In the last Nav Toolbox (“Calculating the time of twilight,” Issue No. 90) looked at calculating the best time for shooting stars. In the morning, calculating the time of nautical twilight gets the navigator on deck when the brightest stars are still visible and the horizon has become distinct enough for sextant work. In the evening, the navigator wants to begin shooting stars at the time of civil twilight, when the brightest stars first appear and yet the horizon is still visible.
How much time does a navigator have for getting a round of star sights at each twilight? That depends on his or her latitude; the farther from the equator, the longer the window of opportunity.
For our exercise, we assumed a date of July 25, 1998, and a DR position of 36° N, 68° W. Calculations for the best time to begin shooting morning stars (at nautical twilight) gave us the answer of 0829 GMT.
Imagine now if we could hit the deck, sextant and watch in hand, already knowing where the brightest stars would be in the sky and what their altitudes and azimuths (bearings) would be. It sure would make our lives easier. There are a few ways to do this. We’ll concentrate on how to do it using HO 249, volume 1.
During morning twilight, when so many stars are visible, this “precalculation” can save the navigator from having to identify a few stars out of the “billions and billions” visible to the naked eye. And, during evening twilight, when the familiar references of constellations are not yet visible, precalculation can allow the navigator to positively identify the few pinpricks of light that illuminate the darkening sky. The wizards who create HO 249, volume 1 have selected, out of the 57 navigational stars (refer to the daily pages of the Nautical Almanac for this entire list), the seven best (brightest) stars visible at any time of the day. Each list of seven selected stars covers 360° in azimuth, so the good crossing angles of the resulting LOPs are maintained, even if only a few of them are shot.To get started in HO 249, we first need to calculate the local hour angle (LHA) of Aries. Aries is an imaginary line on the celestial sphere (much like a line of longitude can be thought of as a line on the globe) established each year at the point where the sun is located at the exact moment of the vernal (spring) equinox. This Aries meridian moves through the sky, 360° every 24 hours, its movements tracked daily in the Nautical Almanac. When we calculate the LHA of Aries, we’re establishing the location of Aries relative to us by measuring the number of degrees to the west between our longitude and the “longitude” of Aries. We know our longitude?68° W?because we needed a DR position to start the twilight calculation. For the longitude of Aries, we’ll use the Greenwich Hour Angle (GHA) of Aries for our twilight time of 0829 GMT. The degrees of GHA of Aries are given on the left-hand column of the left-hand page of the daily pages in the Nautical Almanac. The minutes and tenths of GHA of Aries come from the “Increments and Corrections” pages in the back of the almanac.To find the degrees of GHA of Aries for our example, look under the Aries column and read the value opposite a time of 0800 on July 25. Next, using the minutes (00:29) of our calculated twilight time, search for the 29 minute box in the Increments and Corrections section and grab the top value (corresponding to 00 seconds) under the Aries column. Add them together to get the GHA of Aries.08:00 hours
62° 49.8′
00:29 minutes
+ 7° 16.2′
GHA Aries at 0829 GMT
70° 06 .0′
To get to LHA of Aries, simply subtract our longitude of 68° W:
GHA Aries
70° 06.0′
DR Longitude
–
68° 0’W
LHA Aries 2° (Note that for this calculation it is perfectly acceptable to do some judicious rounding to arrive at an LHA in whole degrees.)
With an LHA Aries of 2° and our DR latitude of 36° N, we are ready to enter HO 249, volume 1. Volume 1 is laid out with north latitudes to the front and south latitudes to the back, with 0° (the equator) in the middle of the book, two pages for every whole degree of latitude (except in very high latitudes, where only one page per degree is given).
Once on the page for 36° N, work your way through the LHA values (0° to 359°) to locate 2° (each page is split into two LHA ranges, so look carefully).
Each block of 15 LHA values is headed by a list of seven selected stars. Reading across the line for the proper LHA value, the navigator can pull out an altitude (Hc) and azimuth (Zn) for each of those seven stars. Further, a diamond alongside three of the seven stars indicates which of the listed stars will yield the best three-star fix. The stars listed in all capitals are first magnitude (brightest) stars.
From the list of stars the navigator can create a page in the sight notebook to carry up on deck. Columns for GMT sight time and the observed altitude allow for the actual star sight values to be jotted down next to each star, as we’ve illustrated in the accompanying sidebar.
On deck, sextant in hand, the navigator can pick a star, say Capella, look at the precalculated values, and be reasonably sure that (in our example) the bright star he’s seeing about 33° up in the sky on a bearing of about 054° is Capella. Presetting the sextant to 33° and looking off in the general direction of 054°, Capella will be seen hovering near the horizon. Some quick sextant adjustments, a time check, and the star is done! With the precalculated list, a round of seven stars can be quickly finished (assuming they’re all visible), and other stars or planets can be shot to add to the collection.
Since I’ve always found it awkward to record bearings of each sight, I get around this by drawing a rough outline of a boat on my notebook page, and sketching in the precalculated stars in their relative bearing around the boat (the accompanying illustration assumes we are headed due north). This helps me find stars much more quickly than by asking someone at the helm to point in a particular direction. This technique also allows me to shoot any star, precalculated or not, sketch the star in its relative position to the bow of the boat, and then compare it with the list later, when I have more time. Once the navigator is finished with the fun of shooting stars the real work begins, of course. The stars must still be reduced and the LOPs plotted. Volume 1 can be used to reduce the stars quickly, but must be reentered for the actual LHA value of the sight. And, since volume 1 is created to last for 10 years, with a central year stated on the cover (currently given as Epoch 1995), the navigator must correct the plot for other years using Table 5 in the back of the book.
With any luck, a beautiful pinwheel fix will result from the sights, assuring the navigator that the boat is right where it is supposed to be. Sight reduction, the use of Table 5, and plotting will be covered in upcoming articles.
Precalculating stars, whether using HO 249, the Rude Starfinder, or a list from a calculator like the Celesticomp, is a tremendous time saver and confidence builder. Plus, it is always worth it when the navigator points to a single pinprick of light in an otherwise blank sky and says with studied nonchalance, “There’s Altair, right where it should be!”
