Sundial



On at least three widely-spaced dates, compare the time shown on a correctly aligned sundial with local mean time. Use these data to determine the accuracy of the sundial used.






So we need two times . . . . . .

Dial time
One is the time on the correctly aligned sundial. The sundial needs to be level and the gnomon (the angled piece of plastic) needs to be pointing north, towards the pole star. The instrument has to be the right way round: the point where the gnomon meets the base plate should be on the south side of the instrument (i.e. pointing towards the sun). The longest lines on the baseplate are the hours, and the central line is 1 pm when we are on BST, so the dial runs from 7 am to 7 pm. The medium length lines are the quarter hours and the shortest lines are at five minute intervals. You should be able to estimate the dial time to the nearest minute, or you can wait until the shadow is exactly on one of the lines. It's the shadow of the top edge of the gnomon that you are are interested in. You do, of course, have to contend with the fact that solar shadows are always fuzzy just because the sun is half a degree wide!

Local mean time (LMT)
Local mean time differs from Greenwich mean time because of where you are. Your wrist watch or phone will give you Greenwich mean time. If you are west of Greenwich (as Winchester and Midhurst both are), then the sun rises a little later, and both places have their local noons a little later. you need to apply a  correction to what your watches tell you in order to arrive at LMT. The correction is 4 minutes for every degree of longitude. Google will tell you your longitude if you tell it your location.
For example, Winchester is at 1.31 W, which corresponds to 5.24 minutes. So when it's 1 pm at Greenwich, it's just before 12.55 in Winchester because there are still 5 minutes to go before the sun crosses the Winchester meridian.

. . . . . . .and we have to compare them.

The Equation of Time (EoT)
The dial time and LMT can only agree on four days of the year. On all other days a correction must be applied, known as the Equation of Time (although it is, on any given day, just a number of minutes rather than an equation in the ordinary sense of the word). You can obtain the correction for any particular day from the well-known graph or from a suitable table, such as that at http://www.ppowers.com/EoT.htm. One way of comparing the two times is to calculate what the EoT should be from the formula
EoT = Dial time LMT
For example, as I write this, my dial is reading 12:34 and my watch is reading 12:50. Applying the 5 minute longitude correction to my watch, I find that LMT is 12.45. Using the formula above, I find that the EoT today is 11 minutes. Unfortunately, this does not agree with the table's value of 5 minutes. So I have a problem which is good in terms of undertaking a project to get to the bottom of it.



Where next?

I took seven readings today. The sundial remained in place all day, so I do not need to worry about inaccuracies in aligning it (well, I do; but we'll come to that). I'm going to switch the formula round and use it to calculate what the sundial should have read on each occasion, and then subtract what it actually read, to find the error.
Error = LMT + EoT Dial time
Here's a graph showing error against time of day.



This is interesting because it shows a trend rather than a random scatter. So what I will do next is to take much more precise time readings. I'll wait until the centre of the shadow is over a 'target' time, and then read the watch, which I will synchronise carefully with GMT.

There are two major difficulties in placing the sundial, names the levelling process and pointing it in the right direction. Once I've refined my time-taking to the point that my graph is reasonably non-random, I'll try deliberately altering the orientation by measured amounts, and see what effect that has.