With the Scan Gauge 2 I can find out a lot about what my engine is doing. I have it set to provide a continuous display of speed (it's about 2 m.p.h. slower than the dashboard speedometer display), r.p.m., instant mileage, and absolute manifold pressure. The manifold pressure is a very sensitive indication of throttle position, since throttling is accomplished by restricting the flow of air through the throttle body.
I've found a few stretches of freeway where it seems like the road is level, or at least its slope is constant (constant slope will suffice for this). Thus, with cruise control on, manifold pressure will remain quite constant on these stretches. This is an ideal time to experiment with turning the air conditioning on and off to see if there is an effect on manifold pressure, indicating that throttle position is increased in order to operate the compressor while still maintaining the selected speed.
So what happens? Well, the manifold pressure increases by approximately 0.4 p.s.i., typically from 9.1 p.s.i. to 9.5 p.s.i. I found this to be a consistent and repeatable result. What does it mean in terms of fuel consumption? I can run a few calculations and come up with a number, but I'm not extremely confident in the accuracy because the indications on the instant gas mileage display are not as dramatic, consistent, or repeatable.
But let's proceed anyway. PV=nRT in an ideal gas, we'll assume (inaccurately) that that's what we have. Since, for a given length of time the volume, V, and the temperature, T, are fixed, and R is the universal gas constant and thus never changes, a change in P means that n, the quantity of the gas (number of moles), must change by the same proportion. A change from 9.1 p.s.i. to 9.5 p.s.i. represents an increase of about 4.4%, so fuel consumption should increase by a similar amount. Since I'm typically looking at about 21.7 m.p.g. or so, I should see a decrease to something like 20.8 m.p.g. It doesn't seem like I see this much of a decrease, but I'm going to be doing some more checking.
In another post I determined the LR3 uses something like 24.5 horsepower to cruise on a level highway at 55 m.p.h. Since burning fuel provides this horsepower, the additional fuel burn should reflect the increased power required to run the air conditioner. How much power? It works out to be just a tiny bit over 1 horsepower, and as I concluded in my previous post on air conditioning, I find that to be a number that squares nicely with my intuition.