The riddle, as posed to the TMIP forum was:
“About 20 years ago a team at UW-Madison received a rather ample grant to train local public officials in the art of traffic flow optimization through signalized intersections, with the specific intent of saving fuel. (The money came from a source that was particularly interested in reducing energy consumption.) So the question I posed was: If all the traffic signals in Wisconsin were to be optimized to reduce delay, would there be any fuel savings?”
Unquestionably, there are lots of good reasons for wanting to optimize signal timing, including improved safety and reduced delay. However, the claim for fuel savings is repeatedly made. Savings of greenhouse gas emissions is just the same; there is a fixed stoichiometric relationship between fuel consumption and CO2 emissions for motor vehicles.
Some well-known traffic operations software packages will tell us the amount of fuel burned for an alternative, and it is a simple matter to subtract the before from the after to learn of the fuel savings. But are these fuel savings real or imagined?
Real in the fleeting short term, but completely imaginary in the long term.
One of the more well-established principles of travel demand is the “travel budget”. With very few exceptions, everyone is granted 24 hours of life each day, and people are willing to spend just so much of it on travel. But the desire for travel is often more than this budget. This leads to a remarkable finding that the total amount of personal travel time by an average individual is relatively unvarying.
Traffic operations software products assume that VMT (vehicle miles of travel) is constant, but they should be assuming instead that VHT (vehicle hours of travel) is constant. Any improvement in delay through signal timing optimization will be (over the long term) reallocated to additional travel, presumably to enjoy an enhanced lifestyle or gain additional income.
So now we can pare down the question to: Assuming travel time for a trip is constant, is there more fuel consumed by continually cruising or occasionally stopping?
To answer this question, I set up a simple numerical experiment using the famous Davis equation, substituting automobile coefficients for train coefficients, to estimate fuel consumption for a compact car. The form of the equation I used weighs automobiles in tons (W), measures speeds in miles per hour (S), measures cross-sectional areas in square feet (A), and measures accelerations in miles per hour per second (a). The equation gives the resistance to forward motion (R) in pounds.
R = 10*W + 0.1*W*S + A*C*0.0026*S^2 + 91.1*T*a
and C is the drag coefficient. I have omitted the grade term, because I am assuming flat terrain. For many years, as a homework exercise, I asked my undergraduate students to verify this equation by comparing it to test track results for a variety of high-performance cars, so I know that it validates quite well.
My experimental automobile, because it lines up with some necessary information from the Internet, is a compact car with a 2-liter engine, weighing 1.5 tons, having a frontal cross-sectional area of 24 square feet and having a drag coefficient of 0.4. The combined thermodynamic efficiency of the engine and drivetrain is 0.27. This is roughly a high-end Honda Civic, non-hybrid.
Let’s compare two trip segments of a 5-minutes duration. One trip is pure cruising at an exactly 30 miles per hour, and the second trip has 1 minute of signal delay. That signal delay consists of 3 seconds of deceleration, 52 seconds of stop, and 5 seconds of acceleration. However, the total time from the beginning of the deceleration to the end of the acceleration is 68 seconds. Let’s concentrate on those 68 seconds, since the rest of the two trips are the same.
The 58 seconds of deceleration and stop consume 0.0026 gallon of fuel, at an idle rate of 0.16 gallon per hour, as reported by the EPA. I assumed idling during slowing, but it might require slightly more or less fuel, depending upon the technology of the automobile.
The 10 seconds of acceleration consume 0.0043 gallon of fuel.
The 68 seconds of pure cruising at 30 mph consume 0.0112 gallon, which corresponds to a fuel economy of 50.4 mpg. Terrain variations and minor accelerations while cruising might raise the fuel consumption rate a little bit.
Bottom line: cruising uses considerably more fuel than stopping, so stopping is better!
An even greater difference in energy consumption would be seen with a hybrid vehicle or an electric vehicle.
This analysis is not at all intuitive. The next time you hear someone claiming global warming benefits of better traffic controls, please refer him or her to this blog post.
Alan Horowitz, Whitefish Bay, March 31, 2017
Note: The delay for a single stop would need to be a quite low 24 seconds (or just 16 seconds of totally stopped time) for the two trips to have the same fuel consumption.