Volvo XC60: A New Green Machine? Not Exactly
I was recently traveling in Europe (including in Switzerland, where 87% of trains are less than 3 minutes late). While I was in Cambridge, England, my old friend and colleague David MacKay, who shares my antipathy for bad numbers, gave me a copy of a recent article in the UK journal Physics World (“Optoelectronics: a green explosion”, May 2011, p. 5 of the optics supplement). The article touted laser-based “green technologies,” including their use in reducing carbon-dioxide emissions:
Volvo’s Johnny Larson says it is possible to shave a few kilograms off the weight of a car’s metal frame by optimizing its design for a laser process. This has knocked up to 2 kg [4.4 lbs] off the XC60, and for every one of these models that clocks up 100,000 km [60,000 miles], 24 kg [53 lbs] of carbon-dioxide emissions will be saved.
So many numbers, so little meaning! Whenever I see so many numbers, I think of what Socrates might have said: “The uncompared number is not worth knowing.” Let’s start with the 2-kg weight reduction. Because it has units, it is meaningless: It gets meaning only in comparison to another, relevant quantity with the same units—for example, the weight of the XC60 (which is an SUV). A typical SUV weight is perhaps 2000 kg [4409 lbs], so the weight reduction is 1 part in 1000 or 0.1 percent.
That number is dimensionless and meaningful, and it suggests that the weight reduction is not significant. However, it’s hard to feel the size of 0.1 percent directly. To give the comparison some bite, convert it to an area of life—salaries—where our perceptions are acute. Thus, imagine that you’re an engineer earning $60,000 per year. In the past year you’ve developed amazing new green technologies. Your supervisor comes to discuss your annual merit raise, saying, “You’ve done fantastic work! We want to thank you by giving you a raise to $60,060!” You might feel cheated by the microscopic raise—just as we should feel cheated by the minuscule weight reduction.
Now let’s apply similar reasoning to the reduction in carbon-dioxide emissions. The 24-kg reduction (over 100,000 km of driving) is, once again, a number with units; thus, it is meaningless. To make it dimensionless, I’ll divide it by the total carbon-dioxide emissions from 100,000 km of driving. Alas, I don’t know that number off the top of my head (whereas I could easily guess the vehicle’s weight when making the weight reduction meaningful).
Fortunately, having made the 2-kg weight reduction meaningful (by dividing it by the XC60’s weight) pays us a bonus dividend: we can reuse that comparison by guessing that the carbon-dioxide emissions are simply proportional to the vehicle’s weight. Thus, the emissions reduction would be 1 part in 1000 or 0.1 percent; and the total carbon-dioxide emissions would be 1000 times larger than 24 kg, or 24,000 kg.
There are at least three lessons in that result. First, and somewhat amazingly, the guess is reasonably accurate: The XC60 is rated at 154 grams of carbon dioxide per kilometer, which is roughly 15,000 kg per 100,000 km (our guess was 24,000 kg). Second, this application of lasers is green because of the color of the money that this misleading marketing will earn for Volvo. Third, a physics journal should know better!