Hostile Vessel Operating in this area
N
E
Lighthouses in the Sky
Junior Navigation
Chapter 1
5
1
Learning Objectives




Define terms: altitude, circle of position,
geographical position, intercept, and celestial line
of position.
Given altitude, determine the radius of a circle of
position and vice versa.
State why accurate time is important in celestial
navigation.
Describe the altitude-intercept method of plotting
a celestial line of position.
2
Apparent
Body
Terms
GHA & Dec
UL
Body
Dec
When body is at your zenith:
Latitude = Dec and
Longitude = GHA
Zenith
ha
Observer’s Eye
Sensible Horizon
Geoidal Horizon he
hs
Ho (Altitude)
DR
GP
dip
3
Nadir
LL
Law of Cosines
(cos LHA x cos Lat x cos Dec) + (sin Lat x sin Dec) = sin Hc
convert sin Hc to Hc (calculated sextant height)
Difference between Hc and Ho provides distance from
your DR to COP.
[sin Dec – (sin Lat x sin Hc)] / (cos Lat x cos Hc) = cos Z
convert cos Z to Zn provides direction (azimuth) to GP.
4
The Fundamental Idea

In AP, a Radar Fix was determined by plotting two
LOPs taken from radar.
5
Plotting a Circle of Position

You need to know:



Direction from observer to the GP of the body;
and
Distance from observer to the GP of the body;
but first –
You need to know how to convert altitude
difference to nautical miles.
6
Angular Distance

Radius of a circle of position is equal to 90°
minus the altitude (1º latitude = 60nm).
90º – 90º = 0º
0º x 60nm = 0nm
90º – 0º = 90º
90º x 60nm = 5400nm
?
90º – 30º = 60º
60º x 60nm = 3600nm
7
COP and Altitude

At 1034 an observer in Galveston measures the
sun’s altitude to be 77°41.5´. What is the
radius of the COP?
90°00.0´
–77°41.5´
12°18.5´
12° x 60 nm/degree
= 720.0 nm
18.5´ x 1 nm/minute = 18.5 nm
Total = 738.5 nm (radius of COP)
8
COP and Altitude

At the same time observer in Los Angeles
measures the sun’s altitude to be 57°34.1´.
What is the radius of the COP?
90°00.0´
–57°34.1´
32°25.9´
32° x 60 nm/degree
= 1920.0 nm
25.9´ x 1 nm/minute =
25.9 nm
Total = 1945.9 nm (radius of COP)
9
Altitude-Intercept Method

At 10-34-15 a sight of the sun is taken.
Recorded altitude = 57°34.1’ COP 1,945.9nm
10
Altitude-Intercept Method

Calculate true bearing (azimuth) and altitude
(Hc) from DR using Law of Cosines
Zn
11
Altitude-Intercept Method

Difference between Ho (observed altitude) and Hc
(calculated altitude) is the intercept
Ho 57º 34.1’
Hc 57º 24.1’
Diff
10.0’ towards
Intercept 10.0nm
When Hc is greater than
Ho,
your azimuth is the
 COP drawn as a straight
reciprocal
of computed
line perpendicular
to the
azimuth. azimuth
12
Altitude-Intercept Method

Label with time of sight and name of body
13
Altitude-Intercept Method

When you have only a single LOP, you obtain an
estimated position (EP)
14
Quiz
1. If two observers at different DR positions measure the altitude
of the same celestial body at the same time,
a. the observer closer to the GP of the body measures the
larger altitude.
b. the observer closer to the GP of the body measures the
smaller altitude.
c. both observers measure the same altitude.
d. the positions of the observers relative to the GP cannot be
determined because the azimuths from each observer are not
given.
15
Quiz
2. Polaris (the North Star) is located exactly over the
earth's north geographic pole.
a. True
b. False
16
Quiz
3. The vertical angle measured with a sextant between a
celestial body and the horizon is called:
a. azimuth.
b. intercept.
c. altitude.
d. zenith.
17
Quiz
4. A navigator determines the altitude of the sun to be
37°26.1'. What is the distance in nautical miles
between the navigator's position and the GP of Sun?
Solution:
90 ° - 37°26.1´ = 52° 33.9´
52° x 60nm/° = 3120.0nm
+ 33.9' x 1nm/' = +33.9nm
3,153.9nm
18
Quiz
5. The difference between the calculated altitude (Hc)
and the observed altitude (Ho) is called:
a. azimuth.
b. co-altitude.
c. altitude.
d. intercept.
19
Quiz
6. The method used in plotting a celestial LOP is called
“the altitude-intercept method”.
a. True
b. False
20
Quiz
7. The geographical position (GP) of a body is defined as
the point on the surface of the earth directly beneath
the center of the body.
a. True
b. False
21
End of
Lighthouses in the Sky
The Sextant
Junior Navigation
Chapter 2
22
Learning Objectives









Identify the parts of a sextant and understand how
a sextant works
Determine index error & index correction
Describe how to handle, maintain & stow a sextant
Describe techniques for taking Sun sights
Describe safety procedures for taking sights on a
boat
Record the time of a sight
Identify the ideal & practical accuracy limits
Identify erroneous sights in a run of sights
23
Describe the sight requirements for JN
Parts of the Sextant
Handle
Lanyard
Frame
Limb
Index Arm
Release Clamp
Arc (degrees)
Sight Tube
Micrometer (min)
Vernier (tenths)
Horizon Glass
Index Mirror
Horizon Shades
Index Shades
Telescope
Horizon
Whole Split
2X or 4X
Telescope
24
How a Sextant Works


The sextant set to 0°00.0´
The horizon will appear as an unbroken line when
the sextant is correctly adjusted
Split Field
Full Field
25
How a Sextant Works


Telescope aimed at the horizon
Index arm adjusted to the appropriate angle
Split Field
Full Field
26
Reading a Sextant

Accurate reading is necessary


Full turn of micro drum


0.1’ of arc equals 0.1 nm
moves index arm one degree
Vernier - auxiliary scale to interpolate the
minute scale of micrometer drum
27
Reading the Measured Angle
1. First read degrees from the arc
2. Then read minutes

from micrometer drum
3. Finally read tenths of minutes

from vernier
28
Reading a Measurement
Read the Arc
Index Mark
Read the Drum
Read the Vernier
40°02’
40°
40°02.6’
29
Reading a Measurement
32.6’
23.0’
51.3’
30
Sextant Error


Non-adjustable error
Adjustable error
 Telescope axis - not parallel to frame
 Index mirror - not perpendicular to frame
 Horizon glass - not perpendicular to frame
 Index mirror and horizon glass are not parallel
when sextant set to 0°00.0´
 Checking & adjustment procedures in Bowditch
 Should only be made by experienced persons
 Frequent adjustment might loosen screws
ASTRA IIIB
ASTRA IIIB
ASTRA IIIB
2000 4 24
31
Index Error (IE)



IE is common
In good quality metal sextants
 IE tends to remain fairly constant
In plastic sextants
 Checking IE critical
32
Determining Index Error (IE)



Set sextant to 0°00.0´
and sight on horizon
If 2 images of horizon
not superimposed OR
If horizon shows as
broken line
 IE present
33
Determining Index Error (IE)
To determine value of IE.
 Adjust micro until horizon
appears as straight line.
 IE is the sextant reading:
 If index mark is below
0°00.0´ is off the arc
 If index mark is above
0°00.0´ is on the arc
OFF THE ARC
ON THE ARC
Full Field
Split Field
34
Index Correction (IC)


IC - value applied to the altitude measured to
correct for IE
IC - always opposite to the sign of IE
 IE ‘on the arc’ requires negative IC


When it’s on, take it off
IE ‘off the arc’ requires positive IC

When it’s off, put it on
ON THE ARC
OFF THE ARC
35
Index Error


When the horizon line is continuous,
the index mark is between 0° and
+1° and the micrometer/ vernier
reads 4.5´
The sextant altitude (hs) is 34°23.6´




On or Off the Arc?
What is the IE?
What is the IC?
What is ‘ha’?
ON the Arc
+ 4.5’ when it’s on
– 4.5’ take it off
34º 19.1’
36
Index Error


When the horizon line is continuous,
the index mark is between 0° and
–1° and the micrometer/ vernier
reads 56.3´
The sextant altitude (hs) is 34°23.6´




On or Off the Arc?
What is the IE?
What is the IC?
What is ‘ha’?
OFF the Arc
– 3.7’ when it’s off
+ 3.7’ put it on
34º 27.3’
37
Caring/Cleaning for a Sextant









Delicate precision instruments
Handle sextant by grasping its frame or handle
- never by its limb, index arm, or telescope
Avoid touching mirrors except to clean them
Set sextant down on its legs - never mirror side
Never put sextant where it can fall
Stow sextant in its case in a secure spot
Clean mirrors with lens paper or soft lint-free cloth
Remove salt spray with fresh water
Lubricate with light coat of fine instrument oil 38
Sight-taking Supplies








Sextant (obviously)
Watch with second hand
Notebook/pencil – record sight data
Chart of the area
Tape measure
THEN
Familiarize yourself with your sextant
Practice taking sights at a beach or pier
 Natural horizon vs. dip short of the horizon
When comfortable, take sights from a boat
39
Bring Down the Sun






Set sextant to 00°00.0´
Move all horizon shades
into position
Aim it up at the sun
Sweep sky to find sun
If sun not visible, remove
shades, one at a time
When visible, select index
shades of same density
40
Bring Down the Sun
When the Sun is caught
 Release and slowly move
index arm forward while
rotating sextant downward
 Keep sun in view in
telescope constantly
 Continue until you are near
the horizon
 Adjust horizon shades, if
needed
 Sun also seen near horizon
41
Bring Down the Sun
When sun’s image near
horizon


Release clamp to
reengage tangent screw
Bring sun to appear on
the horizon, then
42
Swinging the Arc
43
Recording Sextant Altitude




Call out “Stand by” to Recorder
Recorder responds “Ready”
Adjust micrometer drum to place sun on horizon
When sun on horizon, call “Mark”
 Recorder notes time:
 Seconds, minutes, hour – in that order
 Read angle from sextant for Recorder
 Repeat steps for a run of sights
44
Alternate Method
 To take sights at predetermined intervals
 Call out “Stand by” to Recorder
 Recorder responds “Ready in xx seconds” and
begins countdown
 During countdown, adjust micrometer drum to
keep sun on horizon
 Recorder calls “Mark” when countdown complete
 Recorder notes time:
 Seconds, minutes, hour – in that order
 Read angle from sextant for Recorder
45
Taking Sights at Sea



Taking sights at sea can be difficult, sometimes
dangerous
Use a safety harness
Techniques: Hit and Run; Wait and See
46
Special Techniques




Dip short of the horizon
 Acceptable for JN sights
Back sight
 Acceptable for JN sights
Artificial horizon
 Not acceptable for JN sights
 OK for practice sights
See Appendix A for details
47
Accuracy of Sights
Modern marine sextant - readable to 0.1´
 Nautical Almanac data are given to 0.1´
 Sights timed to nearest second
 Error of 1 second in time lead to error of
0.25´ of arc
Practical Accuracy limited by:
 Skill of Observer Practice – Practice – Practice
 Quality of Sextant
 Stability of observing platform
 Visibility & Atmospheric Conditions

48
Runs of Sights


Taking several sights on a body improves
accuracy
Corresponding altitude changes should be
proportionately constant
 Positive direction for rising bodies
 Negative direction for setting bodies
49
Run of Sights
Time
14-16-43
Difference
58s
14-17-41
14-18-37
–10.4´
56s
–10.1´
55s
+5.1´
14-19-32
58s
14-20-30
Difference
–25.2´
Altitude
38°06.2’
37°55.8’
37°45.7’
37°50.8’
37°25.6’
50
Graphing a Run of Sights
51
JN Sight Requirements




Two Sun sights simulating RFix
 One upper and one lower limb sight
 Acceptable accuracy of all sights is 5nm
 Qualified ‘run’ of sights
 Sights with altitude greater than 75° are
discouraged
Recording your sights
 USPS Sight Log Form
Sight Folder must be completed before you can
take exam
Details in Appendix D
52
Art Mollica (E066699)
St Paul
1 of 1
JN Sight Requirements
2012
09-05-40
35º 45.4’
E
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09-06-40
35º 51.4’
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09-07-40
36º 02.8’
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09-08-40
36º 14.2’
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09-09-40
36º 24.8’
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Sun UL 0-00 +6 17-12-45
47º 00.8’
W
29 Jun
2
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3
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4
5
6
29 Jun
Ds 8.5 -0.3 44º 29.9’N 92º 18.7’W
Sun LOP, KP by GPS,
DST, D1.3m fm chart
Sun LL 0-00 +6
1
Ds 8.5 -.03 44º 29.9’N 92º 18.7’W
Sun LOP, KP by GPS,
DST, D180yd fm chart
7
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17-12-45
46º 55.8’
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8
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17-13-45
46º 49.4’
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8
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17-14-45
46º 42.6’
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17-15-50
46º 38.4’
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Arthur
Mollica
Sight Folder will also contain USPS SIGHT REDUCTION FORM
(SR96a)
for each of the selected sights and a USPS CLSSAPS (Form CLS86)
plotting the resulting RFix of these selected sights.
53
Quiz
1. When reading sextant altitude, in what order are
degrees, minutes, and tenths of minutes read?
1st Degrees
2nd Minutes
3rd Tenth of Minutes
Quiz
2. When timing sights, in what order are hours, minutes,
and seconds read from the watch?
1st Seconds
2nd Minutes
3rd Hours
Quiz
3. Before taking sights on the Sun, you sight the horizon
and align the direct and reflected images of the
horizon. Your Sextant reading is 1.8' on the arc.
a. What is the IE?
+1.8'
b. What is the IC?
-1.8'
Quiz
4. Before taking sights on the Sun, you sight the horizon
and align the direct and reflected images of the
horizon. Your Sextant reading is 58.2' off the arc.
a. What is the IE?
-1.8'
b. What is the IC?
+1.8'
Quiz
5. You need to use the shade glasses on the sextant
when taking sights on the sun.
a. True
b. False
Quiz
6. You take a run of sights on the Sun with the following
times of sights and sextant altitudes. Which of the
sights are probably erroneous?
WT
17-42-33
17-43-12
17-43-52
17-44-27
17-44-49
17-45-17
hs
27° 01.4'
26° 57.8'
26° 58.7'
26° 50.1'
26° 50.0'
26° 45.8'
Bad Sight
Bad Sight
Quiz
hs
27.05
Bad Sight
27
26.95
Bad Sight
26.9
hs
hs
26.85
26.8
26.75
26.7
42
42.5
43
43.5
WT
44
44.5
45
45.5
Quiz
7. What is the purpose of "swinging the arc" when taking a sight
with a sextant?
a. To help obtain a clear view of the horizon.
b. To be sure that the sextant is horizontal at the time of the
sight.
c. To help focus the body in the sextant telescope.
d. To be sure that the sextant is vertical at the time of the
sight.
The Sextant
End of
Junior Navigation
Chapter 2
62