Meridian Passage Short Method

Meridian Passage Methods. 

Short Method.  In the case of stationary or very slow moving vessels, it is acceptable to use the Meridian Passage Short Method which involves calculating the time of meridian passage at the current DR position.

Long Method.  For vessels that are making good headway, the long method should be used.  The long method involves calculating the time of meridian passage at the present position an hour or so before noon and then plotting a new DR position for that time.  In this way, the time of meridian passage at the new DR position can then be calculated in advance.

Note.  Since the calculations for position by meridian passage involve the Greenwich Hour Angle and the longitude, the base line for both of which is the Greenwich Meridian, it would seem appropriate to refer to Greenwich Mean Time instead of Universal Time in those calculations. Since the terms GMT and UT are generally considered to be synonymous, no loss of accuracy will arise.

Links:  Understanding Meridian Passage,   What is the point of meridian passage?           Applying the Equation of Time,   Meridian Passage Long Method,   Local Hour Angle and Greenwich Hour Angle,   Converting GMT to GHA ,  Altitude Corrections    Zone Time, 

Meridian Passage – Short Method.

As we learned in ‘Understanding Meridian Passage’, meridian passage (mer. pas.) occurs when a celestial body crosses the observer’s meridian of longitude and at that instant, it will reach its greatest altitude above the observer’s horizon.  We also learned that if we measure the Sun’s altitude at local meridian passage and use the result together with the Sun’s declination, we can calculate our latitude.

The short method is used for stationary or very slow moving vessels and involves calculating the time of meridian passage at the current DR position.

Rules For Calculating Latitude at Meridian Passage. The following rules were fully explained in ‘Understanding Meridian Passage’ but need to be reiterated here:

1. Latitude and declination same names but latitude greater than declination:          LAT  =  DEC + (90^o – ALT)
2. Latitude and declination same names but declination greater than latitude:        LAT  =  DEC – (90^o – ALT)
3. Latitude and declination opposite names:        LAT  =  (90^o – ALT) – DEC

 Short Method Outline. The short method involves calculating the time of local meridian passage at the vessel’s present geographical position shortly before noon and then measuring the Sun’s altitude as that time approaches.

Outline of the Six-Step Proforma for the Meridian Passage Short Method. This easy to follow six-step proforma can be used for calculating a vessel’s position by the Meridian Passage Short Method.

Pre Planning.  As the time approaches noon, calculate your vessel’s geographical position (DR or EP) and note the zone time at that position.

• Step 1.  Using the nautical almanac daily page, find the time of meridian passage (mer. pas.) for today’s date (in GMT).
• Step 2.  Convert the time of mer. pas. from GMT to zone time. (Remember that zone time will not correspond to the Sun’s apparent time so although mer. pas. occurs at noon apparent time, the zone time is likely to be several minutes either side of this).
• Step 3.  From the nautical almanac daily page, find the Sun’s declination at the time of Mer. Pas.  (Note, when correcting declination for the ‘d’ increment, care should be taken to check the daily page to see if declination is increasing or decreasing).
• Step 4.  Measure the altitude of the Sun’s lower limb at mer. pas. and calculate the corrected Meridian Altitude.
• Step 5.  Calculate the vessel’s latitude from the meridian altitude and the Sun’s declination using the rules for Mer. Pas. as explained earlier.
• Step 6.  Calculate the vessel’s longitude by converting the time difference between Mer. Pas. and GMT.

Example.  This example demonstrates the application of the above method of calculating latitude by the meridian passage short method.

Task.  Use the meridian passage short method to calculate the position of the vessel in the scenario below by following the six-step proforma above.

Scenario:  Date:  22 June

Zone Time: 1140 (+4)

Zone:  +4

Mer. Pas.: 12 02

DR Position:  32⁰ 30’N.  61⁰ 55’W.

Speed negligible (Fishing vessel hauling nets).

Sextant altitude at Mer. Pas.: 80^o 55’.8

Index Error (I.E.): -0′.2

Ht. of eye:  2.5m.

Deck Watch Time (DWT) at Meridian Altitude: 16^h 08^m 25.1^s

Deck Watch Error (DWE): 5 sec fast (-5)

Solution.

Pre Planning. Date: 22 June.  Zone Time: 1140 (+4).  DR Pos: 320 30’N.  610 55’W

Step 1. Determine Time of Mer. Pas. at Greenwich.

From the Nautical Almanac Daily Page for 22 June, Mer. Pas. at Greenwich =  1202 GMT.

Step 2.  Calculate time of Mer.Pas.at D.R. Pos. (DR Longitude = 610 55’W.) Convert Longitude to time. Long: 61o 55’W 4 x 61o ÷ 60  = 4.066h      =  4h    04m    57.6s 4 x 55’ ÷ 60 = 3.66m                 =  0h    03m   39.6s =                                               4h    07m   37.2s (≈ 37s) Estimate zone time of Mer. Pas. Mer. Pas. Greenwich     =     12h   02m   00s (GMT) (from daily page) Long (61o 55’W):             = + 04h   07m   37s (Longitude West, GMT Best(+)) Local Mer. Pas (GMT)    =    16h    09m   37s Zone (+4)                           =  –04h                     (+4 for GMT but -4 for zone time). Zone time Mer. Pas.         =   12h    09m   37s        ≈ 1209 (nearest minute)

Step 3. Determine Declination at Time of Local Mer.Pas. Local Mer. Pas (in GMT): 16h  09m 37s  » 16h 10m Dec Sun (16h)                        =    N23o 25′.9  (from Daily Page)  (d = 0′.0) d correction                           =                0′.0 (from increments table) Dec Sun (16h 10m GMT):      =    N23o 25′.9  (= N23o.43)

Step 4.  Calculate Meridian Altitude. Sext. Altitude:                80o 55’.8 I.E.:                                         – 0’.2 Observed Altitude:        80o 55’.6 Dip (2.5m):                            – 2’.8    Apparent Altitude:         80o 52’.8 Altitude Correction:           + 15’.8 True Altitude:                  81o 08’.6      (= 81o.143)
Step 5.  Determine Latitude. DR Latitude = 320 30’N. Declination = N23o.43 (from step 3) Altitude = 81o.143 (from step 4) (Lat and Dec same hemisphere; Lat > Dec = rule 1) Therefore LAT  =  Dec + (90o – ALT) –   (rule 1) = 23o.43 + (90o – 81o.143) = 23o.43 + 8o.857 Therefore LAT  =32o.287N = 32o 17’ 13″.2 N

Step 6.  Calculate Longitude  (from DWT at meridian altitude). DR Long = 610 55’W. Mer. Pas.: 12 02 Calculate time difference. Deck Watch Time             =    16h 08m 25.1s DWE:                                   =                -05s GMT/UT:                             =  16h 08m 20.1s Mer Pas:                              =   12h  02m 00s  Time Diff:                             =+04h 06m 20.1s   ( Longitude West = GMT Best) Convert Time to Arc 4h  = 4 x 15  =       60o 00’  00” 06m = 6 ÷ 4  =         1o  30’  00” 20.1s = 20.1 ÷ 4 =  0o  05’  01″.5 = 61o  35’  01”.5 Therefore Long = 61o  35’ 01″.5 W

Therefore, observed position at zone time 12^h 09^m (local Mer Pas)

= 32^o 17’13″.2N.      61^o 35’ 01″.5W.

(For comparison DR Pos. at 11^h 40^m (zone time) was 32⁰ 30’N. 61⁰ 55’W.)

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Applying Mathematics to Astro Navigation at Amazon .com

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Astronomy for Astro Navigation at Amazon.com

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