Astro Navigation In A Nutshell Part Four

Part 4 – Full procedure for establishing an astronomical position line.

This post brings together all of the information from parts 1, 2 and 3 of this series to demonstrate the full procedure for establishing an astronomical position line.

.Links: Astro Navigation In A Nutshell Part One

Astro Navigation In A Nutshell Part Two

Astro Navigation In A Nutshell Part Three

Please note. There is not sufficient scope in this post to fully explain this topic; however, there are in-depth expositions in my books ‘Astro Navigation Demystified’ and ‘Celestial Navigation – The Ultimate Course’.

Demonstration of the procedure:

Scenario:

Date: 18 July

D.R. Position at Zone Time: 16^h 44^m: 52^oN 21^o43.1’W.

Time Zone +1

Deck Watch Time (DWT): 17^h 50^m 28^s.

Deck Watch Error (DWE) 40^s fast (-40^s)

Body observed: Sun lower limb.

Sextant Altitude at true position: 32^o 10.’4 = 32^o.173

Compass Bearing at true position: 261^o (for rough check on azimuth)

Index error: +0’.54. Ht. of eye: 8m.

Temperature: 28^oC. Pressure: 991mb.

Step 1. Note Lat and Long of DR Position.

Lat: 52^o N

Long: 21^o43.1’W

Step 2. Calculate PZ. (90 – Lat).

PZ = 90^o – 52^o = 38^o

Step 3. Calculate Greenwich Date at time of observation.

Date: 18 July

Zone time: 16^h 44^m

Zone correction: +1^h

Universal Time (GMT): 17^h 44^m

Deck watch time: 17^h 50^m 28^s

Deck watch error: -40^s

Greenwich date: 18^d 17^h 49^m 48^sJuly

Step 4. Calculate Greenwich Hour Angle and Declination.

Date: 18 July

GHA Dec

UT 17^h 73^o 26’.1 N20^o 54’.7 (d:0’.5 decreasing)

Inc. 49^m 48^s: 12^o 27’.0 -0’.4

85^o 53’.1 N20^o 54’.3

= 85^o.885 = N20^o.9

Step 5. Determine if Lat and Dec are ‘Same’ or ‘Contrary’.

Lat = N

Dec = N

Therefore Lat and Dec are same.

Step 6. Calculate PX

(Lat and Dec Same therefore PX = 90 – Dec).

PX = 90^o – Dec. = 90^o – 20^o.9 = 69^o.1

Step 7. Calculate the Local Hour Angle (LHA). (Longitude combined with GHA should equal LHA as a whole number of degrees).

DR Long: 21^o43.1’W

GHA: 85^o.885

DR Long: 21^o.718 West (-)

LHA: 64^o .167

Step 8. Determine Angle ZPX.

ZPX = LHA = 64^o .167

Step 9. Calculate True Altitude at True Position (Observed altitude corrected for IE, Dip, Parallax and Refraction).

Sextant Altitude = 32^o 10′.40

Index error (IE) = +0′.54

Observed Altitude = 32^o 10′.94

Dip (ht. 8m.) = -5′.00 (table 6a)

Apparent Altitude = 32^o 05′.94

Altitude correction = +14′.50 (table 6d)

Added refraction (28^o/991mb) = +0′.10 (table 6c)

True Altitude = 32^o 20′.54 = 32^o.34

Step 10. Calculate Zenith Distance at True Pos. (90^o – Altitude).

Zenith Dist = 90^o – 32^o.34 = 57^o.66 = 3459.6′

Step 11. Calculate Zenith Distance at DR Position. (ZX).

Lat. = 52^oN

Declination = N20^o.9 (From Step 4)

Lat and Dec Same (From Step 5)

ZPX = 64^o .167 (From Step 7)

PZ = 38^o (From Step 2)

PX = 69^o.1 (From Step 5)

Cos (ZX) = [Cos(PZ) x Cos(PX)] + [Sin(PZ) x Sin(PX) x Cos(ZPX)]

= [Cos(38) x Cos(69.1)] + [Sin(38) x Sin(69.1) x Cos(64.167)]

= 0.53

ZX = Cos^-1 (0.53) = 57^o.99

Zenith Distance at DR position = 57^o.99 = 3479′.4

Step 12. Calculate Azimuth at DR Position (PZX)

Cos PZX = Cos(PX) – [Cos(ZX) x Cos(PZ]

[Sin(ZX) x Sin(PZ)]

Cos PZX = Cos(69.1) – [Cos(57.99) x Cos(38]

[Sin(57.99) x Sin(38)]

= -0.119

PZX = Cos^-1(-0.119) = 96^o.8 ≈ 97^o

Azimuth at DR position = 97^o

Step 13. Convert azimuth angle to true bearing (ZN):

Rules for converting Azimuth (PZX) to True Bearing (Zn)
	Lat. North	Lat. South
LHA>180^o	Zn = Z	Zn = 180^o – Z
LHA<180^o	Zn = 360^o-Z	Zn = 180^o + Z