Is it possible to use a projector outside during the day?
The short answer - not really.
The reason why people often think the daylight projection is possible lies in the human eye optics. You may be tempted to think that the luminosity of a well-lit conference hall is comparable to a cloudy sky outside.
However, if you measure the objective illuminance, or amount of lux (brightness of the light reflected from the surface, luminous flux per unit area) you will see that there is more brightness outdoors than in the well-lit indoors. This happens because the human eye is adaptive and equalises the broad band of luminescence.
3 reasons why outdoor projectors can't work properly in daylight
1- Sunlight power
In the very basics of projection lies the ability of a surface (your projection screen) to reflect light. And the problem for the daylight projection is that your projector screen reflects sun light better than the light from your projector.
The sun emits more light than any of the most powerful projectors currently available on the market.
2- Weather always changes
Another property of the daylight is that it can change drastically. In a very cloudy winter day -- right before the sunset -- the sky can be obscured enough to allow for a comfortable viewing experience.
But in 10 minutes time, the sun can overpower everything the overcast sky, which will instantly ruin your attempt at a daylight show.
3- Impossibility of doing that with big screens
There is another interesting aspect here. If your projection screen is small enough it requires less light from your projector to show a bright picture. So if you take a 10,000 lumen projector and concentrate its rays onto a 10'' projection surface - you'll be able to see an image during the day.
But if you would like to light up a significantly larger image of, say, 10 ft - you'll require at least a 10x more powerful projector to compete with the sun.
What if you still want to project during the day, at any cost?
The best alternative (LED panels)
We got you covered here. You may get a dull, low-contrast but still visible image: stacking two or three very powerful projectors - say 40,000 lumens, each. The average cost of these powerful projector models would run at $100K, per unit.
This doesn't make any commercial sense and for showing your content during the day outdoors there are LED panels invented. This would currently be the best solution for the environment described.