Yes, you can have air con!
The idea of running air con from a battery was unheard of a decade ago. It's still unheard of with a lead acid battery, but it's being done right now by a large number of our lithium customers.
I'm going to use a
recent estimate for a customer as an example. This gentleman was looking at
400Ah lithium and had 400 watts of solar. He wanted to run a rooftop air con,
so we looked up the specs for that make and model. Below are the pertinent
figures (Max Rated Current for Heating was 7.4A, which is a lot, so we'll
assume he'll use his diesel heater in the cold).
Now bear in mind that 5.6A is the maximum rated current, in other words the air conditioner is running at 100% load, or possibly this is the locked rotor current - that grunt before it can get past the compression stroke.
Let's make the assumption that in a caravan, it wouldn't take long for the air temperature to come down to the point where it only had to run half the time to maintain that temperature. Therefore we can halve the amount of current required once the air conditioner has brought the room down to the required temperature:
So, at 12V, once the desired air temperature has been reached, this air con requires roughly 62 amps per hour to run.
Can you do this with a lead acid battery?
In short, no. Regardless of the maths (obviously you have only half the available capacity of the 400Ah lithium battery), a lead acid battery cannot supply the amount of power to start the air conditioner as quickly as the air conditioner requires it, regardless of the size of the lead acid battery. This is the fast charge / fast discharge benefit of lithium - it will give the power as fast as you ask for it.
The lure of air conditioning whilst free camping is often what brings customers to us for a lithium battery install. But you also need to think about how much solar you'll need to replace the power you use.
A lithium battery is lighter, faster to charge and discharge, and safer than lead acid. They also have a much longer cycle life and they like to work.
It's obvious that you need to replace what you use, but the health of a lead acid battery actually requires you to replace more than you use. A lithium battery needs you to replace what you use and does not need to be maintained at 100% state of charge. It prefers to work.