There’s a story I’ve heard from a good number of sources about submarines, usually in the Mediterranean or near a Pacific island, coming to periscope depth and finding a yacht with a couple amorously engaged. With newer subs, this is then recorded for the crew’s entertainment. I’ve seen this repeated in a few books too. How visible would such a submarine itself be from the yacht? Obviously the clarity of the water is going to be important, but is it sufficiently important to overcome the low angle?
Well, the critical angle for water is about 49 degrees, and so anything closer than that to the surface is going to be completely invisible no matter how clear the water is.
I’ve heard this many times before, too, but it’s almost certainly just a sea story (i.e. an urban legend).
You know it’s a sea story, because it always starts off the same way: “This is no shit. There we were…” 
If it was that interesting to watch they probably wouldn’t notice the sub even if it surfaced.
Closer than 49 degrees to the surface? What does that mean?
Here’s the USS Key West at periscope depth - cool pic: Los Angeles-class submarine - Wikipedia
If the angle from the sub to the person on a boat is less than 49 degrees, the person on the boat can’t see the sub. It has to do with light refraction.
Think of a sub 50 yards away:
-someone in the crows nest of a boat should be able to see it in clear water
-someone in a rowboat will not, because they don’t have the height to see into the water.
Also, you can see fish directly below you in clear water, but not fish 30 yards away even though the water is clear and there is a direct line.
You can google “critical angle water” and get more information.
And here is a lovely picture of Chicago.
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I’ve gone whale watching in a light airplane many times. They’re visible well below the surface. They’re smaller but about the same color scheme as a modern submarine. Spotting subs at periscope depth in decently clear water would be easy once you knew about where to look.
Obviously that’s looking down on them more or less vertically. Which isn’t the POV two folks shagging on a boat would have.
Most boats that have soft comfy spots to lie down on have some kind of solid railing around them. So our amorous yachts-people would be below decks or behind the cockpit coaming or such. Not laying on some hard fiberglass deck out in the open. So unless the sub was right under them and the periscope mast right alongside the yacht & looking down at a steep angle, there’s nothing to be seen.
To be sure if they’re doin’ the deed on a Hobie cat that’s all out in the open to be seen. But that’s a pretty near-shore boat. IANA submariner, but I’d be skeptical of a sub that close to shore other than entering a harbor channel. Which is not a place Hobie sailors are going to stop for a quick shag. Lest they be run over by a passing freighter.
Ref **robby **above … An old fighter joke:
I don’t know what the rules about surfacing are, but I’ll bet they have a minimum distance requirement from other traffic before surfacing. I’m pretty sure that a sub doesn’t surface while on patrol as it gives away its position. What they see through a periscope is a different thing.
You also have to be careful how and where you surface: Ehime Maru and USS Greeneville collision - Wikipedia
I’ve homed in to a submarine periscope once in a maritime surveillance aircraft. It wasn’t visible at all except for the periscope but the sea was choppy, not rough or anything, but a long way from glassy smooth.
If the sub is moving too quickly or there’s some wind or current action, the wake from a periscope might be visible.
The way I learned it:
Fairy tale: “Once upon a time…”
Sea Story: “This is a no-shitter…”
If I recall correctly, there is a scene in Das Boot in which U-96 surfaces to periscope depth in order to take a closer look a British destroyer. Despite the strong currents and the rain, with the periscope hardly ever appearing above the surface, the U-boat is detected and is forced to make an emergency dive.
For what it’s worth, this wasn’t a normal surfacing. It was an emergency ballast blow surfacing maneuver, which is performed periodically for training purposes. However, it is indeed critical to ensure that no other vessels are in the area before starting the exercise, which the USS Greenville tragically failed to do.
The controversy was that the submarine’s failure to clear the area was likely due in part to the number of VIPs in the control room of the submarine during the maneuver.
1963 report on submerged submarines’s visibility from aircraft.
Notable mainly for how few results it has—every time it seemed they tried to do an experiment, the weather crapped out, or the Cuban Missile Crisis interfered with their work. Still, the paper lists curves measuring the received light on a submarine sail at various depths, and attempts to correlate that with visibility distances.
Statements from the air crew indicated that wake from objects breaking the surface was much more visible than reflected light from the submerged submarine. The antenna whip’s wake was cited a few times as leading the aircrew to the sub.
No doubt the research’s been replicated and improved upon a bunch, with that research informing future sub’s hull coatings and shapes. Still, those are awfully modern subs shown visible under the water, in SCAdian’s and Elendil’s links.
I don’t know if this is done, or if anyone could confirm, but do subs even need a firm, solid connection to the surface, like a periscope or other mast, any more? Why can’t the sub stream a reel of cable to whatever sensor raft needs to break the surface? Said raft could be motionless with respect to the surface, so long as the sub kept playing out cable. A wakeless spar with a bunch of GoPros and radio antennas on it is going to be much harder to see. Plus, the sub can be a lot lower than 50-70 feet or whatever periscope depth is. When the sub is done looking around, sink the raft below the water and reel it in.
I think Das Boot is set before the description in my cite, but this site for the U.S.S. Slater, (DE 766), mentions for its radar that,
Which seems mindboggling to me, considering how small a periscope head and mast is compared to the omnipresent return from water waves breaking around it. If it can pick up a periscope head, then how much further away could it pick up the much larger snorkel head?, and isn’t that far enough away to make snorkeling a false security, given that you couldn’t have a surface watch while you were snorkeling?
In both of those pictures, the sub appears to be moving at some speed, and it’s the wake from the periscope that is most visible.
If they were still, about all you would see is the different color of the sub vs. the water – that would be noticable from overhead, but on the deck of a boat a few feet above the water? seems unlikely.
I’m not sure you could do it with radio. The sub is immersed in a good conductor (salt water), and as I recall radio communication when it can be done at all requires very long wavelengths, which in turn requires very large antennas (or lots of power) and very low bandwidth (so your information throughput is much too slow for video).
What you might be able to do is design an acoustic transceiver, since this is over short distances, to communicate between your raft and the sub (and send commands, like ‘turn the camera to the right’).
The other problem is that if you’re leaving a big visible wake you’re moving along, and so the info you get from a raft you leave behind you becomes fairly rapidly out of date as it falls behind. (And the idea of a data cable means if you’re moving quickly you either need a huge cable or only get a short time.) A better option might be a small UAV keeping pace with the sub and a little bit above the water. It would be much less visible than a wake, or even a raft, and its data would not get out of date – and it could get a little more height than a periscope and let you see further. But now we’re back to the problem of communication, since the acoustic route won’t work if the UAV isn’t touching the water. Maybe a blue-green laser would be penetrating enough at low powers, so an optical link would work.
I understand submarines tow submerged antennae for VLF (Very Low Frequency) communications. The comms are receive only and are very slow, so we’re talking about messages of only 5 characters or so, which are looked up in a code book. The most common type of messages would be “Surface to receive important message”, “Execute OpPlan C”, or “Stand down from OpPlan C”.
But there’s a good chance they reel in this antenna when moving at slow speeds to prevent it from fouling the rudder or screw.