He doesn't use the battery to power the AC, just his computer. Start with the worst case, 5 amps continuous at 120 volts for the AC. That's 50 amps out of the battery at 12 volts, not counting losses in your inverter. So you can run your AC for one hour with your 100 amp-hr battery. If you run your battery consistantly below 50% charge you will need a new battery fairly often.

Also a 100 amp-hr battery is less than 100 amp-hrs at that high of a discharge rate. The rating is based on a 20 hour discharge rate. Caldwell's book shows that a 100 amp-hr battery is only 44 amp-hr at a 43 amp draw. You can fix that by adding a lot more batteries or getting a much bigger battery.

There's a whole section on estimating the output of your solar panels. It came down to about 180 Watt panel to generate 60 amp-hrs in one day.

So you need one 180 watt solar panel and one 100 amp-hr battery (ignoring that 20 hour rating problem, add at least 4 batteries to get around that problem) per 1 hour use of the AC.

If the AC cycles on and off, increase your time proportionally.

John Courter
It's not amp/hr, it's amps x hours.