29 Emissions and Fuel Consumption

29.1 Vehicle-Specific Power (VSP) Emission

Frey, Zhang, and Rouphail (2008) used vehicle specific power as an indicator of engine power demand. For a typical light duty vehicle, VSP is:

\[VSP=0.278v \times [0.305a+9.81 \times \sin(a+\tan (\frac{r}{100})+0.132]+0.0000065v^3\]

where:

\(VSP=\) vehicle specific power (kw/ton),
\(v=\) speed (km/h),
\(a=\) acceleration (km/h/s), and
\(r=\) road grade (%).

VSP Mode Definition NO (mg/s) HC (mg/s) CO (mg/s) CO\({_2}\) (g/s) Fuel (g/s)
1 \(VSP<-2\) 0.12 0.076 1.83 1.30 0.41
2 \(-2 \le VSP<0\) 0.092 0.083 1.86 1.43 0.45
3 \(0 \le VSP<1\) 0.026 0.056 0.90 0.97 0.31
4 \(1 \le VSP<4\) 0.14 0.12 2.59 2.03 0.64
5 \(4 \le VSP<7\) 0.21 0.16 3.68 2.74 0.87
6 \(7 \leq VSP<10\) 0.23 0.20 4.74 3.42 1.08
7 \(10 \le VSP<13\) 0.29 0.24 5.73 4.02 1.27
8 \(13 \le VSP<16\) 0.32 0.28 6.18 4.56 1.44
9 \(16 \le VSP<19\) 0.37 0.31 7.09 5.08 1.61
10 \(19 \le VSP<23\) 0.47 0.35 7.81 5.61 1.77
11 \(23 \le VSP<28\) 0.59 0.38 8.36 6.05 1.91
12 \(28 \le VSP<33\) 0.68 0.42 9.01 6.41 2.03
13 \(33 \le VSP<39\) 0.79 0.46 10.5 6.86 2.17
14 \(39 \le VSP\) 0.97 0.48 10.9 7.41 2.34

The average 95% confidence intervals for these VSP modes in % are \(\pm 5\), \(\pm 2\), \(\pm 3\), \(\pm 1\), and \(\pm 1\) for NO, HC, CO, \(\text{CO}{_2}\), and fuel, respectively. The unit for VSP is kw/ton.

VSP Emissions Settings

Figure 29.1: VSP Emissions Settings

Additional information about how this methodology is incorporated into simulation is described in Washburn et al. (2015).

29.2 OBD-based emissions/fuel use calculations

The following calculation methodology is described in Hu, Frey, and Washburn (2016) and Washburn et al. (2017).

The RPM value used in the calculations of this section is obtained from the calculations described in Maximum Acceleration (rearranged to solve for engine speed).

\[MAP\times RPM=\text{min}(a\times VSP^b\times c,d)\]

where:

\(a=\) scaling parameter,
\(b=\) power parameter,
\(c=\) multiplicative bias correction factor (equals 1.0 for all cases), and
\(d=\) additive bias correction factor.

according to the values in the following Table.

Vehicle Year 2005 2005 2008 2004 2001 2009 1998 2002 2010 1998
Make Chevrolet Mazda Chevrolet Pontiac Volvo Honda Buick Chevrolet Ford Chevrolet
Model Tahoe 6 Impala Grand AM GT S40 Civic Century Silverado F150 S10
\(MAP \times RPM\) \(a\) 38100 58700 44800 44300 59900 59100 55200 37900 36600 43200
NULL \(b\) 0.42 0.39 0.42 0.42 0.37 0.43 0.35 0.44 0.44 0.35
NULL \(c\) 32000 45000 40000 36300 45400 37800 43600 34400 32100 33100
  • Calculate manifold absolute pressure

\[MAP=\frac{MAP\times RPM}{RPM}\]

  • Calculate mass air flow

\[MassAirFlow=\frac{MAP\times EngineDisplacement\times\frac{RPM}{60\times EngineStrokesPerCycle}\times EngineVolumetricEfficiency}{1545.349\times (EngineIntakeAirTemp+273.15)}\]

\[EngineLoad = \frac{{(MAP \times RPM + 66189)}}{{3556.4}}\]

\[{m_i} = a{(MAP \times RPM)^b} \times c + d\]

\[{m_{NOx}} = \frac{{a'}}{{{{(MAP \times RPM)}^{0.5}}}}\text{exp}\left( {\frac{{-b'}}{{MAP \times RPM}}} \right)\]

OBD Emissions Settings

Figure 29.2: OBD Emissions Settings