Gas Mileage and Car Accessories (from Car Talk)

First: Car Talk is awesome. I wish I could come up with some class activities that help students become as good at trouble shooting and critical thinking as Tom and Ray are. Anyway, they are quite entertaining.

So, my Dad called and told me he heard a discussion on Car Talk about the effect DC to AC converters and accessories plugged in to it and how they would effect gas mileage. I skimmed through the last Car Talk podcast, but couldn't find it. He must have heard a re-run on the radio or something (he doesn't really believe in podcasts). Let me calculate the effect a number of things will have. This will be extremely similar to my calculation of the effect of daytime running lights on fuel efficiency.

Just like the daytime running lights (DRL) calculation, the problem is the conversion of energy from fuel to electrical energy. You need to make some assumptions to do this. I assume (with the symbols I will use for each variable):

• The energy density of gasoline is 1.21 x 10⁸ Joules/gallon. (d_g)
• A car is 20% efficient at converting this energy to mechanical energy (e_e).
• The alternator is 70% efficient at converting mechanical energy into electrical energy (e_a).
• The DC to AC converter is 70% efficient (e_DC).

What am I going to plug in? Suppose it was about 100 Watts total. If this is the case, then the hard work is already completed from the DRL post. So, I am going to take it one step further. I am going to let you input whatever you want by embedding a zoho spreadsheet. There is one big difference between this calculation and the DRL one. For this, I don't have a specific speed. This means that I can calculate the gallons of gas per second that a device could use. Starting with the power of a device:

So 100 watts worth of stuff would use 100 Joules every second. How much gasoline would this require each second? Well, what is the power produce by consuming a volume of V (in gallons) of gas in 1 second? (including losses due to the alternator, engine etc...):

With the above expression, I could determine how many gallons per second one would need to run devices with power P. What does this do to the fuel efficiency? Suppose I am going 70 mph. I could determine how far I go in one second and thus get a measure of fuel use in miles per gallon. So, the faster you are going, the less these accessories will reduce your gas mileage. Now, let me put all these calculations in a zoho spreadsheet (so you can change all the variables as you like)

Note: I couldn't not figure out how to force zoho to show a number in scientific notation. To compensate, I just put the power in with the units. So, this says that 100 watts worth of stuff plugged into a DC to AC converter would use 8.43 x 10^-6 gallons per second. If you compare this to a car going 60 mph that gets 20 mpg, that would use 8.35 x 10^-4 gallons per second.

I changed this post slightly. The original zoho sheet calculated the loss of efficiency due to the accessories. I need to re-think that.