We pulled into the gas station next to a Ford Excursion. I made the off-hand comment that it wouldn't be fun to fill that sucker up. "Why?" My daughter asked. "Bigger cars don't get as good gas mileage," I replied. I should have known it wouldn't stop there. She is my daughter, after all. Of course the next question was, "Why do bigger cars get worse gas mileage?"
Why indeed? First, maybe I should check. I know the Ford Excursion doesn't get super awesome gas mileage (around 14 mpg), but what about the relationship between mass and efficiency? Was I just making that stuff up? Sometimes I do that - but hopefully I was correct.
Data
Everyone loves data. Here is some data. First, I went to this giant list of 2009 cars with their listed fuel economy ratings (from Wikipedia). Really, this is too much data but I can't help myself. However, it doesn't have mass data. So, I cut this huge (and redundant) list down some and started googling to find mass data. In this case, I went for the "curb weight" and converted to kilograms. Here is the data, if you want it.
Oh, one more note. I removed any hybrid vehicles and vehicles that I had never heard of. Sometimes, there would be multiple listings for a car. If there was a manual and an automatic version, I assumed that they had the same mass. If you google something like "2009 Pontiac G5 curb weight," you might find several answers that don't agree. For cases like this, I just took the first reasonable number I found. Should I have used "gross vehicle weight" instead of curb weight? If I am looking for a relationship, it shouldn't really matter.
Now for a plot. Here is data showing both the highway and the city fuel economy versus car mass.
Looks linear enough to fit a function. Here are the fitting functions.
What do these equations say?
- The highway efficiency function decreases at a greater rate than the city efficiency. This implies that mass has a bigger effect on highway efficiency. I expected it would be the other way around.
- What does the y-intercept mean? I guess if a car had a mass of 0 kg, it would still just get 32 to 44 mpg. Mass isn't the only thing that limits the fuel efficiency. Think about air drag and stuff.
I still didn't answer the original question.Why Mass?
Back to my daughter's question. Why? My first guess was that with a larger mass, you have to use more energy to get the vehicle up to speed. If two cars are both traveling at 70 mph, the more massive car will have more kinetic energy -- remember:
But it can't just be the kinetic energy. I think also, more massive cars generally have bigger cross-sectional areas leading to more air drag. More massive cars have bigger engines that waste more gas with more moving parts to lose energy to friction. Bigger isn't always better, I guess.
One final note. I just realized that the data I used for fuel efficiency includes some sport cars. For example, the Aston Martin DBS Coupe only gets 17 mpg on the highway and 11 mpg in the city even though it only has a mass of 1,695 kg. Again, the problem is the big engine.
Top image: David Guo's Master/Flickr
