# The Impact of Stopping on Fuel Consumption

## Victor Miller November 19, 2011

### Submitted as coursework for PH240, Stanford University, Fall 2011

 Fig. 1: The culprits.

Improvements in traffic control systems can have a significant impact on reducing vehicle fuel consumption. Traffic control devices, consisting primarily of stop signs and signals, have largely stayed the same since their introduction in the early 20th century. [1] Although some signals have "bumpers" or switches that actively change stop lights from red to green, and some lights are timed to improve the flow of traffic, most traffic control systems used today still remain passive and do not actively route or control the flow of traffic. This passive system not only leads to more time spent travelling in our vehicles, but can result in unnecessary stopping, idling, and starting, which consumes a significant amount of energy.

We can perform simple, 'ballpark' calculations for an average passenger car (something like a 2011 Toyota Camry) to determine the amount of energy expended while decelerating to a stop, idling, and accelerating back up to speed. Kinetic energy is the product of mass and the square of the velocity, divided by 2.

 kinetic energy = 12 × mass × velocity2

A 3500 pound (~1500 kilograms) car moving at 25 miles per hour (17 meters per second) carries about 200 thousand joules (200 × 103) of kinetic energy. This is the energy dissipated as heat in the brakes as a car slows to a stop, and it's the minimum amount of energy expended to accelerate car back up to speed from a stop (neglecting things like drag, rolling resistance, and engine efficiency). And so, the average car expends about 400 thousand joules (400 × 103) of energy every time it comes to a complete stop and then reaccelerates back up to speed.

Once a vehicle has stopped, let's assume the automobile remains motionless for three seconds. If we assume a car engine idles at 500 RPM, a 2.5 liter engine (a modest car engine, like that found in a Toyota Camry) will complete 25 revolutions during those three seconds. For these 25 revolutions, there are 12.5 intake strokes. Because the engine is idling, most of the airflow into the engine is blocked, so let's assume that only 50% of the engine displacement is effectively used. During these 12.5 intake strokes, the engine will draw in about .41 pounds of air (19 grams, or .65 moles) at 1 atmosphere of pressure and 77°F (25°C). If we assume our gasoline consists of C8H18 and that we burn it stoichiometrically, we'll need about 0.05 fluid ounces (1.5 milliliters) of gasoline to keep the engine running during this time. A gallon of fuel (3.8 liters) contains about 130 million joules (or 130 × 106) of energy. [2] So for every three seconds spent idling, about 50 kilojoules (50 × 103 joules) of energy is consumed. Therefore, each time a car comes to a stop, idles for a few seconds, and resumes traveling at its original speed, the energy consumed is equivalent to about 0.5% of the energy content of one gallon of gasoline.

There are roughly 120 million registered passenger vehicles in the US. [3] We can estimate that half of these vehicles are driven in an urban setting each day, and from experience, we assume that each car encounters about 15 stop signs during each day of driving in the city. This results in about 900 million stops every day. We calculated that each stop consumes about 450 thousand joules (450 × 103) of energy; the product of these two numbers energy are expended to decelerate and accelerate our vehicles at stop signs in one day, or 150 quadrillion joules (150 × 1015) annually.

 Fig. 2: One potential solution.

According to the Federal Highway Administration, passenger vehicles consumed approximately 9 quintillion joules (9 × 1018) of energy in 2008. [2] Our estimate of energy consumed by decelerating, idling, and reaccelerating suggests that this process is responsible for about 2% of this annual consumption. 2% of the annual passenger vehicle energy consumption seems petty, however, our estimate was calculated using conservative estimates for vehicle mass and traffic scenarios, and we did not include municipal or commercial (read: heavier) vehicles, other traffic scenarios (e.g., traffic jams), or engine efficiency (a significant factor) in our calculations.

Furthermore, this value of 2% becomes more meaningful when scaled by a gallon of gasoline. A gallon of gasoline contains about 130 million joules (130 × 106) of energy - therefore, these 400 trillion joules (400 × 1012) used to decelerate, idle, and reaccelerate are equivalent to about 3.5 million gallons of gasoline per day, or about 1.2 billion gallons per year. If the average American fills up his 15 gallon gas tank once every other week, this is enough gasoline to satisfy the annual needs of 3 million average Americans.

Unnecessary traffic stops consume a considerable amount of fuel. An "active" traffic control system with integrated sensor networks, GPS, and vehicle-to-vehicle communication might significantly reduce the number of stops we make during our daily commute; however, such a system might currently be too complicated and expensive to supplant the existing traffic control devices given the potential marginal benefits. But even simple solutions, such as wider implementation of the Yield sign will have a positive impact on fuel consumption and get us to our destination sooner.

© Victor Miller. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

## References

[1] G. Morgan, "Traffic Signal," US Patent No. 1475024, 20 Nov 23.

[2] Transportation Statistics Annual Report 2010," U.S. Department of Transportation, December 2010, Table 5-7.

[3] ibid., Table 11-1.