Vehicle-specific power

The concept of vehicle-specific power (VSP) is a formalism used in the evaluation of vehicle emissions. The idea was first developed by J. L. Jiménez (Jiménez 1998) at the Massachusetts Institute of Technology. Informally, it is the sum of the loads resulting from aerodynamic drag, acceleration, rolling resistance, and hill climbing, all divided by the mass of the vehicle. Conventionally, it is reported in kilowatts per tonne, the instantaneous power demand of the vehicle divided by its mass. VSP, combined with dynamometer and remote-sensing measurements, can be used to determine vehicle emissions.

The United States Environmental Protection Agency held a "modelling shootout" in 2001, to help with the development of its (then) new MOVES (motor vehicle emissions simulator) vehicle emissions model. Two of the four modelling metholodogies in the shootout, one from North Carolina State University (Frey 2002) and one internal to the EPA, used vehicle-specific power metrics. MOVES was eventually implemented using vehicle-specific power as its primary metric. (See Koupal et al. 2002, § 7.1.3.1 for the EPA MOVES draft VSP specification.)

Formulae

Jiménez's own formula is:

$\mathrm {VSP} ={\frac {\mathrm {power} }{\mathrm {mass} }}={\frac {{\operatorname {d} \over \operatorname {d} t}(E_{\mathrm {kinetic} }+E_{\mathrm {potential} })+F_{\mathrm {rolling} }\cdot v+F_{\mathrm {aerodynamic} }\cdot v+F_{\mathrm {internal} }\cdot v}{m}}$(Jiménez et al. 1999)

VSP can be simplified using typical coefficient values. Haibo Zhai of North Carolina State University provides the following formula for transit buses:

VSP = v × (a + g × sin φ + ψ) + ζ × v³

where:

v

vehicle speed (in metres per second)

a

vehicle acceleration (in metres per second per second)

g

acceleration due to gravity (gee, in metres per second per second)

φ

road grade

ψ

rolling resistance coefficient (metres per second per second)

ζ

drag coefficient (reciprocal metres)

References

Sources

• National Research Council Committee to Review EPA's Mobile Source Emissions Factor (Mobile) Model (2000). Modeling mobile-source emissions. Compass series. National Academies Press. ISBN 978-0-309-07088-1.
• National Research Council Committee on Vehicle Emission Inspection and Maintenance Programs (1 November 2001). Evaluating vehicle emissions inspection and maintenance programs. National Academies Press. ISBN 978-0-309-07446-9.
• Barth, Matthew; Younglove, Theodore; Scora, George (2005). "Development of a Heavy-Duty Diesel Modal Emissions and Fuel Consumption Model". California Partners for Advanced Transit and Highways (PATH).
• Huai, Tao; Durbin, Thomas D.; Younglove, Ted; Scora, George; Barth, Matthew; Norbeck, Joseph M. (2005). "Vehicle Specific Power Approach to Estimating On-Road NH₃ Emissions from Light-Duty Vehicles" (PDF). Environmental Science and Technology. 39 (24): 9595–9600. Bibcode:2005EnST...39.9595H. doi:10.1021/es050120c. PMID 16475340.
• Zhai, Haibo (2007). Regional on-road mobile source emissions characterization for conventional and alternative vehicle technologies. ISBN 978-0-549-54985-7.

Further reading

• Jiménez, J. L. (1998). Understanding and Quantifying Motor Vehicle Emissions with Vehicle Specific Power and TILDAS Remote-Sensing (Ph.D. thesis). Cambridge, Massachusetts: Massachusetts Institute of Technology.
• Jiménez, J. L.; McLintock, P.M.; McRae, G.J.; Nelson, D.D.; Zahniser, M.S. (1999). "Vehicle Specific Power: A Useful Parameter for Remote Sensing and Emissions Studies" (PDF). Ninth CRC On-Road Vehicle Emissions Workshop, San Diego, California, April 1999. Retrieved 2024-10-08.
• Zhai, Haibo; Frey, H. Christopher; Rouphail, Nagui M. (2008). "A Vehicle-Specific Power Approach to Speed- and Facility-Specific Emissions Estimates for Diesel Transit Buses". Environmental Science and Technology. 42 (21): 7985–7991. Bibcode:2008EnST...42.7985Z. doi:10.1021/es800208d. PMID 19031891.
• Frey, M. (October 2002), Methodology For Developing Modal Emission Rates For EPA's MOVES (PDF), EPA420-R-02-027, retrieved 2024-10-08
• Koupal, John; Cumberworth, Mitch; Michaels, Harvey; Beardsley, Megan; Brzezinski, David (October 2002), Draft Design and Implementation Plan for EPA's Multi-Scale Motor Vehicle and Equipment Emission System (MOVES) (PDF), EPA420-P-02-006, retrieved 2024-10-08