In the recent “Cash for Clunkers” program, policy-makers wanted to boost car sales and reduce fuel consumption. But, the average increase in fuel economy was relatively modest (a jump of 15 to 24 miles per gallon on average). Was this program worth it?
At first glance, it would seem as though small gains in fuel efficiency would likely have little impact on fuel consumption. This is because the “miles-per-gallon” rating is highly misleading. People commonly think that for every increase in m.p.g., there should be an equal decrease in the amount of gas consumed in a certain distance. But this is not the case.
In fact, jumping from 10 to 20 mpg saves more gas than going from 20 to 40 mpg. How is this possible? As described by Richard Larrick and Jack Soll in a June 2008 article in Science, there is actually a non-linear relationship between gas consumption and fuel efficiency.
Claudia Bode, Education Director at the Center for Environmentally Beneficial Catalysis (CEBC), read this article and shared it with high school science teachers who were doing research at CEBC.
“I was so surprised by it,” said Bode. “I just couldn’t believe that small improvements in the least fuel efficient vehicles could really make that much of a difference. We thought this would make a great lesson for students.”
Bode and two of the high school teachers, including Carolyn Pearson (left) and Alan Gleue (right) created a new case study based on this real-world issue. The case and related teaching materials were peer-reviewed and published on the National Center for Case Study Teaching in Science website.
“It’s very useful to have materials to help people learn this math so that they’ll do it automatically,” said Larrick.
“I have used this case study twice with my physics classes,” said Alan Gleue, Lawrence High School physics teacher and co-author of the case. “It really helps reinforce graphing and data analysis concepts.”
Larrick and Soll, “The MPG Illusion,” Science 20 June 2008: 1593-1594.