I said that I would post the answer to my challenge.
Well, I just did the experiment myself. I watched the video on youtube:
to see how consistanly I could read when the shadow touched the mark for 8:45 PST (I marked the sundial for standard time but the video was made at approximately 9:45 PDST) approximately 16:45 GMT on April 19, 2016. My sundial is marked to read out PST. The video starts at 16:43:17 GMT.
So, I watched the video 10 times with the speaker turned off so that I couldn't hear WWV in the background and I covered the watch with my hand. When I saw the shadow touch the mark I moved my hand and read the watch.
My readings were:
16:43:58 three times
16:44:01 three times
The spred is only 4 seconds, the average was 16:43:59.7 and the standard deviation was 1.49 seconds.
So, it is possible to read a sundial with a prcision of less than 2 seconds!
This video was taken on April 19, 2016. At 16:45 GMT the GHA of the sun should be 71° 15' if there was no equation of time. Going to the USNO website and putting in that time gives the actual GHA for that time as 71°30.2' so the sun was 15.2' minutes fast so the equation of time was 60.8 seconds fast. This means that the correct time when the shadow should have touched the 8:45 PST mark is 60.8 seconds sooner at 16:43:59.2 GMT. The average of the times that I observed was 16:43:59.7 GMT so the sundial was in error by only 0.5 seconds. Even looking at my worst reading of 16:44:02 was off from the correct time by only 2.8 seconds.
So, to sum up. Using the sun's shadow to place the markings on the face of the sundial and using the leading edge of the shadow and the first edge of the marks as the fiduciary indexes allows you to read the sundial with a standard deviation of 1.49 seconds. And a sundial made this way has a potential absolute accuracy of 2.8 seconds! I was surprised!!!!!!!
(BTW, I didn't know what the equation of time was when I made the video, I only discovered that it was almost exactly one minute when I did the calculations later. It was just a coincidence that it was reading 8:45 when the standaard time was 8:44, a pleasant surprise. I only did this test one time, I did not cherry pick my data.)
So, you all, go out and make your own sundials so you can have an accurate time for setting your chronometers.
From: Gary LaPook
Date: 2016 May 2, 20:39 +0000
Last chance to determine the precision with which you can read the time from a sundial like mine. Look at the video a few times, after blocking your view of the watch face (so that it doesn't bias your readings), write down the readings and see how consistent they are. Tomorrow I will post the correct answer.
From: Gary LaPook <NoReply_LaPook@fer3.com>
Sent: Saturday, April 30, 2016 1:18 AM
Subject: [NavList] Sundial
So, I decided to make a sundial.
But, if I was going to make one I wanted it to be accurate, not just decorative. There are three things that affect the accurarcy of a sundial, the markings on the dial, the alignment of the gnomon and the precision with which the shadow can be read against the markings on the dial. So I bought a standard twenty inch floor tile for the dial and a piece of aluminum bar stock for the gnomon. The most difficult part was drilling the two holes in the tile for mounting the gnomon, tiles are hard.
I decided to make a vertical sundial and place it on the south side of my house. I measured the alignment of the wall by setting up my aiming circle in a position where I could sight along the surface of the wall and measured the azimuth. I then sighted on the sun and measured its azimuth. Doing the normal calculation for azimuth and comparing the sun's measued azimuth with the measure azimuth of the wall let me determine the alignment of the wall, it was within half a degree of straight east, I was amazed that the builder of the house had gotten it that close since there was no particular reason for the house to be so exactly aligned.
I used four aluminum brackets to mount the tile after I had attached the gnomon that I had bent approximately to my latitude. The fact that the wall happened to be so close to east was not important since the alignment of the dial surface is not important to the accuracy of a sundial. What is important is the alignment of the gnomon since it must run true north and be at the exact angle of the latitude. So I set up my aiming circle again and placed it in line with the gnomon. Repeating the prior steps i was able to adjust the gnomon right and left to get to it to point exactly true north. To set the gnomon for my latitude I used a bubble sextant set to my latitude, 34 16', to sight up along the axis on the gnomon and bent it until it was properly aligned.
To acheive markings that allow a precise way to tell the time I decided that it was too imprecise to see when the shadow aligned with the marks. Instead it would be more precise to observe when he leading edge of the shadow just touched the edge of the markings. I decided that the most accurate way to mark the dial was not to calculate where the markings should be but to simply make the marks by drawing them with a pencil and strait edge along the edge of the sun's shadows at the correct times. My longitude is 118 54.0' so my local apparent time is 4 minutes and 24 seconds fast on the 120th meridian LAT. Rather than marking the sundial to read my LAT or the LAT on the 120th meridian I decided to have it indicate Pacific Standard Time. So, on a number of sunny days, I applied the equation of time and then marked the position of the leading edge of the shadow every 15 minutes. This took a number of days allowing for my schedule and sunny days. So, for instance, if the equation of time was 10 minutes fast I would make a mark 10 minutes early on zone time, say at 11:05 am I would mark the position of the shadow for 11:15 am. I caclulated the equation of time from the sun's GHA to achieve the most accuracy at different times of the day rather than relying on the equation of time table in the N.A. This way i can determin zone time any day of the year by just applying the equation of time to the reading from the sundial.
The remaining issue is how precisely can you detemine the exact time when the sun't shadow just touches the edge of the marks and it turned out to be easy to do this to a high level of precision because the tile is a light color and you can see when this thin sliver of light disappears when the shadow touches the black mark. Here is a link to a short video showing the sun's shadow approaching the mark for 9:45 (16:45 Z), with a watch set to Zulu time positioned next to the mark and you can hear WWV in the background. Watch the video a few times and write down the indcated Zulu time when you see the shadow just touch the mark so you can determine how consistant your readings are. Later I will post the correct answer based on the actual equation of time that exisited when I made this video.
See the attached photos.