Using the growth in hybrid sales in the United States shown in Fig. 13-7 as a starting point, consider the transition pathway to hybrid penetration into the fleet, in the following way. Suppose that the number of hybrid electric vehicles (HEVs) in the fleet, which starts in the year 2000 with 9350

Question

Using the growth in hybrid sales in the United States shown in Fig. 13-7 as a starting point, consider the transition pathway to hybrid penetration into the fleet, in the following way. Suppose that the number of hybrid electric vehicles (HEVs) in the fleet, which starts in the year 2000 with 9350 vehicles added, eventually tapers off to 13,000,000 units, and that each hybrid averages 15 km/L fuel efficiency, versus 8.5 km/L for the internal combustion engine vehicle (ICEV) alternative.

Consider the year 2000 to be the year t = 0. Sales through the year 2006, in order, number 20,287, 35,000, 47,500, 88,000, 207,000, and 253,000. Assume that for each new sale another car is scrapped, so that the overall size of this segment of the fleet does not change, and that each car drives 16,000 km/year.

(a) Use the logistics function to calculate in which year (call it year N) the number of hybrids in the fleet surpasses 99% of the 13M target. (b) Calculate the cumulative fuel savings in liters for the shift to HEVs from years 0 to N, if the new cars are assumed to all be available on day 1 of each new year. For the years 2000 to 2006, use the sales estimated from the logistics curve model, rather than the actual sales, to calculate the number of vehicles in the fleet. (c) Compare the savings to the situation where a fleet of 13 million ICEVs is instantaneously transformed into HEVs at the beginning of year 0, and then driven to the end of year N.

Accepted Answer

(a) We begin by converting sales numbers into cumulative numbers in the fleet. The following table provides this information through year 2006:

	No. of Vehicles
Year	Sales	Cumulative
2000	9,350	9,350
2001	20,287	29,637
2002	35,000	64,637
2003	47,500	112,137
2004	88,000	200,137
2005	207,000	407,137
2006	253,000	660,137

We obtain all necessary parameters for the logistics function as follows. Based on full penetration of the 13 million market, a = b = 1. The presence of 9350 in year 0 leads to a value of p[latex]_0[/latex] = (9350)/(1.3 × 10[latex]^7[/latex]) = 0.00072. The value of x is solved in a spreadsheet by calculating the error between observed and model values for years 2000 to 2006, and then minimizing the square of the error terms, resulting in x = 1.29.

[latex]p(2)=\frac{a \cdot p_{0}}{b p_{0}+\left(a-b p_{0} ight) e^{(-a t / x)}}=\frac{0.00072}{0.00072+(1-0.00072) e^{(-2 / 1.38)}}=0.00307[/latex]

HEV penetration in 2002: (1.3 × 10[latex]^7[/latex] )(0.00307) = 39, 920

Plotting actual versus modeled penetration through 2006 gives the curve shown in Fig. 14-17.

In year N = 17, the penetration surpasses 99%:

[latex]p(16)=\frac{0.00072}{0.00072+(1-0.00072) e^{(-16 / 1.38)}}=0.988[/latex]

[latex]p(17)=\frac{0.00072}{0.00072+(1-0.00072) e^{(-17 / 1.38)}}=0.994[/latex]

(b) Since the total fleet size is constant at 13 million, savings accrue from replacing some fraction of the fleet with hybrids. In each year, the baseline fuel consumption with no HEV penetration is

[latex]\frac{\left(1.3 imes 10^{7} ext { vehicles } ight)(16,000 \mathrm{~km} / ext { year })}{8.5 \mathrm{~km} / \mathrm{L}}=2.45 imes 10^{10} \mathrm{~L} / ext { year }[/latex]

The savings in each year is then the baseline minus the actual consumption, based on the mix of HEVs and ICEVs in the fleet. Taking year 2 as an example again, the HEV and ICEV fuel consumption values are, respectively:

[latex]\frac{\left(3.992 imes 10^{5} ext { vehicles } ight)(16,000 \mathrm{~km} / ext { year })}{15 \mathrm{~km} / \mathrm{L}}=4.26 imes 10^{7} \mathrm{~L} / ext { year }[/latex]

[latex]\frac{\left(1.3 imes 10^{7}-3.992 imes 10^{5} ext { vehicles } ight)(16,000 \mathrm{~km} / ext { year })}{8.5 \mathrm{~km} / \mathrm{L}}=2.44 imes 10^{10} \mathrm{~L} / ext { year }[/latex]

The total fuel consumption is therefore little changed from the baseline, at 2.444 × 10[latex]^{10}[/latex] L.

Repeating the calculation of annual savings for each year and summing to quantify cumulative savings gives the following graph of fuel saved from 2000 through 2017, as shown in Fig. 14-18.

Based on these calculations, at the end of year 17, the savings has reached 8.01 × 10[latex]^{10}[/latex] L.

(c) An instantaneous transition to 13 million HEVs gives the following energy consumption per annum:

[latex]\frac{\left(1.3 imes 10^{7} ext { vehicles } ight)(16,000 \mathrm{~km} / ext { year })}{15 \mathrm{~km} / \mathrm{L}}=1.39 imes 10^{10} \mathrm{~L} / ext { year }[/latex]

On this basis, the annual savings is (2.45 × 10[latex]^{10}[/latex] ) − (1.39 × 10[latex]^{10}[/latex] ) = 1.06 × 10[latex]^{10}[/latex] L/year. Including the savings in year 0, the project has an 18-year time span. Therefore the cumulative savings is (1.06 × 10[latex]^{10}[/latex] )(18 years) = 1.91 × 10[latex]^{11}[/latex] L of fuel.

Discussion Comparing the results of parts (b) and (c) in the example shows that during the time of the project, considering the transition period results in a 58% reduction in the projected savings.

Thus the benefits of reducing the consumption of petroleum or emissions of CO[latex]_2[/latex] would accrue much more slowly when one takes into account a realistic amount of time for the new vehicle technology to penetrate the market.

Question 14.2: Using the growth in hybrid sales in the United States shown ...

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