The car is my 2005 Mercedes CLK320A. This has a 3.2L V6 gasoline engine. It is supposed to use "premium" fuel (91 Octane in the US), but I have been unable to determine any performance difference using what is sold as "regular" fuel (87 Octane in the US) in San Diego, where I live. So I run it using regular fuel, and the results here are with regular fuel.
My set-up for testing this stuff is described in this post.
For the test, I used a warmed-up engine. I ran the engine in my driveway and applied the accelerator pedal to achieve different RPM levels. The RPM levels and fuel usage rates shown are those logged by the setup described in the other post throug the car's OBD2 connector.
For "air conditioner off" condition, everything in the car is turned off including the climate control. The car does have running lights that stay on in the daytime, these were on. No attempt was made to determine the state of the alternator, whether it was charging the battery or not during this test.
For "air conditioner on" condition, the climate control in the car cabin was turned on. The thermostatic control was set to 60° F in order to keep the air conditioner on constantly. The fan blowing air in the cabin was set to its highest setting.
Results are shown above. Minimum mean square error line fit to the data are shown. At lower RPM, results are pretty nice and linear.
Idle Fuel Usage with Air Conditioner turned off
Without applying the accelerator, this engine idles at about 600 RPM. The fuel usage at idle is about 0.25 gallons per hour, with the air conditioner turned off. The idle fuel usage rises to about 1.0 gallons per hour at 2500 RPM. The fitted line, with air conditioner turned off, nearly passes through 0 fuel usage at 0 RPM. Thus for all intents and purposes, the idle fuel usage is:
(1 Gallon per Hour) * ( Engine RPM / 2500 )
What is the meaning of 0.25 gallons per hour of idling loss? This is a car which gets about 22 miles per gallon averaged over my driving. So an hour of idling uses the same amount of gasoline as driving about 5.5 miles. At $4/gallon (as I write this prices in San Diego are as low as $2.40/gallon), idling costs $1/hour or 1.6 cents per minute. My conclusion is that in regular use where idling more than a few minutes would be very unusual, idling is a very inexpensive process and not worth great efforts to avoid.
Fuel Usage by Air Conditioner
The caption of the figure shows the linear fit equations for the fuel usage with air conditioner off and on. The difference between these two linear fits is 0.16 gallons per hour. This suggests that when the air conditioner is running, no matter what the RPM of the engine is, it is demanding fuel at a rate of 1 gallon every 6 hours.
If the car gets 22 mpg with the air conditioner off, adding fuel flow of one additional gallon every 6 hours would correspond to moving the car at about 4 miles per hour. Now this is with the air conditioner running constantly (it was set to 60° F for this test). Since it cycles off and on in actual use, actual usage with air conditioner on will be less than this.
At $4/gallon, air conditioner on constantly costs about 67 cents/hour. Since in actual use air conditioner cycles on and off, a better rule of thumb might be 25 cents/hour.