Answers to Lyra Celestial Navigation Refresher Exercise

Correcting Your Sight Reduction Forms

Below are the sight reduction forms and plotting sheets for the navigation exercise. The sight reduction forms are those used by Tom Cunliffe. They are used here to be consistent with the textbook. In class, we will examine the Starpath Navigation sight reduction form that you may find much easier to use.

The completed forms are included here so you can check your own work. There are five general areas in which one usually makes mistakes:

1- Errors in determination of the Geograpical Position (Local Hour Angle and Declination) of the body from the Nautical Almanac. Among the typical blunders are errors in the correction of Watch Time to GMT (UTC), reading the wrong row or the wrong column for the time and body in the almanac, and applying the wrong sign for the v and d corrections.

2- Errors in picking the assumed latitude and assumed longitude. Remember to pick the assumed latitude in whole degrees within 30’ of the DR latitude. Remember that West longitudes are subtracted from the GHA to get LHA, therefore the minutes of the assumed longitude should match the minutes of the GHA of the body so that the resulting LHA is in whole degrees.

3- Errors in converting the sextant reading (Hs) to observed altitude (Ho). A typical error is reading the wrong column in the correction table (e.g., upper vs lower limb correction). The moon corrections are more complex than other bodies and require some care.

4- Errors in using Pub. 249. Remember to make sure that you pick the table with the correct assumed latitude and double check whether the declination and latitude are have the Same Name or Contrary Name. Double check the rules for converting Z to Zn. Finally, remember GOAT (Greater Observed Altitude Toward). If Ho is greater than Hc, then the Line of Position is offset along Zn Toward the body.

5- Math Errors. Double check your addition and subtraction. The one that seems to crop up here most often occurs when adding and subtracting angles. Remember, when borrowing from the degrees column to the minutes column there are 60 minutes in a degree.

Correcting Your Plotting Sheets

Separate universal plotting sheets are included for each of the two problems. The first plotting sheet is for the pre-dawn Jupiter-Vega-Moon sights. Note that a different plotting convention was used than used in Cunliffe. Here, Zn is plotted as a vector and the arrow is labeled with the symbol of the body. This helps keep the bodies straight and debug cases where the Zn is way off. Each Line of Position is drawn perpendicular to the corresponding Zn vector and the right angle symbol is used at the intersection to clarify which LOP belongs to which Zn vector. The Line of Position is labeled with GMT and the body. Plotting conventions are largely a matter of taste – use what you like the best.

For the morning sights, the LOPs have been drawn for the time of the sight and the full length LOPs have not been drawn advanced to the time of the fix. To do so would create a very cluttered plot in this case. You may be able to make out the two short LOP segments that were advanced to draw the final fix. In this case, the difference between the fix without avancing the LOPs and the fix with advanced LOPs is only about 2 miles. The final fix at 0824 GMT is 34o00’N, 065o52’W. Note that a fix obtained with a calculator (34o00’N, 065o51’W) is less than a mile from the fix obtained with the paper tables.

As we can see, LYRA has been set to the SW of the rumb line, but, with the forecast potential for the wind to back, it might be advisable to hold the current heading for the time being – we can always bear off later and go faster as we approach Bermuda. If we bear off now and get back on the rhumb line, we may get headed later on and have to beat to the finish.

The second plotting sheet shows the running fix from the morning and afternoon sun sights. Note that the morning (0824 GMT) fix has been drawn and the DR re-started from that fix. The plotting convention used here is that an advanced line of position is labeled with the original GMT time of the sight connected by an arrow to the advanced GMT time. The Running Fix at 1732 GMT is 33o05’N, 065o20’W and is 1 mile from the calculator fix (34o00’N, 065o51’W). At 1732 GMT, LYRA is within 3 miles (about 30 minutes) of the 50-mile limit for turning on the GPS. We would need to make good 138o True to fetch the Kitchen Shoal beacon. Since we have been set to the SW, we might throw in an extra three degrees to Port in the hope that when we turn on the GPS, we will be right on course for Kitchen Shoal and will have earned our berth for the trip.