How far away can a human see a human from the air?

[Fiery Diamond]

The Question: Presuming completely clear skies, how far away could you see a human? The horizon isn't relevant here, as we're viewing from the air (from an indeterminate height, such that the distance at which humans are too small to spot is the deciding factor rather than anything else). I've tried googling this to no avail. Everything is only about the curvature of the earth, which is not what I want to know - I want to know how far away you could see a person from above or above+to the side.

Presume 20/20 vision.

You don't need to be able to tell that it's a human, just that it's a thing that exists/is possibly moving.

[Fat Rooster]

https://en.wikipedia.org/wiki/Naked_eye is a good starting point, but 1 arcmin seems to be the general consensus on angular resolution. You would be able to distinguish features of a person (head from legs, meaning it is a person not a deer for example) out to around 4km at a push. Where it gets a little more complicated is that it then becomes much more about how well the person blends in, rather than identifying features. It is possible to spot a person in a bright red jacket on a dark mountain from further than that in the right light conditions. You are looking for the 'pixel' that is redder than the surrounding mountain, particularly if it is moving. Even if you can barely see a car in the distance you might be able to notice somebody walking in front of it based on slight colour flickers, or that there is a slight darkening on the path behind you that seems to be moving at human speed. Does that qualify as seeing the human?

Basically vision is more complicated than just angular resolution. Signal to noise ratio is important too, as well as understanding what qualifies as 'signal'. For a more specific answer you need a more specific question. Does that help?

[jayem]

Something that contains photos from above (e.g. google maps) might be an interesting way of getting a real life feel for relative things in static contexts. You'd then have to 'calibrate' the equivalent distance but similar triangles would give you a start on that.
For me I can just about spot static cars as being 'non road' when 1km takes 15cm of the screen from around 45 cm away from the screen, which vaguely corresponds to 3km height.
That would cover blending in as well as angular resolution, but it would ignore focus and things like that.

You might be able to do something similar with photos from other angles (e.g. top of Eiffel towel) but there I think the photo quality is the limiting factor.
I can see just about see cars on the Statue Of Liberty Bridge (Paris) from the Eiffel Tower (1.3km away) when the zoom is such that the bridge is about 2cm at 45cm screen distance (which would suggest about 4km if I reckon correctly).

[Telok]

US mil did a lot of research and I used some to write up some spotting & hearing rules for a rpg. If what you want isn't in one of these then they should get you started on your search. Check thier bibliography and just copy-pasta into google to start down the rabbit hole.

AD-753 600 TARGET DETECTION AND
RANGE ESTIMATION
James A. Caviness, et al
Office of the Chief of Research and
Development (Army), November 1972

RESEARCH MEMORANDUM,
MOONLIGHT AND NIGHT VISIF1LITY
Thomas F. Nichols and Theodore R. Powers
USAIHRU, January 1964
https://apps.dtic.mil/sti/pdfs/AD0438001.pdf

Jungle Vision IL: Effects of Distance,
Horizontal Placement, and Site on Personnel
Detection in an Evergreen Rain forest
Dobbins, D.A. et al.
U.S. Army Tropic Test Center, Fort
Clayton, Canal Zone, March 1965.

The Effects of Observer Location and
Viewing Method on Target Detection with
the 18-inch Tank-Mounted Searchlight
Louis, Nicholas B.
HumRRO Technical Report 91, June 1964.

Report Bibliography on Target Detection
and Range Estimation
ASTIA, Humans, Armed Forces Technical
Information Agency, Arlington, Virginia,
November 19 60.

Scripps Institution of Oceanography.
Predictions of Sighting Range Based Upon
Measurements of Target and Environmental
Properties
Jacqueline I. Gordon.
http://misclab.umeoce.maine.edu/education/
VisibilityLab/reports/SIO_63-23.pdf

Memorandum RM-6158/1-PR, Target
Detection Through Visual Recognition: A
Quantitative Model
H.H. Bailey, February 1970
https://www.rand.org/pubs/
research_memoranda/RM6158z1.html

RESEARCH ON VISUAL TARGET
DETECTION PART I DEVELOPMENT
OF AN AIR-TO-GROUND DETECTION/
IDENTIFICATION MODEL
Margaret E. Franklin, John A. Whittenburg
June 1965

Detection of random low-altitude jet aircraft
by ground observers (Tech. Memo. 7-60;
AD 238 341)

AD-758 875: CAPABILITIES OF
GROUND OBSERVERS TO LOCATE,
RECOGNIZE, AND ESTIMATE
DISTANCE OF LOW- FLYING
AIRCRAFT
Robert D. Baldwin
Human Resource's Research Organization,
March 1973

[Manga Shoggoth]

You might get some feel for it from the PARIS1 GB Vulture 1 launch (https://www.youtube.com/watch?v=tr-qE2q9ev0) (The Register) - humans (or rather the human scale) viewed from above are very quickly reduced to dots. The images aren't as clear as one might like as a lot of the view is taken up by the titular aircraft and its pilot.

There are probably simillar videos around that may even give altitude information - or at least a better view.


1 Paper Aircraft Released Into Space

[Lvl 2 Expert]

The Question: Presuming completely clear skies, how far away could you see a human? The horizon isn't relevant here, as we're viewing from the air (from an indeterminate height, such that the distance at which humans are too small to spot is the deciding factor rather than anything else). I've tried googling this to no avail. Everything is only about the curvature of the earth, which is not what I want to know - I want to know how far away you could see a person from above or above+to the side.

Presume 20/20 vision.

You don't need to be able to tell that it's a human, just that it's a thing that exists/is possibly moving.

What is the definition of completely clear skies here? Realistic sky, or more "we can see stars thousands of light years away because there is barely any stuff in between" clear?

I'm going to assume that second one, because it makes the question a lot clearer. (It's probably not going to matter anyway, although it could matter for things like spotting a mountain in a world without horizons.) The smallest things you can see from about ten cm away (about the closest you can get without losing focus) are a few tenths of a millimeter/several hundred micrometers in long and wide. The smallest things you can see from around a meter away are a few millimeters in every direction. Let's just round that down to one mm, for a proper lower bound. (And that really is a lower bound, if you can see that well you should be able to spot dust mites (https://en.wikipedia.org/wiki/House_dust_mite) in your bed and carpet.) So let's say a human is about 50 cm's wide, "a few hundred millimeters". We should be able to just about spot one from just about 100m away, or 500 meters as our lower bound. Which can't be true and is a ridiculous number, you can spot a human easily from that distance. Sight may not scale as simple as that, or maybe dust mites are just really good at hiding and we can in fact make out non-mite details ten times as small as I estimated above.

Back of an envelope calculations-man, retreat!

(One of the reasons sight may not scale like that is that it's much easier to focus on large things in the distance than on really small things nearby. Another could be that at such a small scale the thickness of the object you're looking at also hinders its visibility, when things become too small they become transparent.)