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My company produces some out door concerts that will have 15-18k people attend. I'd like to setup a video screen next to the stage that I can use to show a video feed of the concert. I don't have a lot to spend on it, but I would be reusing it for other things, so what do you think? I have a switcher that does hdmi and hd-sdi output, so a projector or system would need to use that.
I'm trying to create something, similar to the picture attached. 
"Most affordable" makes this a very difficult question to answer. The way most festivals do it is by hiring large screens. You could try and do it with a projector, which can work okay at night, but not so good in daylight (like a drive-in cinema).
For bright displays there aren't really any shortcuts -
Technology-wise, it is very simple, as you aren't doing anything clever with video.
There isn't an "affordable" option here. Either you use high intensity light screens or high intensity rear projection with an enclosure around the back side to keep out sunlight. Either option is looking at tens of thousands of dollars per screen to buy.
I'm not particularly familiar with light screens because they tend to be a lot harder to move than the rear projection units, though if resolution isn't super critical, there are hanging displays that use basically strands of Christmas tree lights as pixels that are pretty portable.
For rear projection, you are probably going to want something in the neighborhood of 15 to 30,000 lumens per screen which is around $30,000 to $60,000 worth of projector, plus the cost of the screen itself which is likely to be several grand as well and also the (relatively speaking cheap) box around it all to block out light from hitting the screen from behind. These produce excellent quality images, but as you can see, they are anything but cheap.
You may well end up using two or more projectors and stacking them so that the pixels light up. It is an easy way to get more intensity and you could potentially use a whole rig of smaller projectors, but the more projectors you add, the more complexity you will have in aligning them all for a particular installation and keeping them all properly color balanced.
