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Re: Agnostic gnomon and horary error
From: Geoff Hitchcox
Date: 2024 Jun 10, 05:45 -0700

Frank, is the first message in this thread a "Trick Question" ;-)

When making a Horizontal Sundial, the Gnomon needs to be at an angle to the flat surface equal to the latitude of the installation.

However the 'reference surface' on an Armillary Sundial is the equatorial armilla (Latin for ring) which is aligned parallel to the Earth's equator and thus the axis of rotation, and therefore local latitude. The gnomon must therefore be at an angle of the co-latitude, as shown in the diagram attached from Chapter 17 in the book "Sundials" by Albert Waugh (1973).

Regarding the two photos you took of the Mystic Sundials, armillary and vertical, back in April '24, here is my analysis.

Treworgy Sundial Coordinates = 41° 21.741' N, 71° 57.8292' W.

First Picture

Solar Noon = 16:45:32 UT at Sundial on the 26 Apr 2024.

Photo taken at 26 Apr 2024 14.09.10 EDT = 18:09:10 UTC (1:23:38 after Solar Noon).

I would say the Armillary is about "10 minutes fast", and the Vertical "on time".

Second Picture

Solar Noon = 16:45:15 UT at Sundial on the 28 Apr 2024.

Photo taken 28 Apr 2024 16.35.30 EDT = 20:35:30 UTC (3:50:15 after Solar Noon).

Again, I would say the Armillary is about "10 minutes fast", and the Vertical "on time".

It would be most interesting to have an accurate angle of the (co-latitude) of the actual gnomon, to maybe figure out where the "10 minute" error could be, on the lovely Treworgy Armillary Sphere.

I will have a think about the "hour angle" question Frank, after I have written a little bit of code, to help me understand the issue.

For those that like their trigonometry, here is a nice 11 minute video on the "Trigon", a useful tool, before the age of calculators to mark out sundials.

Regards, Geoff Hitchcox, Christchurch, New Zealand.

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