Cost, Effectiveness, and Deployment of Fuel Economy Technologies for Light-Duty Vehicles(2015)

Chapter: Appendix L: Relationship between Power and Performance

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Suggested Citation:"Appendix L: Relationship between Power and Performance." National Research Council. 2015. Cost, Effectiveness, and Deployment of Fuel Economy Technologies for Light-Duty Vehicles. Washington, DC: The National Academies Press. doi: 10.17226/21744.
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Appendix L

Relationship between Power and Performance

The relationship between power and performance is derived in this Appendix. The propulsion or tractive force to accelerate a vehicle can be calculated from the sum of the tire rolling resistance, the aerodynamic drag, and the inertial force for the vehicle on a level road as follows (Gantt 2011):

 Ttr = Frolling resistance + Faerodynamic drag + Finertia (1)

Expanding this equation yields the following:

 Ttr = Crr m gc + ½ ρ Cd Af V2/gc + m dV/dt/gc (2)1

The following parameters were used in Equation 2 for a typical 3,500 lb midsize car:

Crr = 0.0060 (tire rolling resistance)

m = 3500 lbm (mass of the vehicle)

r = 0.075 lbm/ft3 (density of air)

Cd = 0.30 (aerodynamic drag coefficient)

Af = 25 ft2 (frontal area of vehicle)

V = 60 mph (88 ft/sec)

t60 = 0 to 60 mph acceleration time

During a wide-open throttle acceleration, the tractive force can be expressed as following at the 60 mph condition:

Ttr lbf = 0.0060 × 3,500 lbm × 32.2 ft/sec2/32.2 lbm-ft/lbf-sec2 + ½ × 0.075 lbm/ft3 × 0.30 × 25 ft2 × (88 ft/sec2)2/32.2 lbm-ft/lbf-sec2 + 3,500 lbm × 88 ft/sec2/(t60 sec × 32.2 lbm-ft/lbf-sec2)     (3)
(Note the cancellation of units leaving lbf for each term of Equation 3.)

Power to propel the vehicle is obtained by multiplying the tractive effort force in Equation 3 by velocity at 60 mph (88 ft/sec) and converting the product to horsepower (hp = 550 ft lbf/sec), which yields the following equation for power:

 Hp = 14 + 1530/t60 (4)

Applying Equation 4 yields the following relationship between 0 to 60 mph time and horsepower:

 T60 % Change in 0 to 60 mph time Hp % Change in Hp 8 seconds Base 205 Base 7.2 seconds − 10% 227 + 10.7%

These results show that approximately a 10 percent decrease in 0 to 60 mph time requires approximately a 10 percent increase in power.

REFERENCES

Allen, J. n.d. Concept Review: Unit Systems. Michigan Technological University. http://www.me.mtu.edu/~jstallen/courses/MEEM4200/lectures/energy_intro/Review_unit_systems.pdf. Accessed April 3, 2015.

Gantt, L. 2011. Energy Losses for Propelling and Braking Conditions of an Electric Vehicle. VPI MS Thesis, May.

_____________

1 The force exerted by a mass on earth is given by the following equation, which requires the constant, gc, which is equal to 32.2 lbm-ft/lbf-sec2 (Allen n.d.):

F = m × a/gc

Therefore, a mass of 3,500 lbm (lb mass) has a weight of 3,500 lbf (lb force) on earth, where a = 32.2 ft/sec2, as shown by substituting in the above equation:

F = 3,500 lbm × 32.2 ft/sec2/(32.2 lbm-ft/lbf-sec2) = 3,500 lbf

(Note the cancellation of units leaving lbf.)

This relationship is used throughout Equations 2 and 3 of this Appendix.

Page 395
Suggested Citation:"Appendix L: Relationship between Power and Performance." National Research Council. 2015. Cost, Effectiveness, and Deployment of Fuel Economy Technologies for Light-Duty Vehicles. Washington, DC: The National Academies Press. doi: 10.17226/21744.
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Cost, Effectiveness, and Deployment of Fuel Economy Technologies for Light-Duty Vehicles Get This Book
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The light-duty vehicle fleet is expected to undergo substantial technological changes over the next several decades. New powertrain designs, alternative fuels, advanced materials and significant changes to the vehicle body are being driven by increasingly stringent fuel economy and greenhouse gas emission standards. By the end of the next decade, cars and light-duty trucks will be more fuel efficient, weigh less, emit less air pollutants, have more safety features, and will be more expensive to purchase relative to current vehicles. Though the gasoline-powered spark ignition engine will continue to be the dominant powertrain configuration even through 2030, such vehicles will be equipped with advanced technologies, materials, electronics and controls, and aerodynamics. And by 2030, the deployment of alternative methods to propel and fuel vehicles and alternative modes of transportation, including autonomous vehicles, will be well underway. What are these new technologies - how will they work, and will some technologies be more effective than others?

Written to inform The United States Department of Transportation's National Highway Traffic Safety Administration (NHTSA) and Environmental Protection Agency (EPA) Corporate Average Fuel Economy (CAFE) and greenhouse gas (GHG) emission standards, this new report from the National Research Council is a technical evaluation of costs, benefits, and implementation issues of fuel reduction technologies for next-generation light-duty vehicles. Cost, Effectiveness, and Deployment of Fuel Economy Technologies for Light-Duty Vehicles estimates the cost, potential efficiency improvements, and barriers to commercial deployment of technologies that might be employed from 2020 to 2030. This report describes these promising technologies and makes recommendations for their inclusion on the list of technologies applicable for the 2017-2025 CAFE standards.

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