Re: Video projector suitable for outdoor use
Enclosures are available to solve the outdoor aspect. The throw distance issue is simply a matter of using the appropriate lens. The bigger issue is one of brightness.
The rule of thumb for daylight (not direct sun) visibility is a screen intensity of 5000 nits (this makes some assumptions about required contrast ratio). Assuming a screen gain of .7 (white painted wall), this means that you need ~7k lumens per square foot of screen area. A 120" 4:3 screen is ~50 square feet, so you're well into the multiple-stack 20k+ lumen range. Well over $5k to purchase.
For comparison, computer screens are typically around 300 nits, so if that were sufficient brightness, an 18k projector would get you that level over your 120" screen. A 5k projector (about the max you'd be able to squeeze into your budget with lens and housing) would get you about that intensity over a 60" diagonal area (3'x4')
