diamond geezer

Wednesday, April 15, 2020

A sundial only tells the correct time on four days a year.
One of those days is today.

This is because clocks and sundials tell slightly different times.

Clocks tell mean solar time, a constant based on the rotation of the Earth.
But sundials tell apparent solar time, based on the actual position of the Sun.

If you were to start a stopwatch when the Sun is highest in the sky today and stop it when the Sun is highest in the sky tomorrow, you might expect that duration to be 24 hours precisely. But it isn't.

The length of a solar day varies because...
a) the Earth is tilted on its axis.
b) the orbit of the Earth is an ellipse, not a circle.

These two factors combine to create a variation of almost a minute.

For example, on 21st December a solar day lasts 24 hours 30 seconds. By 25th March it's 48 seconds shorter.

When you have a lot of consecutive solar days that are slightly longer than 24 hours, a sundial starts to lag behind a clock. Conversely when you have a lot of consecutive solar days that are slightly shorter than 24 hours, a sundial starts to catch up with a clock and then overtake it.

The amount by which the Sun runs ahead of a clock is given by the equation of time.

The equation of time varies dramatically throughout a year.
For example in mid-February sundials are 14½ minutes behind.
But at the start of November they're 16 minutes ahead.

Here's a graph.

It's complicated because it's two sine waves combined, one relating to the tilt of the Earth and the other relating to the eccentricity of the Earth's orbit.

The graph shows that at the start of the year sundials lag behind clocks. The gap increases to a maximum of almost fifteen minutes in February. The curve then rebounds until by late April a sundial is marginally ahead. In May the curve slips back again. Sundials spend the summer months lagging a few minutes behind. Then in the autumn they accelerate ahead, hitting a maximum of sixteen minutes in November. They remain ahead all the way to Christmas.

Time the Sun is highest in the sky

Feb 11 Apr 15 May 14 Jun 13 Jul 26 Sep 1 Nov 3 Dec 25

sundial ahead 11:56 11:44

sundial correct 12:00 12:00 12:00 12:00

sundial behind 12:14 12:07

There are four places where the graph crosses the zero axis, hence just four dates on which sundials tell the correct time.
Those dates are 15th April, 13th June, 1st September and 25th December.

n.b. dates can vary by a day due to leap years.
n.b. yesterday and tomorrow are pretty close to zero too.
n.b. three of the dates are BST, so technically Christmas Day is the only valid one.

Which is why, if you're anywhere near a sundial today, it will be correct.

posted 07:00 :

This is the sundial in the Great British Garden in the Olympic Park.
It's an example of an analemmatic sundial.
The first analemmatic sundial was laid out in the French town of Bourg-en-Bresse in 1513.

Around the edge are two rings of numbered discs, each in the shape of an ellipse.

The outer ring is for GMT and the inner ring for BST.

In the centre is a strip aligned north/south on which the months of the year are written.

Stand on the correct month and your shadow tells the time.

Different months need different positions to match the declination of the Sun.
This is the angle between the rays of the Sun and the plane of the Earth's equator.
At the equinoxes declination is zero, which is why March and September appear in the centre of the strip.
At the solstices declination is at its maximum, which is why June and December appear at opposite ends.

It works too. Here's my shadow at quarter to nine in the morning while standing on 'April'.

I should go out and test it again today.

posted 06:00 :