Twilight, often used as a metaphor by poets and writers, is a twice-daily event that also offers tremendous potential for the celestial navigator. The fleeting “windows” morning and evening twilight are used by navigators to shoot stars and planets and obtain multiple LOPs for a fiximpossible when one is only shooting the sun. As an added bonus, knowledge of the time of sunrise and sunset provides a navigator with the opportunity to shoot an amplitude sight, the most accurate type of azimuth sight.
Twilight, both morning and evening, is divided into two periods: civil and nautical. Civil twilight occurs between the time the sun’s upper limb is on the horizon and when its center is six degrees below the horizon. Nautical twilight is that span of time from when the sun’s center is six degrees below the horizon to when it is 12 degrees below the horizon. Since we can’t see the sun, however, we have no way of measuring its angle below the horizon. But we can refer to the Nautical Almanac, which provides the times of civil and nautical twilight on each set of daily pages. So, the sequence in the morning is nautical twilight, civil twilight, sunrise; in the evening we have sunset, civil twilight, and then nautical twilight.
Ideally, navigators wish to shoot stars and planets when the sun is between three degrees and nine degrees below the horizon. During this period, the sky is sufficiently dark that navigational stars are visible, but the horizon is still being illuminated by the sun.
In the morning, a navigator should be on deck and ready to shoot stars at the time of nautical twilight. The sky will stay sufficiently dark for the shooting of stars and planets until the sun rises to three degrees below the horizon, at which point the sun’s illumination will begin to overpower the stars. At dusk, a navigator should be prepared to start shooting stars at civil twilight and continue shooting until nautical twilight.
Once the sun reaches 18 degrees below the horizon there is insufficient light to illuminate the horizon and the sky is as dark as it will get for the nightastronomers refer to the time when the sun is between 12 degrees and 18 degrees below the horizon as astronomical twilight. (The horizon can sometimes be seen at night if other light sources, such as the moon, illuminate it.)
A navigator preparing for star shots or just needing to know when daylight will begin or end would enter the Nautical Almanac on the day of interest and refer to the columns and rows on the right hand pages. The columns on the top half of each page give the times of morning twilight and sunrise. The columns on the bottom half of the page give times of sunset and evening twilight.
The appropriate row, for one’s latitude, is entered using DR latitude. Entries are made for a range of latitudes from N 72° to S 60°, but since entries are tabulated for two-, five- and 10-degree increments of latitude, interpolation is necessary for an accurate determination of time. Interpolation for latitude can be done mentally or with the aid of table I on page xxxii (back of the Nautical Almanac). The tabulated times are the GMT of sunrise, sunset, and twilight and must also be adjusted for one’s longitude. Longitude can be converted to time by using the Conversion of Arc to Time table on page i (the first yellow page) in the back of the Nautical Almanac.
At certain times of the year at high latitudes, twilight, sunlight, or darkness can be continuous. If this is the case, the following symbols are used to show that condition:
sun continuously above horizon
sun continuously below horizon
twilight lasts all night
The times given in the daily pages are for the three days covered and is based on the middle day of the three days. This is sufficiently accurate for determinations over the three-day period.Finding twilight
Finding the time of twilight is best illustrated with an example. We desire to determine the time of civil twilight, nautical twilight, and sunrise on June 21st 1994, so that we can shoot morning stars. Our approximate position on the morning of the 21st is latitude 43° 40′ N and longitude 70° 15′ W. Our first step is to enter the Nautical Almanac and go to the June 21st daily page. First, find the two latitude rows bracketing our latitude of 43° 40′ N. These are 40° N and 45° N. We need to record the times for nautical twilight, civil twilight, and sunrise at 40° N and 45° N and then go to the latitude interpolation table on page xxxii.
To enter the latitude interpolation table we need three pieces of information: (1) the tabular interval between latitudes that bracket our actual latitude,(2) the increment in latitude between the tabulated latitude that is less than ours and our actual latitude and (3) the difference in time(s) between nautical twilight, civil twilight, and sunrise for consecutive tabulated latitudes. In our example, value (1) is 5, the difference between 40° N and 45° N. Value (2) is 3° 40′, the difference between 43° 40′ N and 40° N. Values for (3) are 31 minutes for nautical twilight (0317 – 0246 = 31), 23 minutes for civil twilight (0359 – 0336 = 23), and 18 minutes for sunrise (0431 – 0413 = 18).
Table 1 is now entered using the columns and entries that come closest to the values we just determined. We first enter the tabular interval column with 5. We go down this column until we reach 3° 45′, which is the closest entry to our 3° 40′ value and then we move horizontally to the right to intersect the 20 min., 25 min., and 30 min. columns which are the closet to our time differences of 18 min. (use 20 min. column), 23 min. (use 25 min. column) and 31 min. (use 30 min. column). The corrections we extract are 15 min., 18 min., and 22 min. These time differences are now subtracted from the tabulated entries for 40° N to arrive at the correct times for 43° 40′ N. The time corrections are not always subtracted, one must examine the table to determine if the times between consecutive latitudes are increasing or decreasing. Our times are, for now: 0255 for nautical twilight (0317 – 22 = 0255), 0341 for civil twilight (0359 – 18 = 0341) and 0416 for sunrise (0431 – 15 = 0416).
These times are in GMT for nautical twilight, civil twilight, and sunrise at Greenwich, England. Since we are not in Greenwich, we now need to convert these times to GMT at our longitude of 70° 15′ W. To do this we go to the arc to time conversion Table on page i. First, we convert 70° to time by going down the 60° to 119° column until we reach 70°, where we see directly to the right its conversion to time, which is 4 hours and 40 minutes. This is how long it will take the sun to travel 70° of longitude. We also need to convert the 40′ of longitude to time, so we go to the far right side of the table and go down the minutes column until we reach the 15′ entry and directly to the right of this under the 0.00′ column (we have no tenths of minutes of arc in this case) we find the time conversion for 15′ of arc, which is one minute of time. We now know that 70° 15′ of longitude equates to 4 hours and 41 minutes of time. This time added to the GMT of nautical twilight, civil twilight, and sunrise will give us the GMT time at our position.
Nautical twilight will occur at 0736 GMT (0255 + 0441 = 0736), civil twilight will occur at 0822 GMT (0341 + 0441 = 0822) and sunrise will occur at 0857 GMT (0416 + 0441 = 0857) at our location. We can convert these times to local time by subtracting our zone description. (It is important to remember that when using the Rude star finder or volume 1 of HO 249 to determine which stars will be visible, GMT should be used not local time to find the LHA of Aries at nautical and civil twilight.) In this scenario, our zone description is (-4), this includes daylight savings time, and so the local times of nautical twilight, civil twilight and sunrise would be; 0336, 0422, and 0457 respectively. Taking the difference between nautical and civil twilight, we see we have 46 minutes to shoot our morning stars (0822 – 0736 = 46).
Interpolating by eye
If the thought of entering table I to interpolate for latitude seems too daunting, then “seaman’s eye” interpolation can be done. This involves mentally interpolating between rows of tabulated latitude. In the present example, we can round our actual latitude of 43° 40′ N to the closest whole degree which would be 44° N and then examine the rows for latitudes of 40° N and 45° N. Since our approximate latitude of 44° N is 4/5ths or 80% of the difference between twilight at 40° N and 45° N, we take 80% of those time differences, which is approximately 30 minutes and 23 minutes (0246 – 0317 for nautical twilight and 0359 – 0336 for civil twilight) and average the two times.
We can average these two time differences to 25 minutes, (25 is an easily multiplied number about halfway between 23 and 30), and then take 80% of 25, which gives us 20 minutes (.8 x 25 = 20). We therefore take approximately 20 minutes from 0317 and 0359 to give us 0257 and 0339 respectively.
We still need to adjust these times for our longitude and this can be done by rounding off our longitude to the nearest whole degree and then using the conversation of 1° = 4 minutes of time. Our actual longitude of 70° 15′ rounds off to 70° and then converts to 280 minutes (4 minutes per degree x 70° = 280 minutes). Sixty minutes in an hour then leaves us with four hours and 40 minutes. We add this time, four hours and 40 minutes, to the original GMT times, 0257 and 0339 and the result is 0737 and 0819 GMT at our location. These times compare favorably with the precise times of 0736 and 0822 arrived at by using the latitude interpolation table and arc to time conversation table.It does help to use a pencil and paper when making these calculations! A “seaman’s eye” interpolation for sunset, civil twilight, and nautical twilight at another position, say 5° 30′ S and 60° 00′ W on 21 September, 1994, will show the difference in occurrence and duration of twilight due to season and latitude. For sunset, we look at the columns and rows on the lower half of the daily pages and in this example we see times at 0° latitude as 1757 for sunset, 1817 for civil twilight, and 1841 for nautical twilight. At 10° S the times are 1756 for sunset, 1817 for civil twilight and 1841 for nautical twilight. Taking the difference in times and interpolating for latitude in this case is very simple, other than a one-minute time difference in sunset the twilight times are the same for 0° and 10° S so 5° 30′ S will also have the same times: 1756 for sunset, 1817 for civil twilight, and 1841 for nautical twilight.
Adjustment for longitude still needs to be done and since 1° of longitude = 4 minutes of time, 60° of longitude equals 240 minutes of time or 4 hours. Therefore, the GMT of sunset, civil twilight, and nautical twilight at 5° 30′ S and 60° 00.0′ W are: 2156, 2217, and 2241 respectively. Twilight lasts a short 24 minutes (2241 – 2217 = 24) so a navigator needs to be organized and quick to gather the needed shots.
The length of twilight varies depending on our latitude and the earth’s position relative to the sun. For example, on 21 June at the equator, the length of morning twilight is 27 minutes (0536 – 0509 = 27) while at 40° N, twilight lasts 42 minutes (0359 – 0317 = 42) and at 40° S, twilight is 35 minutes (0652 – 0617 = 35).
Given the right situation, one could even put the twilight information in the Nautical Almanac to other uses. For example, in December 1983, Marvin Creamer, aboard the sailing vessel Globe Star,rounded Cape Horn, marking the halfway point in his “instrumentless” circumnavigation. This safe passage of Cape Horn was done using a technique one might call “latitude by twilight.”
Creamer used no instruments (not even a compass), but he did know that during the middle and end of December, Earth’s position relative to the sun would produce a twilight between 56.5° S and 66.5° S latitude that would last all night.
Cape Horn is located at about latitude 55.5° S. Therefore, as long as Globe Star was sailed far enough south to remain in continual twilight, and did not see complete darkness, the latitude would be below 55.5° S and Globe Star could sail safely to the easthence the “latitude by twilight” technique.