Span calculator using arbitrary spacing?
There are several issues: 1) true load on joists, 2) true existing joist size, 3) joist spacing, 4) joist bearing/ support, 

1) The Code requires a minimum of 40 psf for usable loft/attic rooms. However, the equipment you describe could easily exceed that amount, but that load would be near the perimeter of the room probably. You have about 2’ of head room on the rave sides, but could be substantially higher on the rake sides. (“10’ stud nailed 8’ up.”) of course the sides with substantially more load will require substantially more support. So, a uniform joist installation will probably not be sufficient. 

2) The existing joists appear to be 2x8’s not 2x6’s. However, I’ll use your notation. 

3) Existing joist spacing appears to be 16” o.c. (To match stud spacing.)

4) Existing joist support is in shear (balloon framing) with 3-16d (I assume) at each existing joist. Additional load will require additional support. 

So, in order for the new attic load to be transferred to the footing, the new joists will need to be secured to the existing studs, (because there is no double top plate). 

Without knowing the actual load from the equipment, I’ll assume a minimum of 50 psf plus an additional 30 psf along the gable ends. 

I’d sister 2-2x6’s to the existing 2x6’s (1 on each side of the existing 2x6). I’d add a 2x4 under each joist down to the sole plate.

Along the gable end, I’d add 2-2x6’s on each side of the existing 2x6 joists for the first 2 spaces (32” or 2 joists) with 1-2x4 under each added joist. (I’m assuming the first joist will be nailed to the studs on the gable end.)

Btw, with that much equipment, you’ll need to consider adding cooling equipment too.