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Topic: Theater projector
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I have two needs for a theater projector: 1) display images on a 14ft H X 32ft W psych, and 2) possibly use the same projector to project on a 6ft H X 9ft W screen from a shorter distance. Here are the parameters:

Need 1:
1. Display area of psych will be app. 12ft H X 26-28ft W. Psych is mounted upstage.
2. Projector mount is app. 12ft above the front of the stage and has a straight shot to the top of the psych.
3. Distance from projector to psych is 24ft, so I have a 24ft throw distance to a 12ft H X 26-28ft W display area.
4. Image has to display on psych without hitting the actors.

Need 2:
1. A 6ft H X 9ft W screen will be hung app. 9-10 ft from projector, and will sit lower than the projector. About a 30 degree drop.
2. I have been told that a projector used for Need 1 could be used for Need 2 if software like Q-lab is used to draw a black template around the image. The caveat is that the black display area around the image could be see, however diminished. The recommended contrast ration is 10,000. If this approach is not a good idea, I would consider a second projector.

The projector should also have shutter control.

Thanks for any help.
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Contrast ratio is almost irrelevant. Unless you are in a movie theater, then your contrast ratio will be lucky to go beyond 12:1. Even in darkened conditions, it may be best at 50:1. 10,000:1 is well beyond what most movie theaters which are properly designed can achieve. So, someone saying that to you, is someone who should be questioned on how much real value they are providing to you.

No projectors are in the 26:12 (13:6) asepct ratio. They will be 16:9 or 16:10, most likely 16:10 So, you will have a fair bit of overshoot above/below the image.

I'm not sure how much light you will be contending with, but with a bit of controlled light, you may be able to go as low as 50 lumens per square foot of screen space. Keeping in mind you are basically looking at a screen the size of what is in a movie theater, but in a space that isn't actually designed like a movie theater, and with throw distance requirements that are nothing like a movie theater.

So, from there, it's basic math to calculate required lumen output:
25' wide = 300"
Height = 188" (16:10 projector)
300x188/144 = 392 square feet of screen space.
That comes in at about 20,000 (19,600) required lumens for minimal performance, which puts you into a very high end commercial projection system.

This is the list of models with acceptable (or near acceptable) brightness to work from:
http://www.projectorcentral.com/projectors.cfm?g=1&hide=0&st=1&r=&br=17000&br=50000&c=&w=&ar=Wide+%2816%3A9-10%29&db=&zr=&wt=<g=&ll=&mfg=&p=&wr=&dt=&t=&pjl=0&pjw=0&pjh=0&td=&is=&i=d&tr=&tr2=&oop=1&sort=pop&sz=15

This is a model I would probably take a closer look at. I would pick up a couple of lenses for it and swap them out as appropriate, but you will likely have to adjust the angle/keystone of the projector for the different screen. This is still the way to go for a smaller screen. Keep in mind that a 6' tall screen is about 58 square feet in total and only needs about 3,000 lumens for performance similar to what the 392 square foot screen requires.
http://www.projectorcentral.com/Panasonic-PT-DZ21KU.htm

This falls into a commercial-high-end requirement overall and is not something I would tackle without involving a commercial integrator who can ensure that you get all the parts and pieces that you need.
AV Integrated - Theater, whole house audio, and technology consultation during the build and installation process in the Washington, DC metropolitan area.