Studies on average time by full immersion in 2nd+ language to become conversant?

Question

Are there any studies that have noted some "average"¹ length of time for a brand new 2nd (or 3rd, etc.) language learner fully immersed in a culture to pick up a new language to a level of at least being conversant enough to convey in speech some common thoughts, expressions, and aspects of that culture (which by one standard means about 3,000+ words known)?

Besides the fact that I generally hear that immersion speeds up language learning (and it makes sense), are there actual studies on the average speed of learning when immersed? I'm open to information from any formal studies on the speed of language learning in whatever that study deemed as "full immersion."

Ideally, I'm most interesting in cases of more extreme situations. Consider an explorer or a missionary entering into a never before contacted tribe to learn communication with that tribe. Or in a more academic setting, a case where specific measures for purposes of the study were taken to enter a culture to learn the language specifically by immersion without outside help. So ideally (but again, I'm open to whatever information studies have done):

1. The learner has no prior knowledge of the language.
2. The learner enters into the new culture/language without written resources available about that language other than what may be available in that language (so learning will initially be by speech with native speakers within their culture; any written aspect would come as the learner can interact with literate members of that culture willing to guide in reading/writing).
3. The people of that culture have no knowledge of the learner's native language (so no translating by a bilingual speaker to help).
4. Assume the learner is of normal intelligence, fluent in his/her native language, and has either learned other languages previously or grasps well the more grammar aspects and such of the native language (so the learner is moderately familiar with concepts needed to grasp other languages).
5. The learner is the only person from his/her own culture within the new one (or at least is intentionally not interacting with others of the native culture for purposes of a study if such are there).
6. No electronic helps.
7. The learner is actively seeking to learn the language.

In short, if one shows up as the sole outsider in a non-electronic culture and needs to become conversant, are there studies on the average length of time this takes? But as I noted above, that list is my ideal study points. If studies exist on time frame for circumstances different than what I have described (though still considered essentially immersed), I'm fine with knowing their findings as well (along with their parameters), as it may allow me to interpolate an answer.

UPDATE: Further research on this site has shown me that points #2, 3, and 5 seem to amount to a direct method approach. So while that method does not specifically rule out electronic helps, studies on average speed of learning via the direct method might help inform an answer to this question here.

UPDATE: The first answer posted here has revealed that what I seem to be asking about is studies on the average time it takes to become conversant in a language using a monolangauge approach (where linguists do "monolanguage fieldwork" to gain an understanding of the target language).

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¹ I realize there are a lot of factors involved in how fast any one individual can learn a language, as well as the fact that some languages are harder to learn than others (especially in relation to how similar or not the new language is to one's native tongue). This is why I'm hoping there have been some studies that have been broad enough to average out the time for learning.

Answer 1

I'm not sure such studies exist. There are probably only examples, and there is only one good example that I know of:

Daniel Everett is a famous monolingual fieldworker of the type you're asking about ("extreme situations") and is the only linguist in the world fluent in Pirahã. Here he is demonstrating his techniques. Much patience is required. His TED talk summarizes his story and technique. Here is a short documentary in German with subtitles and at 2:45 it talks about language learning.

He spent many years with the Pirahã people - roughly 10 years in total over a ~30 year period. The point at which he became "fluent" is not specified but it seems to have taken years. His work yielded a great debate with the famed Noam Chomsky about whether universal grammar is real.