Unit 5 – Demonstration of a 3 point fix.
Aim. We saw in unit 4 how a position line is obtained from a single intercept; the aim of this demonstration is to establish a 3 point fix based on the intersection of three intercepts obtained from observations of three celestial bodies as detailed below. For the purpose of clarity, the calculations for the zenith distances and azimuths of the three bodies at the assumed position are not included at this stage. However, the next unit will explain how such calculations are made.
Scenario: A yacht is sailing on a course of 090 at roughly 5 knots. Observations of 3 celestial bodies are made in order to obtain a three point fix. Of course it is not possible to take sextant readings of three celestial bodies at exactly the same time and you will see from the data below that there are small time intervals between each reading. You will also see, from the plot diagram, that the three intercepts are drawn from separate positions along the yacht’s course (i.e. AP1,AP2,AP3).
Assumed Position: 47o 52’N, 47o 35’W.
Index error: + 0’.53
Ht. of eye: 5.8m. Resultant Dip: -4′.2
Celestial Bodies Chosen:
Moon’s lower limb, Saturn, Alphecca
Sextant Altitudes at true position:
Moon’s lower limb = 35o 28’.23
Saturn = 41o 48’.73
Alphecca = 54o 58’.06
Corrections to sextant altitudes (altitude tables not shown here but can be seen in unit 3):
|Moon Saturn Alphecca|
|GMT of sextant reading 23h 48m 08s 23h 49m 37s 23h 50m 50s|
|Sext Altitude 34o 29’.2 41o 53’.50 55o 02’.43|
|I.E. +0’.53 +0’.53 +0’.53|
|Dip (5.8m) -4’.2 -4’.2 -4’.2 .|
|Apparent Alttitude 34o 25’.53 41o 49’.83 54o 58’.76|
|Altitude Correction -1’.1 -0’.7|
|Moon Altitude Correction +56’.8|
|Moon’s HP Correction +5’.9|
|Observed (True) Altitude 35o 28’.23 41o 48’.73 54o 58’.06|
Calculating Zenith Distances at the True Position
Zenith distance of Moon = 90o – 35o 28’.23 = 3271′.77 = 3271.77nm
Zenith distance of Saturn = 90o – 41o 48’.73 = 2891′.27 = 2891.27nm
Zenith distance of Alphecca = 90o – 54o 58’.06 = 2101′.94 = 2101.94nm
Calculated Altitudes at the Assumed Position.
Moon’s lower limb = 35o 50’
Saturn = 42o 03’
Alphecca = 55o 26’
Calculated Zenith Distances And Azimuths At The Assumed Position.
Zenith Distance of Moon = 3250nm. Azimuth = 232o
Zenith Distance of Saturn = 2877nm. Azimuth = 223o
Zenith Distance of Alpheca = 2074nm. Azimuth = 116o
Calculating the Intercepts
Moon Intercept = 3271.77 – 3250 = 21.77nm away from 232o
Saturn Intercept = 2891.27 – 2877 = 14.27nm away from 223o
Alphecca Intercept = 2101.94 -2074 = 27.94nm away from 116o
Plotting the fix. The next step is to plot the fix on the chart. Because of the small errors inherent in astro navigation techniques, the three position lines will very rarely cross at one precise point. Usually, a small triangle known as a ‘cocked-hat’ will be produced and as long as the triangle is not too large, it can safely be assumed that the ship’s position is at the centre of this triangle. The diagram shows how the fix would be plotted on a chart.
Note. Where position lines are derived from astronomical observations, the resultant position is not known as a ‘fix’ but is known as an observed position and is marked on the chart as ‘Obs’.
A thorough treatment of this topic can be found in ‘Astro Navigation Demystified‘.
Where to buy books of the Astro Navigation Demystified series:
Astro Navigation Demystified at Amazon.com
Astro Navigation Demystified at Amazon.uk
Applying Mathematics to Astro Navigation at Amazon .com
Applying Mathematics to Astro Navigation at Amazon .uk
Astronomy for Astro Navigation at Amazon.com
Astronomy for Astro Navigation at Amazon.uk
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