Predicting vehicle carbon emissions on vertical curve sections can provide guidance for low-carbon vertical profile designs. Given that the influence of vertical curve design indicators on the fuel consumption and CO2 emissions of vehicles are underexplored, this study filled this research gap by establishing a theoretical carbon emission model of vehicles on vertical curve sections. The carbon emission model was established based on Xu’s vehicle energy conversion model, the conversion model of energy, fuel consumption, and CO2 emissions. The accuracy of the theoretical carbon emission model and the CO2 emission rules on vertical curve sections were verified by field test results. Field tests were carried out on flat sections, longitudinal slope sections, and various types of vertical curve sections, with five common types of vehicles maintaining cruising speed. The carbon emission rate effects on the vertical curve are closely related to the gradient and irrelevant of the radius. On the vertical profile composed with downhill/asymmetric/symmetrical vertical curve with a gradient greater than the balance gradient, the carbon emission rate is determined by the gradient and radius. The influence of the gradient on carbon emissions of vehicle on these vertical profiles was more significant than the radius. The radius is irrelevant to the carbon emission rate on the other forms of vertical profile. These results may benefit highway designers and engineers by providing guidelines regarding the environmental effects of highway vertical curve indexes.
Global warming caused by CO2 emissions is an environmental issue of urgent public concern. The vertical curve is an important part of the vertical profile section of the highway and thus affects emission properties, such as carbon emissions, in motor vehicles. Previous research on fuel consumption and carbon emissions has centered on vehicle operating conditions [
Scholars dedicated to quantifying vehicle carbon emissions have established various microcarbon emission models including the Mobile Source Emissions Factor Model (MOBILE) [
Fuel consumption is closely related to CO2 emissions. Several mechanical models have been proposed based on the dynamic load of vehicles [
Table
Summary schematic of the articles reviewed.
Models | Model type | Parameters considered | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Vehicle types | Vehicle speed | Gradient | Engine types | Fuel types | Vehicle shape | Wind speed | Pavement type | Pavement conditions | Different fuel efficiency | Mechanical resistance | Braking | Reverse mechanical resistance | ||
MOVES | Micromodel | ✓ | ✓ | ✓ | ✕ | ✓ | ✓ | ✓ | ✓ | ✕ | ✕ | ✓ | ✓ | ✓ |
Chang’s model | Mechanical model | ✕ | ✓ | ✓ | ✕ | ✕ | ✓ | ✕ | ✓ | ✓ | ✕ | ✕ | ✕ | ✕ |
Mehrsa’s model | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✕ | ✕ | |
Xu’s model | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Summary of fuel quality in United States and China.
Fuel type | Region | Indicators specification | ||||||
---|---|---|---|---|---|---|---|---|
RVP (psi) | Sulfur (ppm) | Aromatic (%) | Olefin (%) | Benzene (%) | T50 (°C) | T90 (°C) | ||
Gasoline | USA | 6.9 | 30 | 26.1 | 5.6 | 1 | 218 | 329 |
China | 12.33 | 10 | 40 | 24 | 1 | 120 | 190 | |
Diesel | USA | 7.614 | 10 | 40 | 24 | 1 | 248 | 374 |
China | 12.763 | 10 | 35 | - | - | 355 | 365 |
Considering that the radius affects the gradient of each position on the vertical curve [
The purposes of the present study are to establish a carbon emission model of vehicles on vertical curves and to reveal the low-carbon design indexes of the vertical curve. The carbon emission model of vehicles on vertical curve sections were deduced based on Xu’s [
The remainder of this paper is organized as follows: in Section
The methodological process that was used in this study is shown in Figure
Flowchart of methods.
The gentle slope of the vertical curve replaces the original steep gradient of the longitudinal slope. The carbon emissions of a vehicle on a vertical curve section are closely related to the slope of the vertical curve. Before establishing the energy conversion model on vertical curve sections, the energy conversion relationship of the vehicle on uphill and downhill sections must be clarified. According to numerous previous studies [
Propulsive force is required for the vehicle on a level terrain for the purpose of maintaining a cruising speed as only rolling and air resistance act on the vehicle. A significantly higher propulsive force is required for driving on upgrade sections than flat sections owing to the grade impact (grade resistance). The vehicle propulsive energy necessary to overcome the total resistance on a flat section and an uphill section at the cruising speed are given in the simplest form as
There are three driving behaviors on downhill sections (driving in the gear position and releasing the accelerator pedal, driving while pressing the accelerator, and braking, respectively) [
The force and energy conversion formula of vehicles on these road sections were adapted from Xu et al. [
Propulsive energy is closely related to fuel consumption and carbon emissions [
The IPCC conversion model recommended in the IPCC Climate Change Assessment Report [
At the turning point of the two longitudinal slope sections of the vertical profile, a quadratic parabola is usually adopted as a vertical curve to connect the two longitudinal slope sections [
Schematic diagram of vertical curve elements.
The design elements of the vertical curve mainly include radius
A positive
The carbon emission rate,
The vertical curve’s form is greatly affected by its terminal gradients. When the two terminal longitudinal slopes both are uphill or downhill, and with a tendency of uphill or downhill movement, the curve is referred to as a longitudinal vertical curve. When the terminal longitudinal slopes are uphill and downhill, respectively, the vertical curve is in a crest or sag form. The vertical curve is symmetrical or asymmetrical depending on whether the two terminal absolute gradients are equal or unequal [
The longitudinal vertical curve can be divided into uphill and downhill trends from the perspective of force analysis; this division creates an “uphill vertical curve” and “downhill vertical curve,” respectively. The driving energy on the uphill vertical curve can be obtained according to equation (
The fuel consumption of the engine in the idle state is the source of energy required to maintain the normal operation of the engine and to provide the normal operation of various vehicle parts (e.g., the brake, steering system booster pumps, and air-conditioning compressor). The idling fuel consumption determines the idle carbon emissions
In scenario
The carbon emission rate under scenario
In scenario
Schematic diagram of downhill vertical curve in scenario
The carbon emission rate in scenario
The values for
According to equations (
In scenario
Equations (
The typical fully sag and crest vertical curve forms are classified into symmetrical and asymmetrical depending on whether the absolute terminal vertical curve gradients are equal or not.
As shown in equation (
In scenario
Symmetrical vertical curves in scenario
The carbon emission rate of the vehicle on the symmetrical vertical curve section in scenario
In scenario
Symmetrical vertical curves in scenario
In scenario
The values for
The vehicle’s carbon emission rate can be determined by equation (
It can be seen in equations (
Asymmetric vertical curve: (a) crest; (b) sag.
The quantification of vehicle’s carbon emissions on asymmetric vertical curve sections can also be divided into two parts: the uphill trend and the downhill trend sections from the slope of zero. The goal of this study was to determine the carbon emission rules of different forms of vertical curve sections, so the determined quantitative method was adopted here.
The above analysis indicates that the carbon emission rate of the vehicle on the vertical curve is determined by the balance gradient and the terminal gradients of the vertical curve and is irrelevant to the radius or crest/sag form of the curve. Before predicting the vehicle’s carbon emissions, the type of the vertical curve should be figured out by its balance gradient and terminal gradients.
During the low-carbon design of the vertical curve, controlling the terminal gradient of the vertical curve to be less than the balance gradient can make the carbon emission rate of the two-way traffic on the vertical curve equal to the carbon emission rate of the flat section.
On the vertical profile of the actual road, the vertical curve and longitudinal slope sections are sequential. The cumulative carbon emissions on the vertical profile section can be determined by the following equations:
Field experiments can directly reflect the actual operation conditions and carbon emissions of a given vehicle, so field research was applied in this study. Typical flat, longitudinal slope, and vertical curve road sections were selected to measure vehicle velocity and fuel consumption data of vehicles traversing them. The IPCC conversion model was used to convert fuel consumption to carbon emissions.
An Ecan analyzer was adopted to derive the velocity, travel time, and fuel consumption data of passenger cars in the field test. The fuel consumption, speed, and travel time of trucks were measured with a diesel fuel consumption instrument JDSZ-EP-1-1D. An anemometer monitoring instrument AS8336 was used to measure wind speed. These devices have second-to-second sampling frequencies. The accuracy values of velocity, fuel consumption, and wind speed data are 0.1 km/h, 0.1 mL, and 0.001 m/s, respectively; the measurement errors are within ±3%, ±0.5%, and ±3%, respectively. The wind speed was required to be small and stable during the test. Any breeze with speed below 6.0 m/s has almost no effect on the movement of ground objects. The wind speed was required to be below 6.0 m/s and allowed to fluctuate within the range of 2.0 m/s during the test [
A traffic survey was conducted before the experiment. An AxleLightRLU11 vehicle classification statistical instrument was placed on the test roads prior to select the passenger car and truck with a large traffic volume. This instrument automatically collects and records vehicle performance data consisting of vehicle count, timely speed, vehicle type, and headway time with a high accuracy. It is small enough to be easily placed on the outermost edge of the hard shoulder and without affecting the behavior of passing motorists. Based on the traffic volume data on the test road and the development prospects of vehicles, two types of common passenger cars and three types of common trucks were selected as the dominant vehicle types. In order to ensure the reliability of the test data, 10 of each type of test vehicle were used in the test. The characteristics of the test vehicles are the same as the dominant vehicle types (Table
Test vehicles information.
Variable | Specification | ||||
---|---|---|---|---|---|
Vehicle type | Passenger car | SUV | Medium truck | Heavy-duty truck | Tractor |
Label | Car I | Car II | Truck I | Truck II | Truck III |
Mass (t) | 1.65 | 1.88 | 15 | 28 | 40 |
Frontal area (m2) | 1.80 | 2.0 | 5.64 | 5.64 | 6.08 |
Air resistance coefficient | 0.35 | 0.50 | 0.50 | 0.46 | 0.656 |
Engine type | Naturally aspirated | Compression-ignition | Xichai compression-ignition | ||
Fuel type | 92# gasoline | −10# diesel |
Driver performance varies depending on personal driving preferences and experience, so drivers were screened before the field test to ensure they were sufficiently experienced and familiar with the road. Each driver was given 10 days of training and testing to prevent any incorrect driving operations from affecting the test results. The drivers were required to maintain a normal cruising speed and to maintain a safe distance from the vehicle in front of them. The driving behavior of the test vehicle was not impacted by the other vehicles on the road. Fifty healthy male drivers between 15 and 20 years of driving experience passed the test. Each test vehicle type was assigned 10 drivers.
The field test was conducted on highways of different road grades. On the Xibao Expressway, the Hanzhong-Mianxian first-grade highway, and the S306 provincial highway, the flat straight sections were selected to measure the fuel consumption of vehicles travel at a uniform speed. On the Hanzhong-Mianxian first-grade highway (road I), Xunyi-Qiupotou second-grade highway (road II), and Xianyang-Xunyi expressway (road III), longitudinal sections and vertical curve sections were selected to measure the speed and fuel consumption data on uphill, downhill, and various vertical curve sections.
The speed was controlled within the speed limit requirements of the actual road throughout the test. The Xibao Expressway and Xianyang to Xunyi Expressway are composed of asphalt pavements in excellent condition. The rolling resistance coefficient is 1.25, the wind speed is 1.0 m/s, and the speed limits of passenger cars and trucks are 60–120 km/h and 60–100 km/h, respectively. The first-grade highway from Hanzhong to Mianxian is an asphalt pavement in fair condition. The rolling resistance coefficient is 1.5, the wind speed is 3.0 m/s, and the speed limit for passenger cars and trucks is 60–100 km/h and 60–80 km/h, respectively. The S306 Provincial Highway and Xunyi to Qiupotou second-grade road are composed of asphalt pavement in poor condition. The rolling resistance coefficient is 2.5, the wind speed is 6.0 m/s, and the speed limit ranges of passenger cars and trucks are 40–80 km/h and 40–60 km/h, respectively.
The experimental conditions were strictly controlled to eliminate the impact of any other factors on the vehicle carbon emission data gathered in this study. Experimental segments were required to be basic road sections; test locations were at least 1000 m away from any ramps, toll stations, bridges, and tunnels. The traffic flow in the test road was required to be in a free flow pattern with no other vehicles affecting the drivers’ normal operation of their vehicles. Traffic flow patterns and vehicle operating conditions were monitored in real time with the AxleLightRLU11 vehicle classification instrument. Consistent road pavement type and conditions were maintained throughout the test. The route’s horizontal alignment was a straight line or a curve with a radius greater than 2000 m [
According to probability theory, the tested carbon emission data should conform to the normal distribution [
Normal distribution test of the data: (a) histogram; (b) P-P plot.
Parameter values of the descriptive statistics test.
Descriptive analysis | Shapiro–Wilk | ||||||||
---|---|---|---|---|---|---|---|---|---|
Minimum | Maximum | Mean | Variance | Standard deviation | Skewness | Kurtosis | Statistics | df | Sig. |
15.71 | 24.32 | 20.23 | 4.904 | 2.214 | −0.186 | −0.762 | 0.978 | 35 | 0.681 |
Figure
The field test data were used to evaluate the accuracy of the carbon emission model established here. The influence of vertical curve design indexes on vehicle carbon emissions was determined by comparing the carbon emissions of vehicles on flat sections, longitudinal slope sections, and different forms of vertical curve sections. Each group of experimental results for comparisons was analyzed under scenarios where wind speed, road conditions, and other factors were basically the same.
A clear balance gradient allowed for easy verification of the carbon emission rules of vehicles on vertical curves. The rule of the balance gradient from shallow to steep grades versus velocities was confirmed recently by Xu et al. [
Balance gradients of test vehicles under different velocity conditions.
Road | Vehicles balance gradient (%) | |||||
---|---|---|---|---|---|---|
Car I | Car II | Truck I | Truck II | Truck III | ||
Road I | 40 | 2.80 | 3.00 | 2.00 | 1.90 | 1.90 |
50 | 3.30 | 3.50 | 2.30 | 2.00 | 2.00 | |
60 | 3.60 | 4.00 | 2.60 | 2.30 | 2.30 | |
70 | 4.20 | 4.50 | — | — | — | |
80 | 4.60 | 5.00 | — | — | — | |
Road II | 60 | 2.40 | 2.00 | 1.70 | 1.30 | 1.30 |
70 | 2.80 | 2.50 | 1.90 | 1.50 | 1.50 | |
80 | 3.20 | 3.00 | 2.20 | 1.70 | 1.70 | |
90 | 3.50 | 3.50 | — | — | — | |
100 | 4.00 | 4.00 | — | — | — | |
Road III | 60 | 2.00 | 4.50 | 1.30 | 1.20 | 1.20 |
70 | 2.50 | 5.00 | 1.50 | 1.30 | 1.30 | |
80 | 2.80 | 3.00 | 1.80 | 1.50 | 1.50 | |
90 | 3.00 | 3.50 | 2.00 | 1.60 | 1.60 | |
100 | 3.50 | 4.00 | 2.20 | 1.80 | 1.80 | |
110 | 4.00 | 4.50 | — | — | — | |
120 | 4.80 | 5.00 | — | — | — |
During the field tests, test trucks I, II, and III consumed 3, 5, and 7 liters of urea additives, respectively, for every 100 liters of diesel consumed.
Table
Vehicle carbon emissions on longitudinal vertical curve sections.
a
Table
When the test passenger cars and trucks traversed the downhill vertical curve with one of the terminal gradients greater than the balance gradient (nos. 20–22 and 14–22), the carbon emission rate appears to be determined by the balance gradient and terminal gradients. There is a large difference between the carbon emission rates on the vertical curve and those on the longitudinal slope with an average gradient.
When the terminal gradients of the downhill vertical curve are greater than the balance gradient, the carbon emission rate is equal to that in the idle state.
The carbon emission measurements of 12 test cases on the symmetrical vertical curve sections are shown in Table
Vehicle’s carbon emissions on symmetrical vertical curve sections.
The carbon emissions of vehicles on the vertical curve with the terminal gradients greater than the balance gradient are indicated by green shading.
The measured carbon emissions of car I, car II, truck I, truck II, and truck III maintaining cruise speeds of 100 km/h and 60 km/h on the flat section are 15.68 kg/100 km, 16.70 kg/100 km, 22.17 kg/100 km, 20.77 kg/100 km, and 60.30 kg/100 km and 79.55 kg/100 km, 79.06 kg/100 km, 103.68 kg/100 km, 108.74 kg/100 km, and 154.83 kg/100 km, respectively. When the gradients at both ends of the symmetrical vertical curve are less than the balance gradient, the carbon emission rate of any vehicle is almost equal to that on the flat road; the maximum relative errors for passenger cars and trucks are 8.88% and 8.22%, respectively. Compared to the flat road section, the difference in carbon emissions between the uphill and the downhill sections of the vertical curve appear to offset each other. Moreover, there is no energy loss due to braking as the vehicle travels downhill and no additional propulsion energy during uphill driving.
When the terminal gradients of the symmetrical vertical curve are greater than the balance gradient, the carbon emission rate is greater than that on flat road. More driving energy is necessary on the upward curve segment where the gradient is greater than the balance gradient to offset the braking energy loss during downhill driving. Carbon emissions increase as the terminal gradients of the symmetrical vertical curve increase. In the design process, the gradient of the longitudinal slope should be kept below the balance gradient to minimize vehicle carbon emissions on symmetrical vertical curve sections.
Table
The tested carbon emission data of 19 test cases on the asymmetric vertical curve sections are shown in Table
Vehicle’s carbon emissions on asymmetric vertical curve sections.
No. | Indexes | Predicted CO2 (kg/100 km) | Tested CO2 (kg/100 km) | Diff. (%) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Car I | Car II | Truck I | Truck II | Truck III | Car I | Car II | Truck I | Truck II | Truck III | ||||||
1 | 100 | 0.8 | −1.40 | 13000 | 15.15 | 18.76 | 54.81 | 65.69 | 95.08 | 14.82 | 19.49 | 56.94 | 62.41 | 96.66 | 5.26 |
2 | 100 | 1.4 | −0.80 | 13000 | 18.02 | 22.03 | 73.72 | 97.16 | 140.15 | 16.62 | 24.22 | 69.86 | 92.43 | 136.12 | 9.05 |
3 | 100 | 1.476 | −1.64 | 13000 | 16.20 | 19.95 | 61.68 | 77.39 | 111.70 | 15.61 | 21.55 | 59.50 | 78.04 | 108.65 | 7.44 |
4 | 100 | 1.64 | −1.48 | 13000 | 16.98 | 20.84 | 66.85 | 85.73 | 123.78 | 16.24 | 19.16 | 65.83 | 90.93 | 122.60 | 8.77 |
5 | 100 | 1.5 | −0.76 | 16000 | 18.36 | 22.41 | 75.92 | 100.83 | 145.41 | 17.42 | 21.44 | 77.69 | 98.47 | 140.60 | 5.40 |
6 | 100 | 0.76 | −1.50 | 16000 | 14.82 | 18.38 | 52.60 | 62.04 | 89.82 | 15.51 | 16.89 | 54.35 | 59.88 | 84.99 | 8.80 |
7 | 100 | 1.7 | −1.54 | 16000 | 16.97 | 20.83 | 66.78 | 85.67 | 123.65 | 18.41 | 22.65 | 65.46 | 83.70 | 121.21 | 8.04 |
8 | 100 | 1.54 | −1.70 | 16000 | 16.21 | 19.96 | 61.74 | 77.69 | 112.08 | 15.63 | 21.75 | 58.88 | 79.11 | 109.36 | 8.24 |
9 | 100 | −2.2 | 0.80 | 10000 | 13.24 | 16.58 | 42.52 | 49.48 | 71.20 | 14.65 | 15.75 | 46.47 | 46.04 | 74.57 | 9.63 |
10 | 100 | −0.8 | 2.20 | 10000 | 19.94 | 24.21 | 86.32 | 118.14 | 170.20 | 21.63 | 22.92 | 80.31 | 112.21 | 172.73 | 7.82 |
11 | 100 | 2.44 | −1.40 | 12000 | 19.08 | 23.23 | 80.65 | 108.70 | 156.68 | 18.38 | 21.43 | 74.64 | 101.05 | 158.81 | 8.39 |
12 | 100 | 1.4 | −2.44 | 12000 | 14.10 | 17.56 | 48.84 | 60.69 | 87.23 | 12.95 | 18.53 | 46.91 | 59.30 | 86.91 | 8.89 |
13 | 100 | −1.93 | 2.85 | 12000 | 18.79 | 22.90 | 78.76 | 106.75 | 153.64 | 18.47 | 22.66 | 76.85 | 108.10 | 153.05 | 2.48 |
14 | 100 | −2.85 | 1.93 | 12000 | 14.39 | 17.88 | 52.40 | 67.87 | 97.42 | 13.83 | 16.97 | 52.46 | 70.88 | 102.58 | 5.39 |
15 | 100 | 3.2 | −1.40 | 12000 | 20.90 | 25.30 | 92.62 | 128.62 | 185.23 | 23.13 | 26.67 | 85.08 | 123.81 | 183.09 | 9.66 |
16 | 100 | 1.4 | −3.20 | 12000 | 12.28 | 15.49 | 41.20 | 51.45 | 73.65 | 11.61 | 14.52 | 39.20 | 52.10 | 76.84 | 6.65 |
17 | 60 | −2.2 | 4.00 | 4800 | 21.88 | 26.13 | 103.34 | 156.84 | 223.35 | 20.16 | 27.99 | 99.52 | 153.41 | 214.47 | 8.55 |
18 | 60 | −5 | 2.50 | 1500 | 12.61 | 15.39 | 51.59 | 76.66 | 107.89 | 11.55 | 16.46 | 48.74 | 71.04 | 109.04 | 9.21 |
19 | 60 | 6 | −3.20 | 2000 | 24.28 | 28.85 | 120.67 | 187.33 | 266.87 | 22.55 | 29.01 | 109.87 | 181.19 | 252.71 | 9.83 |
Tables
Cumulative carbon emissions of car I on vertical curve and vertical profile sections.
No. | Indicators | Cumulative predicted CO2 emissions (g) | Cumulative tested CO2 emissions (g) | Diff. (%) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Vertical curve | Vertical profile | Vertical curve | Vertical profile | |||||||||||
Forward | Reverse | Forward | Reverse | Forward | Reverse | Forward | Reverse | |||||||
1 | 100 | 1.2 | 0.6 | 54000 | 530 | 64.38 | 40.29 | 104.02 | 65.10 | 63.27 | 38.31 | 106.37 | 62.77 | 5.16 |
2 | 100 | 1.2 | 0.5 | 20000 | 530 | 27.14 | 17.53 | 102.75 | 66.37 | 28.25 | 16.65 | 105.86 | 69.43 | 5.29 |
3 | 100 | 3.5 | 2.2 | 24000 | 850 | 90.35 | 9.76 | 246.14 | 29.62 | 89.75 | 9.86 | 245.09 | 30.05 | 1.42 |
4 | 100 | 3.5 | 2.2 | 50000 | 850 | 188.23 | 20.33 | 246.14 | 27.72 | 179.06 | 21.93 | 242.41 | 26.53 | 7.29 |
5 | 60 | 4.5 | 1 | 4000 | 500 | 36.63 | 7.77 | 130.82 | 34.76 | 38.68 | 7.45 | 134.50 | 32.98 | 5.41 |
6 | 60 | 4.5 | 0.95 | 4600 | 500 | 42.53 | 9.23 | 130.23 | 34.88 | 40.69 | 9.21 | 132.41 | 35.61 | 4.53 |
7 | 60 | 4.45 | 1.1 | 9000 | 500 | 79.25 | 16.26 | 131.42 | 30.66 | 80.54 | 15.50 | 136.11 | 29.11 | 5.34 |
8 | 100 | 2 | −2 | 16000 | 1160 | 106.17 | 106.17 | 192.44 | 192.44 | 99.77 | 100.14 | 182.66 | 182.66 | 6.42 |
9 | 100 | 2 | −2 | 24000 | 1160 | 159.26 | 159.26 | 192.44 | 192.44 | 151.15 | 152.08 | 193.98 | 191.98 | 5.36 |
10 | 60 | 2 | −2 | 16000 | 1160 | 112.49 | 112.49 | 203.88 | 203.88 | 107.09 | 108.54 | 200.08 | 189.18 | 7.77 |
11 | 60 | 2 | −2 | 24000 | 1160 | 168.73 | 168.73 | 203.88 | 203.88 | 156.14 | 156.28 | 208.41 | 189.82 | 8.06 |
12 | 60 | 5 | −5 | 1500 | 710 | 27.51 | 27.51 | 149.90 | 149.90 | 26.54 | 28.53 | 141.39 | 138.08 | 8.56 |
13 | 60 | 5.1 | −5.08 | 5000 | 710 | 93.88 | 93.48 | 138.29 | 137.80 | 87.14 | 89.11 | 135.77 | 129.85 | 7.74 |
14 | 60 | 6 | −5.88 | 2000 | 800 | 45.85 | 44.80 | 182.22 | 179.55 | 45.04 | 45.28 | 174.13 | 170.45 | 5.34 |
15 | 60 | 6.01 | −6 | 5000 | 800 | 114.99 | 114.77 | 163.41 | 163.14 | 115.60 | 114.09 | 159.13 | 153.50 | 6.28 |
16 | 60 | −4 | 4.05 | 1750 | 565 | 25.19 | 24.89 | 108.24 | 107.43 | 24.05 | 23.10 | 100.11 | 100.57 | 8.12 |
17 | 60 | −3.95 | 4 | 4600 | 565 | 65.31 | 64.52 | 104.10 | 103.07 | 60.27 | 62.04 | 96.76 | 97.15 | 8.37 |
c
The field test data confirm that the quantitative CO2 emission model on vertical curve and vertical profile sections is valid, as is the vehicle CO2 emission rules on various forms of vertical curve sections.
To further explore the distribution trends and dispersion degrees of the simulation results, a descriptive statistical test was performed on the residual values, as shown in Figure
Normal distribution test of model residuals: (a) histogram; (b) P-P plot.
Parameters of descriptive statistics test.
Minimum | Maximum | Mean | Variance | Standard deviation | Skewness | Kurtosis |
---|---|---|---|---|---|---|
−14.16 | 15.77 | −0.46 | 10.682 | 3.268 | 0.753 | 5.676 |
Figure
The actual vertical profile section is a combination of longitudinal slopes and vertical curves. The effects of radius on the carbon emissions of vehicles on the vertical profile section were also determined in this study followed by a sensitivity analysis of vertical curve design indexes on carbon emissions. The indexes studied here include the gradient and radius.
The vertical profile was divided into six cases by the balance gradient for analysis, as illustrated in Figure
Six cases vertical curves in vertical profile: (a) uphill vertical curve; (b) downhill vertical curve; (c) symmetrical crest vertical curve; (d) symmetrical sag vertical curve.
The carbon emissions of car I on the vertical profile sections of cases I–VI were obtained using the proposed carbon emission model, as shown in Figure
Vehicle carbon emissions on vertical profile sections of cases I–VI: (a) carbon emission rate; (b) cumulative carbon emissions.
As shown in Figure
When vehicles travel along the uphill vertical profile sections of cases I-II, the carbon emission rate is equal to that on the longitudinal slope section with the average gradient regardless of the radius. The radius has no effect on the height difference to be overcome on the uphill vertical profile. The mileage of the vertical profile section is fixed. Therefore, the cumulative carbon emissions remain unchanged. The same rule emerges in uphill vertical profile sections with terminal gradients larger than the balance gradient.
In case III, the vehicles always require some amount of driving force to traverse downhill vertical profiles with gradients at any point less than the balance gradient, again regardless of the radius. The carbon emission rate and cumulative carbon emissions are independent of the radius and equal to those on the longitudinal slope with the average gradient.
When the gradients at both ends of the symmetrical vertical curve are not greater than the balance gradient (case V), the carbon emission rate is equal to that on the flat section regardless of the radius. The extracarbon emissions on the uphill section appear to offset the reduced carbon emissions on the downhill section as compared with the flat sections. The cumulative carbon emissions on the symmetrical vertical curve are the same as those on the equal-mileage flat section.
In case IV, the downhill vertical profile has one terminal gradient greater than the balance gradient while the other is not. The cumulative carbon emissions in this case can be obtained by the following equations:
According to equation (
In case VI, the terminal gradients of symmetrical vertical profile are greater than the balance gradient, and the cumulative carbon emissions can be obtained according to the following equations:
The extracarbon emission rates on the uphill section were greater than the reduced carbon emission rates on the downhill section. According to equation (
A larger radius results in less cumulative carbon emissions on the downhill vertical profile in case IV and on the symmetrical vertical profile in case VI. The same rules were found to apply for asymmetric vertical curve sections with gradients larger than the balance gradient. The radius is irrelevant to the carbon emissions on the other forms of vertical profile.
When a vertical curve is designed with a general radius higher than the standard, it necessitates extra construction costs for the earthwork for curve flattening [
The Shaanxi Provincial Department of Transportation provided relevant data in 2020 for Shaanxi Province, China: the average cost of one cubic meter of earthwork equals 7.4 RMB, and the average unit prices of gasoline and diesel are 5.41 RMB and 5.02 RMB, respectively; the average annual growth rate of passenger cars is 3%. Table
Estimated benefits and costs on vertical profile sections.
Case | Extra construction cost (RMB) | Fuel cost saving (RMB) | Health cost saving (RMB) | Benefit-cost ratio | |
---|---|---|---|---|---|
13 years | 16 years | ||||
IV | 219.31 | 50.37 | 3.12 | 0.77 | 1.02 |
VI | 2539.06 | 779.48 | 50.44 | 1.03 | 1.37 |
On the downhill vertical profile in case IV, symmetrical vertical profile in case VI, and asymmetric vertical profile with the gradient larger than the balance gradient, the flattened-curvature vertical curve design is beneficial to the environment and economy throughout the life cycle of the expressway.
The radius affects the vehicle’s carbon emission rate on the vertical profile in cases IV and VI. A schematic diagram of the sensitivity analysis results for the gradient and radius under cases IV and VI is shown in Figure
Passenger car carbon emission trends under changing indexes.
In case IV, as radius increases by 10% from 1500 m to 3000 m, the carbon emission rate decreases by 24.68%. In case VI, as the radius increases by 10% from 1500 m to 3000 m, the carbon emission rate decreases by 11.81%. In case IV, as the front gradient increases by 10% from −6% to 0%, the carbon emission rate increases by 212.34%. This is consistent with the rule of equation (
Figure
This paper proposes a carbon emission model for vehicles on vertical curve sections based on Xu’s energy conversion model on longitudinal slopes [
This study centers on the carbon emissions of vehicles on vertical curve sections. The horizontal alignment was required to be straight or with a radius greater than 2000 m during the field test, which eliminated the influence of horizontal alignment on vehicle carbon emissions. The influence of vertical curve design indicators on the carbon emissions of common passenger cars and trucks was explored here where the vehicle was assumed to travel at a cruising speed, thus eliminating the influence of velocity fluctuations on carbon emissions. The quantitative carbon emission model has limited ability to forecast the carbon emissions of vehicles on vertical curve sections when fluctuating in speed during travel. The propulsive energy of a vehicle with fluctuating speed is closely related to its inertial resistance during acceleration and the characteristics of its engine gearbox [
Five typical vehicles comprising majority of highway traffic in China were selected as the test vehicles in this study. Different regions have different fuel characteristics, vehicle performance, road pavement types, and pavement conditions. The model presented here can be modified by adjusting certain parameters (e.g., vehicle type, engine type, fuel type, road condition, vehicle load, frontal area, and tire type) for application of other types of fuel-powered vehicles in other regions. Mechanical efficiency and fuel utilization rates were also idealized here, which may have had some impact on the results.
The model proposed in this paper was shown to accurately quantify the fuel consumption and carbon emissions of vehicles on vertical curve sections in China. The carbon emission rules on different forms of vertical curves as well as the influence of vertical curve indicators (gradient and radius) on carbon emissions were determined. The results can reduce the uncertainty in engineering judgments for environmentally friendly highway vertical profile designs. The main findings can be summarized as follows: The vehicle’s carbon emission rate on the vertical curve is independent of the radius, as well as the crest or sag form of the vertical curve. The carbon emission rate of vehicle on the vertical curve is determined by the difference between the terminal gradients of the vertical curve and balance gradient. When a vehicle traverses a vertical curve with an uphill trend, the height difference that the vehicle needs to overcome is fixed; the carbon emission rate is equal to that on the longitudinal slope with the average gradient. When the terminal gradients of the downhill vertical curve are both less than the balance gradient, driving energy is required during the travel, and the carbon emission rate is determined by the terminal gradients. When a vehicle travels downhill on a vertical curve with one of the terminal gradients greater than the balance gradient, braking is necessary at certain road sections to maintain the cruise speed; the vehicle’s carbon emission rate is thus determined by terminal gradients and balance gradient. When the terminal gradients of the downhill vertical curve are greater than the balance gradient, vehicle can slide downhill in the gear position and the carbon emission rate is equal to that during idling. When the gradients at both ends of the symmetrical vertical curve are less than the balance gradient, the carbon emission rate of the vehicle is almost equal to that on the flat road section; the uphill and downhill sections balance each other. When the terminal gradients of the symmetrical vertical curve are greater than the balance gradient, the carbon emission rate is greater than that on flat sections. More driving energy is needed on the upward curve segment where the gradient is greater than the balance gradient to offset the braking energy loss during downhill driving. The greater the carbon emission rate increases as the terminal gradients increase. On the vertical profile composed of downhill/asymmetric/symmetrical vertical curves and with a gradient greater than the balance gradient, the carbon emission rate is determined by the gradients and radius. A larger radius results in a smaller carbon emission rate because the mileage and driving force are reduced on downhill sections with gradients less than the balance gradient and on uphill sections with gradients greater than the balance gradient. The radius has less impact on the carbon emission rate of vehicles on these vertical profile sections than the terminal gradients of the vertical curve. The radius is irrelevant to the carbon emission rate on other forms of vertical profile. The gradient should be kept below the balance gradient in the vertical profile design to conserve energy and minimize carbon emissions from two-way traffic. If the gradient requirements cannot be met due to terrain restrictions or other reasons, the radii of the downhill vertical curve, symmetrical vertical curve, and asymmetric vertical curve should be increased to reduce carbon emissions.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Y.D. and J.X. prepared methodology for the study. Y.D. and J.X. validated the study. Y.D. did formal analysis. Y.D. and J.X. curated the data. J.X. investigated the study. Y.D. reviewed and edited the manuscript and wrote the original draft. J.X. helped in obtaining funding acquisition, administrated the project, supervised the study, and visualized the study.
The authors are grateful to the Shaanxi Provincial Department of Transportation for generously providing relevant information and the highway design documents of the test road sections. We also thank the drivers for their cooperation during the field experiment. This research was funded in part by the National Key Research and Development Program of China (no. 2016YFC0802208) and the Transport Technology Project of Shaanxi Province (Grant no. 18–23R).