 |
| 1941 | 29,624,269 | 14,364,893 |
| 1942 | 27,972,837 | 15,479,763 |
| 1943 | 26,009,073 | 16,672,451 |
| 1944 | 25,566,464 | 17,947,008 |
| 1945 | 25,796,985 | 19,307,482 |
| 1946 | 28,217,028 | 20,757,878 |
| 1947 | 30,849,353 | 22,302,107 |
| 1948 | 33,355,250 | 23,943,941 |
| 1949 | 36,457,943 | 25,686,956 |
| 1950 | 40,339,077 | 27,534,467 |
| 1951 | 42,688,309 | 29,489,465 |
| 1952 | 43,823,097 | 31,554,544 |
| 1953 | 46,429,270 | 33,731,825 |
| 1954 | 48,468,418 | 36,022,883 |
| 1955 | 52,144,739 | 38,428,667 |
| 1956 | 54,210,901 | 40,949,423 |
| 1957 | 55,917,897 | 43,584,625 |
| 1958 | 56,890,558 | 46,332,903 |
| 1959 | 59,453,984 | 49,191,985 |
| 1960 | 61,671,390 | 52,158,650 |
| 1961 | 63,420,580 | 55,228,689 |
| 1962 | 66,085,289 | 58,396,886 |
| 1963 | 69,038,443 | 61,657,017 |
| 1964 | 71,994,795 | 65,001,863 |
| 1965 | 75,257,588 | 68,423,251 |
| 1966 | 78,124,688 | 71,912,111 |
| 1967 | 80,398,967 | 75,458,556 |
| 1968 | 83,604,514 | 79,051,985 |
| 1969 | 86,857,794 | 82,681,197 |
| 1970 | 89,243,557 | 86,334,529 |
| 1971 | 92,718,395 | 90,000,000 |
| 1972 | 97,082,060 | 93,665,471 |
| 1973 | 101,985,442 | 97,318,803 |
| 1974 | 104,856,341 | 100,948,015 |
| 1975 | 106,705,934 | 104,541,444 |
| 1976 | 110,188,640 | 108,087,889 |
| 1977 | 112,287,522 | 111,576,749 |
| 1978 | 116,573,394 | 114,998,137 |
| 1979 | 118,428,730 | 118,342,983 |
| 1980 | 121,600,843 | 121,603,114 |
| 1981 | 123,098,411 | 124,771,311 |
| 1982 | 123,701,665 | 127,841,350 |
| 1983 | 126,443,782 | 130,808,015 |
| 1984 | 128,157,682 | 133,667,097 |
| 1985 | 127,885,193 | 136,415,375 |
| 1986 | 130,003,574 | 139,050,577 |
| 1987 | 131,482,123 | 141,571,333 |
| 1988 | 133,835,532 | 143,977,117 |
| 1989 | 134,559,193 | 146,268,175 |
| 1990 | 133,700,497 | 148,445,456 |
| 1991 | 128,299,601 | 150,510,535 |
| 1992 | 126,581,148 | 152,465,533 |
| 1993 | 127,327,189 | 154,313,044 |
| 1994 | 127,883,469 | 156,056,059 |
| 1995 | 128,386,775 | 157,697,893 |

### Interpretation of the Results

These results allow analysis to be carried out on the accuracy of the model and the potential for its use in future studies. The results and their implications are explained in the sections below.

#### Construction of S Curves

By plotting the data from the table of values gathered through research as well as values predicted by the model, the below S curves were generated:
By simple observation it is clear that these curves line up fairly well, especially between the years 1960-1980.

#### Interpretation of the S Curves

By simple observation it is clear that these S curves are not perfect matches, and also that there are regions that correlate particularly well and particularly poorly between the model and the data that was gathered from studies.
The first ten or so years as predicted by the model are very accurate by comparison of the graphed points as seen in the plot, where the lines for both the gathered data and the model projections are equal. However, upon comparison of the actual data points it is clear that these values differ significantly, by a factor of up to almost seventy. Yet as these values are insignificant in comparison to those that are both measured in the data and projected by the model, these initial results can be treated as being relatively accurate.
The early middle period of the graph, between approximately 1920 and 1960 shows that the data from real life is significantly greater in magnitude than the figure projected by the model. This difference is significant enough to say that the model is not at all accurate at predicting the number of automobiles in the U.S. at this time. This is likely due to a significant period of accelerated growth of the automobile as it became both more popular and more widely available in the U.S., leading to increasing purchase of this technology by consumers and so a greater number of automobile registrations. This growth was not able to be predicted by the model due to the significance of its acceleration, which was far greater than any other change that occurred over the current stages of the automobiles life cycle. This means that when considering the number of automobiles in the U.S., the model should not be used for this stage of history.
The region with the strongest correlation occurs between approximately 1960 and 1980, meaning that the numbers generated by the model match those gathered in real life are very similar. It can also be observed that the gradients of these sections are fairly similar, meaning that the growth rate for this time as predicted by the model matches that which was observed in reality. This means that for this section of the model, relative accuracy is achieved.
A strange occurrence happens in the gathered data from approximately 1990, where the total number of automobiles in the U.S. drops. The cause of this is beyond the scope of this study. However, this drop before the number again begins to rise cannot be predicted by the model due to the restraints of theorising any data set, which do not have the capacity to allow for what are likely external effects on the study at hand. So although the model in this case differs significantly from the data set, while not completely accurate it still gives a good prediction of the typical trend for the number of automobiles in the U.S. during this period.

### Projections for Future Numbers of Automobiles in the United States

From observation of these S curves it is clear that the projected curve as determined by the model is not a complete S shape, meaning that there are still years to go before it reaches its final capacity. This means that there are more data points that can be determined by using the model until it reaches a point where the number of automobiles in the U.S. does not increase at any significant rate, i.e. when the life cycle has reached maturity.
The data that was predicted using this model is shown below in the table, and also displayed in the figure.
| Year | Projected Number of Automobiles |
| 1996 | 159,242,122 |
| 1997 | 160,692,518 |
| 1998 | 162,052,992 |
| 1999 | 163,327,549 |
| 2000 | 164,520,237 |
| 2001 | 165,635,107 |
| 2002 | 166,676,186 |
| 2003 | 167,647,441 |
| 2004 | 168,552,758 |
| 2005 | 169,395,921 |
| 2006 | 170,180,598 |
| 2007 | 170,910,326 |
| 2008 | 171,588,505 |
| 2009 | 172,218,389 |
| 2010 | 172,803,083 |
| 2011 | 173,345,542 |
| 2012 | 173,848,570 |
| 2013 | 174,314,819 |
| 2014 | 174,746,797 |
| 2015 | 175,146,865 |
| 2016 | 175,517,247 |
| 2017 | 175,860,031 |
| 2018 | 176,177,173 |
| 2019 | 176,470,509 |
| 2020 | 176,741,752 |
| 2021 | 176,992,505 |
| 2022 | 177,224,264 |
| 2023 | 177,438,422 |
| 2024 | 177,636,277 |
| 2025 | 177,819,037 |
| 2026 | 177,987,827 |
| 2027 | 178,143,690 |
| 2028 | 178,287,596 |
| 2029 | 178,420,446 |
| 2030 | 178,543,072 |
| 2031 | 178,656,251 |
| 2032 | 178,760,698 |
| 2033 | 178,857,079 |
| 2034 | 178,946,009 |
| 2035 | 179,028,056 |
| 2036 | 179,103,749 |
The combination of this data and the figure allow for an estimation of the phases of the life cycle of the automobile, especially in the U.S.

### Dates for Phases in the Life Cycle

The dates for the different phases of the life cycle of the automobile were estimated using a combination of the data points that were from both the model projections and gathered data, as well as the interpretation of the s curves generated by these data points.

#### Birthing

The birthing phase occurred between 1900 and 1914, as these are the dates between growth was the slowest. In 1914, this growth rate began to accelerate.

#### Growth

The growth phase of the automobile occurred between 1915 and 1990. At the beginning of this time period, the growth of the automobile’s popularity and acceptance by society dramatically increased, as seen in the steep gradient of the S curve for gathered data in this period. This growth only began to slow significantly in approximately 1990, meaning that the growth phase was coming to an end.

#### Maturity

The technology of the automobile came into maturity in approximately 1991 and this phase continues until the present day. This can be seen from the models s curve which has begun to flatten out at this time, before almost coming to a halt in growth of any kind in 2030. However, as the latter half of this phase is based purely on speculation and remains in the future, the exact accuracy of the dates for the maturity phase of this technology remains unknown.

### The Accuracy of the Model

The model that was used in this analysis included three parameters which each played a role in predicting the amount of automobiles registered in the United States at any time. However, due to the complexity of the model this mean that the initial values of these parameters was difficult to estimate. Projections needed to be made according to genuine estimates made by real world observation in regards to the saturation level of the number of cars in the U.S. in order to the be able to begin analysis on number of values that fall around this predicted range.

#### The Reality of Comparing Real Life to a Model

The reality of any technology or product is significantly different to any kind of model and prediction, as no model can perfectly predict all of the influences that will occur in regards to a certain technology. What this looks like in a plot of this data is that all data values gathered from surveys and experience will not follow a smooth flow, although they may display a trend, whereas a model will display a perfectly smooth flow according to a trend. This means that no model will be able to perfectly match or predict a set of data corresponding to a real phenomenon, meaning that the results of a model must be properly interpreted in order to be effectively applied to the real world.

#### Assumptions

The model employed in this research uses the following assumptions
*There is a limiting capacity to automobile usage, meaning that automobiles will reach a maturity phase

#### The Available Data

The data that is available for the number of automobiles in the U.S. that was used in this study runs only from 1900-1995, meaning that the values for a considerable number of years need to be predicted in order to be able to continue to use the model.
Also, the fact that the life cycle of the automobile has not been completed makes any analysis of the stage of automobile ownership difficult to ascertain. This is as it is currently impossible to determine whether the use of automobiles in the U.S. is in the birthing, growth, or maturity stage, as all of these stages have not been yet completed and so there can be no benefit in hindsight. This makes it difficult to create projections for future ownership of automobiles, as these projections depend upon where the industry is currently situated in the life cycle. If automobiles are still in the birthing phase but projections are made as if they are in the growth phase, then the predicted number of automobiles will be significantly lower than what will actually occur. Similarly, if automobiles are still in the growth phase but projections are made as if they are in the maturity phase, then the predicted number of automobiles will be significantly higher than what will actually occur. So, it is clear that the projections made by this model cannot perfectly determine the future amount of automobiles that will be used in the future of the U.S., as the life cycle of the automobile cannot be fully understood since it is not yet complete.

#### The Value of R2

The r2 value of any data series is important as it is an indicator of the accuracy of a model when compared to a real set of data. An r2 value of 1 is ideal, as this represents a perfect correlation between model and data, however this is almost never achievable with any kind of data. This means that values that are close to 1 are deemed to be suitably accurate. The r2 value for this analysis was 0.871, which means that the model can be deemed to be accurate to an extent that means it can be used in the analysis of automobiles in the U.S. However, it also shows that there is significant room for improvement, meaning that there exist models that will correlate to this data more accurately. This means that the model as determined by the parameters of this experiment can be used and accepted as accurate, however for further analysis to continue other models should be consulted in order to attempt to create a higher degree of accuracy.

## Bibliography

James J Flink, The Automobile Age, The MIT Press, London, England
Stephen Parissien, The Life of the Automobile: A New History of the Motor Car, Atlantic Books, London, England
Andrew Jamison, The Steam-Powered Automobile: An Answer to Air Pollution, Indiana University Press, Bloomington, The United States of America
William L. Garrison, David M. Levinson, 2014, The Transportation Experience, Oxford University Press, Oxford, England
Investopedia, copyright 2018, How the U.S. Automobile Industry has Changed, viewed May 10 2018, https://www.investopedia.com/articles/pf/12/auto-industry.asp
The History Channel, copyright 2018, Connecticut Enacts First Speed-Law, A&E Television Networks, viewed May 10 2018, https://www.history.com/this-day-in-history/connecticut-enacts-first-speed-limit-law
Encyclopaedia Britannica, copyright 2018, Automotive Industry, viewed May 10 2018, https://www.britannica.com/technology/automotive-industry
U.S. Federal Highway Administration, copyright 2018, State Motor Vehicle Registrations by Year (1900-1995), Washington DC, viewed May 6 2018, https://www.fhwa.dot.gov/
Everyday Mysteries, copyright 2017, Who Invented the Automobile?, viewed May 10 2018, https://www.loc.gov/rr/scitech/mysteries/auto.html
Statista, copyright 2018, Number of passenger cars and commercial vehicles in use worldwide from 2006 to 2015 in (1,000 units), viewed May 6 2018, https://www.statista.com/statistics/281134/number-of-vehicles-in-use-worldwide/
Business Dictionary, copyright 2018, Automobile, viewed May 10 2018, http://www.businessdictionary.com/definition/automobile.html
Daimler, copyright 2018, History of Suspension, from Independent to Active Suspension, viewed May 10 2018, http://media.daimler.com/marsMediaSite/en/instance/ko/History-of-suspension-from-independent-to-active-suspension.xhtml?oid=9361881