NavList:

When I read the Wikipedia article, it seems to imply that WW II Loran (Loran-A) gave an accuracy of tens of miles *worst case.*   Later in the article it speaks of "accuracies of 1~2 miles" in at least some experiments with the system.

Almost all electronic positioning systems (Loran, GPS, ...) require very precise measurement of the time of arrival of electronic signals.  (Radio signals travel at 1000 feet per microsecond).  Today measuring the timing of signals to nanosecond accuracy is commonplace.   In WW II, a tenth of a microsecond or worse was pretty much state-of-the-art.  So I wouldn't expect a WW II technology to yield the results we can see with today's electronics.

Also (and something I didn't realize until I read the article) is that Loran-A was intended as much more of a long-range positioning system than the later Loran-C that many of us may have had experience with pre-GPS.  WW II aircraft flew below the clouds, not above them as we are used to today.  So celestial on a cloudy day was impossible.  There are several stories of transatlantic aircraft delivery flights being caught by unexpected tailwinds and almost landing in occupied Europe instead of Britain.   I suspect Loran-A was a welcome adjunct to celestial to WW II aircraft navigators.   And an accuracy of "tens of miles" is acceptable for aircraft navigation (or ships on similar trans-oceanic voyages).