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SvennoJ on 02 November 2013
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JoeTheBro said:

Distance distance distance.

Let's use math!

Omega=2*arctan(9(screen size in inches)/((337)^(1/2)*2*(vertical screen resolution)*(distance from screen in inches)))

For a 1080p image on a 50inch screen at 5 feet, omega=.02167

For a 720p image in the same setting, omega=.03251

For a 1080p image on a 5 inch screen at 1 foot, omega=.01084

For a 720p image in the same setting, omega=.01626

 

The results are conclusive! It's the same percent change for each setting! However with diminishing returns, the 50inch screen going from 720p to 1080p would be more noticable! Math!

Disclaimer!
Omega represents the observed size of a pixel.
I don't know math.

I know what you're getting at but let me simplify it a bit.
Indeed who wants to sit 8-10 ft away from a 30" screen in 2015...

THX standard specifies a 40 degree field of view for optimal visual experience. That corresponds to 1.2 times the diagonal for sitting distance with a 16:9 screen. 3ft from a 30" screen, or 6ft from a 60" screen. 1080p isn't even very nice to look at at that distance, 4K will finally full fill the THX specifications.

SMPTE standard specifies a 30 degree field of view for optimal 1080p experience. Or 1.62 times the diagonal of a 16:9 screen, hence 4ft for 30", or 8ft for 60". Very noticeable difference between 720p and 1080p.

Or to simplify your Omega factor, the number of pixels per degree you see is easier to compare:
For 16:9 720p, perceived ppd = distance * 25.62 / diagonal
For 16:9 1080p, perceived ppd = distance * 38.45 / diagonal

For example
1080p 50" at 5ft (60") = 46 pixels per degree (92 pixels per degree at 1ft from a 5" screen)
720p 50" at 5ft (60") = 31 pixels per degree (61 pixels per degree at 1 ft from a 5" screen)

The human eye can distinguish individual pixels upto 60 pixels per degree while people report a better smoother more detailed looking picture upto 200 pixels per degree. Makes more sense to go higher on your tv then on your phone.

Ofcourse you can be happy sitting 8 ft away from 30" 720p at 82 pixels per degree. But I rather have a more immersive experience in 2015 then a 16 degree field of view. Horizontal fov in degrees = 2 * arctan ((0.436 * diagonal) / distance)