Fuel economy of a vehicle as a function of airspeed: the concept of parallel corridors
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In this investigation, it is shown that when a highway vehicle is driven at a constant speed on a level road, what actually determines its fuel economy is the airspeed of the vehicle rather than its ground speed or its speedometer reading. A theoretical model is then developed for the first time that describes the fuel economy of a highway vehicle as a function of its airspeed. The functional form of this model turns out to be in good correlation with the experimental data that have been collected by the authors over the last 2 years. Finally, the concept of parallel corridors is introduced and a design for highway construction is suggested that can significantly improve fuel economy of vehicles where traffic is heavy, by establishing a controlled driving environment. The results of this investigation apply to any vehicle using any source of energy.
KeywordsFuel economy; Airspeed; Highway vehicles; Parallel corridors
kilometers per hour
kilometers per liter of fuel.
Although the invention of internal combustion engines (ICE) dates back to before 19th century, their widespread applications were hindered until mid 1850s when commercial drilling and production of petroleum began . Since then, fossil fuel has been the main source of energy in transportation and travel. However, as the world became more aware of the limited supplies of fossil fuel and resource depletion as well as economical and ecological impacts of its usage, concerns began to grow. As a result, for many decades, at least as far back as the time of Great Depression in the USA, the nation has been concerned with fuel efficiency and conserving energy resources. However, the issue is not quite as simple and straightforward as it seems and there are challenges. For instance, improving fuel efficiency triggers an economic reaction causing additional travel that partially offsets the original energy saving. In other words, as the energy becomes cheaper, it provides an incentive to increase its use, a phenomenon known as the ‘rebound effect’ .
In general energy usage has direct impacts on the economy . Furthermore, almost in every country in the world, transportation takes up a large portion of the fossil fuel consumption. For example, in the USA today, 70% of the total oil consumed is directed to fuels used in transportation - gasoline, diesel, and jet fuel . In Nigeria, 96% of the total gasoline consumed and 40% of the diesel fuel consumed go to road transportation . In addition to economical consequences, fossil fuel consumption results in the emission of toxic gases (CO, CO2, NO x , SO2, HC, and PM)  that affects local and regional air quality, specially in urban areas, which can pose serious health hazards and cause other ecological issues. Today the emission of CO2, which is directly related to the consumption of carbon-based fuel, is regarded as one of the most serious threats to the environment through greenhouse effect , and transportation alone is responsible for about 21% of the global CO2 emission .
Shortages of gasoline and other petroleum fuels from time to time, as well as ecological concerns, have renewed interest in identifying factors that affect fuel efficiency of vehicles. To this end, various proposals for reducing fuel consumption have been made. These include simple modification of vehicle components such as replacement of bias-ply tires with radial tires and development of alternative fuel sources and new engine designs to optimize combustion. In addition, a noticeable trend toward smaller and more efficient vehicles has appeared in the last few decades. This is done through reducing vehicle weight by using new materials and by improving vehicles’ exterior design to achieve lower aerodynamic drag . Thus, fuel efficiency has become a selling point in the automotive industry. Although most of the proposals for conserving fuel resources have been focused around vehicle design changes, some external factors have been considered as well. The national reduction of highway speed to 55 mph (88.5 km/h), mandated in the USA in the 1970s, is one example. Other examples include maintaining a constant highway speed or maintaining a constant throttle setting .
Oil dependency and global warming have stimulated research and development activities toward utilization of secondary biofuels and renewable energy sources including solid waste and vegetable oil [11, 12, 13]. In addition, alternative fuel sources and engines have become popular in recent years, and the endeavor toward production of the so called ‘greener’ vehicles continues. These include electric, hybrid, and fuel cell vehicles. Today, hybrid passenger cars are widely in use and quite popular. Electric cars have zero emission but suffer from the disadvantage of having to be recharged frequently with a long recharging time and having a relatively short range. The fuel cell vehicles, on the other hand, combine the advantages of an electric vehicle, i.e., almost zero emission, high efficiency, and silent operation, with the advantages of conventional internal combustion engine vehicles, i.e., long range and short refueling time. In addition, they have about twice the efficiency of an internal combustion engine during a typical driving cycle . Although hydrogen is the most common fuel, other fuels such as natural gas and methanol have occasionally been used in fuel cells . Hydrogen fuel cell vehicles, however, are very expensive due to the cost of the platinum used in them as catalyst, which has hindered their large-scale production. While fuel cell vehicles may someday replace those with internal combustion engines, various disadvantages, specially the cost of the fuel cells, mean that the market is unlikely to see their large-scale production for decades .
Returning to the internal combustion engine vehicles, other factors that influence fuel consumption and exhaust emission in transportation are those related to driving style and independent driving pattern [6, 7, 17, 18]. It has been shown that nine driving pattern factors have important effect on fuel consumption and emission. These factors include acceleration and deceleration, gear changing, as well as the speed of the vehicle .
As a result of the ever-increasing cost of fossil fuel as well as the air pollution concerns, vehicle fuel consumption and emission have become two critical aspects in the transportation planning process of highway facilities. To this end, several mathematical models have been developed that predict vehicle fuel consumption and emissions using instantaneous speed and acceleration [19, 20, 21]. It is a well-known fact that fuel consumption (and emission) increases substantially as the speed of a vehicle increases, an issue that has been extensively discussed in the literature [22, 23]. Some references have referred to this increase as being ‘exponential’  although technically, this statement is not correct.
Although the effect of speed on fuel consumption of a vehicle has been extensively investigated, the effect of its air speed has not been studied. This is because all of the investigations in the past have focused on vehicles moving in still air, in which case the ground speed becomes the same as the airspeed. However, if the vehicle moves upwind or downwind, the results would be quite different. In fact, any experienced truck driver would testify that fuel consumption of the vehicle varies substantially between driving upwind or downwind all day and, to some extent, driving through crosswind. In this article we show that what really determines the fuel consumption of a vehicle under normal driving conditions is the airspeed of the vehicle rather than its ground speed. However, as mentioned above, if the vehicle travels in still air, its airspeed and ground speed are obviously the same.
The objective of this paper is to develop a theoretical model for the rate of fuel consumption of a vehicle (especially of a highway vehicle) as a function of its airspeed, taking into account the fuel consumption due to the moving parts of the vehicle as well. To the best of our knowledge, the effect of these factors on fuel consumption of a vehicle has not been investigated or addressed in the literature, not at least from a quantitative point of view. We then compare this model to the actual experimental data that we have collected and show that they are in good correlation. We also show that this model is consistent with those previously developed as well as the existing experimental data for vehicles moving in still air. Finally, based on our results, we suggest a new design for highway construction which could substantially reduce the rate of fuel consumption of vehicles on busy highways.
The fuel consumed by a vehicle is responsible for four different types of work: (a) vehicle acceleration, which increases the kinetic energy of the vehicle, (b) vehicle climbing a hill, which increases the gravitational potential energy of the vehicle, (c) work done against all internal frictional forces as well as the rolling friction of the wheels, and (d) work done against air resistance. Here we are not interested in parts (a) and (b). We only consider cases where the vehicle travels on a straight level road with a constant speed.
Consider a vehicle traveling on a straight level road, which we take to be the x direction, at a constant speed. Assuming no air resistance and no internal friction between the moving parts of the vehicle, according to the Newton’s first law of motion, the net force on the vehicle would be 0 and the vehicle would consume no fuel. But in reality, there is internal friction between the moving parts as well as the rolling friction of the tires. However, these frictional forces are all proportional to the normal forces acting between the moving parts, and the proportionality constants are all, to a good approximation, independent of the speed of the moving parts [25, 26, 27]. Therefore, for a vehicle traveling on a straight level road, to a good approximation, the contribution from these frictional forces is a constant k0, independent of the speed of the vehicle. The value of k0 depends on the details of the design of the vehicle.
For intermediate values of the Reynolds number, both the linear and the quadratic terms are present.
For a typical vehicle, the characteristic length is of the order a few meters. The density of air at sea level and normal temperatures is about 1.3 kg/m3, and its dynamic viscosity is about 1.8 × 10-5 Pa s. Therefore, for a typical vehicle even at speeds as low as a few kilometers per hour, say 5 km/h which is about 1.4 m/s, the Reynolds number is of the order of 105 to 106, which is much greater than unity, and the force of air resistance on the vehicle is in the Newton regime.
where the first term is the contribution from all internal frictions in the vehicle as well as the rolling friction of the wheels, and the second term is the contribution from air resistance. Once again we stress that in this equation v is the airspeed of the vehicle, not its ground speed.
Note that in this equation we have used new constants c0 and c2, instead of k0 and k2, because Φ is only proportional to -(d x/d W), not equal to it. This proportionality depends on a number of factors, including the efficiency of the engine and the limitations set by the second law of thermodynamics. This is because in an internal combustion engine, the chemical energy of the fuel is first converted into heat before it is converted into mechanical energy.
where the new constants a and b are related to c0 and c2 by a = 1/c2 and b = c0/c2. The graph of this equation has the correct functional form for the experimental data that have been collected for various vehicles . Equation 9 also conforms to the functional form of the regression model of Rakha et al. for fuel consumption rate as a function of speed  as well as the Oak Ridge National Laboratory experimental data , both for vehicles moving in still air.
Results and discussion
During several trips from Wisconsin to Arizona and back in the 1990s, one of us (CHH) noticed a marked difference in fuel consumption between the westward trips out and the eastward return trips. Based on this observation, a 2003 Chevy Suburban was equipped with a Pitot tube  and an airspeed indicator (Wag-Aero 0-120 mph). The Pitot tube was mounted in the front of the vehicle, flush with the front bumper and center of the radiator. The device was calibrated by driving the vehicle in still air and comparing the speedometer readings with the airspeed indicator. The agreement was remarkably good, within 2 mph (3.2 km/h). The vehicle was also equipped with an electronic device which was plugged into the OBD2 engine analyzer to read out the instantaneous fuel economy.
Finally, to confirm the above results, we equipped a 2005 Volkswagen Passat for the test and collected over 200 measurements at various airspeeds, but at a ground speed of 60 mph (about 97 km/h). These measurements confirmed all the results obtained for the Chevy Suburban, but of course, with different parameters for Equation 9. The graphs for the Volkswagen Passat are qualitatively nearly identical to those for the Chevy Suburban, therefore we do not duplicate them here.
which would be the fuel economy of the vehicle if it traveled with an airspeed of 0.
Unlike in an aircraft, in an automobile, the Pitot tube is parallel to the airstream only when driving exactly upwind or downwind. Consequently, the automobile Pitot tube responds only to the parallel component of the airstream. Thus, in a 90° crosswind, the airspeed indicator in an automobile would read the same as the speedometer, regardless of the wind speed. This phenomenon contributes to data error, because a strong crosswind requires front wheels ‘crabbing’ into the wind to hold the road lane, contributing to more fuel consumption, while the airspeed indicator shows the same as the speedometer. This is one reason for the scatter in our data as shown in Figure 1. Another is the difficulty of finding a level stretch of road long enough to get stable airspeed and readings of the fuel economy.
In view of the above results, the question is how can the fuel economy of vehicles be improved? Of course, the first factor is to streamline the vehicle. This has been done by all manufacturers to the point that all new automobile profiles resemble each other. Streamlining the vehicle simply reduces the drag coefficient. Thus, the value of k2 in Equations 3 and 4 are lowered as much as possible, which maximizes a and minimizes b in Equation 9 accordingly. The second factor is to control the driving environment in order to expose vehicles to lower airspeeds. This is where we introduce the concept of parallel corridors. To this end, an enormous opportunity exists on heavily traveled roads to reduce fuel consumption by significant amounts without changing the vehicle or driving habits. In addition, parallel corridors could eliminate crosswind effects as well.
Recently, on a trip west, one of us (CHH) drove on the middle lane of seven lanes of traffic leading east out of Phoenix, Arizona, on Highway 60. While driving in the center lane between closely spaced vehicles, all traveling at 70 mph (113 km/h), the airspeed indicator registered 30 to 40 mph (48 to 64 km/h), illustrating the fact that vehicles carry air along with them.
Several years of driving experience with an airspeed indicator has revealed that natural conditions sometimes resemble the parallel corridor concept. In the mountainous states, for example, lanes are sometimes separated and flanked by cuts or berms, where a substantial reduction in airspeed is noted if traffic is heavy. This unique situation was first observed on Interstate 17, between Phoenix and Flagstaff.
The first phase might be to construct a 10-km test strip on a busy lane to confirm the benefits. Design guidelines could be established for exits, snow accumulation, and barrier heights, etc. A cost-benefit ratio could be obtained to determine payback time. Various barrier types might also be evaluated. In some areas, a single center barrier might suffice.
Finally, for anyone wishing to explore the parallel corridor concept personally, we would suggest mounting the indicator in such place that both airspeed and speedometer could be read at the same time. It is customary in mounting the Pitot tube (any tube will do) that the first bend behind the opening to the air be inclined upward to prevent water (from rain) to accumulate and block pressure. In our case, a small diameter silicone rubber tube connected the Pitot tube to the airspeed indicator.
The results of this investigation apply to any vehicle regardless of its size, shape, engine design, or type of fuel consumed as well as electric vehicles.
CHH received his degree in Industrial Engineering in 1947, from Iowa State College. As a child during the Great Depression of 1929, he became motivated and impressed with the need for resource conservation as he grew up. He was actively involved in the Southeastern Wisconsin industries in various areas, including making fuel pumps for oil burners and making silicon rubber parts for the medical industry. He retired in 2007. As an amateur pilot, CHH became an expert in aviation and flight dynamics. He has always been interested in and an advocate of energy conservation.
PM is a professor of physics at the University of Wisconsin-Parkside. He received his PhD in Materials Science and Engineering from the University of California, Berkeley, in 1975. He has published extensively in a wide variety of areas, ranging from bicycle stability to cancer research. His current research interest is thermodynamics and statistical mechanics of small systems.
We would like to thank Adam J. Reck, Krista J. Reck, and Emma H. Jung for recording the data. We would also like to thank Kathryn H. Thompson for her help during the preparation of this manuscript.
- 1.Wikimedia Foundation Inc: History of the internal combustion engine. . (2013) Accessed 7 April 2013. http://en.wikipedia.org/wiki/History_of_the_internal_combustion_engineGoogle Scholar
- 4.Institute for Energy Research. Petroleum: Percent of US transportation sector. (2013) Accessed 7 April 2013 http://www.instituteforenergyresearch.org/energy-overview/petroleum-oil/Google Scholar
- 8.Gorham R: Air Pollution from Ground Transportation: An Assessment of Causes, Strategies and Tactics, and Proposed Actions for the International Community. The Global Initiative on Transport Emissions. A Partnership of the United Nations and the World Bank, New York, USA; 2002.Google Scholar
- 19.Biggs DC, ARFCOM: Models for Estimating Light to Heavy Vehicle Fuel Consumption. Australian Road Research Board, Victoria; 1988.Google Scholar
- 21.Akçelik R, Smit R, Besley M: Calibrating fuel consumption and emission models for modern vehicles. Paper presented at IPENZ transportation group conference, Rotorua, March 2012 Paper presented at IPENZ transportation group conference, Rotorua, March 2012Google Scholar
- 25.Halliday D, Resnick R, Walker J: Fundamentals of Physics. Wiley, New York; 2005.Google Scholar
- 26.Barger V, Olsson M: Classical Mechanics: A Modern Perspective. McGraw-Hill, New York; 1995.Google Scholar
- 28.Dodge RA, Thompson MJ: Fluid Mechanics. McGraw-Hill, New York; 1937.Google Scholar
- 30.Marion JB, Thornton ST: Classical Mechanics of Particles and Systems. Saunders, New York; 1995.Google Scholar
- 32.Tom Murphy: MPG for electric cars? http://physics.ucsd.edu/do-the-math/2011/08/mpg-for-electric-cars/. (2011) Accessed 6 April 2013Google Scholar
- 33.Farlex Inc: The free dictionary by Farlex. Fuel consumption rate. http://www.thefreedictionary.com/fuel+consumption+rate. (2013) Accessed 28 March 2013Google Scholar
- 34.Dictionary.com: Fuel consumption rate. http://dictionary.reference.com/browse/fuel+consumption+rate. Accessed 28 March 2013
- 35.Definitions.net. STANDS4 LLC, Fuel consumption rate http://www.definitions.net/definition/fuelconsumptionrate. (2013) Accessed 28 March 2013
- 36.Rakha H, Van Aerde M, Ahn K, Trani AA: Requirements for evaluating traffic signal control impacts on energy and emissions based on instantaneous speed and acceleration measurements. Transportation Research Board 79th Annual Meeting, January 9–13, 2000, Washington, D.C Transportation Research Board 79th Annual Meeting, January 9–13, 2000, Washington, D.CGoogle Scholar
- 37.West B, McGill R, Hodgson J, Sluder S, Smith D: Development of data-based light-duty modal emissions and fuel consumption models. Soc. Automotive Eng. Paper No. 972910 1997.Google Scholar
- 38.Encyclopedia Britannica Inc. Pitot tube http://www.britannica.com/EBchecked/topic/462113/pitot-tube. (2013) Accessed 16 March 2013
- 39.Gould H, Tobochnik J: An Introduction to Computer Simulation Methods. Addison-Wesley, New York; 1996.Google Scholar
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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.