Electrics and Wiring Questions

I don't foresee any productions bringing a couple of 96 racks into an 18' tall black box, or even a 48. Chances are most rentals are going to use house gear I'd assume, and even if they bring a 24 rack, you can swap the bussing in most of those really easily.
 
Both legs from a single phase system are "in phase" with each other, not 180 degrees as some people claim; the increased voltage by connecting a load between both legs is achieved because you are connected across more windings on the secondary side of the transformer, not because of a vectorial sum in a polyphase system.

With a split phase service, the 2 legs will, neccessarily, be of opposite polarity. We could talk about flux linkages and other magnetic constructs in the context of a transformer or we can just accept that it's what happens... If they were not there would be zero potential between hots yet we know there is 240V.

When we represent AC voltages using phasors, we are using complex numbers which gives us a magnitude and a phase.
When using complex numbers in polar form, there is no such construct as a negative, the magnitude is an absolute value and thus must ALWAYS be positive. A negative in the rectangular form of the complex number will shift its position in the complex plane and the only way we can represent that in polar form is to use a phase shift.
So, because convention dictates that we talk about voltages as a magnitude and a phase, the 2 phases MUST be out of phase with one another.
 
My most recent position was running a black box theater. It was larger than yours (50x50) but in the smallest of stage configurations (20x20 stage arena seating) I needed at least 50 fixtures for a good looking light design. My larger stage configurations (40x20 proscenium) ran around 100 fixtures. You may only have the budget to start out with 20 fixtures but your designers and your renters are going to want to use more than that. So plan for more circuits and more power.

The shoeboxes I would trust for permanent use are the ETC Smart Bar (not really a shoebox) and the Leprecon ULD's. The Smart Bars and ULD's both come in edison and stagepin configurations which is excellent. Since the Smartbar's are ETC products they are of course well built and well supported. I installed some ULD's in a small rental hall and I was really impressed with the build quality, and as far as I know they've been very reliable with moderate regular usage. I haven't seen the Strand Light Pack in person but it appears to be a product worth a solid look if you can.

The Elation/AMDJ/Chauvet level of shoeboxes are very cheap. You are buying a disposable product. They definitely have their place in the industry but as far as I'm concerned a rental facility is not the place for them. I would not want to rely on them to keep my rig going day in and day out when my facility's reputation is on the line.
 
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Also, hire a theater planning and electrical professional. It may seem redundant, but 95% of architects, electrical companies, and engineers know nothing about the lighting needs of a theater. Get someone who does.

I have been BEGGING my theatre company who is getting a new space remodeled for them to do this, but no one wants to listen to me, and instead want to take my free, un-professional advice about how to run power and how much would be needed. I tell them I'm not sure what the power requirements and equipment needs are without a professional theatre planner to help in that regard, but I keep being asked these questions over and over. This building only has a 200A supply, which I think was fed via 3phase YDelta for the entire building, and that includes upstairs offices, HVAC and everything else. Any advice on how to convince them to hire someone to tell them how to install circuits and what the lighting needs of the space would be?
 

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