The sun angle helps a little but still not enough. As seen in the image above, with that sort of ambient light level, then without a proper canopy / roof / awning to shade the screen you're not really going to see much until it starts to get dark. In the summer that could be as late as 10pm.
The average cheap 75" TV (<£800) can produce somewhere around 300 to 400 Nits of image brightness. There's a 1:1 translation between Nits and cd/m2 which is the more common measuring standard used for TVs. You'll see cd/m2 referred to in the proper TV reviews from rtings.com and AVForums.
Ignoring the problems of poor black level and a lack of contrast that come from projecting in daylight, and the lack of colour saturation that will happen as a consequence, then just to get the same image brightness on say a 100" diagonal (8ft) 16:9 white screen from a projector will need a genuine 3000 - 4000 ANSI lumens. The word
genuine is important. The light power claims for most projectors are deceiving. When being measured they're set up in a way to maximise image brightness. The resulting image looks awful. When the projector is set for a watchable image you'll get a drop in brightness by roughly 25-40%. In reality then you're looking for a projector of around (best case) 4000 and (worst case) 6500 ANSI lumens to equal the brightness of an £800 75" telly.
The telly has some other advantages. First, the screen is black. That helps image contrast immediately. Second, you're looking directly at the thing making the light and not at a reflected image so you don't need to worry about the quality of a screen. Next, a TV doesn't flap about in a light breeze, and the surface doesn't ripple due to inadequate support from the roller tube. The TV will have smart features and a sound system built in. It's cheap and easy to hang a TV and equally cheap and easy to add a sound bar for more audio oomph. A TV doesn't have fan noise and there are no lamps to replace.
There are relatively cheap 4000 ANSI lumen projectors available with the right kind of throw ratio, but they're designed for Powerpoint presentations and not for video, streaming and gaming; therefore the video processing in them is very basic (read that as 'a bit crap') compared to even basic tellies. Also, they're not even 1080pHD resolution. You're looking at 1280x800 res which is HD Ready. They'll handle 1080p but there's no support for native 4K. Guide pricing: Optoma W400+ (lamped) @ £650. Optoma ZW400 (laser) @ £900. These prices don't include screens or sound systems or any smart features. I'll stress right now that these are at the very very shallow end of the price pool. These are not high-end, nor even mid-range. They're about as cheap as it gets to tick the brightness and throw distance requirements....
that's it.
In the home entertainment / gaming projector category then the entry-level Benq TH585 @ £600 claims to be 3500 ANSI lumens. The real world brightness then will be around 2000-2500 ANSI. Allowing for the depth of the projector and the corresponding small reduction in throw distance, and with the lens set to its widest to give the biggest image, you'll get a 78" diagonal image.
Yep, just 3" different to the TV.
It's the same story with the Optoma HD145X. The Epson EH-TW740 isn't as bright but does have a slightly shorter zoom lens. It will do a 90" diagonal image.
You might get the impression that I'm anti-projector, but nothing could be further from the truth. I could show you projected images that would make your jaw drop, and that's without throwing UHD and HDR in to the mix. But in each situation the room would be in almost complete blackout and the projector and screen set up to work together perfectly.
I'm very pro projection, but also realistic about its capabilities in adverse conditions. Also, I've been around the block more than enough times when someone has seen projectors as a cheap alternative to a big telly without really understanding just how different the final results will be or what it takes to get there. Stuff you might take for granted such as dealing with multiple sources or handling sound becomes a magnitude more complicated with projectors; and that means it costs more too.
Big tellies got cheap. The screen sizes for what you spend are tremendous value. They're easy; everyone understands a telly. They're pretty much self-contained, and they're now light enough that they're easy to move and store at the end of the season. Have a think about a big telly. Put it on a wall bracket. Add a sound bar. Cover the whole lot with a waterproof outdoor cover along the lines of
this for use during the season and then put the TV inside over winter. You'll do the whole thing for under a grand. It'll be simple, and you'll be able to use it from 6:00pm rather than waiting until 10 o'clock.