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1 INTRODUCTION
In the age of electronics, of constellations of satellites
meant to determine the position of the ship anywhere
on the Earth's surface, astronomical navigation
continues to be the subject of study by future
seafarers. We can consider astronomical navigation as
a reserve means in keeping navigation that cannot
miss from the necessary professional knowledges of
the navigator just as neither the lifeboat nor the
collective life raft can miss on board of any ship,
regardless of its size or destination.
"Ars Navigation" – “the art of sailing” called the
ancient Latins this wonderful human occupation,
although they possessed, at that time, modest
knowledge in the field of celestial mechanics and
spherical trigonometry. And they were right,this is an
art! What else can be reading an ECDIS device or a
GPS display today? This ancient art, also known to the
Arabs, has become routine!
But what can happen if these modern, ergonomic,
smart systems fail? Art exists but we no longer have
artists!
This paper intends to bring back to the stage of
navigation the method of determining the fix of the
ship using astronomical observations, a method that
has proved particularly useful and accurate during
ocean voyages both in peacetime and during major
military events of the last century.
In the vastness of the Atlantic Ocean, the Sun and
the stars were the guides of those who had taken on
the noble mission of navigator.
But why in the era we were talking about at the
beginning could astronomical navigation still be
needed? Why use the formulas and tools we already
see in museums, now that everything is computerized
and is about to become robotic? Why right now when
we start talking about artificial intelligence?
For the simple fact that under certain conditions
the modern systems I mentioned may be "out of
work" or may be the victims of a large-scale cyber
attack.
Therefore, this paper presents a method for
determining the fix of the ship with astronomical
observations approved by the IMO as an international
regulatory body in the field, based on the use of a
Fix Position Using Two Astronomical Line Of Position
A. Buslă
Constanta Maritime University, Constanta, Romania
ABSTRACT: The Intercept Method (originally known as the Intercept Azimuth method) was created in 1875 by
the French captain (latter admiral) Marq de Saint Hilaire. The method is still used today and is accepted by the
International Maritime Organization as an component element of the Standards of Training, Certification and
Watch-keeping for Seafarers. This paper aims to present the way of graphically determination of the vessel's fix
position with two astronomical position lines computed using the intercept method.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 15
Number 2
June 2021
DOI: 10.12716/1001.15.02.17
396
simple mathematical formula and the use of a pocket
scientific computer to which are added the correction
tables for the height measured with the sextant.
The determination of the coordinates of the
astronomical fix of the ship is done through a
graphical process that only needs the classic tools for
chart work.
Incredible but true, the accuracy offered by the
method is high enough, the error not being greater
than 0.1 Nm. [1–4]
2 LOP’S COMPUTATION
On October 10, 2020, at the chronometer time
CT=19h14m11s in DR position: Lat =34°13.4’ N ; Lon =
023°44.3’ W the following sights were taken and
recorded: Deneb star - sextant altitude Hs= 67°40.9'
and the Altair star – sextant altitude Hs=62°09.5'.
Height of eye is 14 m and index correction IC = +1.5'.
The chronometer correction is CC= + 1m12s. The
astronomical fix coordinates are required.
Meridian angle (t) and declination (Dec)
computation
Table 1. LOP 1 Deneb
Computed altitude (hc) and intercept (a)
computation
The following formula is used to determine the
computed altitude (Hc):
. . .
part a partb
Hc sin Lat sin Dec cos Lat cos Dec cos t=+
Table 2. Computed altitude (Hc)
Zenith angle (Z) and azimuth (Zn) computation
Zenith angle (Z) is computed using the formula
below:
The zenith angle given by this formula has a
quadrantal size.
Table 3. Quadrantal size of zenith angle
The following table helps to find the quadrant of
horizon where the body is sighted.
Table 4. Quadrantal size of zenith angle
NOTES:
HPV represents the altitude of the celestial body in
Prime Vertical. HPV is computed using the following
formula:
PV
sin H = sin Dec cosec Lat
To convert the zenith angle (Z) into azimuth (Zn)
the following Conversion Table has to be used:
Table 5. Conversion table
LOP 2 Altair
Computed altitude (hc) and intercept (a)
computation
Table 6. Computed altitude (Hc)
Zenith angle (Z) and azimuth (Zn) computation
397
Table 7. Quadrantal size of zenith angle
Table 8. Quadrantal size of zenith angle
Usually the method requires a few steps:
1. take the sights (the optimal situation is to be two
observers on the bridge)
2. note the chronometer time (CT) to be able to
compute UT for the moment of sight and the DR
position of the vessel for the moment of sight
3. identify the two sighted bodies (if necessary)
4. compute the intercept (a) and azimuth (Zn) for each
sight
3 GRAPHICAL CONSTRUCTION
Algorithm
1. prepare a graphical scale of latitude and longitude
on a blanc piece of paper (see the picture bellow)
− draw a vertical line in the middle of the white
paper and mark its top with an arrow; label it as
TN (True North). This vertical line represents
for us the true meridian of vessel’s DR position
− draw a horizontal line which will be used as
longitude scale; mark the intersection point as
origin (O) of a latitude-longitude graphical
scale
− divide the horizontal line into equal segments
from the origin to the edge and label the
obtained points as minutes of longitude (1’,
2’,…etc.)
− from the origin (O) draw a line that makes with
the longitude scale an angle equal to DR Lat
− from each point on the longitude scale draw
perpendiculars till to the intersection with the
line drawn before; mark the intersection points
as minute of latitude. We have obtained a
graphical scale of latitude
2. plot the two LOPs on the blanc paper:
− choose a point for DRP on the meridian
(vertical line) and label it DRP
− draw a horizontal line through DRP which
represent DRLat
− plot the two azimuths from DRP using a
protractor and label them Zn1 and Zn2
− plot the two intercepts on each azimuth line
(points I1 and I2) from DRP toward the celestial
body (CB) if intercept is positive or away the
CB if intercept is negative. Measure the size of
intercepts on the latitude scale!
− draw the two line of position (LOP1 and LOP2)
as perpendiculars through the intercept points
I1 and I2. At the intersection of the two
astronomical LOPs there is the astronomical Fix
of the vessel
3. extract the fix coordinate as follows:
− draw a horizontal line through the Fix (the Fix
parallel of latitude) and a vertical one (the Fix
meridian)
− the difference of coordinates – difference of
latitude and difference of longitude - will be
sized as follows: the difference of latitude on
the DRP meridian or between the parallel of Fix
and parallel of DRP and the difference of
longitude between the two vertical lines
(meridians) or on the parallel of FIX position
− the difference of latitude will be measured on
the graphical latitude scale
− the difference of longitude will be measured on
the graphical longitude scale
− the geographical coordinates of the Fix position
will be computed using following formulas:
Lat DRLat DLat
Lon DRLon DLon
=+
=+
Inputs:
34 13',4
023 44',3
1 2,4
052 ,6
2 2,0
151 ,7
Lat N
DRP
Lon W
LOP a Nm
DENEB Zn
LOP a Nm
ALTAIR Zn
=
=
=+
=
=+
=
Figure 1. Graphic representation
398
Solution:
34 13',4
0',5
34 12',9
023 44',3
4',1
023 40',2
34 12',9
023 40',2
DRLat N
DLat
Lat N
DRLon W
DLon
Lon W
Lat N
Fix
Lon W
=
+ = −
=
=
+ = +
=
=
=
4 CONCLUSION
The application of the described method is carried out
in two steps. The first step is to perform the
calculations needed to determine the elements of the
astronomical position lines (LOP) that are azimuth
and intercept. The second step is to create the
graphical solution needed to determine the
geographical coordinates of the ship's position for the
moment when the observation were done.
The method is useful for verifying the accuracy of
the indications of the existing navigation systems on
board the ship as well as for substituting their work in
case of their failure.
The accuracy offered by the method is high enough
given the size of the aquatic space at ocean crossings.
To facilitate the use of method, it is recommended
to prepare by the time observation and computation
sheets whose fields should be completed step by step
in real time.
Mastering the method but especially its application
does not mean a return to the past but rather an
additional safety measure in keeping the navigation
accurate.
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