Printer Friendly

Application of Chebyshev's theorem for estimating C[O.sub.2] emissions due to overloading of heavy duty diesel trucks/Aplicacion del teorema de Chebyshev para estimar las emisiones de C[O.sub.2] por sobrecarga de las unidades de transporte terrestre de carga.

A certain amount of emissions from the trucking industry operating within regulated load and speed parameters is inevitable. However, overloaded and speeding trucks generate additional pollution that can be avoided. It is therefore important to ensure truck compliance to weight regulation (Jacob and Feypell, 2010). Measuring emissions for heavy duty diesel trucks in any transportation system, considering their payload, speed, road type and road surface conditions, represent an impractical and very costly effort. In contrast, application of Chebyshev's theorem allows, with the use of an experimental sample, to validate a truck's theoretical formulation so as to obtain its fuel efficiency and hence its C[O.sub.2] emissions.

This paper proposes a methodology to estimate emission levels from overloaded trucks, based on the amount of fuel consumed. The procedure presented here, based on the application of Chebyshev's theorem, allowed the use of different truck and emission models, according with the degree of statistical confidence to be achieved. Using known truck fuel efficiency, emission models and data, an application is herein developed for the Mexican case. An assertion can be made that there is an important increment in C[O.sub.2] emitted by an overloaded and speeding truck, compared to emissions produced by trucks operating within the legal weight and speed limits. Application of the proposed approach considers overload level, operating speed, type of road surface and road slope. Results are presented for five axle articulated and double trucks, which are the most representative trucks for this case.

Methodology to Estimate Fuel Consumption and C[O.sub.2] Emissions of Overloaded and Speeding Trucks

Approach taken for validating the theoretical formulation

Run a limited number of test trips ([n.sub.1]) registering fuel consumption, type of terrain, road surface conditions, load levels and average travel speed.

Gather as much information as possible from trucking companies ([n.sub.2]) related to their fuel consumption and trips operating conditions.

Choose a truck, fuel consumption and emission model, and considering truck's and road characteristics from the test trips ([n.sub.3]), calculate fuel efficiency and C[O.sub.2] emissions.

Using Chebyshev's theorem, calculate Chebyshev's intervals in order to validate within certain confidence statistical level, data coming from the chosen models.

Conduct the validation considering the Chebyshev's intervals, the results produced by the chosen models and the experimental data collected.

Chebyshev's theorem

Validation of the theoretically calculated data, based on that experimentally gathered, is carried out by constructing Chebyshev's intervals (Kasmier, 1998), assuming a predetermined confidence level. Coefficients of variability are also calculated for these intervals. Construction of Chebyshev's intervals is carried out as follows.

The probability that any set of fuel efficiency values (X), expressed in km/l (with mean [mu] and variance [[sigma].sup.2]), takes values within the standard deviation of the mean value, is at least 1 - 1/[k.sup.2]. That is:

P([absolute value of X - [mu]] < k[sigma]) [greater than or equal to] 1 - 1/[k.sup.2] (1)

p([mu] - k[sigma] < X < [mu] + k[sigma]) [greater than or equal to] 1 - 1/[k.sup.2] (2)


Considering sample size n ([n.sub.1], [n.sub.2], [n.sub.3]) and looking for a high degree of results reliability (Kasmier, 1998), Chebyshev's intervals can be calculated with a significance level a. Therefore, from expression [alpha] = 1/[k.sup.2] and a confidence level of 1-[alpha], k, can be obtained from 1 - 1/[k.sup.2] = 1 - [alpha] for any k > 1. This means that the minimum proportion of fuel efficiency values that are within k times the standard deviation from the population mean is at least 1-[alpha]. In other words, it means that 1-[alpha] out of 100 samples of size n contain the population average fuel efficiency values.

The set of fuel efficiency values X satisfies the properties of a discrete random variable (Walpole, 1978; Daniel, 2011), as

a) P(X = x) = f(x) [greater than or equal to] 0

b) [[summation].sub.x] P(X = x) = 1

X is a random variable with sampling distribution for a sample size n (Blalock, 1972; Daniel, 2008). Since the population mean and standard deviation are unknown, they are replaced by the sample mean and its standard deviation, calculated as

[bar.x] = [summation over x] x/n (4)

[s.sub.[bar.x]] = [square root of [[[summation].sup.n.sub.i-1][([x.sub.i] - [bar.x]).sup.2]]/n-1] (5)

It is stressed that Chebyshev's inequality is rarely used to set mean value confidence intervals (in our case fuel efficiency average for both data, experimental and calculated). However, in this case, this is the best method to apply given a population that is not normal and only small samples are available (Kasmier, 1998).

From Eq. 3, Chebyshev's intervals are set as

[bar.x] [+ or -] k x [s.sub.[bar.x]]/[square root of n] (6)

Considering the proposed methodology, Chebyshev's theorem guarantees that mean values of the experimental [n.sub.1] and sampled [n.sub.2] data are within the Chebyshev's interval obtained for the calculated [n.sub.3] data, within a 1-a statistical confidence level.

Fuel Consumption and C[O.sub.2] Emission

Although there are few recent estimates of the global fuel consumption and related C[O.sub.2] emissions of road transport (Halenka and Uherek, 2010), the effects of vehicle weight and road grade have not been studied in detail (Naguib, 2011). A majority of emission models include a number of vehicle characteristics, travelled mileage, and driving modes, but other important factors, such as vehicle weight, road grades, and weather effects, are not sufficiently addressed as they are difficult to predict or measure (Chunxia, 2005; Suzuki, 2011). The main types of emission models are speed-based, modal, and fuel-based models. The first two types are the most commonly used. In speed-based models, the main input is the average speed; simplicity and limited data needs are their main advantages, but they do not account for driver (speed fluctuations) and roadway influences. Examples of speed-based emissions models include EPA MOBILE (EPA, 2009; COPERT, 2009; EMFAC, 2007). Modal models are based on vehicle's operating mode determined from roadway, driver, and traffic factors to calculate emissions.

In order to illustrate the methodology presented, the well-known relations involving road slope, rolling and aerodynamic resistances found in (Fitch, 1994), Chunxia and Seungju (2005) and Morales et al. (1995) are used for a truck model. For fuel consumption and C[O.sub.2] emission estimation, the models proposed by Torres (1998) and by Zadek and Schulz (2010) are used.

Tractive force

This model assumes there is a tractive force equal to the sum of forces opposing the truck's movement. It is assumed that the truck travels at a constant speed, thus the tractive force [F.sub.t] available at the wheels is:

[F.sub.t] = [F.sub.s] + [F.sub.s] + [F.sub.r] (7)

with each force given by

F = g x m x sin([theta]) (8)

[F.sub.a] = d/2 x [C.sub.d] [A.sub.f] x [V.sup.2] (9)

[F.sub.r] = ([C.sub.8] x W + [C.sub.v] x W x V) x r (10)

Considering international units for expressing all forces in Newtons, the tractive force available is obtained by multiplying truck's speed by the factor 0.0003714 (Fitch, 1994) in order to obtain the required motor power as horse power (HP) or by 0.000498 for kW.

The following expressions are used to evaluate the truck's fuel efficiency and the amount of C[O.sub.2] emitted (Torres, 1998; Zadek, 2010). Using the proper units, fuel efficiency can be expressed in km/l and C[O.sub.2] emission in kg/100km travelled. Thus,

[F.sub.e] = V / [[P.sub.r] x SC x 1/[rho]] (11)

C[O.sub.2] = D/[F.sub.e] (HV x EF) (12)

Mexican Case Example. Field vs Calculated Data

According to the Mexican Transport Institute (IMT), vehicles transporting the highest load volume in Mexico are those shown in Table I. These heavy-duty diesel trucks (HDDT) are the two-axle truck, three-axle truck, five axle articulated and double. Of these vehicles, the five axle articulated and the double stand out, both for transporting most of cargo in the country and for being the most overloaded units. As an example, in 2007 (Table I), these units carried 68.7% of total load moved on Mexican roads, representing 83.2% of total load economic value for that year. These trucks are also the most overloaded, with an average extra gross vehicle weight of 22.1% for the five axle articulated and 31.1% for the double truck.

The truck overweight problem is associated with short term profits (EMFAC, 2007). But overloading is not necessarily associated with lower operating costs; on the long run an overloaded truck requires a more intensive maintenance. Additionally, an overloaded truck is more prone to be involved in accidents, causing more casualties (Chan, 2008) and road damage (Jacob and Feypell, 2010), and increases fuel consumption (Naguib, 2011). Due to this extra fuel consumption, truck overloading causes an increment on C[O.sub.2] emissions (Halenka and Uherek, 2010).

In 2002, C[O.sub.2] emissions in Mexico were estimated in 643,183,000 tons (SEMARNAT, 2007). According to the greenhouse gases national emission inventory of 2002 (Mar, 2005), the total C[O.sub.2] emissions from the transport sector were 111,942,170 tons. From this amount, 91% was emitted by trucks, 6% by airplanes, 2% by ships and the remaining 1% by railroad cars. This estimation was carried out (Gonzalez, 2007) following the Good Practice Guidance and Uncertainty Management (GBPMI) of the Intergovernmental Panel on Climate Change (IPCC). Similar figures of C[O.sub.2] emissions in Mexico were obtained using the Highway Development and Management System HDM-4 (Torras et al., 2005). To this regard, the IMT is carrying out a sensitivity analysis for determination of appropriate values to be used in the HDM-4 operating costs sub model (Arroyo and Aguerrebere, 2002).

Measuring emissions for the 141,000 five axles articulated and double trucks (SCT, 2009) operating in Mexico, considering their payload, speed, road type and road surface conditions represent an impractical and extremely costly effort. Thus, fuel efficiency was obtained for nine test runs. At the beginning of each test, the truck fuel tank was 100% full. At the end of each test, the amount of consumed fuel was divided by the traveled distance. Experimentally obtained fuel efficiency for the test runs, is shown in Table II. Table III shows the percentage of total traveled distance, indicating slope and surface road condition, for each route. Data taken from Tables II and III were used to calculate fuel efficiency and C[O.sub.2] emissions by applying Eqs. 7 to 12. Table III also shows these average fuel efficiencies.

Chebyshev's intervals, calculated with different percentages of confidence level and values, are presented on Table IV. Data sources for these calculations are experimental trips ([n.sub.1]), truck's company ([n.sub.2]) and those calculated ([n.sub.3]) with Eqs. 7 to 12.

The calculated Chebyshev's intervals contain the sample means experimental and truck's company ones, which also can be seen in Table IV. In particular for k= 3.16 there is a likelihood that 90 out of 100 samples of size 9, contains the population mean. Variation coefficients are calculated using the expression

CV = [s.sub.[bar.x]]/[absolute value of [bar.x]] (13)

For each set of data, the variation coefficients are [CV.sub.1], calculated from experimental data ([n.sub.1] = 9); [CV.sub.2], calculated from truck's company data ([n.sub.2]= 52); and [CV.sub.3], calculated from theoretical data ([n.sub.3] = 9)


[n.sub.1] [right arrow] [CV.sub.1] = 0.4896/2.25 = 0.2176 < 1

[n.sub.1] [right arrow] [CV.sub.1] = 0.4911/2.0378 = 0.2410 < 1

[n.sub.1] [right arrow] [CV.sub.1] = 0.647/1.926 = 0.3359 < 1

The variability coefficients [CV.sub.1], [CV.sub.2] and [CV.sub.3] is <1. This value implies that there is low data variability from their respective mean values. Also [CV.sub.1]>[CV.sub.3]>[CV.sub.2], means that the calculated data are more heterogeneous than the experimental and truck's company sample data.

For different levels of confidence, theoretical data Chebyshev's intervals, contain the experimental and company samples averages. Mean values for the experimental data, company sample data, and that given by theoretical data, are 2.25, 2.03 and 1.92, respectively. Thus, formulations that yield the theoretical data are validated with a sample, n= 9, within a 90% confidence interval.

Statistical Inference for calculating fuel efficiency (km/l)

It has been established that Eqs. 7 to 12, validated in previous section, allow to simulate truck's fuel consumption within a 90% confidence interval. So, using these expressions, the following two conditions were simulated: 1) keeping truck's weight and speed constants, traveling on hilly terrain managing slopes of 1, 1.5, 2 and

2.5% (Avila, Alarcon, 2002), and 2) keeping the slope constant, trucks traveling at different loads (loaded and overloaded) and speeds (60, 80 and 110km/h).

Estimation of C[O.sub.2] emissions (kg/100km)

C[O.sub.2] emissions were calculated according to Ecs 7-12. Table V presents C[O.sub.2] levels (kg/100km) emitted by five axle articulated and double trucks traveling on a regular condition road surface, negotiating various slopes at different speeds and load levels. On this table it can also be seen the emission's level increase when a truck is traveling overloaded or speeding. From this information it can be evaluated one of the worst cases for C[O.sub.2] emissions, that is, when a truck travels overloaded and speeding. In this situation a truck generates in the range of 60% more C[O.sub.2] than allowed by the operating standards set by the authority.


The methodology presented allows simulating different scenarios. These scenarios reflect with a very good approximation the extra pollution that speeding and overloaded trucks emit. So, based on the available data related with the amount of overloaded and speeding trucks, as well as the trend of growth in the number of units, estimation of C[O.sub.2] emitted by trucks can be carried out. For the Mexican case, Figure 1 shows the annual C[O.sub.2] (kg/100km) emitted by five axle and double trucks, both with weight and average speed regulated and not regulated. Figure 2 shows the results of annual C[O.sub.2] (kg/100km) emitted by both types of trucks, both with weight and average speed regulated and not regulated.


1. A methodology for estimating C[O.sub.2] emissions from overloaded and speeding heavy duty vehicles, based on Chebyshev's Theorem was presented.

2. The methodology presented ensures, within a certain statistical confidence level, validation of fuel efficiency data coming from different sources.

3. For the example presented, the theoretical calculated Chebyshev's intervals, contain experimental and sampled (truck's company) data means.

4. Using the validated model, estimation within a 90% confidence level of C[O.sub.2] emissions produced by overloaded and speeding trucks were carried out.

5. Considering the growth in vehicle numbers and the overloading and speeding in the past nine years in Mexico, it was estimated that due to such overloading and speeding, an average of 60% more C[O.sub.2] was annually emitted.


X: random variable; in this case it is efficiency (km/l)

x: fuel efficiency values (km/l)

[mu]: average fuel efficiency of truck's population

[sigma]: standard deviation of the population

f(x): probability of value x

k: number of a from the population mean

[bar.x]: sample mean

[s.sub.x] : standard deviation of the sample

n: sample size

[F.sub.1]: tractive forve available

[F.sub.2]: slope resistance force

[F.sub.a]: aerodynamic force

[F.sub.r]: rolling resistance force

g: gravity acceleration

[theta]: angle of inclination

d: air density

[A.sub.f]: truck's front area

V: truck's velocity

[C.sub.d]: aerodynamic coefficient

[C.sub.[theta]]: rolling static coefficient

[C.sub.r]: rolling dynamic coefficient

r: rolling friction coefficient

m: mass

W: weight

[F.sub.e]: fuel efficiency

[P.sub.r]: required power

SC: specific fuel consumption

[rho]: diesel density

D: travelled distance

HV: diesel heath value

EF: emission factor

CV: coefficient of variation

Received: 02/19/2013. Modified: 04/09/2014: Accepted: 04/25/2014.


Arriaga PM, Garnica AP (1998) Indice Internacional de Rugosidad. Aplicacion en la Red Carretera de Mexico. Technical Report No. 108. Instituto Mexicano del Transporte. Queretaro, Mexico. 47 pp.

Arroyo OJA, Aguerrebere SR (2002) Estado Superficial y Costos de Operacion en Carreteras Technical Report No. 202. Instituto Mexicano del Transporte. Queretaro, Mexico. 76 pp.

Avila R, Alarcon J (2006) Calculo de los costos de operacion vehicular en la carretera Cuitzeo--Puruandiro--Zinaparo y su impacto en los usuarios. Ciencia Nicolaita No. 45: 85-96.

Blalock HM (1986) Estadistica Social. Fondo de Cultura Economica. Mexico. 603 pp.

COPERT 4 (2009) Estimating Emissions from Road. European Emissions Agency. http:// (Cons. 06/22/2012).

Chan YC (2008) Truck Overloading Study in Developing Countries and Strategies to Minimize its Impact. Thesis. Queensland University of Technology. 164 pp.

Chunxia F, Seungju Y (2005) Data Needs for a Proposed Modal Heavy-Duty Diesel Vehicle. 98th AWMA Meeting. Minneapolis, MN, USA. Paper 1072.

Daniel W (2008) Bioestadistica. 4th ed. Limusa. Mexico. 755 pp.

EMFAC (2007) Air Resources Board. California Environmental Protection Agency. www. (Cons. 06/15/2012).

EPA (2009) Air Quality Management Online Portal Emissions Inventory. U.S. Environmental Protection Agency. aqmportal/management/emissionsinventory (Cons. 05/14/2012).

EPA (2012) Heavy Duty Engine Emission Conversion Factors for MOBILE 6 Analysis of BSFC. National Service Center for Environmental Publications. http:/ (Cons. 06/24/2012).

Fitch JW (1994) Motor Truck Engineering Handbook. Society of Automotive Engineers. Warrendale, PA, USA. 433 pp.

Gonzalez S (2007) Inventarios de Gases Efecto Invernadero segun el IPCC. Instituto Nacional de Investigaciones Agricolas. La Platina, Chile. (Cons. 07/18/2012)

Gutierrez HJL, Villegas VN, Soria AVJ (2008) Estudio Estadistico de Campo del Autotransporte Nacional. Analisis Estadistico de la Informacion Recopilada en las Estaciones Instaladas en 2007. Technical Document No. 40. Instituto Mexicano del Transporte. Queretaro, Mexico. 100 pp.

Gutierrez HJL, Villegas VN, Soria AVJ (2010) Estudio Estadistico de Campo del Autotransporte Nacional. Analisis Estadistico de la Informacion Recopilada en las Estaciones Instaladas en 2009. Technical Document No. 45. Instituto Mexicano del Transporte. Queretaro, Mexico. 121 pp.

Halenka T, Uherek E (2010) Transport impacts on atmosphere and climate. Land Transp. Atmos.c Environ. 44: 4772-4816.

Jacob B, Feypell V (2010) Improving truck safety: Potencial of weight-in-motion technology. IATSS Res. 34: 9-15.

Kasmier L (1998) Applied Statistics and Economics Management Schaum Series..131 pp.

Mar E (2005) Inventario Nacional de Gases de Efecto Invernadero 2002. Instituto Mexicano del Petroleo, prepared for Instituto Nacional de Ecologia. Mexico. 100 pp.

Morales-Rafael M, Hernandez-Guzman A (2012) Manual de Conduccion Tecnica de Vehiculos Automotores Diesel. 2a ed. Reporte No. 360. Instituto Mexicano del Transporte. Mexico. 93 pp.

Naguib H (2011) Leveraging Weigh-In-Motion (WIM) Data to Estimate Link-Based Heavy-Vehicle Emissions. Thesis. Portland State University. USA. 110 pp.

SCT (2007) Estadistica Basica del Autotransporte Federal. Secretaria de Comunicaciones y Transportes. Mexico. 76 pp.

SCT (2007) Norma Oficial Mexicana NOM 012-SCT-2-2008. Secretaria de Comunicaciones y Transportes. Mexico. 50 pp.

SCT (2009) Anuario Estadistico. Secretaria de Comunicaciones y Transporte. Mexico.

SEMARNAT (2007) Bases de Colaboracion en Materia de Calidad del Aire. Plan Nacional de Desarrollo. Secretaria de Medio Ambiente y Recursos Naturales. Mexico. 9 pp.

Suzuku Y (2011) A new truck-routing approach for reducing fuel consumption and pollutants emission. Transp. Res. Part D 16: 73-77.

Torras OS, Tellez GR, Mendoza SJF (2005) Analisis Parametrico del Submodelo Efectos Ambientales del HDM-4. Technical Report N' 266. Instituto Mexicano del Transporte. Queretaro, Mexico. 66 pp.

Torres M (1998) Logistica de la Flores en Mexico y su Competitividad Internacional. Thesis. Universidad Nacional Autonoma de Mexico. 78 pp.

Walpole RE, Myers RH (1992) Probabilidad y Estadistica. 4a ed. Mc Graw Hill Interamericana. Mexico. 791 pp.

Zadek H, Schulz R (2010) Methods for the calculation of C[O.sub.2] emissions in logistics activities. In Dangelmaier W, Blecken A, Delius R, Klopfer S (Eds.) Advanced Manufacturing and Sustainable Logistics. Lecture Notes in Business Information Processing. Vol. 46, part 3: 263-268.

Maria del Consuelo Patricia Torres Falcon. Actuary and Master of Transport Engineering, Universidad Nacional Autonoma de Mexico (UNAM). Ph.D. student, Centro de Investigacion en Ciencia Aplicada y Tecnologia Avanzada (CICATA)--Instituto Politecnico Nacional (IPN), Mexico. Lecturer, Universidad Autonoma de Queretaro (UAQ), Mexico. Address: CICATA-IPN Queretaro Unit, Cerro Blanco No. 141 Colinas del Cimatario, Santiago de Queretaro, Mexico 76800. e- mail:

Alejandro A. Lozano Guzman. Control Communications and Electronics Engineer, and Master in Mechanical Engineering, UNAM, Mexico. Ph.D. in Mechanical Engineering, University of Newcastle upon Tyne, UK. Professor, IPN, Mexico. e-mail:

Mercedes Rafael Morales. Ph.D. in Mechanical Engineering, UAQ, Mexico. Lecturer, Instituto Tecnologico de Celaya (ITC), Mexico. Researcher, Instituto Mexicano del Transporte. e-mail:

Jose Antonio Romero Navarrete. Mechanical Engineer and Master in Mechanical Engineering, IPN, Mexico. Ph.D. in Mechanical Engineering, UNAM, Mexico. Lecturer, UAQ, Mexico. Consultant, Instituto Mexicano del Transporte and Instituto de Investigaciones Electricas, Mexico. e-mail:

Maximiano Ruiz Torres. Mechanical Engineer, Instituto Tecnologico de Morelia, Mexico. Master in Management, Instituto Tecnologico de Estudios Superiores de Monterrey, Mexico. Professor, IPN, Mexico.

Israel Aguilera Navarrete. Master in Mechanical Engineering, ITC, Mexico. Ph.D. student, IPN, Mexico.


Type of truck                                 Two     Three
(allowed GVW, tons)                           axle    axle
                                             (17.5)   (26)

Average gross vehicle weight                  17.3    14.5
  (percentage exceeded, 1991-2007) *
Percentage of total carried load on Mexican   6.40    6.40
  roads (2007) *
Percentage of total carried load economic        6      NA
  value on Mexican roads (2007) *

Type of truck                                 Five axle    Double
(allowed GVW, tons)                          articulated   (66.5)

Average gross vehicle weight                       22.1     31.1
  (percentage exceeded, 1991-2007) *
Percentage of total carried load on Mexican       36.50    32.20
  roads (2007) *
Percentage of total carried load economic         54.70     28.5
  value on Mexican roads (2007) *

* SCT (2009), Gutierrez et al. (2008, 2010).

GVW: gross vehicle weight (PROY-NOM-012-SCT-2-2003), NA: not


Route   Vehicle    GVW     Load level     Travelled
         class    (tons)                distance (km)

1       double      30       empty           249
2       double      85     overloaded        646
3       double      30       empty           46
4       double      85     overloaded        452
5       double      30       empty           110
6       double      35       loaded          789
7         faa       20       empty           789
8         faa       25       loaded          885
9         faa       20       empty           885

Route       Average       Fuel efficiency
        velocity (km/h)       (km/l)

1             90               2.57
2             70               1.40
3             60               2.45
4             60               1.40
5             60               2.50
6             70               2.48
7             80               2.55
8             80               2.30
9             90               2.60

GVW: gross vehicle weight (PROY-NOM-012-SCT-2-2003), faa:
five axle articulated.


Type of terrain *   Flat +    Flat     Hilly     Hilly    Mountainous

Surface road         Good    Regular    Good    Regular      Good
conditions **        (%)       (%)      (%)       (%)         (%)


1                     90        5        5         0           0
2                     81        0        17        0           2
3                     85        0        15        0           0
4                     53        0        45        0           2
5                     73        0        27        0           0
6                     63        0        33        0           4
7                     63        0        33        0           4
8                     60        0        35        0           5
9                     60        0        35        0           5

Type of terrain *   Fuel efficiency
Surface road
conditions **         T        E


1                    2.17    2.57
2                    1.06    1.40
3                    2.66    2.45
4                    0.70    1.40
5                    2.43    2.50
6                    1.81    2.48
7                    2.38    2.55
8                    2.02    2.30
9                    2.06    2.60

* Patino (1998), ** Fitch (1994), Arriaga (1998). T: theoretical,
E: experimental.


Significance   Confidence     k      Theoretical   Experimental
level            level      values
(%)               (%)

1                  99         10      (0-4.05)     (0.65-3.85)
5                  95        4.47    (0.99-2.87)   (1.53-2.96)
10                 90        3.16    (1.26-2.59)   (1.74-2.75)
15                 85        2.58    (1.38-2.47)   (1.83-2.66)

Significance      Truck
level            company
(%)               data

1              (1.35-2.70)
5              (1.73-2.32)
10             (1.81-2.24)
15             (1.85-2.20)


                          Five axle articulated

(a) Slope    Speed     GVW           Extra C[O.sub.2]
(%)          (km/h)   (ton)           emitted due to

                        45     65

1              60      237     331        39.66
               80      270     369        36.60
              110      330     437        32.42
                        Worst case        61.85

1.5            60      283     397        40.28
               80      316     435        37.65
              110      376     503        33.77
                        Worst case        59.17

2              60      329     463        40.72
               80      361     501        38.78
              110      422     569        34.83
                        Worst case        58.71

2.5            60      374     529        41.44
               80      407     567        39.31
              110      467     635        35.97
                        Worst case        56.01


(a) Slope    Speed     GVW           Extra C[O.sub.2]
(%)          (km/h)   (ton)           emitted due to

                       66.5    98

1              60      338     486        43.78
               80      376     533        42.55
              110      445     614        37.97
                        Worst case        63.29

1.5            60      406     585        44.08
               80      444     632        42.34
              110      513     713        38.98
                        Worst case        60.58

2              60      473     685        44.82
               80      512     732        42.96
              110      580     813        40.17
                        Worst case        58.78

2.5            60      541     785        45.10
               80      579     831        43.52
              110      648     913        40.89
                        Worst case        57.68

(a) Sin([theta]) x 100 = % (Fitch, 1994). GVW: gross vehicle
weight (PROY-NOM-012-SCT-2-2003).
COPYRIGHT 2014 Interciencia Association
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2014 Gale, Cengage Learning. All rights reserved.

Article Details
Printer friendly Cite/link Email Feedback
Title Annotation:articulo en ingles
Author:Torres-Falcon, M.C. Patricia; Lozano-Guzman, Alejandro A.; Rafael-Morales, Mercedes; Romero-Navarret
Date:Apr 1, 2014
Previous Article:The sponsorship of a scientific journal/El patrocinio de una revista cientifica/O patrocinio de uma revista cientifica.
Next Article:Concentracion de metales traza en el agua condensada de la humedad atmosferica en el Valle de Mexico.

Terms of use | Privacy policy | Copyright © 2021 Farlex, Inc. | Feedback | For webmasters |