Lectures in Navigation Part 13

To find an azimuth of the sun: Note the time of taking the azimuth by chronometer. Apply chronometer correction, if any, to get the G.M.T.

Convert G.M.T. into G.A.T. by applying the equation of time. Convert G.A.T. into L.A.T. by applying the longitude in time. The result is L.A.T. or S.H.A. With the correct L.A.T., lat.i.tude and declination, enter the azimuth tables to get the sun's true bearing, i.e., its azimuth. Example:

March 15th, 1919. CT 10h -- 4m -- 32s. D.R. lat.i.tude 40 10' N, longitude 74 W. Find the TZ.

G.M.T. 10h--04m--32s Eq. T. --09 --10

G.A.T. 9h--55m--22s

G.A.T. 9h--55m--22s Lo. in T. 4 --56 --00 (W--)

L.A.T. 4h--59m--22s Lat.i.tude and Declination opp. name.

TZ = N 101 30'W

We will take up later a further use of azimuths to find the error of your compa.s.s. Right now all you have to keep in mind is what an azimuth is and how you apply the formulas already given you to get the information necessary to enter the Azimuth Tables for the sun's true bearing at any time of the astronomical day when the sun can be seen. In consulting these tables it must be remembered that if your L.A.T. or S.H.A. is, astronomically, 20h (A.M.), you must subtract 12 hours in order to bring the time within the scope of these tables which are arranged from apparent six o'clock A.M. to noon and from apparent noon to 6 P.M. respectively.

We are taking up sun azimuths today in order to get a thorough understanding of them before beginning a discussion of the Marc St.

Hilaire Method which we will have tomorrow. You must get clearly in your minds just what a line of position is and how it is found. Yesterday I tried to explain what a line of position was, i.e., a line at right angles to the sun's or other celestial body's true bearing--in other words, a line at right angles to the sun's or other celestial body's azimuth. Today I tried to show you how to find your azimuth from the azimuth tables for any hour of the day. Tomorrow we will start to use azimuths in working out sights for lines of position by the Marc St.

Hilaire Method.

Note to Instructor: Spend the rest of the time in finding sun azimuths in the tables by working out such examples as these:

1. April 29th, 1919. D.R. lat.i.tude 40 40' N, Longitude 74 55' 14" W.

CT 10h--14m--24s. CC 4m--30s slow. Find TZ.

2. May 15th, 1919. D.R. lat.i.tude 19 20' S, Longitude 40 15' 44" E. CT 10h--44m--55s A.M. CC 3m--10s fast. Find TZ.

Note to Instructor:

If possible, give more examples to find TZ and also some examples on lat.i.tude by meridian alt.i.tude.

a.s.sign for Night Work reading the following Articles in Bowditch: 371-372-373-374-375. Also, examples to find TZ.

FRIDAY LECTURE

MARC ST. HILAIRE METHOD BY A SUN SIGHT

You have learned how to get your lat.i.tude by an observation at noon. By the Marc St. Hilaire Method, which we are to take up today, you will learn how to get a line of position, at any hour of the day. By having this line of position intersect your parallel of lat.i.tude, you will be able to establish the position of your s.h.i.+p, both as to its lat.i.tude and longitude.

Now you have already learned that in order to get your lat.i.tude accurately, you must wait until the sun is on your meridian, i.e., bears due North or South of you, and then you apply a certain formula to get your lat.i.tude. When the sun is on or near the prime vertical (i.e., due East or West) you might apply another set of rules, which you have not yet learned, to get your longitude. By the Marc St. Hilaire method, the same set of rules apply for getting a line of position at any time of the day, no matter what the position of the observed body in the heavens may be. Just one condition is necessary, and this condition is necessary in all calculations of this character, i.e., an accurate measurement of the observed body's alt.i.tude is essential.

What we do in working out the Marc St. Hilaire method, is to a.s.sume our Dead Reckoning position to be correct. With this D. R. position as a basis, we compute an alt.i.tude of the body observed. Now this alt.i.tude would be correct if our D. R. position were correct and vice versa. At the same time we measure by s.e.xtant the alt.i.tude of the celestial body observed, say, the sun. If the computed alt.i.tude and the actual observed alt.i.tude coincide, the D. R. position is correct. If they do not, the computed alt.i.tude must be corrected and the D. R. position corrected to coincide with the observed alt.i.tude. Just how this is done will be explained in a moment. Put in your Note-Book:

_Formula for obtaining Line of Position by M. St. H. Method._

I. Three quant.i.ties must be known either from observation or from Dead Reckoning.

1. The S. H. A., marked "t."

Note: The method for finding S. H. A. (t) differs when the sun or star is used as follows:

(a) For the Sun: Get G.M.T. from the corrected chronometer time. Apply the equation of time to find the G.A.T. Apply the D.R. Lo.

(-W) (+E) and the result is L.A.T. or S.H.A. as required.

(b) For a Star: (Note to pupils: Leave this blank to be filled in when we take up stars in more detail.)

2. The Lat.i.tude, marked "L."

3. The Declination of the observed body, marked "D."

II. Add together the log haversine of the S.H.A. (Table 45), the log cosine of the Lat. (Table 44), and the log cosine of the Dec. (Table 44) and call the sum S. S is a log haversine and must always be less than 10. If greater than 10, subtract 10 or 20 to bring it less than 10.

III. With the log haversine S enter table 45 in the adjacent parallel column, take out the corresponding Natural Haversine, which mark N_{S}.

IV. Find the algebraic difference of the Lat.i.tude and Declination, and from Table 45 take out the Natural Haversine of this algebraic difference angle. Mark it N_{DL}

V. Add the N_{S} to the N_{DL}, and the result will be the Natural Haversine of the calculated zenith distance. Formula N_{ZD} = N_{S} + N_{DL}

VI. Subtract this calculated zenith distance from 90 to get the calculated alt.i.tude.

VII. Find the difference between the calculated alt.i.tude and the true alt.i.tude and call it the alt.i.tude difference.

VIII. In your Azimuth Table, find the azimuth for the proper "t," L and D.

IX. Lay off the alt.i.tude difference along the azimuth either away from or toward the body observed, according as to whether the true alt.i.tude, observed by s.e.xtant, is less or greater than the calculated alt.i.tude.

[Ill.u.s.tration]

X. Through the point thus reached, draw a line at right angles to the azimuth. This line will be your Line of Position, and the point thus reached, which may be read from the chart or obtained by use of Table 2 from the D. R. Position, is the nearest to the actual position of the observer which you can obtain by the use of any method from one sight only.

Example:

At sea, May 18th, 1919, A.M. (_) 29 41' 00". D.R. Lat.i.tude 41 30' N, Longitude 33 38' 45" W. WT 7h 20m 45s A.M. C-W 2h 17m 06s CC + 4m 59s.

IE--30". HE 23 ft. Required Line of Position and most probable position of s.h.i.+p.

WT 18d -- 7h -- 20m -- 45s A.M.

-- 12 ------------------------ WT 17d -- 19h -- 20m -- 45s C-W 2 -- 17 -- 06 Corr. + 9' 34"

------------------------ IE -- 30 CT 17d -- 21h -- 37m -- 51s ------------ CC + 4 -- 59 + 9' 04"

------------------------ G.M.T. 17d -- 21h -- 42m -- 50s (_) 29 41' 00"

Eq. T. + 3 -- 47 + 9 04 ------------------------ ------------ G.A.T. 17d -- 21h -- 46m -- 37s -(-)- 29 50' 04"

Lo. in T 2 -- 14 -- 35 (W--) ------------------------ log hav 9.48368 L.A.T.(t) 17d -- 19h -- 32m -- 02s log cos 9.87446 Lat. 41 30' N log cos 9.97473 Dec. 19 21' 25" N -------- log hav S 9.33287 N s .21521 L - D 22 08' 35" N D L .03687 -------- Calc. ZD 60 16' 30" N ZD .25208 -- 90 00 00 ------------- TZ found from table to be Cal. Alt. 29 43' 30" N 90 E.

-(-)- 29 50' 04"

------------- Alt. Diff 6' 34" Toward.