Jeo100,
You mention that "Tzais R' Taam is off by 15 minutes". My first
assumption would be that you assume Tzais Rabainu Tam to be 72
minutes, something that is not 100% accurate. To quote the sefer
הזמנים בהלכה by הרב חיים פ. בניש regarding using 72 minutes year round
in any location for calculating Rabainu Tam Tzais as "ומנהגם זה מוקשה
הן מההלכה, הסברא והמציאות". He is not targeting this comment at
Rabainu Tam ח"ו, but rather to those who calculate Rabainu Tam's Tzais
using 72 minutes. Using 72 minutes in all locations year round, is
something that was first mentioned rather "recently" by talmidim of
the מהר"ש מבעלז and the דברי חיים (they never mentioned this
themselves) . Also Note that הרב ישראל דוד הארפענעס of Williamsburg in
his sefer ישראל והזמנים discusses this and in his calendars has
columns for 7 different ways to calculate Rabainu Tam Tzais, one of
them the 72 minute calculation that you expect. In other parts of his
sefer he shows additional opinions on the way to calculate Tzais
Rabainu Tam, so the 72 minute calculation is one of many, though I
can't argue on the fact that many (but far from all, see
myzmanim.com)
calendars do use this.
To explain this, here are some details on calculating zmanim. 72
minutes is based on a person being able to walk 4 mil at 18 minutes a
mil. At this point a level of darkness is reached that is considered
night. The fact is that at 72 minutes after shkiah in the winter is
much darker than 72 minutes after shkiah in the summer. The farther
north or south you travel from the equator, the greater this
difference is. Travel to Gatshead, England in the summer solstice on
June 21, and at 72 minutes after shkiah the sun will only be 7.6
degrees below the horizon, something that takes only 32 minutes in
Eretz Yisroel on the equinox. For this reason, many calculate Tzais
Rabainu Tam as measure by the degrees the sun is below the horizon in
Eretz Yisroel right before the equinox when the day is exactly 12
hours. This level of darkness can be matched on any day in any
location in the world by calculating when the sun will be 16.1 degrees
below the horizon on that day in the location you are in. This is the
exact method used by the iPhone Siddur Zmanim section. The typical
reason given as to why many use 72 minutes year round anywhere is "it'
is simpler to calculate", something that is no longer relevant.
That said, I would suggest that Barry and Ronni add the "using 72
minutes as 16.1 degrees" note that they already add for MGA Krias
Shema when Tzais R' Tam is tapped, or better yet, have 'Tzais R"T 72
Minutes' and Tzais R"T 16.1°' to prevent misunderstandings.
By the way, in the siddur on Motzai Shabbos, an additional zman of
Havdala is available, and this is configurable in the settings to 72
minutes. There are 2 minor issues with this display. One that it shows
in the list before the early Tzais (it should be sorted by time), and
secondly (something that only became an issue when I was looking at it
while typing this email and is not really a bug) the Havdala display
disappears at midnight, when it should probably be displayed till Alos
(I am not advocating having it display till Tuesday, the latest time
for Havdala, since the time of havdala is moot at that point).
Have a good voch, and feel free to continue asking or complaining :)
about zmanim (easy for me to say).