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A general description is here.
(Unix-alike) For ‘http://’ URLs and the default method (‘"auto"’),
‘download.file()’ switches to ‘method = "libcurl"’ if a redirection to
a ‘https://’ URL is encountered.
For ‘url()’ with method ‘"default"’ and an explicit ‘open’ argument, if opening fails because of redirection to an ‘https://’ URL then ‘method = "libcurl"’ is tried.
Changes when redirection of a ‘http://’ URL to a ‘https://’ URL is encountered:
The internal methods of ‘download.file()’ and ‘url()’ now report that they cannot follow this (rather than failing silently).
(Unix-alike) ‘download.file(method = "auto")’ (the default) re-tries with ‘method = "libcurl"’.
(Unix-alike) ‘url(method = "default")’ with an explicit ‘open’ argument re-tries with ‘method = "libcurl"’. This covers many of the usages, e.g. ‘readLines()’ with a URL argument.