First observation. Romeo-class = Soviet diesel-electric submarine, built in the 1950s = loud = easy to detect by US sonar. If the US knows a NK sub happens to be in the area where there was a launch, then I think they can draw a reasonable conclusion.
Second observation: Wikipedia says "Range: 14,484km (9,000 miles) at 9 knots".
Great circle distance from Pyongyang to Lima is 10,100 miles. http://www.gcmap.com/mapui?P=ZKPY-SPJC&DU=mi . That direct route goes through Utah, so the ocean-only route will be longer.
Pyongyang to Lima via Hilo is 10,550 miles. http://www.gcmap.com/mapui?P=ZKPY-ITO-SPJC&DU=mi . That's not much longer. Still, it's a reminder that we're talking about a spot almost at the other side of the world from NK.
On the other hand, http://www.russianwarrior.com/STMMain.htm?1947vec_Romeo.htm&... says that the range at snorkel is "7,000 nautical miles at 5 knots" while on the surface it's "16,000 nautical miles at 10 knots". That's 8,000 and 18,000 miles, respectively. Which means about 3,000 miles on the surface (=visible by satellite) followed by the rest at snorkel depth. And a one-way trip.
If I were the US Navy, and saw a NK sub travel towards the Americas for thousands of miles, I think I would keep a close eye on it.
Third observation: The NK Sinpo class submarine appears to have been built to 1) replace the Romeo class subs, and 2) be armed with an KN-11 ballistic missile. See https://en.wikipedia.org/wiki/Pukkuksong-1 . The longest estimated range for that missile is 2,000-2,500 km . Then again, the submarine itself has an estimated range of only 2,800 km.
The GC distance from Lima to Brownsville, TX is almost 3,000 miles, so well further than NK's relatively small ballistic missile can manage from that gap in US satellite surveillance.
So even if a Romeo-class submarine weren't detected via sonar, and had the range to get to that gap, and were modified to support a submarine-launched ballistic missile, it doesn't seem like that missile could reach the US.
Or, to quote from the last Wikipedia link:
> The Korean People's Navy has no nuclear submarines, and no diesel-electric submarines equipped with air independent propulsion (AIP), so the launch submarine's range (and by extension the missile's) is limited and assuredly prevents it from threatening America's western seaboard.
> Given their submarines' insufficient power to outrun U.S. Navy nuclear attack submarines and lack of aerial and surface coverage to protect them out to long distances, they cannot venture far out to sea, ..
> ... because of its finite power capacity, the sub would have to surface or snorkel for air to recharge its batteries if it remains hiding for an extended period, making it vulnerable to anti-submarine warfare (ASW) efforts.
