# How to read the Alumni Association Sundial at Caltech

It is possible to get routine accuracy of ~5 minutes from this sundial, but the instructions on the posted brass plaque are not clear enough for anyone who doesn't already understand sundials to follow. This webpage is meant to serve as a step-by-step recipe that anybody can follow!

## Step 1. Stand on the date

The Roman numerals going up one side and down the other of the line on the rectangular granodiorite slab represent the months of the year: January = I, February = II, and so on up to December = XII. The lines labeled with the Roman numerals correspond to the first of the month. In this picture you see III for March on the right side, and IV for April further up the right side. The right side of the line corresponds to the time between midwinter and midsummer when the sun is getting higher in the sky, and the correct place to stand is moving up the line. On the left side of the line you see IX for September in the upper half of the image, X for October further down, and XI for November just right at the bottom. The left side of the line corresponds to dates from midsummer to midwinter when the sun is getting lower in the sky and the correct place to stand is moving back down the line.

You need to estimate the position for today's date by interpolating. To make this totally clear, see the next picture, where I have marked each day of March with a red line.

In detail, the spacing between days is not constant, but using linear interpolation within a given month introduces only a small error.

Now, the important question to get high precision is: with what part of your foot should you stand on the indicated date? The sundial is really designed for a 6-foot high vertical stick to be placed right on the date, casting a shadow on the number ellipse. Your head is only an approximation of this ideal geometry. So, I find that I get the most accurate reading when I put the balls of my feet on either side of the meridian line at the position indicated by the date. Toes is too far back, heels is too far forward. Your posture may be different, though. Here I am standing on March 23 (yes, I wear Birkenstocks with socks. What about it?):

## Step 2. Read the local solar time

Now look at your shadow and find the point where it crosses the ellipse defined by the series of little granodiorite circles with Arabic numbers on them (these are the hours of the day). You see in this picture that the shadow of my head is between 11 and 12, closer to 12:

Once again, you need to interpolate; I think it is reasonable to do so to the nearest 5 minutes. The center of each hour circle marks the hour; near noon, the edges of the circles are about 10 minutes before and after the hour. So, in this picture you see that the center of the shadow of my head falls at 11:43 AM.

## Step 3. Correct to local mean time

A sundial does not read the same kind of time as a clock because the sun does not move across the sky at a constant rate. The raw reading in step two is local solar time, but we want to get standard mean time (or daylight mean time, see below). Mean time is clock time, which goes at constant speed. The first correction, from solar time to mean time, is called the equation of time, and it varies from -10 to +15 minutes over the course of the year. The equation of time has two sinusoidal components: an annual cycle with an amplitude of ~7.5 minutes due to the eccentricity of the earth's orbit around the sun, and a semiannual cycle with an amplitude of ~10 minutes due to the obliquity of the earth's spin axis. There is a very good and detailed explanation of the origin of the equation of time at http://www.analemma.com. For our purposes, you read the correction from the graph on the brass plaque on the south wall of Hameetman Center:

The curved line is a graph of equation of time (in minutes, on the y-axis) vs. day of the year (given as Julian day counting from January 1 = 1 to December 31 = 366, and as roman numerals for the first of each month, on the x-axis). So, I took my sample measurement on March 23, for which date the equation of time is +7.5 minutes:

## Step 4. Correct to standard time

This correction is almost explained on the brass plaque. The sundial reads local time, at the longitude of Caltech. But the Pacific time zone is centered on 120° West longitude, which is 1°52'35" west of here. It takes the sun 1 day = 1440 minutes to go around the Earth (360 degrees of longitude), so it takes 1440/360 = 4 minutes to go each degree. Hence, whatever solar time it is here, now, it is 7.5 minutes earlier at 120° W – whatever position the sun is at here and now, it will be at the same position 7.5 minutes from now at 120° W. So what we do is subtract 7.5 minutes from your reading. Hence Pacific Standard Time is 11:50 – 7.5 min ~ 11.43 AM. Let me emphasize that it is complete coincidence that on March 23 these two corrections cancel; on any other day (well, except January 10) they will not exactly offset one another.

## Step 5. Correct for daylight savings time, if needed

Under current US law, March 23 falls during daylight savings time, i.e. after the "Spring Forward". So, we have to add one hour to our reading the get it to match the way we currently have our clocks set. Thus, the final reading in this example is 12:43 PM PDT. What time was it actually? It was 12:45 PM, so we made an error of –2 minutes. What is the source of this error? Near noon it is sensitive to whether you stand straight up or lean a bit right of left. Early in morning and late in afternoon it is more sensitive to leaning forwards or backwards. Also, it is hard to interpolate between hours much more accurately than plus or minus 5 minutes.

## Summary

So, I hope this tutorial has been helpful to you and you can actually use the sundial now. To summarize:

1.     Stand on the date