In my apartment, I have two window air conditioning units. Both have different settings for the fan speed: one has two speed options and the other has three. Both have the design that the room circulation fan and the condensor coil cooling fan run on the same shaft, so the speeds of the two fans are identical.
My main question is, which fan speed setting should I use if my goal is to make the rooms these A/C units are in as cool as possible? I had originally guessed I would want to use the lowest speed setting, since that's when the air comes out the coolest and also (since I live in a humid area) less air passes the coils per minute and thus less of the cooling power of the unit is being invested in dehumidification but rather spent directly on cooling the air.
However, as I thought about it more, I realized my picture of the situation was oversimplified. For example, running the fans faster moves more air through the unit per minute and thus the temperature of the air coming out is cooler, but there's more air coming out at the not-as-cool temperature so it probably balances out (by energy conservation, it should balance out). Also, running the fans faster means the outside fan is better able to cool the coolant, possibly allowing the unit to run at a cooler temperature overall. And finally, maybe investing more cooling power in dehumidifying the room will help reach a cooler temperature overall since eventually the room will be at a lower humidity and the A/C unit will be investing less cooling power pulling the water out of the air.
Poking around online, I found this statement from an energy.gov website:
Set the fan speed on high, except on very humid days. When humidity is high, set the fan speed on low for more comfort. The low speed on humid days will cool your home more effectively and remove more moisture from the air because of slower air movement through the cooling equipment.
So, according to the US government, running the fan speed on high is the best course of action except on very humid days (but no explanation why). They also say that running on a low fan speed on humid days will both cool your home more effectively and remove more moisture.
So, my questions: If I want to get my rooms as cool as possible, what is the best fast speed setting to use on my air conditioners and why? Does this answer change depending on how humid the day is, and if so, how? Is the advice from energy.gov sound?
(I have a strong physics background, so I'm fine with a detailed physical or mathematical explanation.)