## Wednesday, December 13, 2023

### How to Remember the Equation of Time

On Valentine’s Day, February 14, the sun is late on the meridian by 14 minutes (LAN at 1214); three months later, it is early by 4 minutes (LAN at 1156). On Halloween, October 31, the sun is early on the meridian by 16 minutes (LAN at 1144); three months earlier, it is late by 6 minutes (LAN at 1206).

These four dates mark the turning points in the Equation of Time. You can assume that the values at the turning points remain constant for two weeks on either side of the turn, as shown in Figure 12-7. Between these dates, assume the variation is proportional to the date.

There is some symmetry to this prescription, which may help you remember it:

14 late three months later goes to 4 early

16 early three months earlier goes to 6 late

but I admit it is no catchy jingle. Knowing the general shape of the curve and the form of the prescription, however, has been enough to help me remember it for some years now. It also helps to have been late sometimes on Valentine’s Day! An example of its use when interpolation is required is shown in Figure 12-7.

The accuracy of the prescription is shown in Figure 12-8. It is generally accurate to within a minute or so, which means that longitude figured from it will generally be accurate to within 15′ or so.

This process for figuring the Equation of Time may appear involved at first, but if you work out a few examples and check yourself with the almanac, it should fall into place. If you are going to memorize something that could be of great value, this is it. When you know this and have an accurate watch, you will always be able to find your longitude; you don’t need anything else. With this point in mind, it is worth the trouble to learn it.

Also remember that the LAN method tells you what your longitude was at LAN, even though it may have taken all day to find it. To figure your present longitude, you must dead reckon from LAN to the present. Procedures for converting between distance intervals and longitude intervals are covered in the Keeping Track of Longitude section below.

For completeness, we should add that, strictly speaking, this method assumes your latitude does not change much between the morning and afternoon sights used to find the time of LAN. A latitude change distorts the path of the sun so that the time halfway between equal sun heights is no longer precisely equal to LAN. Consider an extreme example of LAN determined from sunrise and sunset when these times are changing by 4 minutes per 1° of latitude (above latitude 44° near the solstices). If you sail due south 2° between sunrise and sunset, the sunset time will be wrong by 8 minutes, which makes the halfway time of LAN wrong by 4 minutes. The longitude error would be 60′, or 1°. But it is only a rare situation like this that would lead to so large an error. It is not easy to correct for this when using low sights to determine the time of LAN. For emergency longitude, you can overlook this problem.

In preparing for emergency navigation before a long voyage, it is clearly useful to know the Equation of Time. Generally, it will change little during a typical ocean passage. Preparing for emergency longitude calculations from the sun involves the same sort of memorization required for emergency latitude calculations. For example, departing on a planned thirty-day passage starting on July 1, you might remember that the sun’s declination varies from N 23° 0′ to N 18° 17′ and the time of LAN at Greenwich varies from 1204 to 1206. Then, knowing the emergency prescriptions for figuring latitude and longitude, you can derive accurate values for any date during this period.

Anonymous said...

I have the book Emergency Navigation, love this stuff! So the EqT formula in the example was a subtraction because the slope was negative? If the date was in November would the Formula be an addition as the slope is positive?

David Burch said...

Yes, the correction is positive, but you are staring with 16 min early, so it is just less early throughout Nov. ie, -16 + 5 = -11 or 11 min before 1200 = 1149. The full graph at the start of the note can help check the reasoning for various dates.

Mike J said...

By the way, the subscribe button does not seem to be working...

David Burch said...

Thanks for that notice. Must have been broke a long time. It seems Google no longer allows such links and also the original link to our YouTube channel was not working. So it seems the only way to follow the blog is to do so within your own blog settings. I did add a link to get to our videos section. Thanks again.