In addition to roadway agency costs, Vehicle Operating Cost (VOC) is important because it varies by vehicle depending on which roadway surface it travels. The book Economic Analysis on Highways states that the VOC on gravel roads is approximately 1.35 times that on paved roads (Winfrey, 1969). Therefore, VOC must be a consideration in the conversion of a roadway surface type or determination of the most economical roadway surface type. VOC components include fuel cost, maintenance cost, tire cost, and depreciation. The book by Winfrey includes tables to calculate the VOC (referred as running costs by the author) for five classes of vehicles, which represent real traffic flow on roads. As a separate classification for school bus is not mentioned, it can be considered under single unit truck type of vehicle. The five classes of vehicle types, shown in Figure 4.1, are passenger cars, commercial delivery trucks, single-unit trucks, 2-axle tractor semitrailers (2-S2), and 3-axle tractor semitrailers (3-S2).
(Source: Winfrey, 1969)
Figure 4.1 Five classes of vehicles used in calculating VOC
The detailed tables in Economic Analysis on Highways contain empirical values of cost for all five classes of vehicles for various speeds, gradients, and horizontal curves along roadways.
All the tables are provided in Appendix D. Running cost values in the tables are for 1,000 VMT
for one mile for one year must be accurately converted to a present dollar value using proper consumer price index (CPI). CPI is a measure of the average change over time in prices paid by urban consumers for consumer goods and services. CPI is the cost of goods or services in any year as compared to the cost of that good or service in the base year (Officer and Williamson, 2015).
Since VOC values in Economic Analysis on Highways correspond to the year 1970, it was converted to the present year or the year of consideration, such as 2013. The VOC was successfully calculated for any ADT on the roadway with known percentage of vehicles in various classes of vehicles, with roadway gradients, and in the presence of horizontal curves. Economic Analysis on Highways also considered roadway surface type when calculating the VOC. The following equations were used to compute the VOC for any combination of vehicles on any type of roadway surface (paved or gravel) with any gradient and horizontal curve. The VOC of all vehicles for a known ADT on a paved road for a particular speed s for 1000 VMT is calculated as:
VOCP = ADT × ∑ pi
5
i=1
× [Cgi+ Chi] (4.9) where,
VOCP = vehicle operating cost of given vehicles on a paved road ADT = average daily traffic on the road under consideration i = class of vehicle type (i = 1 to 5)
pi = percentage of each vehicle class i
Cgi = running cost of vehicle class i on any gradient g for a given speed s Chi = running cost of vehicle class i on any horizontal curve h for given speed s
The VOC of all vehicles for a known ADT on a gravel road for particular speed s for 1000 VMT is calculated as shown in Equation 4.10.
VOCG= ADT × ∑ pi
5
i=1
× [Cgi+ Chi] × CFg (4.10) where,
VOCG = vehicle operating cost of given vehicles on a gravel road
CFg = conversion factor to obtain the running cost on a gravel road for given speed s The VOC of all vehicles for a known ADT on a paved road for a particular speed s for 1 VMT for 1 year is calculated as shown in Equation 4.11.
VOCP = ADT × 365
1000 ×∑ pi
5
i=1
× [Cgi+ Chi] (4.11) The VOC of all vehicles for a known ADT on a gravel road for a particular speed s for 1 VMT for 1 year is calculated as shown in Equation 4.12.
VOCG = ADT × 365 with the correct transportation CPI index value for the given year of consideration according to the Bureau of Labor Statistics using the CPI Inflation Calculator (Bureau of Labor Statistics, 2015). The Equation 4.13 and Equation 4.14 show the VOC for present dollar value using CPI for paved road and gravel road, respectively.
VOCP = CPI × ADT × 365
CPI = transportation consumer price index to convert the 1970-dollar value to present
CPI value is 6.004 to convert the 1970-dollar value to 2013-dollar value (Bureau of Labor Statistics, 2015). The year 2013 is considered in this study to maintain uniformity in costs because most available details on agency cost are averaged for the year 2013.
Various combinations of percentages of vehicle classes (pi), vehicle speeds (s), gradients (g), and horizontal curves (h) could exist in a real-world scenario. Therefore, a computer based program was designed using Visual Studio 2015 in order to obtain the running cost of any number of vehicles. The program calculates the running cost value for any given speed, gradient, and horizontal curve from specific tables according to vehicle class. After obtaining the running costs, various cost components are precisely added and the VOC is given as an output. Inputs for calculating the VOC on a roadway surface for given traffic are type of roadway surface (paved or gravel), ADT on a given roadway, traffic distribution by vehicle class (% of vehicle types), speed of all vehicles (generally the posted speed limit for a given roadway), gradient of the road, if any (default = 0), and horizontal curve of the roadway, if any (default = 0).
Roadway surface type is usually known, and traffic volume can be approximately assumed for the current location if it is not measured or known. Distribution of vehicle types can be obtained at least approximately, and the speed of all vehicles can be assumed to be the posted speed limit of the roadway. If a variable such as gradient of the road or horizontal curvature is difficult to know, then it is assumed to be zero for simplicity.
The VOC calculated using tables provided in Economic Analysis on Highways gives the running cost of a vehicle on a roadway surface. It does not consider ownerships costs such as insurance costs, registration, and taxes because ownership costs is constant and does not have any significance depending on roadway surface type (i.e., ownership cost is identical irrespective of vehicle traveling on a paved road or a gravel road).
Using the tables provided in Appendix D and properly adjusting the cost with the appropriate CPI index for the year 2013, the VOC for 1 mile of travel by each of the five vehicle classes was calculated as shown in Table 4.1.
Table 4.1 VOC per mile on paved and gravel surfaces for five vehicle classes
No. Vehicle Class On paved surface On gravel surface
1 Passenger car $0.21 $0.29
2 Commercial delivery truck $0.24 $0.33
3 Single-unit truck $0.41 $0.59
4 2-axle tractor semitrailer (2-S2) $0.63 $0.91
5 3-axle tractor semitrailer (3-S2) $0.60 $0.90
NOTE: Values were computed for an average speed of 40 mph, zero gradient, and zero horizontal curve.
American Automobile Association (AAA) estimated the average operating cost per mile for a sedan (passenger car) on a paved surface to be 20.42 cents and 22.39 cents for a minivan (commercial delivery truck) (AAA, 2013). Therefore, the proposed method to calculate the VOC using the literature (Winfrey, 1969) and proper CPI value is nearly identical and can be considered.