What is origin of the phrase "tits up"
Solution 1:
'Tits Up' was in common usage in the British Armed Forces, post WW2. It may have originated earlier. The common consensus was that it originated in the Royal Navy. Its use meant 'complete failure' (e.g. "the HF radio is tits up"), and was apocryphally ascribed to drowned female bodies floating 'tits up' whereas male bodies float face down. I've never managed to drown anybody as a yacht skipper, but I've tried experiments (with volunteers) in a swimming pool, and relaxed women with at least a C cup tend to float face up, and men face down (the sacrifices I make for science ! ;) ). The RAF used a euphemism of this - 'Pear-shaped' - when socially necessary. Pear-shaped is quoted by the OED to have originated from RAF usage in 1983 (used in the book 'Air War South Atlantic'), and I was an RAF pilot in 1983, so can confirm this meaning.
Solution 2:
According to the The Phrase Finder it is might be of military origin, but there is no real evidence to support this view:
Inoperative; broken. The term is also used to mean fallen over (on one's back)
Tits up:
This is a 20th century phrase, probably of military origin. There's certainly no mention of it in print prior to WWII. It has been suggested that the term derives from the behaviour of aeroplanes' altitude indicators, which turn upside down when faulty and display an inverted 'W' resembling a pair of breasts.
There's no real evidence to support this speculation and it seems more likely that the phrase is just a vulgar alternative to the earlier 'belly-up', which has the same meaning.*
'Belly-up' is an allusion to fish, which float that way when 'dead in the water'. This expression was known in the USA by the 1920s, often related to bancruptcy or other commercial disasters; for example, this extract from John Roderigo Dos Passos' Letters, 1920:
Solution 3:
Dictionary and glossary definitions of the phrase
From Eric Partridge & Paul Beale, A Dictionary of Slang and Unconventional English, eighth edition (1984):
tits-up. ‘Unserviceable, out of action (used of aeroplanes, cars, plans, people: tits-up on the runway)’ ([Colin] Strong & [Duff] Hart-Davis, Fighter Pilot [Queen Anne Press for BBC], 1981): RAF: later C.20. Formed on comparable balls-up, ballsed-up.
From Rick Jolly & Tugg Wilson, Jackspeak the Pusser's Rum: Guide to Royal Navy Slanguage (1989):
tits up (esp. FAA) Lying on its back, i.e. broken or useless: *"We were due to launch at oh seven dubs, but the aircraft went tits up as we taxyed out.."
From Marion Robertson, The Chestnut Pipe: Folklore of Shelburne County (1991) [quotation not shown in snippet window]:
Tits up: To have fallen upon one’s back when drunk ...
Shelburne County is in Nova Scotia.
From Jonathon Green, Chambers Slang Dictionary (2008):
tits-up adj. {1970s+} (Orig. Can. prison) dead, i.e., laid out on one’s back; thus in fig. use, ruined, destroyed, esp. in phr. go/gone tits-up.
From Paul Dixon, Intoxerated: The Definitive Drinker’s Dictionary (2009/2012):
T.U.B.B. (abbreviation for “tits up—but breathing”): This term was reported by C.W. Sande, M.D., an emergency room physician and surgeon [from Caldwell, Idaho] who heard it from his paramedics, in a letter to the author, July 13, 1983.
Matches for the phrase in the wild
A Google Books search for “tits-up” yields two relevant nondictionary matches from the 1970s, one from 1981 (not the one cited in Partridge & Beale, above, which it did not find), and no other from before the 1990s. All three of the earliest Google Books matches come from Canadian publications.
From an unidentified story in Journal of Canadian Fiction, issues 16–18 (1976):
Maybe you got the message now that Henry ain’t average, eh. He saves his money like he was tighter'n a nun's snatch and off he goes on one of these nights on the town, spends two or three hundred bucks sometimes, him and his girl friend Betty. They get all dressed up and eat at the real swank joints and he even rents a car for the day. He does it two times a year, once in February cause Henry says everybody needs a good time then. The other time he just goes when he feels like it. Did it twice in February one year, said it was a lousy winter and his old lady almost went tits up that Christmas.
From a letter by Mark Starowicz to the editor of The Canadian Review (February 1977):
When Mr. Black came into my office to do a piece on CBC Radio's Sunday Morning, he was probably chagrined to find that I wasn't firing an M 16 out the window at passing cops. And since I didn’t throw pies at him during the interview or denounce him as a rootless cosmopolitanist, he had his evidence that the producer of such hothead programmes as Five Nights, Commentary, Radio Free Friday and As It Happens had gone tits up as a revolutionary.
From an unidentified story in Saturday Night, volume 96 (1981) [excerpt not shown in snippet window]:
"He's tits up."
"Cleve Rackle's dead?"
"It was in the Saturday paper. Found dead in his own bedroom. I phoned Veeweger about it."
Saturday Night is (or was) a Canadian publication, headquartered in Toronto, Ontario.
Conclusions
The evidence that I looked at supports the assertion in Chambers Slang Dictionary that “tits up” in the relevant sense arose in Canada in the 1970s, first with the literal meaning “dead” and then with the figurative meaning “hopelessly nonfunctional.” Reference works find it in the UK by 1981 and in Idaho in 1983.
These research results lead me to doubt claims that this usage arose in the immediate aftermath of World War II or that it originated in the Royal Air Force. It is significant that Eric Partridge, who had a particular interest in British military slang of the two world wars and after, never mentions this usage; Paul Beale is responsible for the entry in the eighth edition of DS&UE.
I would love to know where Green got his information that the phrase originated as Canadian prison slang, but even absent that data I think that the 1976, 1977, and 1981 matches from Canadian publications make more sense as occurrences near the point of origin than as an early and briefly popular import from elsewhere.
Solution 4:
Personally, I like the acronym explanation as provided by acronymfinder: Total Inability To Support Usual Performance.
It aligns nicely with one of the other classic expressions - SNAFU.
It is reasonable the true origin was military and the acronym invented to ( ~ politely) fit on some form.