How Big Of An A/C Unit?

How big of an A/C unit will be required to cool a 12x18x8 room with 4000 watts of HPS in a normal mid-west summer. Our summers are usually in the 80's with a couple days in the 90's. 100's are rare. There is a window 16" away from the wall in my flower room. I was planning on just buying the biggest window A/C unit I could find and cutting it to fit through the wall. But I know so little about HAC (HVAC minus the V), and I know some RIU'ers are brilliant on the matter. So hopefully someone will be able to tell me exactly what I need.

curious to know myself, i have a veg and bloom room needing cooled, though slightly smaller. 12x12x10 each.

I had a 10,000 BTU haier window unit in a 6kw 18x10x10 and it had enough power to drop my temps to 65F with all the lights on (tested it before I planted) took about 15 mins to go from 95F to 65. You need really really good circulation fans though. I had huge problems with mine originally because all the cold air would situate on one side of my room. The air that blows out of the unit I have comes out around 30F so if you dont have proper placement/circulation you end up with major coldspots and hot spots across the other side of room.