### How Can You Figure Out How Much Gas Your Car Burns While You Sit At Stoplights?

The basic idea is that since the Average Fuel Economy display is showing a value calculated from the cumulative distance (since reset) and the cumulative fuel flow (since reset), if you know the distance your car’s computer is using in this calculation, you can calculate back to the cumulative fuel consumed. Then you can see how this number changes as you sit and idle.

**Reset your meters**. While you are parked, use the button next to your multi-function odometer to reset the trip odometer and the avg mpg display. For most units, you press and release the button to shift between functions, then press and hold to reset that function back to zero. Make sure that the mpg display you’re resetting is the long-term average display. If you have an instantaneous display, it probably won’t display anything when you are not moving anyway, and it cannot be reset in any case. Now switch back to display the reset trip odometer before you move.**Drive 1.0 mile**. Just drive around the block a few times until the trip odometer reads 0.9. Slow down so that you can jump on the brakes and stop within a few feet of the odometer rolling over to 1.0, but if you find you’re in an intersection, just keep going until you hit 1.1 exactly. It’s not so important what the number is, but very important that you know exactly what it is to within a few tens of feet. (50 feet would be 1% error if you use 1.0 in your calculations and it was really 50 feet longer.)**Switch the display back to avg mpg**. Leave the car in drive with your foot on the brake, just like you’d do at a stoplight. You should see the mpg display dropping. Get your stopwatch ready and the next time the mpg value changes, start the clock. In my experiment, it read 22.6 when I first saw the display, dropping 0.1mpg about every four seconds. I started the stopwatch the instant I saw 22.5 change to 22.4. Jot down the number that you chose to start at.**Idle while the mpg reading plummets.**We’re not interested in what the display started at, which is why it didn’t matter how efficiently or poorly we drove that first mile. We’re only interested in how fast the reading drops. This test can be done with pretty good precision in 3-4 minutes, but I let it idle for almost ten which, in hindsight, was overkill. When you get tired of idling, get ready to stop the stopwatch as the next new value comes up on the mpg display. For me, just as the reading changed to 13.5. Jot down that number and note the time on the stopwatch. (for me 9 min 42.2 sec = 9+42/60 = 9.70min)**Go home and calculate.**Since the mpg display is showing you Cumulative_miles/cumulative_gallons, and we know the cumulative miles exactly, since both meters were reset in the same location and counted the same distance to our idling spot, we can calculate the cumulative gas usage to each of our stopwatch moments. Taking the difference between those gives us the gas burned between stopwatch clicks, and from there we can calculate gallons per minute used while idling. The whole formula is (Dist/StopMpg – Dist/StartMpg)/ElapsedTime. I calculated: (1.0/13.5 – 1.0/22.4)/9.703 = (0.0741 – 0.0446)/9.703 = 0.0294/9.703 = 0.00303 gallons/minute. If you express the time in seconds, then the answer will be in gallons/second.**Extra credit.**Any good scientist wants to know how accurate his/her measurement is. The only measured quantities are the distance and the time. We have a good idea of the error in the distance; let’s say 10 feet out of 5280, or 0.2%. So what’s the error in our timing data? You could guess at the variability in your reaction time on the stopwatch, but that neglects any variability in the actual measurements the car is making. You can estimate the timing measurement uncertainty as well. Instead of a stopwatch, I wrote an Excel macro on my laptop to log a timestamp whenever I press CTRL-shift-Z, which I did EVERY time the mpg meter changed to a new value. This enabled me to calculate the cumulative gas value every time the mpg meter changed, not just on the first and last. This chart shows the time difference between each logged point and the next, showing some variability. The uncertainty of any time difference is half the width of the "fuzz" around the underlying curve, in my case, about 0.021 minutes. (Any time difference that has one of those pilot-error spikes as the start or stop time will affect the point-to-point calculation, so you could also use this plot to ensure that you don’t use bad endpoints for the final result.) A 1-sigma uncertainty of 0.02minutes is about 0.2% of the total 9.7minute test interval. (Even without getting better at the stopwatch, I could have done a 5x shorter test and still gotten a 1% accurate measurement). Lastly, there may be some systematic errors in the car’s internal fuel measurement, but we trust that gauge for every other measure of gas consumption, so why would we distrust it now? A test that is more immune to that error would be to fill up the tank, idle for an hour or two while sitting at the gas station, then fill it up again to the same point. We replace the error of the fuel measurement system with the (un)repeatability in the fill volume of the gas tank, but it would eliminate any nagging doubts that the fuel measurement system is wildly inaccurate at the low fuel usage rates of concern here. I don’t have plans to do it, so if anyone else wants to try it, please add a comment.