I am interested in "pixels per viewing distance" as a measure of what our visual systems detects.
It may not be easy to pin it to a single number because it depends on (assuming 'optimal' viewing conditions) contrast, resolution and the individual's eyes (and degree of optical correction).
For a meaningful (and fixed contrast, to eliminate one variable in the) measurement, one could use a resolution target that allows quantification at multiple scales of magnification. One could use a print of a target with many resolution levels, such as a 'Siemens' star target
. When printed as instructed, 600 or 720 PPI to a 130mm square output size, at the perimeter of the 'star', the resolution is: (144 / Pi) / 100mm = 0.458 cycles/mm (~0.916 lines or pixels/mm, or 0.916 x 25.4 = 23.27 PPI).
When we increase our viewing distance to the target, there comes a point that the outer perimeter will no longer be resolved by our eyes. For me that point is approx. at 4.50 metres (4500mm) viewing distance, or 15x normal reading distance of 300mm. When we multiply 15 x 23.27 PPI we would get a resolution of 349 PPI at reading distance. This is for regular visual resolution, not Vernier acuity. Higher contrast features would give higher resolution and thus require higher PPI, and lower resolution obviously gets away with lower PPI.
That allows to determine the minimum required PPI at any distance (assuming our eyes have the same angular resolution at various distances). The additional printer resolution capability, 600 or 720 PPI, is used to allow Vernier acuity, higher contrast detail, and sharpening.
Hopefully one is close to the effective full image width of 81cm, since my observations in galleries suggests that this is a common range for the viewing of large prints. (Paintings by the way are typically viewed from further away, further than the "normal" distance of image diagonal length. But most paintings are very low res. by photographic standards!)
At 81cm the above situation would suggest 4500/810 = 5.56, multiplied by 23.27 PPI that gives 129 PPI resolution, and I'd use the double of that to allow for Vernier acuity / higher contrast detail / sharpening, so 258 PPI as a minimum for that viewing distance. Closer viewing will produce a sense of lacking resolution, for my eyes anyway.
This approach could produce a simple rule-of-thumb, e.g. in my case something like 105 PPI at 1 metre distance, 52.5 PPI at 2 metres, 210 PPI at 50cm, etc., and double that PPI for higher contrast detail, Vernier acuity, and sharpening.
Printing that amount of minimum detail would of course require up-sampling to the native printer resolution, to avoid suboptimal interpolation by the printer driver, and allow artifact free sharpening at that output resolution for the specific print material.