Hehe. This is probably why the author of the document summarized the discussion of the Hz to say:
'Use of "Hz" will cause communication problems, errors, and make one party or another look insane in the eyes of the other.' LOL.
* Every physicist or electrical engineer or high school physics student has "known" for the past 100 years that a Hz is 2 pi radians/s. And it was defined that way for a long time, as the document referenced shows, and almost everyone follows this convention.
* Everyone who follows the current rules of the SI exactly (as per JadeNB's analysis above) "knows" that a Hz is 1 radian/s. His analysis is not hard to follow. It's utterly unambiguous and machine-parseable. There is no possible other answer.
So, you can see there's a problem there. The document correctly traces the changes in the definition of the Hz and radian at different times that led to this situation. (e.g. the Hz used to be defined as "cycles/s")
The funny part is seeing what different units-aware software packages do to try and make themselves seem reasonable. :)
* Frink (the package from which this data file emanates.): Follow the currently-written rules of the SI (that is, 1 Hz = 1 radian/s) but rant about it in the data file. Also, if you read the data file closely, it allows you to switch between radians having their own dimensions or being dimensionless (but warns against the former.)
* GNU Units: Follow the currently-written rules of the SI (that is, 1 Hz = 1 radian/s) Not sure if there's a rant.
* Wolfram Alpha: This was an interesting one. At launch, they followed the currently-written rules of the SI but this evidently led to lots of bug reports and a current inconsistent state. They used to report that "1 Hz = 1 radian/s" but soon they hacked and patched around these in some inconsistent ways. For example, it would work differently if you put in "1 Hz in radians/s" and "1.0 Hz in radians/s".
Nowadays, if you do "1 Hz in radians/s" in Wolfram Alpha, it gives you the answer "6.283 rad/s" which is more acceptable (but wrong according to strict interpretation of the SI) but has a little disclaimer where it says below (in gray)
"(using 1 Hz = 1 rps (revolution per second))"
A revolution meaning a rotation of 2 pi radians, I hope.
But it's a single-case kludgey workaround. You can see
that their system is hacked and self-inconsistent, because if you divide both sides of that calculation by something else, say, seconds:
"1 Hz/s in radians/s/s"
which of course should give the exact same numerical value as above, 6.283, but this time it gives 1!
* Wolfram Language / Mathematica: Follow the currently-written rules of the SI (that is, "Convert[Hertz, Radian/Second]" gives "Radian/Second") Note that seems to be a different result than Wolfram|Alpha.
* Google calculator: At the start, Google Calculator would follow the currently-written rules of the SI (that is, "1 Hz in radians/s") would return 1. But this caused lots of consternation and bug reports: http://productforums.google.com/forum/#!topic/websearch/kudd...
The funniest part about that nowadays is that Google Calculator utterly refuses to do anything with the Hz, even if you force it with a preceding equals sign. The interactive interface only lets you turn Hz into kHz, MHz, etc, and other multiples. LOL. I'm sure that other self-consistent environments wish they had this latitude. Like a politician, any question they don't like, they just pretend not to hear, and give you somebody else's search results instead. :)
This problem with the definition of the Hz is nothing new, and is well known in the literature. For example, see:
M.P. Foster, Quantities, units and computing, Computer Standards & Interfaces (2013), http://dx.doi.org/10.1016/j.csi.2013.02.001
In short, the author of the rant might be messed up in the head from having to 1.) deal with these inconsistencies and 2.) try to look non-insane to two groups of people who are simultaneously both right and both wrong.