Chapter 9
3. With your D.R. latitude, declination and Time Interval from Meridian Passage, enter Table 26 to get the proper amount of Variation of Altitude in one minute from meridian passage.
4. With the Time Interval from Meridian Passage and the Variation, enter Table 27 to get the total amount of Variation of Altitude.
5. Add this total amount of Variation to the true observed altitude taken before or after noon, and the result is the corrected altitude.
6. Then proceed to get your latitude according to the rules already given you for latitude by meridian altitude.
Example: At sea, Jan. 23rd, 1919. CT 4h 22m 14s. CC 1m 10s fast. Longitude 66 deg. 04' W. Latitude by D.R. 19 deg. 16' 00" N. (_) 50 deg. 51' 00" S. HE 49 ft. IE--1' 30". Required latitude in.
CT 4h - 22m - 14s CC - 1 - 10 --------------------- G.M.T. 4h - 21m - 04s Eq. T. - 11 - 50 --------------------- G.A.T. 4h - 09m - 14s Lo. in T 4 - 24 - 16 (W-) --------------------- L.A.T. 22d - 23h - 44m - 58s
24h - 00m - 00s - 23 - 44 - 58 ----------------- 15m - 02s = Time Interval from Meridian Passage.
Dec. 19 deg. 34' 48" S Table 26 = 2.8 Variation Lat. 19 deg. 16' 00" N For 1 min. 0 altitude.
* * * * *
Time Interval from Meridian Passage 15m 02s - 2.8" Variation for 1 minute (Table 27) 2" = 7' 30" .8 = 3 00 ------------- 10' 30" +
IE - 1' 30" (_) 50 deg. 51' 00" HE + 8 42 + 7 12 --------- ----------- Corr. + 7' 12" -(-)- 50 deg. 58' 12" + 10 30 ----------- 51 deg. 08' 42" - 90 00 00 ----------- ZD 38 deg. 51' 18" N Dec. 19 34 48 S ----------- Lat. in 19 deg. 16' 30" N
Assign for work in class room and Night Work, examples similar to the following:
1. At sea, July 11th, 1919. Latitude by D.R. 50 deg. 01' 00" N. Longitude 40 deg. 05' 16" W. Observed ex-meridian altitude (_) 61 deg. 45' 30" S. HE 15 ft. IE--4' 10". CT (corrected) 2h 38m 00s. Required latitude in.
2. At sea, June 6th, 1919. Latitude by D. R. 49 deg. 21' N, Longitude 18 deg. 18' W. Observed ex-meridian altitude (_) 61 deg. 30' 22" S. HE 42 ft. CT 1h 06m 18s. CC--1m 14s. IE 0' 30" off the arc. Required latitude in of ship.
If any time is left, work similar examples by Marc St. Hilaire Method.
FRIDAY LECTURE
EXAMPLES: LATITUDE BY EX-MERIDIAN ALTITUDE OF THE SUN
1. Jan. 1st, 1919. WT 11h 53m 18s A.M. C-W 5h 56m 16s. Latitude by D. R. 58 deg. 05' S. Longitude 89 deg. 00' 48" W. (_) ex-meridian 55 deg. 16' 30" N. IE 2' 00" off the arc. CC 1m 28s fast. HE 36 ft. Required latitude in.
2. March 11th, 1919. CT 11d 9h 14m 39s A.M. Latitude by D. R. 39 deg. 20' N, Longitude 39 deg. 48' 16" E. (_) ex-meridian 46 deg. 17' 30" S. IE 2' 00" on the arc. CC 1m 16s slow. HE 29 ft. Required latitude in.
3. April 26th, 1919. CT 26d 4h 46m 38s A.M. Latitude by D. R. 24 deg. 25' S, Longitude 107 deg. 16' 56" E. (_) ex-meridian 52 deg. 18' 50" N. IE--2' 40". CC 3m 56s slow. HE 33 ft. Required latitude in.
4. May 10, 1919. CT 2h 18m 46s A.M. Latitude by D. R. 23 deg. 54' S, Longitude 143 deg. 20' 18" E. (_) ex-meridian 48 deg. 26' 20" N. IE 3' 20" on the arc. CC 4m 18s fast. HE 41 ft. Required latitude in.
5. June 21st, 1919. CT 4h. 56m 18s. Latitude by D. R. 42 deg. 01' N, Longitude 75 deg. 00' 18" W. (_) ex-meridian 71 deg. 29' 40" S, IE--2' 30". CC 3m 04s slow. HE 28 ft. Required latitude in.
6. Dec. 18th, 1919. WT 11h 50m 18s A.M. C-W 3h 14m 18s. Latitude by D. R. 11 deg. 55' S. Longitude 48 deg. 02' 29" W. (_) ex-meridian 78 deg. 32' 30" S. IE 3' 30" on the arc. CC 2m 44s slow. HE 35 ft. Required latitude in.
If there is any time left, give examples of latitude by meridian altitude, Marc St. Hilaire Method by sun or star sight, etc.
SATURDAY LECTURE
FINDING THE WATCH TIME OF LOCAL APPARENT NOON
Noon at the ship is the pivotal point of the day's work at sea. It is then that the navigator must report to the commanding officer the latitude and longitude by dead reckoning, the latitude and longitude by observation, the course and distance made good, the deviation of the compass and the course and distance to destination. Apparent noon, then, is a most important time to calculate accurately, and to do so when the ship is under way, is not so easy at it first appears.
If the ship is stationary, and you know the longitude you are in, the problem is simple. Then it is merely a question of starting with L.A.T. of 00h-00m-00s, adding or subtracting the longitude, according as to whether it is West or East, to get G.A.T.; applying the equation of time with sign reversed to get G.M.T.; applying the C. Cor. with sign reversed to get the C.T.; and applying the C-W to get the WT. If, for instance, this WT happens to be 11h-42m-31s, when the watch reads that number of hours, minutes and seconds, the sun will be on the meridian and it will be apparent noon.
When the ship is moving, the problem is more difficult. At first thought you might imagine that all you would have to do would be to take the difference between the L.A.T. of the morning sight and 24 hours, calculate the distance the ship would run in this time and from that determine the longitude you would be in at noon. Then proceed as in the case of the ship being stationary. But such a calculation does not take into consideration the easting or westing of the ship itself. Suppose that at the morning sight the L.A.T. is found to be 20h-10m-30s. If the ship does not move, it will be 3h-49m-30s to noon. But suppose the ship is moving eastward. Then, in addition to the speed at which the sun is approaching the ship, there must be added the speed at which the ship is moving toward the sun--i.e. the change in longitude per hour which the ship is making, expressed in minutes and seconds of time. Likewise, if the ship is moving westward, an allowance must be made for the westing of the ship. And this change of longitude in minutes and seconds of time must be subtracted from the speed of the sun's approach since the ship, in going west, is traveling away from the sun.
There are various ways to calculate this allowance for the ship's speed, among the best of which is given in Bowditch, Art. 403, p. 179. Another, and even easier way, is the following, which was explained to the writer by Lieutenant Commander R.P. Strough, formerly head of the Seamanship Department of this School:--
1. Take the morning sight for longitude when the sun is on or as near as possible to the prime vertical.
2. Subtract the L.A.T. of the morning sight from 24 hours. This will give the total time from the morning sight to noon if the ship were stationary.
3. From the course to noon and speed of the ship, figure the change in longitude per hour in terms of seconds of time. For instance, suppose a ship were steaming a course of 275 deg. at the rate of 11 knots per hour in approximately 38 deg. North latitude. The change of longitude per hour for this speed would be 14' of arc or 56s of time.
4. Now the sun travels at the rate of 60 minutes or 3600 seconds per hour. To this hourly speed of the sun must be added or subtracted the hourly speed of the ship according as to whether the ship is going in an easterly or westerly direction. If, as mentioned above, the ship is steaming a course of 275 deg. (W 1/2 N) and hence changing its longitude at the rate of 56s per hour, then the net rate of approach of the sun per hour would be 3600s - 56s, or 3544s per hour.
5. Divide the total time to noon from the L.A.T. of the morning sight (expressed in seconds of time) by the net rate of approach of the sun per hour. The result will be the corrected time to noon--i.e. the time at which the sun will be on the ship's meridian when the ship is changing its longitude to the westward at the rate of 56s per hour.
6. One more step is necessary. To the watch time of the morning sight, add the corrected time to noon. The result will be the watch time of Local Apparent Noon. Thirty minutes before will be the watch time of 11:30 A.M. and at 11:30 A.M. all deck clocks should be set to the local apparent time of the place the ship will be at local apparent noon.
The following example illustrates the explanation just given and should be put in your Note Book:--
Example:--At sea, August 7th, 1919. About 7:30 A.M. by ship's time, position by observation just found to be Latitude 30 deg. 05' N, Longitude 58 deg. 08' W. WT of morning sight 6h-53m-13s A.M. C-W 4h-37m-21s. CC + 3m-38s. Course 275 deg.. Speed 11 knots. TZ N 90 deg. E. What will be the Watch Time of Local Apparent Noon?
WT 6h -- 53m -- 13s A.M. + 12 ------------------- 18 -- 53 -- 13 C-W 4 -- 37 -- 21 ------------------- CT 23 -- 30 -- 34 CC + 3 -- 38 ------------------- G.M.T. 23 -- 34 -- 12 Eq. T. -- 5 -- 42 ------------------- G.A.T. 23 -- 28 -- 30 Lo. in T. 3 -- 52 -- 32 ------------------- L.A.T. 19 -- 35 -- 58 24 -- 00 -- 00 ------------------- Total time to Noon 4h 24m 02s
Course -- 275 deg. Change in Lo. per hr.-- 14', 56s.
3600s -56 ----- 3544s, Net rate of approach of sun
4h 60 ---- 240m + 24 ----- 264m x 60 = 15840s
15840s + 02 ----- 15842s, Total time to noon. 3544) 15842 (4.47 hours 14176 ----- 16660 14176 ----- 24840 24808 -----
Corrected time to Noon 4h -- 28m -- 12s WT of A.M. sight 6h -- 53m -- 13s ----------------- WT of L.A.N. 11h -- 21m -- 25s WT of 11:30 A.M. 10h -- 51m -- 25s
When, therefore, the watch reads 10h--51m--25s, the deck clocks should be set to 11.30 A.M. and thirty minutes later it will be apparent noon at the ship.
In all these calculations it is taken for granted that the speed of the ship and hence the change in longitude can be gauged accurately. A check on this can be made by comparing the longitude of the A.M. sight with the D.R. longitude of the same time. Any appreciable difference between the two can be ascribed to current. Now, if a proportionate amount of current is allowed for in reckoning the speed of the ship from the time of the A.M. sight to noon, then a proper correction can be made in the net rate of approach of the sun and the corrected time to noon will be very close to the exact time of noon. Of course there will be an error in this calculation but it will be small and the result gained will be accurate enough for ordinary work.
So much for finding the watch time of Local Apparent Noon. Careful navigators carry the process further and get the watch times of 15, 10 and 5 minutes before noon, so that by the use of constants for each one of these times, an accurate check on the noon latitude can be quickly and easily secured. We have not time in this course to explain how these constants are worked out but it is well worth knowing. The information regarding it is in Bowditch Art. 325, p. 128, and Art. 405, p. 181.
A word about the watch used by the navigator should be included here. This watch should be a good one and receive as much care, in its way, as the chronometer. It should be wound at the same time every day, carefully handled and, in other respects, treated like the fine time-piece that it is.
While authorities differ on this point, the best practice seems to be not to change the navigator's watch to correspond with the apparent time of each day's noon position. The reason for this is two-fold. First, because constant moving of the hands will have an injurious effect on the works of the watch, and second, because, by not changing the watch, the C-W remains approximately the same, and thus a good check can be kept on both the watch and the chronometer as well as on the navigator's figures in reckoning the times of his various sights.
Assign for night reading the following Arts. in Bowditch: 323, 324, 333. Also problems similar to the following:
1. At sea, July 28, 1919. Position by observation just found to be Latitude 44 deg. 58' N, Longitude 22 deg. 06' W. WT of morning sight 6h-02m-20s. CC 3m 34s slow. Course S 24 deg. W. TZ N 90 deg. E. Speed 9 knots. What will be the watch time of Local Apparent Noon?
2. At sea, August 9th, 1919. Position by observation just found to be Latitude 38 deg. 48' N, Longitude 70 deg. 46' W. WT of morning sight 8h-15m-01s A.M. C-W 3h-56m-32s. CC 3m-43s slow. Course 272 deg.. Speed 12 knots. TZ N 90 deg. E. What will be the watch time of Local Apparent Noon?
WEEK VII--NAVIGATION
TUESDAY LECTURE
COMPASS ERROR BY AN AZIMUTH
The easiest and most accurate way to find the error of your compass is, first, to find the bearing of the sun by your pelorus. If you set your pelorus, so that it will exactly coincide with the course you are steaming as shown by the compass in your chart house and then get a bearing of the sun by noting where the shadow from the pelorus vane cuts the circumference, this bearing will be the bearing of the sun by compass. At the same time, get your true bearing of the sun from the Azimuth Tables. The difference between the two will be the compass error, marked East or West according to the following rule which put in your Note-Book:
1. Express your Compass Bearing and your True Bearing by NEW compass reading.
2. If TZ is to the right of CZ, C.E. is East. Formula: True--Right--East.
3. If TZ is to the left of CZ, C.E. is West. Formula: True--Left--West.
You must now remember that what you have is a Compass Error, consisting of both Variation and Deviation. To find the Deviation, the Variation and C.E. being given, is merely to apply the rules already given you under Dead Reckoning. For instance, if you had a C.E. of 10 deg. W and a Variation of 4 deg. E, the Deviation would be 14 deg. W.
Put this example in your Note-Book:
LAT 20h 59m 57s Lat. 4 deg. 55' N Dec. 10 deg. 39' 30" N
Ship heading N 11 deg. W. CB of (.) S 88 deg. E. Variation 10 deg. W. What was the ship's true course and Deviation of Compass on direction ship was heading?
CZ 92 deg. (New compass reading) TZ 80 deg. (New compass reading) --- CE 12 deg.
CE = 12 deg. W Variation 10 deg. W ----- Deviation 2 deg. W
True course being sailed N 23 deg. W or 337 deg..
Let us now work out some of the following examples:
1. L.A.T. 22h--14m--18s Lat. 30 deg. 29' S Dec. 17 deg. 28' 44" N Ship heading S 84 deg. W Compass Bearing 44 deg. Variation 10 deg. W.
Required T.C. and Deviation on ship's loading.
2. August 29th, 1919. CT 2h 29m 18s A.M. Longitude 120 deg. 19' 46" E. Latitude 44 deg. 14' N. Ship heading 98 deg.. Compass Bearing S 42 deg. E. Variation 4 deg. E.
Required T.C. and Deviation on ship's heading.
3. June 17th, 1919. CT 4h 18m 44s A.M. Longitude 60 deg. 14' 59" E. Latitude 38 deg. 48' 00" S. Ship heading SW x S. Compass Bearing 40 deg. Variation 12 deg. W.
Required T.C. and Deviation on ship's heading.
Etc.
WEDNESDAY LECTURE
CORRECTING LONGITUDE BY A FACTOR
We are now almost ready to begin the discussion of a day's work at sea. The only method we have not taken up is the one which is the subject of today's lecture. It is a method to correct your longitude to correspond with the difference between your latitude by Dead Reckoning and your latitude by observation.
Suppose you take a sight in the morning for longitude. The only latitude you can use is a D. R. latitude, advanced from your last known position. Now suppose you run until noon and at that time take a sight for latitude. In comparing your D. R. latitude, advanced the true course and distance steamed to noon, and your latitude by observation taken at noon, suppose there is a difference of several minutes. The question is--How can we correct our longitude to correspond with this error discovered in the latitude? This is the method which put in your Note-Book:
Find the difference between the latitude by D. R. and the corresponding latitude by observation (in most cases secured from a sight at noon or from the Star Polaris). Call this the Error in Latitude. With the D. R. Latitude of the preceding sight and the azimuth or bearing of the preceding sight (always expressed as a bearing of less than 90 deg., old compass reading) enter Table 47 for the correct Longitude Factor. Multiply this Factor by the Error in Latitude. The result is the correction to apply to the Longitude. It is applied East or West according as to whether the Latitude by Observation is to the East or West of the D. R. Latitude on the Line of Position (the line at right angles to the Azimuth) of the preceding sight.
Example:
Position about 7:30 A.M. Latitude by D. R. 25 deg. 40' S, Longitude (just secured by observation) 104 deg. 05' 38" E. L.A.T. 7h 32m 30s A.M., Declination 4 deg. 59' N. Thence ship ran to noon 109 deg., true course, 46 miles, when the latitude by meridian altitude of the sun was found to be 25 deg. 52' S. Required corrected longitude at noon.
7:30 A.M. D.R. Lat. 25 deg. 40' S Lo. 104 deg. 05' 38" E 109 deg.--46 k. 15 S 48 18 E ---------- -------------- Noon--Lat. by D.R. 25 deg. 55' S Lo. 104 deg. 53' 56" E Noon--Lat. by obs. 25 deg. 52' S ---------- Error in Lat. 3'
Enter Table 47 with azimuth (S 105 deg. E) N 75 deg. E as bearing and Latitude 25 deg. 40' or 26 deg., Factor is found to be .3.
3' (Error in Latitude) times .3 (Factor) = .9' or 54", Correction in Longitude. Is it East or West? Since azimuth is N 74 deg. E, Line of Position is N 16 deg. W. The D. R. Latitude and Latitude by Observation are plotted on this line as follows:
\ * Lat. by obs. (25 deg. 52' S) \ * Lat. by D.R. (25 deg. 55' S) \
Latitude by observation is West of Latitude by D.R. Hence correction in longitude of 54" is applied West. Position by observation, therefore, is as follows:
Lo. 104 deg. 53' 56" E Corr. in Lo. 54 W -------------- Lo. by obs. 104 deg. 53' 02" E
Lat. by obs. 25 deg. 52' S
Note to Instructor:
Assign the following examples for work in the class room:
1. April 20th, 1919 A.M. at the ship. G.M.T. 20d 10h 28m 24s A.M. (_) 31 deg. 55' 40". HE 30 ft. No IE, CC. Latitude by D. R. 26 deg. 30' N. Longitude 36 deg. 55' West.
Ship then sailed a true course of S 36 deg. E--40 knots until noon when observed altitude (_) 75 deg. 40' 50" S. What was the position at noon corrected for Longitude? (Note: Work the A.M. sight by both Time Sight and Marc St. Hilaire Method.)
2. June 25th, 1919, A.M. Latitude by D. R. 36 deg. 20' S. Longitude 96 deg. 30' E. CT 1h 37m 16s A.M. CC 1m 30s fast. IE 2' 30" off arc. HE 36 ft. (_) 7 deg. 34' 20". Log registered 114.
True course to noon S 76 deg. E. Log registered 174. Same IE, HE, CC. Observed altitude (_) 29 deg. 44' 40" N. Required position at noon by Longitude factor. (Note: Work A.M. Sight by Marc St. Hilaire Method.)
3. At sea, May 30th, 1919. In D. R. Latitude 38 deg. 14' 29" N. Longitude 15 deg. 38' 49" W. Observed altitude (_) 39 deg. 05' 40" and bearing by compass 259 deg.. IE 1' 00" on arc. HE 27 ft. WT 3h 04m 49s. C-W 1h 39m 55s. CC 1m 52s fast.
Changed course to 94 deg. p.s.c. and steamed 75 knots to about 8 o'clock. WT 8h 06m 18s. C-W 1h 39m 58s. At this time observed altitude of Star Arcturus 68 deg. 30' 40", East of meridian. Same IE, HE, CC.
Changed course to 95 deg. (true). Steamed 60 knots until midnight when ran into heavy fog. Slowed down to 7 knots per hour until 8 A.M. when observed altitude (_) 48 deg. 45' 10". CT 9h 45m 18s A.M. Same HE, IE, CC.
Required fix at 8 A.M. by Marc St. Hilaire Method, laid down on chart.
Note to Instructor:
Spend rest of period in familiarizing pupils with laying down runs and intersecting lines of position on Mercator plotting charts.
THURSDAY LECTURE
THE NAVIGATOR'S ROUTINE--A DAY'S WORK AT SEA
You are now familiar with the principal kinds of sights and the methods used in working them as explained in the foregoing pages. This information, however, relates only to each individual kind of sight. Today I will explain briefly how those sights are made use of in your daily work at sea. Such an explanation necessarily cannot include the navigator's work under all conditions and on all classes of ships. It merely gives a brief outline of and a few suggestions relating to navigating conditions on board a medium-sized transport, in time of war. I say "in time of war" because navigating then is different, to some extent, from the ordinary routine in time of peace.
Suppose you are ordered to a ship as navigator. What are your duties (a) before leaving port, (b) while at sea, and (c) on entering pilot waters?
_(a) Before Leaving Port_
Ascertain the height of the eye of the bridge and any other place on the ship where you would be likely to take sights.
Have posted in the chart room and on the bridge the deviation of the compass on each 15 deg. heading, so that it can be easily referred to.
Keep in each chronometer case or in a book nearby the error and daily rate of all chronometers on board.
Test each sextant for index error and record the result where you can refer to it easily.
See that all charts of the harbor out of which you are to steam are corrected to date and are familiar to you, both as to sailing directions and buoys, and also as to lights and other aids to navigation.
Examine, in detail, the steering engine and steering apparatus. In case of its disarrangement your intimate knowledge of it may be most valuable.
See that the patent log and sounding machine are in good order. See that the lead lines are well soaked in water, stretched, and properly marked.
See that the lighting system in the chart room and the navigator's room is such that when any door is not tightly closed the lights in the room are extinguished. Likewise, when the doors are closed, see that the lights will light and without repeated slamming of the doors.
If possible, provide yourself with a flashlight set back in a metal tube so that the rays of the light are not diffused but can be focussed only on one spot at a time.
See that your charts are arranged neatly in the drawers provided for them in the chart room. If, as is usual, the charts must be folded to get them in the drawers, mark them legibly on the outside and in the same place on each chart. Put in the top drawers those charts you know you will use most frequently. This will save endless time and confusion.