# Cruising with Minimal Wallet Bruising

How fast should you drive on long road trips?

One common piece of financial advice is to drive slowly. Per FuelEconomy.gov, “gas mileage usually decreases rapidly at speeds above 50 mph. You can assume that each 5 mph you drive over 50 mph is like paying an additional \$0.25 per gallon for gas.”

That’s a big deal, and it can lead to some significant savings. However, this piece of advice ignores a giant cost of driving slowly: it takes more time. Therefore, I’ve created back-of-the-envelope cost estimates at various speeds. This is part of my ongoing quest to optimize literally everything.

Without further ado, here’s a graph of the total cost of driving 500 miles at a sustained cruising speed. I’ve assumed leisure time is worth \$30 per hour, and I’ve used the same fuel assumptions specified at the above link. With these parameters, the cost of the entire trip is minimized at 95 miles per hour.

All of these can be adjusted in the workbook attached below. For instance, changing the value of leisure time to \$10 per hour changes the optimal speed to 67 miles per hour.

I was somewhat surprised to see the cost of time completely dominate the cost of fuel at the interstate speed limit. Fuel is expensive, but you can always buy more of it.

Amusingly, one can use Excel’s goalseek function to back into the value of time of the losers you pass in the right hand lane. Someone driving at 55 miles per hour is implicitly valuing their time at \$5.64 an hour. As a persistent leadfoot, I was comforted by this analysis. However, I can already hear my mother begging me to exercise caution. Those who drive quickly are more likely to get into an accident, and that’s worth considering.

Fortunately, I’m not the only person to ask this question. Wikipedia led me to a discussion of the Solomon Curve, a graphical representation of driving risk. Apparently, the log of crash risk has a quadratic relationship with driving speed. Drive either above or below the median speed, and your risk of crashing exponentially increases.

Table 7 of the original paper presented a fairly detailed risk of injury and death depending on the driving speed and the time of day (day vs night). I used this data, the aforementioned relationship and two regressions to develop risk curves for day-time and night-time driving. This is old data, and someone else could probably improve the results by looking at more contemporary sources. However, it suits my back-of-the-napkin purposes.

To translate the risks of crashes into the expected value of crashes, I had to assume costs for both injuries and deaths. For injuries, I assumed \$50,000. After insurance, that’s probably a little high, but it’s good enough for our purposes.

The next assumption I had to make is slightly more complicated. How does one value the threat of losing their life? What cost do you assign to daylights, sunsets, midnights and cups of coffee forever squandered in a driver’s overzealous haste to get to the next red light? Sure, in 1999, the EPA estimated a life’s value at \$5.5 million while calculating the value of air regulations, but just because I’m an economist doesn’t mean I’m a monster. Who am I to blindly annoint a dollar value to an anonymous other’s very existence? It would go against everything I hold dear to say lives are worth \$5.5 million each.

First, we must adjust it for inflation. In 2013 dollars, one life is worth roughly \$7.7 million. Moving on…

Due to the quadratic and exponential nature of speed and collisions, the right side of the graph quickly balloons. With the original assumptions, the back of my envelope recommends going 65 miles per hour in the day and 60 miles per hour at night. For my non-American readers, that’s roughly 105 kmh and 97 kmh, respectively. For my pirate readers, that’s 56 and 52 knots, respectively.

The day chart is provided below. Please note that the x-axis has been restricted to 90 miles per hour, unlike the prior graphs.

Of course, all of this assumes you have a radar detector, an average driving ability and an average love of life. The Solomon Curve is anchored on the speed of your fellow travelers, not the speed of an old data set. Take everything into account, and don’t be afraid to disregard FuelEconomy.gov.