Transportation Deployment Casebook/2018/Natural Gas Vehicle

Description
Natural gas vehicle (NGV) is a fuel vehicle that used compressed natural gas or liquefied natural gas as its fuel. Natural gas vehicles birth as there is concern in the energy dependence, air quality, the pollution in emission and the change of global climate. Quesstar Corporation is now the biggest natural gas companies in USA. Natural gas give 10 to 20 percent of greenhouse gasses compare to diesel vehicle. In heavy vehicle application, the natural gas can cut nitrogen oxide by nearly 50 percent when compare to diesel engines. The lists of actors in birthing stage included natural gas vehicle component manufacturers, natural gas distribution, transmission, production companies, natural gas development organizations, non-profit advocacy organizations, state, local government agencies and fleet operators

Characteristics
Methane gas (CH4) merged with Oxygen (O2) are entered the atmosphere through the combustion. This can form form carbon dioxide (CO2) and vaporized water (H2O) through its combustion machine. Methane is regard as the most environmental friendly hydrocarbon. Natural gas is also renewable. Natural gas offer lower in-use emission then other engines such as diesel. Natural gas have a high upfront capital cost and low ongoing fuel costs. Natural gas now is abundant in the world. The engine of natural gas vehicle is also larger in size. Renewable natural gas fuel can run the fuel required for 18 wheelers, making 90 percent of reduction of greenhouse gases and leverage existing infrastructure.

Advantages
Natural gas vehicles have lower fuel cost, give clean energy and have efficient services. Low fuel costs can accelerate the phase to remove dirty diesels in heavy vehicles and other vehicles niches. The fuel is also safe when compare with petroleum. Expanding the use of natural gas can save the declining energy business. The consumers money can also be saved by reducing the transport cost and helping the communities to discuss issues such as smog and greenhouse gas emission. Using natural gas can cut the dependent in petroleum or diesel. The birth of natural gas vehicles also create jobs for the investing, marketing and producing the vehicle. The vehicle is sold in discount compare to diesel prices. The vehicles can help to fulfil policy goals immediately such as increase U.S. Jobs, reduce greenhouse gases, urban pollution and import of oil.

Main markets
Nowadays there are 63 percent of customers using Natural Gas vehicles to get to work, with another 22 % uses Natural Gas Vehicles to travel to school and universities. Natural gas is currently providing 24% for primary energy used while only providing 1% for transportation. Switching to natural gas for long-haul track can cut 20000 gallons of diesel fuel each year. Switching to natural gas can cut 250000 gallons each year of diesel fuels. Switching to natural gas for ferry vessels can reduced 800000 gallons which is more than 40 trucks in a single year. A small container ship to natural gas can displace 35 million gallons of fuel per year. Therefore the fuel itself has a high potential.

Past Modes
One of the similar mode is the Diesel vehicles. Diesel vehicles are as fuel-efficient as Natural Gas Vehicles. Diesel vehicles have more power and smaller engine. The torque produced by high-compression of air result in high forces on connecting the road. Diesel has 12.5% averagely more energy than gasoline. It enter the economy by its ignition of the fuel and is injected to the combustion chamber. There are different temperature of air in the cylinder as there are mechanical compression.

Another similar mode is gasoline vehicles. Gasoline vehicle has an internal combustion engine with spark-ignition and is volatile for combustion. Gasoline engines revolves at a high rotation speed than diesels due to lighter pistons and cranks connecting the road. Gasoline vehicles can cover wider distances. Gasoline is also one of the most compare to other fuels. The gasoline vehicle can also create more power as gas is more powerful for fuel efficiency.

Limitation of Predecessors
Diesels engine does not work well for short trips. For short trips, there is risk of the particulate filter blockage which is used for collecting soot. The cost of Diesel-powered vehicle also increased a lot compare with petroleum. The Diesel fuel is greasy the service cost is high. Diesel vehicles also produce large noise and do not have high-speed performance.

Gasoline vehicles made much pollutions and health hazard to global warming. The pollution cased by the burn of petroleum can create lungs problem and lead to cancer. The breathing of petroleum can result in confusion, dizziness and even death. The liquid nature of petroleum also is easy to contaminate water. The fossil fuel of petroleum is running low and there is proof that the world does not have enough supply in few decades. Petroleum also exist vastly in some countries, such as Saudi Arabia. Those countries can result in other countries dependent of its supply. Therefore, they can make the price when and whatever possible.

Market Evolvement
The lack of amount in refuel of the fuel in the commercial stand point is a fundamental obstacles for the involvement in any alternative mode. The market relies heavily on hydrogen and electric vehicle. In 2014, the cruel oil prices crashed and the market favors the use of gasoline. vehicles There is a spread in the shift to gasoline-maximizing stage. However in 2015, the market swing back to diesel-maximizing stage and the market interest moving between the diesel and gasoline. There is no winner between both fuels and the market is on balanced with several variation such as more users used diesel in winter and more commuters buy gasoline in summer.

Catalyst for New Modes
The economics becomes favourite for natural gas when the market cannot decide whether to favors Diesels vehicle or Gasoline vehicles. The cost difference between natural gas and petroleum reduced. At the same time, the price difference between Natural Gas Vehicle and gasoline/diesel vehicles reduced. There is also the support of the energy industry of using gas. The technology of natural gas vehicle also enough to support to growth market. Government and politician interest in the low emission as fuel.

Physical artifacts
There are high ductility and strength natural gas pipelines across medium-length stretches of water for the transport of natural gas There is also the  conversion kit for swapping gasoline or diesel for natural gas. There is also the increase in natural gas station all around the world. This is also growing in the US. There is also the investment of home refueling facilities.

Transportation Artifacts
Many transport mode can adapt to this raw fuel, such as trucks, transit and lightweight vehicles. The increase in adaptive brings alternative to user. Therefore the retailer is more readily to deploy more stations for the supply of natural gas. The current network offer refuel gasoline station. There is also a lot advertisement of how much better is using natural gas engine. The governmental in US also wishes to provide less price for the usage of natural gas as fuel and the government in US have planned to provide subsidy on the sales of natural gas vehicles.

Technological Expertise
The natural gas vehicle powered by internal combustion engine. For the compressed nature gas fuel, the gas deliver to refuel station through pipes and compressed pressure before pumping back to the fuel tank. For the liquefied natural gas, the gas pressurized in a form of liquid with its shrinkage volume of 600 times. The liquid form of natural gas enable natural gas ships and loads to large trucks. The technology of fluid or gas under high pressure is an ability where other vehicle fuel lack of.

Methodology
There are two types of common supply for natural gas. They are compressed natural gas (CNS) and liquefied natural gas (LNS). For compressed natural gas, the gas stored in a large compact tank with pipes. Coselle carrier included the coiling of small pipes. Another type is lower pressure option, VOLTRANs method, which consists of large and lengthy diameters pipes being stored in an insulated shell. A third type is C-Natural Gases method which included the coiling of pipes and allow shipping with the current vessel design. For liquefied natural gas, the gas cool and keep up in a temperature of negative 111 Kelvin. Therefore, there is a capital investment in the infrastructure to keep the temperature for cold natural gas.

Modification of Design
Another branch in the technology is to modified the design for motorcar racing. The car run with natural gas. In 2012, another change carried on with the conversion kit of Cavagna/ Bigas fuel or in other name, 500 EcoAbarth. The motorcar team won several titles in the Ecorally Sarino-Vantican and CSAI Alternative Energy Pilot. The spark ignition decreases by at least 80 percent. The adaption in the form of motor car also promote the deployment and growth.

Initial and Predominant Technology
The technology included Spark Ignited Natural Gas Engine, Compression Cycle Engine for Natural Gas with Diesel Pilot Ignition and Fuel Injection Conversion Kit. The Spark Ignited Natural Gas Engine is an engine that can combust when the air-fuel mixture ignite by any spark. This is useful for medium and heavy tractors, trucks and buses. The compression cycle engine for natural gas with diesel pilot is injecting very little of diesel to engine to start combustion. Heavy tractor uses in this technology. The fuel injection conversion kit enable the retrofitting of gasoline engine for making the vehicle run with natural gas. Automobile can perform predominantly by this technology.

Market Development
The early switch to natural gas result in the lost of traction. This is because the supply of domestic natural gas decreased and the price of the natural gas increased in 2005 and lasted for a year. The operators have confident issue of whether the cost of natural gas can stay low enough to give existing customers as well as give an alternative to new users. At the same time, there is a large expansion in United states about natural gas production and the reserves in natural gas. This result in the lowering of price and this created sustainable attraction for later usage. Several parties are move their fuel to natural gas. They also willing to pay the cost which required to limit the natural gas vehicles supply.

Market Niches
The sales of natural gas vehicles to United states has been restraint to very little markets. This includes the medium to heavy mode like buses, tractors, trucks and fleet truck. Natural gas transit buses is also established as the mode mostly use natural gas. In 2007, there are 15% of transit vehicles powered by natural gas. The only penetration to the market is to deploy on Civic GX by Honda. Honda Civic GX is now the only vehicle run by natural gas vehicle. The last production is in 2015. In UK, the market niche is to deploy on roads which gasoline vehicles must to pay congestion charges. Overall the market niche of natural gas concentrate on fleets.

Functional enhancement
The greatest mode for enhancement are trucks and bus. Despite the selling of natural gas trucks increased about 20 % in 2014, the technology keep on improving. There is commercial plan to have more than 1000 compressed natural gas and liquefied natural gas truck for renting and leasing. The natural gas operators also give maintenance facilities in eight states. Normal truck maintenance required about 90 days. There are also few enhancement in natural gas buses services. There is also regular removal of undesirable constituents of pipeline natural gas and oil carryover produced during gas compression in the refuel station. With the increased in safety compressed natural gas tanks, the tank place on top of the buses to increase space within the bus.

Functional discovery
In the market in the Americas, natural gas allow to trade with a 50 % discount to other fossil fuel. This create attraction for vehicle owner to switch mode. There is also a discovery of market. The world first car ferry design in Norway in the name of GHLTRA. There will carry 1000 private cars for the car ferry. The ferry operates by natural base. The four gas engine generator gives power to electric driven compass thruster and it can propel the car ferry. There is storage of liquid natural gas below the main deck. The liquefied natural gas shipping is decent for further expansion of trucking as the fuel is transfer between land and sea.

Role in birthing phase
For the birthing stage, the empowering of that the producer can make use of the new and excellent vehicle and have a mass-production. This empowerment introduces new things to the commuters. The innovations as natural gas are uses in the power station for energy. However, natural gases in vehicles works on existing technology and develops a new use in vehicles. The adopted technology is then entering the market niches. The typology of innovation is end-driven as the innovation is directly developed from the research. Policies makes for the new mode and discouragement of old saturated mode.

Precursor Policies
Purchase price subsidies was first implemented in diesel technology when it was a development industry. The subsidies were a measure made to keep the prices below affordable commuters. The global fossil fuel subsides contributed 6.5% of the global GDP in 2015. The subsidies use in the 20th centuries to make sure the price of Diesel was low enough and similar to petroleum. The subsidies are also used to offer economic benefits in a form of reducing price to stimulate new customers. Natural Gas in the mean time has the same scenario as diesel did a hundred years ago. Therefore purchasing price subsidies can make sure the price are low enough to attract users from using diesels or gasoline.

Innovated Policies
Affordable vehicle conversion and home refilling facilities can arise new users to drive natural gas vehicles. The vehicle conversion kit can enable the retrofit of gasoline engine to work with natural gas. This can largely reduced the capital cost of that the commuter have to buy an expensive new car. This can also attract customers to use natural gas with the conversion kit when the petroleum price rises. To have policy subsidizing the conversion kit can enable the usage of natural gas as fuel. Once the customers have good experience in this fuel, they can have the wish to buy a natural gas vehicle. Home refilling facilities can also motivate the usage of natural gas vehicles. In United States, South Coast residents allow to spend less than 2000 dollars to have a home fuelling appliance. In Europe, there are nearly 1200 small vehicle refuelling appliance which can allow the users to refuel their natural gas vehicles at home by using gas connection. The payment is convenient through gas bill. Government can also give subsidy to the home refueling technology. This technology can help to cut the cost, provide safety and increase capacity for natural gas vehicle fuel tanks.

Governmental Policies
Government purchasing programme for vehicles such as public transport buses and garbage trucks made. Buses and trucks have compromised most of the total number of natural gas vehicles. In Europe, natural gas vehicles uptake encourage through agreeing with the government to adopt natural gas-powered buses. The research from AECOM also shows that compressed natural gas fuelled trucks will be cheaper option over diesel till 2030. Therefore adopting garbage truck can implemented the usage of cheap natural gas. The government can also carry out fuel tax to encourage natural gas in vehicles. The net refueling cost with fuel tax rebates are around $0.95 cents per litres. This is about 20 percent cheaper than the net cost of diesel. Fuel tax exemptions or reduction is solely applied on natural gas vehicles. With the fuel tax, more commuters switch to natural gas vehicle mode. Vehicle fleet emissions standards can also be applied to the industry by having the standard of different fuel tax for different fuel. Natural gas vehicles are able to reduce greenhouse gas emissions. The transport make up around 17 percent of Australia total green house gases and diesel is responsible for two fifth of it. Higher tax on dirty fuels such as diesels can encourage the usage of environmental friendly natural gas.

Locked in Policy
Gas prices and supply locked in policy. Gas prices and supply fix after standardisation when natural gas vehicles deploy. Increasing natural gas vehicle penetration will increase the demand for natural gas. Therefore the adequate supply of natural gas is important. As a result, the domestic gas markets locked in and work effectively to supply natural gas. The government should also make policy for the exploration and production of allowable gases. This include the policies from government to fixed the price to allow enough consideration on the local users and the picture of natural gas in the economy. This can make sure the natural gas is enough to support domestic and export for incentives. The inconsistent changing of the supply of natural gas which result in the decrease of the price of natural gas. Therefore lock-in required.

Description
For the development and growing phase, the efficiency innovation is that this product provides attractions of that it can cut cost and in a form of magic bullet. This is the systems grow as the bigger it is the more advantages they have over the smaller systems. These economies of scale work compromise and expand a system. The economies of scale of that the property has average cost decreases as the demand increases. The cost reduction can create profit to the producer in uncompetitive situation. The more natural gas vehicles, the lower the cost of it and the better of the production and as a result, this attract more commuters after that.

Public and Private
The public sectors include the commuters who is using natural gas vehicles, the commuters who is using other modes and the local community. With the number of natural gas vehicles in the market growing in a fast rate, the commuters who is using the natural gas vehicles enjoy the vehicle improvement, safe driving and cheap subsidy from the government and they stay as one of the natural gas vehicle commuter. The commuter who is using other mode switch their fuel to natural gas through the government subsidy on the conversion kit. This is because the fuel price of petroleum or diesel is higher than natural gas. With the conversion kit, these commuters can enjoy the service of natural gas vehicle and join as one of the member in the development or growth phase. Local community can enjoy the less pollution environment and some of them are willing to have a try on natural gas vehicles. They also join the development or growth part of the S-curve. Private sector included the natural gas vehicle manufacturer, natural gas distributor and fleet operators. Natural gas vehicle manufacturer enjoy the high demand of the vehicles and can earn incentives in selling high demand transportation mode. They can also enjoy the subsidy from the government for the further design and further produce of vehicle. The natural gas distributor switched from working in gas station to bill collector due to home refuelling facilities. They will also give maintenance and repair work of the facilities and inspecting any flaws or leakage in pipes. The fleet operators enjoy the low-cost of natural gas over petroleum or diesel. With government, the petroleum fleet abandons and the natural gas vehicle uses to give service. As a result, the number of natural gas vehicles rises and they join one of the users on the development or growth part in the S-curve.

Issues
According to the study of Lessons on the role of market failure in markets for alternative fuel vehicles, we can find that coördination, competition, imperfect information, bounded rationality and principle-agent problem are the main issues in this stage. Coordination happens the market is not independent. Failure of competition occur when only very few user using non-natural gas vehicles. Imperfect information happens when any actor can change the data stock. Bounded rationality occur when the user do not have enough understanding of the product. Principal-agent problem occur when there is no common principle between parties. This five issues generally occur in the growth stage and that it will result in probably downfall in the production or failure to reach the capacity. It happened in Germany in 2013 that deploying natural gas vehicles failed to reaches saturation level.

Solution
In order to solve the issues arise during the growth of number of natural gas vehicles. It is important to maintain a stable supply side by improving the cooperation between the vehicle manufacturer, fuel distributer and transmission. On the demand side, the awareness on trust and acceptance of each customers should be arise such that the demand can keep stable. Reliable, realistic, positive and stable expectation and environment are required to build the trust between each list of actors. The imperfect information can be resolved by policymaking of the government over the dominating users. Bounded Rationality can be resolved by having more advertisement regarding the advantages of this mode. In this condition, the effective research and development in the natural gas vehicle industry. Finally, a system optimal can be achieved.

Policymaking
The policy environment influence the policymaking in this period by the number of supply available and number of natural gas vehicles demand by the public. When the number of supply do not match the number of demand, there will be the S-curve. As a result, the market failure in natural gas vehicle market in Germany occur again. Therefore if the demand is too high, the government can decrease the fuel price for diesel and gasoline to prevent the customers waiting for the product. If the supply is too high, the government can decrease the fuel price for natural gas. As a result, more and more people are interested in buying the natural gas vehicles on stock.

Description
For the mature or declining stage, the sustaining innovation makes that the old product replace by new. Natural gas vehicle transits from the entrepreneurs to engineers and to the managers. The society becomes more cautious on risks and there is dilemma on who captures the mature system. Imperatives occur and there are imperatives for keeping the vehicle produced healthily. The aging process of the natural gas vehicle can no longer attract users to drive it. The number of natural gas vehicles cannot be higher since the demand is already at greatest value.

Adaption
The new producers of a new mode invade the market with similar product with higher quality or lower cost, the producer of natural gas vehicle react by imitating the new mod or dampen international competition through tariffs and quotas. This is how adaption occur. Currently there is a new mode which is hybrid electric vehicle. The vehicle is a type of hybrid electric vehicle consist of internal combustion and electric propulsion system. To adopt with the low-cost and fuel for hybrid electric vehicle, the price of the natural vehicle drops and there will be a conversion kit converting between electricity and fuel to adapt to the new mode.

Competition
The winner of the current competition are neither hybrid electric vehicles or natural gas vehicle. This is because of autonomous vehicle. This type of vehicle can drive themselves with the data presented in the database. However there are recent accident in US that terms the future of the project as a question mark. Nevertheless, this brings the same competition of hybrid electric vehicles and natural gas vehicles. Natural gas vehicles are currently developing in the technology of absorbed natural gas which can drive down the cost of natural gas vehicles infrastructure and vehicle tank to compete with hybrid electric vehicles.

Scheme
The scheme or policy value in this stage are to give for competition of natural gas over other fuel. The highway exercise tax treatment of liquefied natural gas is disincentive to invest in new liquefied trucks and fueling station. Some fleet operators like UPS and Ryder are switching to natural gas vehicles. There are still good policy supporting natural gas vehicle by competing with other fuel. Currently, liquefied natural gas taxed at a higher rate than diesel fuel heavy truck market. Policy of resetting the tax rate so that the tax act on energy content. The alternative fuel tax credit reset trough government policy to apply energy-content basis for natural gas fuels like liquefied natural gas and compressive natural gas. It is important to support a level of playing field that allows natural gas vehicle to compete in the market.

Constraint of Locked in
The locked in policy included the subsidy of the fuel for natural gas vehicles. Although there is competition between natural gas vehicles, electric vehicles and hybrid electric vehicles. The government should lock-in the subsidy and add tax for diesel and gasoline so that only clean fuels use. In economical view, the decrease in the demand of diesel and gasoline vehicles can increase natural gas vehicles in the market. Gas prices and supply fix after standardisation when natural gas vehicles deploy. Locked in constraints adaption as it does not allow the producer to imitate the lower cost producer. However, since the locked in policy is to subsidy the fuel for natural gas, the producer relies too much on the help of the government and does not change for better. Therefore the competitiveness of the product will be lower.

Re-invention
To better serves the needs of today and tomorrow, I suggested that conversion kit used in the natural gas vehicles are re-invented to converting between electricity, natural gas and gasoline. This can make the converter more efficient and attract more potential users. I also suggested some government adopted buses as movable portable natural gas fuel tank. This portable nature can give more freedom for users since the vehicle usually running off power while on street.

Data
Table 1: Raw data from NGV Global, Natural Gas Vehicles Knowledge Base

Logistic Function
The following logistic function is being used S(t) = K/[1+exp(-b(t-t 0 )] Logistic function, S-curve, is to model the behavior of the data. The data include year and number of natural gas vehicles corresponding to the year. The year and number of natural gas vehicles donate by t and S(t) . The limits in the equation include K, which is the saturation level of natural gas vehicles in the world. In mathematical view, S(t) is equal to 0 when time approaches negative infinity, which means that there is no natural gas vehicle deployed before it invented. This can easily prove by mathematics, since when t approach negative infinity, the exponential term become very big and so as the denominator. On the other hand K is the number of natural gas vehicles when time approaches infinity. This can easily prove by mathematics, as when time approaches positive infinity, the exponential term becomes 0, and therefore S(t)=k. t0 is the time when the number of natural gas vehicle equal to half of K. This can also be proved by mathematics as the exponential term equal to one. t0 is also the inflexion point of the graph due to the rotational properties of the graph. Since,

dS(t)/dt = kbexp(-b(t-t0))/(1+ exp(-b(t-t0)))^2

d^2S(t)/dt^2 = (-kb^2(exp(-b(t-t0))-2kb^2(exp(-b(t-t0))^2-kb^2 (exp(-b(t-t0))^3+2kb^2 (exp(-b(t-t0))+2kb^2 exp(-b(t-t0))^2)/(1+ exp(-b(t-t0))^4= -kb^2(-1-2-1+2+2)/ (1+ exp(-b(t-t0))^4

and at t= t0, d^2S(t)/dt^2 = 0.

Linear Regression
For linear regression, we can expression straight line equation as y=Bx+C

Where B is the slope, C is the y-intercept for any variables of y and x

Rearranging the terms of the logistic equation, we have

(1+exp(-b(t-t0))=K/S(t)

exp(-b(t-t0)=K/S(t)-1

ln(exp(-b(t-t0)))=ln(K/S(t)-1)

ln((K-S(t))/S(t)=-bt+bt0

-ln(K-S(t)/S(t))=bt-bt0

ln(S(t)/(K-S(t)))=bt-bt0

By comparing the terms, we have b=B, C=bT0, x=t

And y=ln(S(t)/K-S(t))

Identification of Stages
According to table 1, we found that S(t) approaches largest in 25000 in 2017. Therefore, we have a first guess of K is equal to 32000 as from figure 3. By establishing the value of S(t) corresponding to K=32000, we can find out the build up a matrix of expression ln(S(t)/(K-S(t))) for all years and K which is about 1000 different from 32000. We can then calculate the R square for every year for a particular K values. We obtained the most R square value of 0.993598 when K equal to 32000, where R square is a determinant illustrating the variance in ln(S(t)/(K-S(t))) which is predictable from the year. Then we run a linear regression in excel for K= 32000 in figure 2. We obtained the y intercept is -504.98662 and slope is 0.25101958.

Therefore, b is equal to 0.25101958 and t0 = -504.98662/b = 2011.74194.

S-Curve Modelling
Therefore we can established the predicted number of natural gas vehicle in a certain year t by

S(t)=32000/(1+-exp(-0.25101958(t-2011.74194))).

Forecasting of Curve
We can further forecast the year and predicted number of natural gas vehicle until S(t) reaches 32000, which is in the year of 2055. The S-curve is then show in figure 1.

From the curve in figure 1, we can find that from the year of 1996 to 2004, the growth of vehicles per year is less than 1000, which is quite slow. Therefore we can close that this is the stage of birthing of natural gas vehicle. Between the year of 2005 and 2019, the growth rate maintains at least 1000 natural gas vehicles being used in the market per year. After the year of 2019, the product attains a maturity or decline stage which the curve reaches asymptotic.

Graphs and Excel Result
Table. 2 The Predicted and Actual number of NGV in the world. Figure. 1. The S-curve of NGV Figure 2: Linear Regression of Data Figure 3: Data and Calibration of the parameters

Accuracy
The logistic equation expect to have stability, symmetric and stimulation. For stability, the curve fits the data very well before year 2018. The model is quite correct with the value of R square for K=32000 are nearly equal to one. This is with less than 6% and is quite right. The t-statistic value is 51, which is a lot higher than 2 which guarantee the result is correct and significant at least for 95%. The t-statistic is the ratio of the departure of the estimated value of the number of vehicles from its predicted number of vehicles to its standard deviation of sampling distribution. The graph also shows that the red curve stays pretty close to blue curve. This means that the real and predicted numbers of vehicle are in a correlated and similar shape. The curve stays still in asymptotic of S(t)=31000. The curve also have a symmetry of t0 = 2011.74194 when the number of natural gas vehicles half the overall saturation value. The Stimulation of the curve also occurs as the deployment time decreases with time. This is a fact in the curve since the number of vehicles depends on the duration taken between the start time rather the effect of same duration and different start time.

Errors
The model has difficulties for analyzing the stage before year 1996 due to the insufficient data. It is because it is hard for anyone to record the time of the start of a vehicle in the deployment. However there is less error in forecasting the past once we have the birthing stage. Although the most error occurs between the growth stage and birthing stage or growth stage and mature stage, there is still an error and a danger of extrapolation for extrapolating the birth stage. In this model, it expects the number of vehicle exist in the world before 1996 is less than the extrapolating value. The model is however not correct after the maturity stage. It expects the model to decrease due to the market movement and deploying of a new product.