Kinds Of Time

Time: the general idea, relation, or fact of continuous or successive existence; infinite duration or its measure. (Webster)

Timekeeping is based upon the period in which the earth makes one complete revolution upon its axis. This period is called a day, which is divided into 24 hours, each hour having 60 minutes and each minute 60 seconds. This period of time, the day, is complete when the sun starts and returns to the same point on the earth. As the earth rotates 360° in a 24-hour period:

1 hour = 15° or 1° = 4 minutes

Hour Angle (h, HA): the angle corresponding to the sun's position around its daily (apparent) orbit. Measured westward from local noon, it increases at a rate of 15° per hour.

A particular geographical location on earth is described by its latitude and longitude.

Latitude (ø): is the angular position of a place on the Earth's surface measured north or south of the equator. Positive values in the Northern hemisphere, negative in the Southern.

Longitude (λ): is the angular location of a place on the Earth's surface measured east or west of the Prime meridian through Greenwich. Longitudes west are positive and east are negative.

Figure 1: Lines of Latitude and Longitude

As the earth rotates and the sun appears to move, it will be over only one particular longitude at a given time. As an observer, this particular longitude, which passes through your location is called a meridian. If you are using the sun to tell the time, no two observers will share the same time unless they are on the same meridian.

Local Apparent Time (L.A.T.): this is solar time, as derived from the real sun at any particular location.

This is the kind of time that is shown on most sundials. Telling time by this method is very inconvenient. In a large city there could be a significant time difference between the east and west ends of the city. How would you ever make it to a meeting on time?!

There is a second problem with this method of telling time. This is the fact that measuring time using the sun results in days of varying lengths during  the year. Instead of the real sun, we use an imaginary mean sun that moves at a constant speed equal to the average speed of the real sun. Divide this day into twenty-four equal parts and you have:

Mean Solar Time: a measure of day based conceptually on the diurnal (daily) motion of the mean fictitious sun, under the assumption that the earth's rate of rotation is constant.

If you start the real sun and the mean sun at a time when they coincide, over the year, the mean sun will sometimes lag or lead the real sun. At the end of the year, though, they will meet again. Like the real or apparent sun, the mean sun is over only one particular meridian at a given time. Mean solar time is still localized.

Local Mean Time (LMT): this is solar time which has been corrected for the Equation of Time but not for longitude.

The difference between the Local Mean Time and the Local Apparent time is known as the Equation of Time.

Equation of Time (E, EoT): the time difference between Local Apparent Time (apparent solar time) and Mean Solar Time at the same location. Its value varies between extremes of about +14 minutes in February and -16 minutes in October. It arises because of the elliptical orbit of the earth, and the tilt of the earth's axis to the ecliptic. The preferred usage by diallists is:

Mean Solar Time = Apparent Solar Time + EoT

but this convention is by no means universal and the opposite sign is used in modern almanacs. Irrespective of the sign convention adopted, the sundial will appear slow compared to the mean time in February, and fast in October/November.

EoT varies continuously, but is usually tabulated for noon each day at a particular location. Figure 2 is a graph of the Equation of Time.

Figure 2: Equation of Time - Graph (SHADOWS)

Note that Mean Solar Time and the Apparent Solar Time coincide four times a year. Figure 3 illustrates the Equation of Time in the form of an analemma.

Analemma: is a graphical plot with the Equation of Time on one axis and the sun's declination on the other. In appearance, a tall thin figure of eight. The dates of various points around the curve are often shown. The shadow of a point falling onto an arbitrary plane at the same clock time each day will trace out an analemma over the course of a year.

Figure 3: Equation of Time - Analemma (SHADOWS)

By applying the Equation of Time to a sundial that indicates Local Apparent Time, it is possible to obtain the Local Mean Time of the place where the dial is located. This correction can be made by using an EoT graph as shown above and adding or subtracting the appropriate number of minutes from the sundial reading. There are also sundials with specially designed gnomons that will account for the EoT.

Clocks, however, indicate standard time.

Standard Time (ST): is mean solar time at the central meridian of a given time zone.

Or as a further definition civil time.

Civil (Clock) Time: the legally accepted time scale in a particular country or region. It is based on the standard time for that standard time zone, but may have fixed differences (e.g. BST/DST). Measured in modern hours from the most recent midnight, with either a 24 hour or 2 x 12 hour format.

Standard Time Zone (TZ): a geographical region which uses the same civil (clock) time. These are approximately regions between two lines of longitude, set 15° apart, and hence 1 hour time between adjacent zones.  For the UK, which is in Zone 0, the standard meridian is the Prime Meridian at Greenwich, and the zone extends nominally 7½° west to 7½° east.

Within a given time zone, a sundial located at the central meridian of that time zone will indicate clock time with the appropriate application of the EoT. If the sundial is located to the east, it will read fast and if it is located to the west it will read slow. As every 1° movement of the sun is equivalent to 4 minutes of time, a correction for longitude can be applied to a sundial that indicates Local Apparent Time as follows:

Longitude Correction = (Central Meridian - Local Meridian) * 4 minutes

The longitude correction can be applied manually to the sundial indication or it can also be incorporated into the graph of the Equation of Time. The correction can also be incorporated into the design of the hour line angles of the sundial which would then indicate Zonal Solar Time.

Zonal Solar Time: denotes solar time at a time zone meridian. Thus it is Local Apparent Time with a longitude correction but without EoT.

One last correction that can be made is for:

Daylight Saving Time (DST): civil time during the summer in much of the USA (and some other countries) obtained by advancing clock time by one hour from local standard time.

This can be done by having two sets of numbers for the hour lines or in locations where the dial is covered with snow for a long period of time, you may choose to number it to read DST. Some sundials have an adjustment for DST.

Now, to correct the time indicated by a sundial designed to read Local Apparent Time and obtain Standard Time:

Standard Time = Local Apparent Time + Longitude Correction + Equation of Time + Daylight Saving Time

where:

Longitude Correction: positive west of the central meridian; negative east of the central meridian

Equation of Time: positive when the dial is slow; negative when the dial is fast

Daylight Saving Time: 1 or 0

It should be noted that there may also be variations in the standard time due to local legislated time zone variations. Be sure to check for this.