Finding accurate directions using a watch

Method for finding accurate directions by a common analogue watch.
by tonytran2015 (Melbourne, Australia).

#find North, #finding North, #compass, #direction, #by Sun, #bisector, #using watch, #with watch, #tilted watch, #inclined watch, #navigation, #without compass

This method uses a common 12-hour watch with analogue face for finding directions. Unlike the traditional method of using the hour hand of a flat lying watch, my method uses a watch tilted from the vertical and gives better accuracy for both North and South hemispheres including tropical zones. When applied to the arctic and antarctic regions, the watch is tilted by more than 67 degrees and lies almost flat on the ground; it becomes the traditional method using flat lying watch.
This method use the position of the Sun, time and known latitude angle to determine directions and Sun declination (therefore estimation of current month of the year).
The method for Northern latitudes is described below.

Method for Northern latitudes.
The word “bisector” here is used to mean the bisector of the angle between the midnight/midday marking and the hour hand.

DirectionBySun_12N

The red line is the bisector. The line CB is drawn on a card representing the half-plane to enable accurate alignment to the Sun

WatchCompass_22NL

The bisector is in the opposite direction of a corresponding 24 hr hand on a 24 hr dial

1/- Hold the watch so that its AXIS rises above the horizontal plane by an angle equal to the latitude of the region. That is its face points to somewhere in the sky and its back is angled downwards into the ground.
2N/- Determine the half-plane limited by the axis of the watch and containing the bisector. This half plane revolves clockwise about the axis of the watch once every 24 hour and goes through the mid-day marking at noon.
3N/- Hold the watch in such composure and rotate your whole body around your vertical axis by your feet until the Sun lies in the above half-plane.
4N/- Alternative to step 3N, observer can determine on the semi-plane a half-line CB from the centre C of the watch dial, forming with the watch axis an angle equal to the angle between the direction to the Sun and the Celestial axis. The half-line CB starts from the center of the dial and is nearly in the direction of the bisector. It rises above the dial toward the glass and points through the glass of the watch during summer time and dives below the dial into the movement compartment of the watch and points through the movement of the watch during winter time. This half-line always points to the Sun if this watch displays the local time and the face of the watch and its axis point to the North Star. Instead of trying to have the half-plane containing the Sun, observer can try to have CB pointing to the Sun. This gives better accuracy.
5N/- At that position, the watch face and its AXIS are POINTING to the North Star. Tilt the watch further, until it lies horizontally. In this horizontal position, the mid-day marking is pointing South and the 6 o’clock marking is pointing North.

watchcompassJ

Figure: Summary of finding North by a watch. Red hand is the bisector of 0 hr direction and the hour hand; green hand is its reflection across the (6-12) axis. Axis C-BN for Northern hemisphere is parallel to red hand at equinox days and is (raised above)/(dipped below) the watch dial by 23 degrees at local summer/winter solstice. Axis C-BS for Southern hemisphere is parallel to green hand at equinox days and is (raised above)/(dipped below) the watch dial by 23 degrees at local summer/winter solstice. Green drawing marks are for Southern hemisphere and are the mirror reflection of red drawing marks.

Method for Southern latitudes.
The word “left-right flip of bisector” here is used to mean the the bisector the bisector of the angle between the midnight/midday marking and the hour after being flipped left-to-right, that is after being reflected across the line mid-day to 6 o’clock on the dial.

1/- Hold the watch so that its AXIS rises above the horizontal plane by an angle equal to the latitude of the region. That is its face points to somewhere in the sky and its back is angled downwards into the ground.
2S/- Determine the half-plane limited by the axis of the watch and containing the left-right flip of bisector . This half plane revolves anti-clockwise about the axis of the watch once every 24 hour and goes through the mid-day marking at noon.
3S/- Hold the watch in such composure and rotate your whole body around your vertical axis by your feet until the Sun lies in the above half-plane.
4S/- Alternative to step 3S, observer can determine on the semi-plane a half-line CB from the centre C of the watch dial, forming with the watch axis an angle equal to the angle between the direction to the Sun and the Celestial axis. The half-line CB starts from the center of the dial and is nearly in the direction of the bisector. It rises above the dial toward the glass and points through the glass of the watch during summer time and dives below the dial into the movement compartment of the watch and points through the movement of the watch during winter time. This half-line always points to the Sun if this watch displays the local time and the face of the watch and its axis point to the Southern Celestial pole. Instead of trying to have the half-plane containing the Sun, observer can try to have CB pointing to the Sun. This gives better accuracy.
5S/- At that position, the watch face and its AXIS are POINTING to the Southern Celestial pole. Tilt the watch further, until it lies horizontally. In this horizontal position, the mid-day marking is pointing North and the 6 o’clock marking is pointing South.

No ambiguity in equatorial latitudes.
The watch is placed almost vertically in equatorial latitudes by both methods. Methods for both Northern and Southern latitudes gives exactly the same outcomes.

Extension application for both hemispheres.

6/ This method applies equally well to the Moon when its declination as well as lateness relative to the Sun is known. If the Moon can be seen in day light, a navigator should continue from the so determined direction of the Celestial axis to take the declination of the Moon as well as its lateness (and its angular distance, which can be accurately measured using the divider) relative to the Sun for that day. He can then continue his accurate determination of Celestial axis during the Moon lit part of that night by replacing the unseen Sun by the Moon together with its value of declination and its lateness supplied by himself. (Remember that the Moon increases its lateness relative to the Sun by a further 50 minutes in every 24 hours).

Figure: Summary of finding North by a watch.

Actual field test.
The author has tested these methods and found them to be applicable, easy and accurate to much better than 30 degrees for latitudes from 0 to 40 degrees. The accuracy is better than 10 degrees when the Sun has low altitude.

Explanation notes.
N1/- The word “watch” here applies to any watch or clock.
N2/- When a watch or a clock dial is hung on a vertical wall, its midnight marking is at the highest position. If the hour hand of a watch completes one revolution in 24 hours the watch is called a 24-hour watch; if it completes in 12 hour the watch is called a 12-hour watch. Most watches and domestic clocks are 12-hour ones. The bisector of the midnight marking and the hour hand of any 12-hour watch complete one revolution in 24 hour. It moves like an imaginary 24-hour hand on that watch.
N3/-The axis of the watch is the oriented line (Note that it is more than “the oriented half-line”.) going through the center of the watch at right angle to its dial disc and is parallel to the rotation axes of both the minute pointer (or “minute hand”) and the hour pointer (or “hour hand”). The direction chosen on the line is from the back to the front face of the watch.
N4/- A watch display local time when it shows 12 o’clock when the Sun reaches its highest point in the sky.
N5/- The angle between the North Star and the Sun varies like a sine wave with amplitude of 23.5 degrees; it should be 90 degree during Spring and Autumn equinoxes and 90-23.5 degree at Northern Summer solstice (21st June) and 90+23.5 degree at Northern Winter solstice (21st of December).
N6/- To tilt the watch accurately as required by step1, we can carry out the following steps:
1a/- Note that hour markings on 12hr watch dials are separated by 30 degrees. Other angles can be similarly worked out.
1b/- Hold the watch verticaly with 0hr at highest position.
1c/- Rotate the watch (either left or right, it does not matter) by angle lamda, keeping its dial plane unchanged. The line 0hr-6hr now makes an angle lamda with the vertical line.
1d/- Keep the axis 0hr-6hr fix in space, rotate the watch around it until the dial is pointing upwards evenly. The watch dial is now tilted upward by the angle lamda.

Relevant to this topic is also a method of finding North and time using neither watch nor compass [1].

Reference

[1]. tonytran2015, Finding North direction and time using the Sun and a divider, https://survivaltricks.wordpress.com/2015/05/06/finding-directions-and-time-using-the-sun-and-a-dividing-compass/
posted on May 06th, 2015.

RELATED SURVIVAL BLOGS (Added in December 2016) 

Caution in finding North by bisector line of a horizontal watch. Posted on October 28, 2015

Finding directions and time using the Sun and a divider., posted on May 6, 2015<<<—This is my MOST USEFUL novel technique.

wpid-dividermwp3e2c2.jpg

Finding North direction and time using the hidden Sun via the Moon . Posted on July 6, 2015This is a useful technique.

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Finding North and time by stars. Posted on August 28, 2015
PolrNorthNC20const8

 wpid-bstarsn20b.jpg

Finding North and time with unclear sky. Posted on October 17, 2015

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Finding accurate directions by a watch .

Method for finding accurate directions by a watch in any latitude.

by tonytran2015 (Melbourne, Australia).

#find North, #finding North, #compass, #direction, #bisector, #using watch, #with watch, #tilted watch, #inclined watch, #navigation, #without compass

This method uses a watch with analogue face for finding directions. Unlike the traditional method of using the hour hand of a flat lying 24-hour watch, my method uses a 24-hour watch tilted from the vertical and gives better accuracy for both North and South hemispheres including tropical zones. When applied to the arctic and antarctic regions, the watch is tilted by more than 67 degrees and lies almost flat on the ground; it becomes the traditional method using flat lying 24-hour watch.

The method assumes an analogue 24-hour watch is in use. For any analogue 12-hour watch, the bisector between its midnight marking and its 12-hour hand can serve as an imaginary 24-hour hand. From the latitude of the place, the position of the Sun in the sky and the local time shown on the watch, the method gives out the Cardinal directions and declination of the Sun (therefore an estimation of the date and month in the year.

The method for Northern latitudes is described first and is followed by the method for Southern latitudes.

Method for Northern latitudes:

WatchCompass_22NL

A 24-hour watch shown only with hour hand

1/- Hold the watch so that its AXIS rises above the horizontal plane by an angle equal to the latitude of the region. That is its face points to somewhere in the sky and its back is angled downwards into the ground.

2N/- Determine the half-plane limited by the axis of the watch and the backward pointing direction of the 24-hr pointer (the hour hand of the 24hr watch). This half-plane will contain the Sun if this watch displays the local time and the face of the watch and its axis points to the North Star.

3N/-Determine ON THIS SEMI-PLANE a half-line CB from the centre C of its dial, forming with the watch axis an angle equal to the angle between the direction to the Sun and the Northern Star. The half-line CB starts from the centre of the dial and is nearly in the opposite direction of the 24-hour hand (pointer). It rises above the dial toward the glass and points through the glass of the watch during summer time and dives below the dial into the movement compartment of the watch and points through the movement of the watch during winter time. This half-line always points to the Sun if this 24-hr watch displays the local time and the face of the watch and its axis point to the North Star.

4N/- Hold the clock in such composure and rotate your whole body around your vertical axis by your feet until the above half-line CB points towards the Sun (Therefore the Sun lies in the half-plane limited by the watch axis and the backward pointing direction of the 24-hour pointer). At that position, the watch face and its AXIS are POINTING to the North Star.

5/- The projection of the Celestial axis onto the horizontal ground is then the terrestrial Northern-South direction.

The method for determining the North-South direction in the Southern hemisphere is different but is very similar to this method for the North. Paragraphs 2N, 3N and 4N are appropriately replaced by 2S, 3S and 4S for Southern latitudes as in the following.

Method for Southern latitudes:

2S/- The UP-DOWN REFLECTION OF THE HOUR HAND of a 24-hour watch is its imaginary hour hand going anti-clockwise, pointing downwards at midnight and upwards at midday. It is the reflection of the hour hand of a vertically hung 24-hour watch through any water surface below it.

Determine the half-plane limited by the axis of the watch and the up-down reflection of the hour hand. This half-plane will contain the Sun if this 24-hr watch displays the local time and the face of the watch and its axis point to the Southern Celestial pole, while the back of the watch points through the ground to the North Star.

3S/-Determine ON THIS SEMI-PLANE a half-line CB from the centre C of its dial, forming with the watch axis an angle equal to the angle between the direction to the Sun and the Southern Celestial pole. The half-line CB starts from the centre of the dial and is nearly in the direction of the up-down reflection of the 24-hour hand. It rises above the dial toward the glass and points through the glass of the watch during Southern Hemisphere’s summer and dives below the dial into the movement compartment of the watch and points through the movement of the watch during the Southern Hemisphere’s winter. This half-line always points to the Sun if this 24-hr watch displays the local time and the face of the watch and its axis point to the Southern Celestial pole.

4S/- Hold the clock in such composure and rotate your whole body around your vertical axis by your feet until the above half-line CB points towards the Sun (Therefore the Sun lies in the half-plane limited by the watch axis and the up-down reflection of the 24-hour pointer). At that position, the watch face and its AXIS are POINTING to the Southern Celestial pole while the back of the watch points through the ground to the North Star.

No ambiguity in equatorial latitudes.

The watch is placed almost vertically in equatorial latitudes by both methods. Methods for both Northern and Southern latitudes give exactly the same outcomes.

Adaptation for use with any common 12 hr watch.

The method is easily  modified for application to any common 12 hr watch. In the following figure, the red hand (the bisector of the 0hr direction and the hour hand of a common 12hr watch ) is in the opposite direction of the hour hand of a 24hr watch.

WatchCompassG

Figure: Summary of finding North by a watch. Red hand is the bisector of 0 hr direction and the hour hand; green hand is its reflection across the (6-12) axis. Axis C-BN for Northern hemisphere is parallel to red hand at equinox days and is (raised above)/(dipped below) the watch dial by 23 degrees at local summer/winter solstice. Axis C-BS for Southern hemisphere is parallel to green hand at equinox days and is (raised above)/(dipped below) the watch dial by 23 degrees at local summer/winter solstice. Green drawing marks are for Southern hemisphere and are the mirror reflection of red drawing marks.

 

 

 

 

 

 

 

 

 

 

 


Figure: Summary of finding North by a watch.

Actual field test

The author has tested these methods and found them to be applicable, easy and accurate to within 30 degrees for latitudes from 0 to 40 degrees.

Explanation notes:

N1/- The word “watch” here applies to any watch or clock.

N2/- When a watch or a clock dial is hung on a vertical wall, its midnight marking is at the highest position. If the hour hand of a watch completes one revolution in 24 hours the watch is called a 24-hour watch; if it completes in 12 hour the watch is called a 12-hour watch. Most watches and domestic clocks are 12-hour ones. The bisector of the midnight marking and the hour hand of any 12-hour watch complete one revolution in 24 hour. It moves like an imaginary 24-hour hand on that watch.

N3/-The axis of the watch is the oriented line (Note that it is more than “the oriented half-line”.) going through the centre of the watch at right angle to its dial disc and is parallel to the rotation axes of both the minute pointer (or “minute hand”) and the hour pointer (or “hour hand”). The direction chosen on the line is from the back to the front face of the watch.

N4/- A watch display local time when it shows 12 o’clock when the Sun is highest in the sky.

N5/- The angle between the North Star and the Sun varies like a sine wave with amplitude of 23.5 degrees; it should be 90 degree during Spring and Autumn equinoxes and 90-23.5 degree at Northern Summer solstice (21st June) and 90+23.5 degree at Northern Winter solstice (21st of December).

(Added in December 2016) RELATED SURVIVAL blogs

Finding directions and time using the Sun and a divider., posted on May 6, 2015.

Finding accurate directions using a watch, posted on May 19, 2015 .

Finding North direction and time using the hidden Sun via the Moon . Posted on July 6, 2015

Finding North and time by stars. Posted on August 28, 2015

 

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Using polarized light to locate the Sun when it is hidden from view.

Using polarized light to locate the Sun hidden behind clouds.

by tonytran2015 (Melbourne, Australia).

#find, #finding, #Sun, #North,  #navigation, #survival, #find the Sun, #polarize, #light, #ray, #Sunlight, #Sunray, #sunglasses, #compass, #direction, #time

Anti-glare polarizing sunglasses reduce horizontally polarized rays. They can also be useful in locating the Sun even when it is hidden from view by clouds or by the horizon. Locating the Sun enables determination of compass direction and time for navigation without any compass.

1. Basic information

Two walkie-talkies are in the best condition for communication when their two antennas are parallel and at right angle to their line of view. The electric waves traveling between them have their electric field parallel to the emitting antenna and the varying electric field is at right angle to the line of transmission. The electromagnetic waves is said to be polarized in the direction of the emitting antenna.

Light is just electromagnetic waves at much higher frequencies than our familiar radio waves. Light can be polarized too. Light rays from incandescent sources are randomly polarized like radio waves coming from a walkie-talkie which is randomly orientated before each transmission. On the average we don’t see any polarization from a source with randomly changing orientation. However after a partial reflection (accompanied by a partial transmission) at an interface between two transmission media, the reflected and the transmitted rays from an non-polarized ray are partially polarized.

Polarizing sunglasses can favour light polarized in one direction and discriminate against light polarized in the other direction. With the same pair of sunglasses we can see two different colours and brightnesses depending on the orientation of the glasses when viewing the same source. This is illustrated in the following figure.

Be certain that your polarizing glasses really reduces sunlight reflecting off horizontal road surfaces before trying subsequent instructions here; each of the glasses must be individually tested and its direction of polarization verified.

2. Different colours and degrees of brightness seen from the same source of light through polarizing sunglasses

skylight through polarizing sunglasses

The cross with two different colours on the source denotes the two different colours seen through two orientations of the same sunglasses.

3. Seeing the polarized lights of the sky

polarization of scattered blue sunlight

The polarization of scattered blue sunlight in the sky

Blue light from the sky is the result of Rayleigh scattering of photons from sunlight by molecules in the sky. This scattered light is highly polarized as seen in the following practice:

Search for a large clear patch of sky with no cloud. Look through the polarizing glasses. Rotate the glasses about the axis of view to see the sky lightens and darkens alternatingly with the angle of rotation. The darkening is most profound when the Sun is at right angle to the line of view.

4. Locating the hidden Sun.

Locating the hidden Sun using polarized light

Locating the hidden Sun from two patches of clear sky.

1/- Search for a large clear patch of sky with no cloud. Rotate the glasses about the axis of view until the clear sky becomes most darkened. The Sun is then on the great circle perpendicular to the line joining the left and right spectacles (Being the intersection of the Celestial sphere and the symmetry plane of the sunglasses). The darkening is most profound when the Sun is at right angle to the line of view.

2/- Repeat with a second clear patch of the sky. Two large clear patches of the sky can give out the position of the hidden Sun. It is at the intersection of the two so obtained great circles in the sky.

3/- The position of the Sun below the sky-line can also be found using polarized light-rays from the clear sky above its (underground) line of view. If this picture is turned up side down with a horizon line added above its Sun it will illustrate how to find the Sun when it is below the horizon (The polarization is most profound on the clear sky at 90 degree to the (underground) line of view of the Sun.).

Reference [2] gives some interesting history of the early applications of polarization of light. Currently there have even been hypotheses that the Vikings had used polarized light to locate the Sun since antiquity with pieces of birefringent calcite crystals [1].

References.

[1]. Cahal Milmo, Not just the stuff of legend: Famed Viking ‘sunstone’ did exist, believe scientists,
The Independent, http://www.independent.co.uk/news/science/archaeology/not-just-the-stuff-of-legend-famed-viking-sunstone-did-exist-believe-scientists-8521522.html, 06 March 2013, 21 May 2015.

[2]. Unknown Authors, Polarization (waves), Wikipedia, http://en.wikipedia.org/wiki/Polarization_%28wave… 26 May 2015

[3]. Unknown Authors, Following the Light of the Sky, polarization.net, https://www.polarization.com/compass/compass.html… Accessed 16 May 2015 05:40:14 GMT.

[4]. tonytran2015, Finding North direction and time using the Sun and a divider, http://www.survivaltricks.wordpress.com/, 06 May 2015.

(The following is added after 20 May 2017)

[5]. Israel Ramirez, https://www.quora.com/What-can-animals-that-can-see-the-polarization-of-light-see-that-other-animals-cannot, 28 Nov 2016.

[6]. tonytran2015, Finding North in the polar zones using equatorial stars and the Sun, https://survivaltricks.wordpress.com/2017/05/24/finding-north-in-the-polar-zones-using-equatorial-stars-and-the-sun/, posted May 24, 2017

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Finding North in the polar zones using equatorial stars and the Sun, posted May 24, 2017Navigating with an AM MW radio receiver, posted January 17, 2017The Scorpius constellation, posted January 8, 2017, The Orion constellation., posted December 26, 2016, Rice as emergency food.Using GPS in off-grid situationsSlide Sky-Disks with grid masks showing azimuths and altitudesSlide Sky-Map for displaying tropical stars.

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Finding directions and time using the Sun and a divider.

by tonytran2015 (Melbourne, Australia).

#find North, #finding North, #compass, #direction, #time, #Sun, #divider, #navigation, #survival, #bare hands.

There are times when you neither have your watch nor can use any magnetic compass in the location but you want to find out the time and the North-South directions. This method is useful for those such difficult situations. The divider or the dividing compass in the title of this article is actually not necessary, it is helpful but it only improves the accuracy of the method and can be replaced by any two straight sticks or even by your two stretched arms. Those situations are not very unlikely and one such situation may arise if you get lost without having your watch while traveling or if you find yourself without your watch while traveling inside a bus or a train. The method from this article gives both the North direction and the local time (local time starts its noon when the Sun is highest, local time is close to but is not the same as the official zonal time declared by the local government there.) from the position of the Sun in the sky, the latitude and the day of the year.

1. Finding North in 7 steps.

DividerMethod2Cb

Figure: Finding North direction and local time with a divider (viewed against the Sun).

DividerMWP3e2c2.jpg

Figure: Finding North direction and local time with a divider (viewed against the Sun).

1.1/- Let the two legs of the divider be CA and CB. Let CA and CB of the divider form an angle ACB equal to that from the lower Celestial pole to the Sun.  This angle is obtainable from the declination of the Sun and can also be easily worked out by the observer. (A divider or a dividing compass is a compass with two long legs having pointed ends. The lower Celestial pole is the Celestial pole below the ground plane of the observer.)

1.2/- Point the second leg CB of divider to the Sun. Rotate the divider about its second leg CB so that its first leg CA points slightly downwards to the ground, inclined to the ground by an angle equal to the local latitude while leg CB still points to the Sun.

1.3/- There are usually two such dipping positions for leg CA, each has its dipping angle equal to the latitude angle. Only one position for CA is the correct one.

image

Figure: Aligning the divider along the directions of Sun rays and the laying of compass points.

1.4/- The correct choice for the position of leg CA is given by the following rules: 4a/- In Northern latitude and during sunrise half-day (alternatively in Southern, during sunset half-day): Downward axis points to the left of the ray from the Sun. 4b/- At Noon: The two possible positions of leg CA coincide and there is only one single position for leg CA. 4c/- In Northern latitude and during sunset half-day (alternatively in Southern, during sunrise half-day): Downward axis points to the right of the ray from the Sun. 4d/- Observer must be absolutely certain of being in which half (sunrise or sunset) of the day as any mixing up between the sunrise and the sunset halves of the day will give an error in direction of more than 90 degree. 4e/- The correct choice makes leg CA points downwards to the lower Celestial pole and leg CB rotates around leg CA exactly one whole turn every 24 hours. (Users can easily make up ways to remind themselves of the choice dictated by 4a, 4b and 4c.)

image

Figure: Finding North direction and time using the Sun and a divider.

1.5/- The terrestrial North-South is the projection of leg CA onto the ground surface. This method gives directions with an accuracy of better than 15 degrees of angle when the Sun is far away from the zenith of the observer.

divider80cl.jpg

Figure: Reading time from the divider.

SunCelestSphereFigure: Daily travel of the Sun on the Celestial sphere.

1.6/- Imagine having a 24-hr watch dial mounted onto the leg CA of the divider with the marking for 0th hour on the highest position. The local time is then given by the position of leg B relative to this imaginary dial. Time reading from the position of CB gives local time with an accuracy smaller than 30 minutes.

66CL3

Figure: Summary of the steps for all solar position (above and below the horizon).

The author has been using his method for more than ten years and found it to be applicable, convenient and accurate for both Northern and Southern latitudes.

1.7/ If the Moon can be seen in day light, a navigator should continue from the so determined direction of the Celestial axis to measure the declination of the Moon and its angular distance from the Sun for that day. He can then continue his accurate determination of Celestial axis during the Moon lit part of the night by replacing the unseen Sun by the Moon together with its value of declination and angular distance from the Sun supplied by himself.

2.Cautionary notes.

C1/- Newcomers to this method should only practice it when the Sun has low elevation angle to get used to the right and left hand selection rules and to the judgement on the amount of dipping of the leg CA to find the Celestial axis.

C2/- People who fall asleep because of exhaustion or sickness may get confused between the two halves of the day on waking up and may make mistakes when using this method at that moment.

3.Explanation notes.

N1/- There are the North and South Celestial poles in the Celestial sphere. The line joining the North and South Celestial poles is called the Celestial axis. The lower Celestial pole is the one that is under the horizontal plane of the observer, therefore it can not be seen by the observer ! The Southern and Northern Celestial poles are respectively the lower Celestial poles of the Northern and Southern hemispheres of the Earth. The sunrise half-day is from midnight to noon (0 hr at midnight to 12 hr at noon). The elevation angle of the Sun increases during this time. The sunset half-day is from noon to midnight (12 hr at noon to 24 hr at midnight). The elevation angle of the Sun decreases during this time.

N2/- The Celestial axis for any location can be easily found by the following method: Have three similar thin sticks. Tie one of the ends of each stick to a common point P. Let the three sticks point respectively to the positions of the Sun at sunrise, sunset and noon. This can be easily done on any level sandy surface as two sticks can lay on the ground pointing from point P to sunrise and sunset directions while the third stick already has one of its ends resting on P on the ground and only needs small help to be kept in position. Let a sphere (e.g. an orange fruit or a soccer ball) with suitable size touch all three sticks at the same time (The surface may have to be dug around the sphere so that it can touch all three sticks at the same time.). The line joining P to the centre of the sphere is the Celestial axis.

image

Figure: Declination of the Sun from a rough graph.

N3/- The angle from the lower Celestial pole to the Sun varies like a sine wave with amplitude of 23 degrees 27minutes and period of nearly 365.25 days. It varies slowly and periodically during the year. It is the sum of 90 degrees and the declination of the Sun. The angle is exactly equal to 90 degree on Spring and Autumn equinox days (21st of March and 23 rd of September) It reaches a maximum value of 90+23.5 on local summer Solstice days (21st of June for Northern hemisphere and 21st of December for Southern hemisphere). It reaches a minimum value of 90-23.5 on local winter Solstice days (21st of December for Northern hemisphere and 21st of  June for Southern hemisphere). Equinox and Solstice days of the years are the principal days for working out these values .

N4/- The markings on the dial of any analogue watch can be used to measure the angles used for the divider. Any quarter of the watch dial gives an angle of 90 degrees. One hour marking on any 12-hr watch therefore gives an angle of 30 degrees.

N5/- A watch face can be drawn on the ground to obtain more accurate value of solar declination as in the following figure (see reference [1]).

solar-declination-by-a-watch-face

Figure: Determining solar declination using a watch face. (The lines “SOLAR DECLINATION Its rough estimate is required for Fine Alignment of the watch” are to be ignored.)

4.Additional notes.

image

Figure: Improvised instructional divider made from a stylish, pen-styled compass by extending its legs using plastic drinking straws.

The instructional divider is built from a pocket, pen-styled (Vietnamese, Thien-Long brand) compass. The two legs are extended by pushing two plastic drinking straws (in yellow colour) onto the cylindrical ends of the compass. Fortunately, the fit is just right. The device works very well and costs me under $3USD !

Reference (added 09 Mar 2017)

[1]. tonytran2015, , survivaltricks.wordpress.com, posted on February 13, 2017

RELEVANT  SURVIVAL blogs (Added after February, 2017) 

, posted on February 13, 2017

Finding accurate directions using a watch, posted on May 19, 2015

Finding North direction and time using the hidden Sun via the Moon . Posted on July 6, 2015

Finding North and time by stars. Posted on August 28, 2015

Finding North and time with unclear sky. Posted on October 17, 2015

wpid-bstarsn20b.jpg

, posted July 22, 2016

NorthByKnownStar

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