## Save money by driving

Do you enjoy driving? Do you care about pollution? Do you like money? If your answer to one of these questions is yes, the following may be of interest to you.

Last summer it was quiet on the road during my daily commute. This enabled me to do a little experiment that I have been wanting to do. I know my car uses less fuel when driving slower, but how much less?

To test this, every day I would drive 100 km/h on the highway in the morning and 120 km/h in the evening when coming back, or vice versa, chosen more or less randomly. Every time I recorded fuel consumption for my Fiat 500, travel time, and temperature.

This gave me some data points, that I could analyze. Now to be fair, I have only 13 data points, so it is not all very scientific. But citizen science is mostly about the fun, right?

Here are the data points I recorded, plotted against temperature:

Now be careful, the fuel consumption is for the whole trip, while the change in driving speed was only applied to the highway part. Let’s see if the trip time correlates with the speed.

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)     21.143      3.391   6.235 6.39e-05 ***
inverse_speed   40.714      6.098   6.677 3.48e-05 ***

Residual standard error: 1.096 on 11 degrees of freedom
Multiple R-squared:  0.8021,    Adjusted R-squared:  0.7841
F-statistic: 44.58 on 1 and 11 DF,  p-value: 3.483e-05



(sorry for being confusing with the inverse speed, but it is the physically correct quantity to use). That correlation is certainly significant, but there is some variation. Probably this is due to random events, like traffic lights or small traffic jams. The correlation is 40.714 km, meaning that effectively 40.7 km of the 60 km drive was on highways.

The question rises whether it is better to use the correlation of fuel consumption with speed, or with travel time. Because of the variations mentioned above, I actually find a more significant correlation with speed. I will use this to calculate how much money you save when driving slower.

Here are the correlations with all parameters that seem relevant:

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  2.055750   0.655437   3.136 0.011996 *
speed        0.028449   0.004505   6.316 0.000138 ***
temperature -0.028659   0.027249  -1.052 0.320333
direction    0.290119   0.144276   2.011 0.075223 .

Residual standard error: 0.1496 on 9 degrees of freedom
Multiple R-squared:  0.8734,    Adjusted R-squared:  0.8312
F-statistic:  20.7 on 3 and 9 DF,  p-value: 0.0002236


Indeed, the correlation with speed is very significant. There is also a correlation with direction (morning or afternoon drive), probably due to typical wind conditions. The correlation with temperature is not very significant, but in my experience it really becomes significant when you compare summer and winter driving conditions.

The speed / fuel consumption coefficient is 0.028449, or, in other words, by driving 20 km/h slower I save 0.56898 liter per 100 km. But I assumed that the savings were only due to the highway part of our trip. So I should calculate the absolute numbers: the full trip is 59.9 km, so the saving is 0.3408 liter. For just the highway part, this is 0.8374 liter per 100 km.

The average price of Euro95 right now is 1.600 euro/liter. This means that I save 1.34 euro per 100 km. When driving 120 km/h, driving 100 km takes 50 minutes, but at 100 km/h, it takes 60 minutes, a difference of 10 minutes.

Of course, I assume here that all the correlations are linear, but I know that they are not. In fact, if you drive faster, say 130 km/h or 140 km/h, your fuel consumption will increase more dramatically, and the savings will be bigger.

# Conclusion

By driving slower on the highway, you can save 1.34 euro, but you arrive 10 minutes later. This means you save 8 euro by driving for one hour. Maybe not enough to earn a living, but if you have the time: relax and drive slower!

If you are interested, you can get the  data and the R script that I used.
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