Fan speed does not really affect efficiency a lot. I’m not 100% sure on this, but I believe AC is either fully on or off, and temperature is more controlled by how much heat is added. The heat is neutral efficiency-wise, because it’s just the losses from the Engine. If you don’t want it in the cabin and turn it down, it’s redirected to go out.
The ac is either on or off as indicated by a lamp or snowflake symbol and while modern cars may offer an eco button that may or may not cycle ac as part of that, we should just assume it’s on. So the only effect there is if it’s running or not, temp setting doesn’t matter because it never cycles it just blends hot and cold air in different ways.
Increasing fan speed however does have an effect that’s more immediate though not as impactful as ac compressor on or off. An ac might pull 2-3HP while a fan on highest setting might pull 1/4 HP. Also we should consider that the engine fan will also turn on or run faster when AC is enabled and that saps power too, probably another HP or 2 depending on the car and design at least.
There’s an old (accurate) joke that turning off the ac is smaller cars before climbing hills, etc was a requirement because they suck so much performance. I’ve had cars where I could visibly feel the difference in performance when the ac is on.
The ac compressor is belt driven off the engine, using and sucking engine power.
The fan is electric and consuming almost none of it.
It somewhat depends on the age of your car. If it’s less than 20 years old or so, changing the requested temperature will make a somewhat significant difference to the efficiency. The fan speed is basically inconsequential. The difference in engine load between fan off and full speed is probably similar to a couple of psi in your tires.
Mythbusters did a few shows on this. The thing that most folks don’t consider is that the compressor is part of the serpentine belt and is always there. So the difference of amount of cooling or fan speed is a much smaller drain than the fact that its there. I knew someone who pulled the AC out (in the 60s when AC was new and attached to outside of the engine.) You’ll save more gas accellerating slowly…. Don’t fly a flag, that almost like a parachute adding drag/resistance.
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