Finding true North and time from the Sun with your fingers.

Finding true North and time from the Sun with your fingers.

by tonytran2015 (Melbourne, Australia).

Click here for a full, up to date ORIGINAL ARTICLE and to help fighting the stealing of readers’ traffic.

(Blog No. 149)

#find North, #finding North, #find true North, #North, #true North, #navigation, #find time, #time, #Sun, #fingers,

Finding true North and time from the Sun with your fingers.

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 North-South directions and the time. This method is useful for those such difficult situations. Those situations 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 true North direction and the local time from the position of the Sun using only your fingers.

Required preparatory practices

1. Practice holding each of your hands in the three principal postures as illustrated in the following three figures.

Summer Solstice

Equinox

Winter Solstice

Figures: Hand postures for Summer Solstice, Equinox and Winter Solstice. Click on individual figure to enlarge.

If this practice cannot be carried out due to body deformity or illness (such as rheumatism) then some other method of finding North should be used instead.

The equinox posture is to be used around Mar 21st and Sep 23rd equinoxes while Summer and Winter Solstice postures are to be used around your local Summer and Winter solstices respectively.

The index finger in these postures is always aligned with the forearm and is to be kept in line with the line from the elbow to the tip of the index finger.

The angle between the index and the middle fingers should have value of:
90 degrees for Equinox posture
90-23= 67degrees for Winter Solstice posture and
90+23= 113 degrees for Summer Solstice posture. The above angles for Summer Solstice, Equinox and Winter Solstice postures are equal to the angles between a clock hand pointing at 0 minutes and
19 minutes,
15 minutes,
11 minutes respectively. These angles are represented by angles between positions of watch hands on a watch face shown in two following figures.

EcoDriveDuo

Summer Solstice

EcodriveDuo2

Winter Solstice

Figures: Angles between fingers for hand postures at Summer Solstice, Equinox and Winter Solstice are represented by angles between positions of watch hands on this watch face. The long white hand pointing at 0 minute of the watch-face represents the direction of the left index finger of the user of this method while the long red hand represents the direction of his left middle finger (see text).

The long white hand pointing at 0 minute of the watch-face represents the direction of the left index finger of the user of this method while the long red hand represents the direction of his left middle finger.

The angle between the hands on each watch-face has been chosen to match the angle between the line to the Sun on the respective date and the line to the Celestial pole below the horizon. The angle between the red hand and the thick white hand pointing at 15 minutes represent the declination angle of the Sun (or its negative, depending on the observer being in the Southern or Northern terrestrial hemisphere). The variation of that angle through various dates of the year can be found in previous blogs [1,2].

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.)

2. Determine the slope to your Celestial pole.

Sun on Celestial Sphere

Figure: The Sun, the Moon and the stars are attached to a Celestial sphere which encloses the Earth like a giant rotating cage. The cage rotates around the Celestial axis (in cyan-blue color) joining the its two points called the Celestial poles. The horizontal ground of an observer at the center of the celestial sphere is represented by the horizontal great circle of the Celestial sphere while his line of sight to the Celestial pole is represented by the cyan-blue arrow.

The slope from level ground surface to the line of sight to the visible Celestial pole is called the latitude of your place. Practice recognizing it.

Find a level ground. On a clear night set up a stick pointing from the ground to the Celestial pole. In the Northern hemisphere the Celestial pole has a star (Polaris) while in the Southern hemisphere it is only a point on the geometrical figure formed by circum-polar stars. Such a stick is constructed as a shadow rod in any “builder clock”.

Figure: A “builder clock”. The shadow rod of this clock is set to point towards the Celestial pole in the sky.

The inclined shaddow rod on a “Builder Clock” points toward the Celestial pole in the sky when the clock is properly setup with its base in the true North-South direction.

The angle between the stick pointing to the Celestial pole and the ground is called the latitude of the location. The angle between the stick and a vertical plumb line is (90° – latitude). You need to practice recognizing this angle. (Knowing this angle also help you quickly find the Celestial pole from the stars).

Figure: The Northern Celestial pole is the center of this map of the Northern sky.

Figure: The Southern Celestial pole is the center of this map of the Southern sky.

3. Practice reading in degrees the angles between positions of hands on a clock face.

The angle between a hand pointing at 0 minute and another one pointing at
5 minutes is 30 degrees,
10 minutes is 60 degrees,
15 minutes is 90 degrees,
20 minutes is 120 degrees,
25 minutes is 150 degrees,
30 minutes is 180 degrees.

8 Steps for finding true North and time.

1. Determine the current season in the year to select the appropriate hand posture.

The equinox posture is to be used around Mar 21st and Sep 23rd equinoxes while Summer and Winter Solstice postures are to be used around your local Summer and Winter soltices respectively (Each posture can be used for its whole month and a solstice posture can also be used for two adjacent months.).

If the season in the year cannot be determined (as in the case of inhabitants living in artificial environment for years), use the hand posture for equinox days.

2. Determine whether you are in the Northern or Southern hemisphere.

3. Determine if you are in the morning (the Sun is rising before noon) or in the afternoon (the Sun is setting after noon)

This step is needed to select the appropriate hand for the task.

4. Select and use only the appropriate hand for the task:

4a. Northern hemisphere: LEFT hand in the morning THEN RIGHT hand in the afternoon.
4b.Southern hemisphere:RIGHT hand in the morning THEN LEFT hand in the afternoon.

5. Point the index finger to the Sun with your middle finger in its comfortable, nearly horizontal position.

6. Twist the forearm and hand until the middle finger makes with the level ground an angle equal to the latitude angle.

This is illustrated in the two figures.

Find North by Left Hand

Figure: Finding the meridian (true North-South) line with the left hand.

Find North by Right Hand

Figure: Finding the meridian (true North-South) line with the right hand.

7. The projection of the middle finger onto the ground now points exactly away from the terrestrial pole of your hemisphere.

The middle finger now points to the Celestial pole below the horizon, in other terms it points directly away from the visible Celestial pole in the sky.

8. Looking along that direction pointed by the middle finger and imagining a 24-hour clock dial attached to that axis give a natural clock giving time in the day.

Find time by divider

Figure: The line CB to the Sun form the hour hand of a 24 hour clock. This clock face is for Northern hemisphere. In Northern hemisphere the hand sweeps clockwise while in Southern hemisphere it sweeps anticlockwise.

The time given by the natural clock is the local time which has noon when the Sun is highest in the sky. Local time differs from the zonal time selected by the government.

9. Around noon time, either left or right hand can be used. The terrestrial North South line is determined with least accuracy around noon time.

10. On the terrestrial equator, either selection of 4a or 4b can be applied. The middle finger of the selection 4a points at true terrestrial South while that of 4b points at true terrestrial North.

Figure: Summary of the method of finding true North and time from the Sun.

References.

[1]. tonytran2015, Finding directions and time using the Sun and a divider., posted on May 6, 2015.

wpid-dividermwp3e2c2.jpg

find North by the Sun

[2]. https://survivaltricks.wordpress.com/2017/02/13/good-approximation-to-solar-declination-by-a-watch-face/

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Finding North and time by stars in the tropics

Finding North and time by stars in the tropics

by tonytran2015 (Melbourne, Australia).

Click here for a full, up to date ORIGINAL ARTICLE and to help fighting the stealing of readers’ traffic.

#find North, #finding North, #direction, #by stars, #Mercator, #sky map, #star map, #declination, #right ascension, #tropic.

This posting gives a method of using stars in the tropics under adverse effects of high skyline and bright sky. It is applicable whenever more than 30% of the night sky is seen.

It is based on the traditional tropical Oriental country methods, with the added improvement by using accurate data on dates and angular distances between stars for their identification. It is useful when the sky is unclear and restricted such as in cities with high skyline and bright sky.

1. Identifying bright stars in the tropics.

BrightStars20Plus2

Figure 1: Table of 20 brightest stars plus two additional easily identifiable stars for navigation in the tropics.

People in the tropics learned using stars differently from people in the temperate zones.

In the tropics it is difficult to see the polar and circumpolar stars to start identifying stars. Traditional (not influenced by Western astronomical knowledge) country methods by tropical people ignore the polar stars and rely on the dates of tropical stars and their order of succession in the sky to identify them.

Any tropical star is visible nightly (either from Sunset to its setting or from its rising to Sunrise) for more than 10 months each year. The visibility cycle for each star begins with the star seen rising near the Eastern horizon few minutes before Sunrise. On subsequent days, the star rises earlier and earlier, it travels gradually towards the West and remains for longer and longer duration in the night sky until one day it stays for the whole night. The star is therefore called a star of that date. After that day, the star is seen setting in the West in the night. On subsequent days, its lead on the Sun gradually increases and it sets on the West at earlier and earlier time. Near the end of the cycle, the star is visible above the Western horizon for only few minutes after Sunset. It then sets on the West. At the end of this cycle, the star is too close to the Sun to be visible in the sky. The cycle then repeats from the beginning.

Mercator star map

Figures 2,3: The Mercator map of the sky for inhabitants of Tropical Zone. North direction is on its top. 24hr of R.A. is near the center and R.A. increases towards the left (East) of the map. The map is to be read South side up in the Southern hemisphere. Click to enlarge figure.

The table of this step shows the stars in their order of appearance in the year. The date of a star is the night when the star attains its highest elevation at mid-night (when the hidden Sun has the most negative elevation) and it is visible for that whole night.

2. Identifying stars positively using patterns in the map.

mercator8gc30.jpg

Figure 1: Sky map for the tropic. It is a Mercator map of the central strip of the night sky for printed side down reading. An observer looking up will see that the continuous strip made up of this map and its identical copies slowly and repeatingly moves from its left (aligned to rise on the East of the sky line) to its right (aligned to set on the West of the sky line).

The bright stars for the date near to the current date are then joined to its neighbours of similar brightness to reveal their relative directions and distances. These directions and distances form shapes and sizes to positively identify the stars.

As only the 20 brightest stars are used with large unique patterns in the sky, there is no possibility of having two similar patterns with equal sizes. A user of this method matches the observed shapes in the sky and compare them with those given in the map to identify stars positively.

The map of this step (for printed side down reading) shows the stars in a central strip of 120 degree width going across the sky starting from the Eastern horizon and ending at the Western horizon. An observer lying on his back, looking upwards vertically will see a part of a long continuous strip made up of the map in this step joined by its identical copies slowly rises from the Eastern horizon, moves across the sky (the right hand side of the map leads, left hand side trails) then sets on the Western horizon. He can only see those stars of this map within a window of 12 hours width (in the direction of left to right on the map) when there is no sunlight. The window remains stationary while the continuous strip, being the map here followed by its identical copies, moves across the sky (the right hand side of the map leads and left hand side trails). This is illustrated in the following four maps of the tropical mid-nights and their four approximate zenithal maps to be found at the end of this section.

Merc12

Figure 2: Reading the Mercator sky map (with a grid of azimuth and elevation lines) at midnight Dec. 21st from the equator.

Merc03

Figure 3: Reading the Mercator sky map (with a grid of azimuth and elevation lines) at midnight Mar. 21st from the equator.

merc0621b

Figure 3: Reading the Mercator sky map (with a grid of azimuth and elevation lines) at midnight Jun. 21st from the equator.

Merc09

Figure 3: Reading the Mercator sky map (with a grid of azimuth and elevation lines) at midnight Sep. 23rd from the equator.

The users of this method should keep in their minds that some bright planets (especially the outer planets Mars, Jupiter, Saturn) may wander on the ecliptic (drawn on the map) and cross some area under observation to confuse the identification of stars and constellations. The positions of those such slowly moving bright planets should be noted when observation condition is favourable.

Example:

For May 15th, the star to use is Antares (of May 29th) in the Scopii. The nearby stars to use are

Spica (201.3 deg R.A., -11.1 deg decl.),

Arcturus (213.9 deg R.A., +19.2 deg decl.),

Antares (247.3 deg R.A., -26.4 deg decl.),

Vega (279.2 deg R.A., +38.8 deg decl.).

3. Mercator maps and the distances on them.

Zenith12

Figure: Approximate zenithal map of the tropical midnight sky for December 21st. Positions of stars near the horizon are not accurate in these maps. The maps are obtained by placing circular windows of 12h width on the Mercator map.

Zenith03

Figure: Approximate zenithal map of the tropical midnight sky for March 21st. Positions of stars near the horizon are not accurate in these maps. The maps are obtained by placing circular windows of 12h width on the Mercator map.

Zenith06

Figure: Approximate zenithal map of the tropical midnight sky for June 21st. Positions of stars near the horizon are not accurate in these maps. The maps are obtained by placing circular windows of 12h width on the Mercator map.

Zenith09

Figure: Approximate zenithal map of the tropical midnight sky for September 23rd. Positions of stars near the horizon are not accurate in these maps. The maps are obtained by placing circular windows of 12h width on the Mercator map.

The map in the preceding step uses a Mercator projection to preserve angles. This projection specifies that

(Vertical distance to equator on Mercator map)/(dist. to equator by rectilinear scale) =

(180deg/3.14159rad) × ln((1+tan(0.5×decl.))/(1-tan(0.5×decl.))) / declination.

The projection makes small shapes look similar to the original shapes on the Celestial sphere. Equatorial shapes on the Celestial sphere are faithfully represented. However shapes near the polar regions of the Celestial sphere are enormously overstretched by this type of maps. The distortion can be easily seen by comparing the Mercator map given here and the two polar maps given in reference [2].

The equator line of a Mercator map can be used as a scale to measure distances between stars near to the equator. The vertical lines for of Right Ascension divides it into hours. Each hour of R.A. corresponds to 15 degrees on the Equator line.

The distance between two close stars anywhere on the map is their distance measured on the map multiplied by the cosine of the declination angle of their midpoint.

When the two stars are widely separated, the great circle arc joining them is divided into (about 3) small segments and their distances are added together to give the total distance.

Example:

The distance between Sirius and Canopus on the map of step 2 is measured (using the equator line as a scale) to be nearly 47 degrees in length.

Their midpoint is nearly at 40 degrees (in absolute value) in declination.

Their great circle distance on the Celestial sphere is therefore nearly

47deg X cos(40deg) =36 deg.

This is reasonably close to the actual distance of 36 degrees deduced from the values obtain from their declination and R.A. values given in the table of step 1

4. Measuring the angle between any two stars.

The actual angular distance between any two stars in the sky can be measured using a compass divider with each leg pointing to a star and their angle measured on a protractor.

The two legs of the compass divider can be substituted by two stretched fingers on one hand. The protractor can be substituted by a 12h clock face with each hour marking representing 30 degree angle separation.

(Instrumental navigators use sextants for highly accurate measurements of angles between stars and they can quickly decide on the identity of stars.)

5. Finding time with stars.

On its date, a star reaches its meridian at midnight. Every month before/after that the star reaches its meridian plane two hours later/earlier.

The user of the method should add the difference between zonal time and local time (when noon is at 12am) to obtain the zonal time.

6. Conclusions.

1/- I have tested this method in Saigon, a city with unclear sky and high-rise buildings and found it to be applicable in 80% of the non-rainy nights.

2/- Users of this method should take care not to mistake planets for dimmer stars along the ecliptic.

Reference.

[1]. tonytran2015, Finding North direction and time by stars, survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2015/08/28/finding-north-and-time-by-stars/ , posted on August 28, 2015.

Added after 2018 July 20:

[2]. https://misfitsandheroes.wordpress.com/2012/08/28/ancient-navigators/

[3]. http://www.ancient-wisdom.com/zodiac.htm

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Finding North direction and time accurately from the horn line of the Moon.

Finding North direction and time accurately from the horn line of the Moon.

by tonytran2015 (Melbourne, Australia).

Click here for a full, up to date ORIGINAL ARTICLE and to help fighting the stealing of readers’ traffic.

 

#find North, #finding North, #direction, #time, #Sun, #hidden Sun, #navigation, #survival, #Moon, #phase, #horn line, #half Moon,
Here I add two more steps to the common horn line method for the Moon to obtain more accurate North direction and time from its horn line. The modified method uses position of the Moon, shape (phase) of the Moon, solar declination and user’s latitude to work out North direction and rough local time.

1. Basic information on the Moon for navigation.

mooncrescent.jpg

moonshapesnangles4c.jpg

The Moon is a satellite of the earth. Everyday Moon-rise and Moon-set time is retarded by about 50 minutes. This allows the Sun to travel further on its journey every subsequent night. Therefore after full moon the partial bright side stays on the East (trailing) side and dark crescent appears on the West and dark area gets fatter daily until the whole moon is dark. Similarly, from new Moon a bright crescent appears on the West and grows fatter and bright area gets fatter daily until full Moon is reached. From the shape of the Moon, it is easy to say how late the Moon is trailing the Sun (new Moon trails by 0 degree and 0 hour, new half-Moon by 90 degree and 6 hours, full-Moon by 180 degrees and 12 hours, and late half-Moon by 270 degrees and 18 hours .). The shape and the position of the Moon allow some guessing of its trajectory for the night.

The Moon completes its orbit in space in 27.321 days, and it completes one full revolution on the Celestial sphere in that time. Its angular velocity on that sphere is 1/27.321 (rev/day) = 0.036601 (rev/day) .

The Sun apparent travel on the ecliptic takes 365.256 days. Its angular velocity on the elliptic is 1/365.256 (rev/day). The Moon revolves on the Celestial sphere faster than the Sun by an angular velocity of 1/((1/27.321)-(1/365.256)) = 1/29.530 (rev/day). When the Sun is one full turn ahead of it, the Moon will catch up, and they will be both in the same direction again on the Celestial sphere after a period of about 29.530 days. So the intervals between consecutive full Moons will be something like a pattern of (30days, 29days).

By keeping records of previous full Moon nights people know it is a WAXING or WANING Moon.

The simple Waxing-Waning rule is that the bright side of the Moon is on the West for waxing and East for waning Moon.

It is natural for people to desire to use the horn line, which is the line connecting the two horns of the Moon, to draw the North South direction. However it has been found that the intersection between the horn line and the horizon does not accurately give the North direction.

Here we find out the reasons for that inaccuracy and show a more accurate method of using Moon’s horn-line.

It may be easier for some readers to first read step 5 then come back to read steps 2, 3 and 4.

CAUTION: The horn line of the partial Moon can point far away from the terrestrial principal North or South directions.

2. Estimating the current solar declination

wpid-divider10l.jpg

Estimating the current declination.

The whole Celestial spherical shell rotates around its two Celestial poles. The Sun moves slowly on that sphere on a great circle called the ecliptic. Its distance to the two opposite Celestial poles varies periodically, and its distance to the Celestial equator is call the declination of the Sun.

You can make a rough sketch of this declination from the principal values and estimate the declination for the current day.

3. The horn line is not easily transformed to the ground meridian line.

image

Figure: Panoramic view of the travel of a partial Moon in the sky. The Celestial axis is always at right angle to the path. This picture is for the winter, with the Sun in the other hemisphere and the bright side of the Moon tilts toward the ground. In the summer, it tilts toward the sky.

The horn line is at right angle to the plane containing the very slender triangle formed by the Earth, the Moon and the Sun but the Celestial axis is at angle of (90-23.5) degrees to that plane. So the horn line usually form an angle of that size to the Celestial axis.

Near to half-moons the horn line is easily defined, and it is also easy to see that the projection of the Celestial axis onto the half-moon makes with it an angle equal to solar declination.

On top of those complication, the Moon also has its own declination and an observer has additional difficulty working out the direction of the horn line as it is usually not at right angle to his line of view.

4. Twisting the horns of the partial Moon.

MoonShapesNAngles5C

Figure 1: Moon phase chart for a Solar declination of (-20) deg (South).

At half Moon, it is possible to twist the horn line about the line of view to generate a line KL parallel to the Celestial axis. The amount of twisting is opposite to the declination angle of the Sun.
Similarly, when the angle Sun-Moon-Earth is about 90°+/-30° (=120° or 60°) the amount of required twisting is about 0.85*declination of the Sun.

The required twisting is varied with the phase of the Moon as in the following:

Half Moon requires twisting by full Solar declination,

15% or 85% bright area requires twisting by half Solar declination,

full or no-Moon requires no twisting.

Remember that if the Sun is into your hemisphere (in your summer) the bright side of the half Moon has to be twisted downwards (toward the Celestial equator) by an angle equal to the solar declination angle. The opposite should be done in your winter.

This correction here already causes a difference between the results from the old horn line method and the current method. There will be another difference caused by drawing the “spear line” parallel to Celestial axis in the next section.

Note:

The required twisting on the horns of the Moon varies sinusoidally with time and peaks to the values of minus/plus Solar declination when the Moon is half-full.

5. Finding North direction from a Celestial North South line seen on the Moon.

image

Observing a Celestial axis KML drawn on the Moon: U is observer, E center of the Earth, N terrestrial North pole, S terrestrial South pole, M Moon, UV local vertical, KL a line parallel to Celestial axis, EQ normal to plane UKL, UP a line parallel to Celestial axis. The red circle through U is the intersection between the plane UKL and the Earth’s surface.

Suppose that there is on the Moon M a line KL parallel to the Celestial axis, as illustrated in the figure. We draw a plane through the observer containing the line KL. On that plane UKL draw a line PU nearly in the direction of KL, descending into the ground at latitude angle.That is

(|angle /(PU,KL)| <90° ) and (angle /VUP = 90 deg. – latitude angle).

The line UP is then parallel to the Celestial axis, and its projection on the ground gives the local North South (meridian) direction.

When the Moon is high in the sky and the plane UKL is steeply inclined to the local horizontal, the last condition is the satisfied by

( angle /MUV < angle /MUP ) and (angle /VUP = 90 deg. – latitude angle).

The line UP is then parallel to the Celestial axis, and its projection on the ground gives the local North South (meridian) direction.

For Southern latitudes draw UP’ close to the direction of LK (PUP’ is a straight line).

6. On the ground view of the horn line method.

image

Figure: Finding out North direction more accurately using horn line.

On half-Moon nights, when the angle Sun-Moon-Earth is 90°, twist the horn line by the declination of the Sun to generate on the Moon the line KL parallel to the Celestial axis, and similarly, when the angle Sun-Moon-Earth is about 90°+/-30° (=120° or 60°) the amount of required twisting is about 0.85*declination of the Sun.

When properly carried out, the plane UKL always makes with the horizontal plane an angle not less than the latitude angle. The line KL is the observer’s view of the Celestial axis. All lines co-planar to UKL generate the same view to the observer! Draw a “spear line” PU co-planar to UKL and spearing the ground at an angle equal to latitude angle. The spear line PU so obtained is then pointing exactly along the Celestial axis, towards the lower Celestial pole. The projection of PU onto the ground gives the terrestrial North-South line. North direction is then found.

When the Moon is high in the sky and the plane UKL is steeply inclined to the local horizontal, the lower end U of the spear line is nearer to the line KL than its upper end P.

Note:

The intersection line between the plane PKL and the ground surface is generally NOT in the North-South direction unless the observer is on the terrestrial equator circle. The drawing of the spear line PU cannot be by-passed in this method.

7. Summary of steps in this method.

moonsungreatcircle.jpg

wpid-divider10l.jpg

MoonShapesNAngles5C

wpid-wp-1439376905855.jpeg

To apply this method, the navigator has to go through all the following steps:

a. Working out the ROUGH (+/- 45 degrees) principal North-Sout-East-West directions, from the Waxing-Waning rule and the knowledge that the horn line direction is being close to an RA arc,

b. Estimating the Solar declination for the current time of the year,

c. Working out the proportion of Solar declination used for twisting the horns of the Moon from the Moon phase,

d. Twisting the horns of the Moon by the required angle and waving a stretched arm along the adjusted horn line to establish the plane through the Earth, Moon containing the direction of the Celestial axis,

e. Drawing a spear line inside that plane, inclined by latitude angle, aligned roughly to the ROUGH direction of the lower Celestial pole to establish its exact direction, and

f. Projecting the Celestial axis onto the ground surface to obtain the terrestrial North-South direction.

New users to this method should initially only use it as a double check for another method using the position of the hidden Sun, given earlier as part 1, in a previous Instructables article [2]. The agreement between the two methods would make users confident on their results.

8. Avoiding hasty and perilous conclusions when using the horn line.

image

Figure: A rare (or not so rare?) failure of the simplistic, traditional horn line method. The horn line intercepts the horizon near to the terrestrial North (wrong by 180 degrees!) in a place in Northern hemisphere. The traditional horn line rule really requires amendments.

At latitude less than 28 degrees, the horn line may point to Northern skyline at high Moon although most of the times it points to Southern skyline ! There is a peril of being sent astray by 180 degrees for unreserved navigators.

At high Moon the horn line only gives North South direction near to equinox times ! The error can be due East or West by the declination value of the Sun.

If the steps for using this method seem to be too complex, the Moon navigators may have to accept reduced accuracy from the Moon and use only Waxing-Waning rule in combination with the stars to navigate !

There is a third part to this topic, with the title “Finding North direction and time using the Moon p3- Moon surface features”.

Conclusions:

It is possible to work out accurately North direction from the horn line of the Moon.

The twisting of the horn line and the drawing of the spear line PU are two additional steps of this modified method.

References

[1]. Tristan Gooley, How to navigate using the Moon, the natural navigator,
http://www.naturalnavigator.com/find-your-way-using/moon, accessed 2015aug12

[2]. tonytran2015, Finding North direction and time using the hidden Sun via the Moon, https://survivaltricks.wordpress.com/2015/07/06/finding-north-direction-and-time-using-the-hidden-sun-via-the-moon/, posted on July 6, 2015

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Finding North direction and time using the hidden Sun via the Moon

Finding North direction and time using the hidden Sun via the Moon.

by tonytran2015 (Melbourne, Australia).

Click here for a full, up to date ORIGINAL ARTICLE and to help fighting the stealing of readers’ traffic.

(Blog No.006).

#find North, #finding North, #compass, #direction, #time, #Sun, #hidden Sun, #navigation, #survival, #Moon, #phase,

Finding North direction from the Moon cannot not be as accurate as from the Sun. There are many causes for this:
1/- The Moon does not always rise on the principal East (at 90 degree of the compass rose).
2/- We cannot work out by heart the Moon’s declination (up to +/- 5.1 degrees to the ecliptic, and 23.5+5.1 degrees to the Celestial equator ).
3/- We cannot easily work out when the Moon reaches its highest elevation angle at its meridian time. The Moon does not often cast strong shadows for shadow sticks to work.
Here I describe my new method to find out North direction and time with improved accuracy. The method uses shape and position of the Moon, solar declination and user latitude to work out the position of the hidden Sun, then work out North direction and approximate local time with an accuracy of 30 minutes. Literally, the user can work out North direction and the local time with his bare hands.
I have field tested this method and I have relied on it for many years.

1. Basic information on the Moon for navigation.

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Figure 1: Moon phase chart. Figure 2: A crescent Moon may not align itself to the terrestrial East or West horizon points (see texts).

The Moon is a satellite of the earth. Everyday Moon-rise and Moon-set time is retarded by about 50 minutes. This allows the Sun to travel further on its journey every subsequent night. Therefore after full moon the partial bright side stays on the East (trailing) side and dark crescent appears on the West and dark area gets fatter daily until the whole moon is dark. Similarly, from new Moon a bright crescent appears on the West and grows fatter and bright area gets fatter daily until full Moon is reached. However the bright and dark sides of a partial Moon rarely point accurately to East or West directions.

Figure 2 of this section shows a crescent Moon on the Celestial sphere. The horizontal great circle represents the horizon of the observer. The inclined great circle represent the Celestial equator and the arrow through the center of the sphere represents the Celestial axis. The circle parallel to the Celestial equator is a constant declination circle being the trajectory of the Moon during the hours. The two intersection points of the two great circles are the terrestrial East and West points of the horizon. This picture shows that the crescent Moon may point its bright to dark line far away from the terrestrial East or West points when there is a combination of high declinations of both the Moon and the Sun on the same side of the Celestial equator.

Each Lunar (Moon) cycle begins with the Moon being visible as a thin bright arc in the sky (called a New Moon), trailing the Sun by less than one hour. After Sunset this thin Moon is seen bright on the West until it sets. On subsequent days, the Moon is more and more behind the Sun, its position shifts gradually towards the East and the Moon remains for longer and longer duration in the night sky till full Moon day. After full Moon day, the Moon (now called a Late Moon) becomes thinner and thinner and is seen risen in the East in the night, it remains visible in the sky after Sunrise, and travels ahead of the Sun. On subsequent days, its lead on the Sun gradually reduces. Near the end of the cycle, the Moon is visible as only a thin bright arc rising in the East for less than one hour before Sunrise and after Sunrise it can still be seen leading the Sun by that same amount of time. At the end of the Lunar cycle, the Moon sends no reflection of Sunlight to Earth and is too close to the Sun to be visible in the day sky.

Keeping diaries of past days of full and new Moon helps people know where their time is in the current cycle, and so they know whether the leading (West) side of the Moon should be bright (new to full Moon) or dark (full to new Moon). Fortunately, the users of my method described here do not have to refer to any such records of the Moon.

It is interesting to note that Buddhist East Asians use lunar calendars and observe fasting at new and full Moon. From their calendar and their fasting festivals , they already know whether the Moon is waxing or waning. This may help explaining why they are good at finding North direction using the Moon.

CAUTION 1: The bright to dark line of the partial Moon can point far away from the terrestrial principal East or West directions.

CAUTION 2: The horn line of the partial Moon can point far away from the terrestrial principal North or South directions.

2. Moon shapes giving Moon-Earth-Sun alignment.

The various shapes of the Moon under various angles of lighting by the Sun are given in the illustration picture. The Moon goes through this cycle every 29.5 days. The picture is drawn for the principal values of the angle of Moon-Earth-Sun. The picture allows determination of the direction of the Sun from the shape of the Moon.
The angle Moon-Earth-Sun will be more accurately known if the navigator is in the habit of directly measuring and recording it before Sunset (few hours earlier) whenever the Moon is seen during day light.

3: Direction of the Sun from the Moon

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The line joining the two horns of the Moon is always at right angle to the plane of Sun, Earth and the Moon. Draw a half-line from you to the Moon and extending far past the Moon. Imagine the Sun is at the far end of this half-line. Swing this half-line in the direction of the bright side (at right angle to the line joining the two horns) of the Moon to have the angle of Moon, Earth and Sun giving a matching shape for the brightened part of the Moon. The half-line then gives the direction of the Sun.
Alternatively, you can think of placing a sphere between you and the Moon, and a torch is is used to shine on the sphere and the torch is placed in various directions until it gives a partially brightened sphere similar to the current Moon shape.

4. Finding North direction and time.

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divider43.jpg

With the direction of the Sun known, the technique given by my previous blogpost “Finding North direction and time using the Sun and a divider” [1] can be applied to find North direction and local time.
The selection rule of right or left hand placement of CA in “Finding North direction and time ising the Sun and a divider” has been generalized.

The generalization is:
(Northern latitudes with rising Sun or Southern lat. with setting Sun) ==> CA on the left of CB,
(Northern latitudes with setting Sun or Southern lat. with rising Sun) ==> CA on the right of CB.
The time for rising Sun here is from 0hr to 12hr (AM) and time for setting Sun here is from 12hr to 24hr (PM).
The rest of that method applies to the hidden Sun to give North direction as well as time.

I have tested and found that this method gives direction accurately and easily. The additional benefit is that it also gives approximate time.

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

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, posted on 2018 July 10

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Finding North direction and time accurately from the horn line of the Moon. posted on August 12, 2015. This is my novel technique.

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Finding directions and time using the Sun and a divider.

Finding directions and time using the Sun and a divider

by tonytran2015 (Melbourne, Australia).

Click here for a full, up to date ORIGINAL ARTICLE and to help fighting the stealing of readers’ traffic.

#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.

find North by a Divider

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

Find North by Divider

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.

Find North by Divider

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/- At a Northern latitude and during sunrise half-day : Downward axis points (Southwards) 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/- At a Northern latitude and during sunset half-day : Downward axis points (Southwards) to the right of the ray from the Sun. 4d/- On the other hand, at a Southern latitude and during sunrise half-day downward axis points (Northwards) to the right of the ray from the Sun while during sunset half-day it points (Northwards) to the left of the ray from the Sun. 4e/- 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. 4f/- 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.)

Find North by Sun and Divider

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.

Find time by divider

Figure: Reading time from the divider.

Sun on Celestial Sphere

Figure: 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.

Find North by Sun n Divider

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.

Solar Declination versus time

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.

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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 !

References (added 09 Mar 2017)

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

[2a]. (same topic on youtube) https://www.youtube.com/watch?v=iWgqO9CsQvU&t=58s

[2b]. (same topic on youtube) https://www.youtube.com/watch?v=noo2OoJ84tU

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Finding North direction and time accurately from the horn line of the Moon. Posted on August 12, 2015. This is my novel technique.

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Finding North direction and time using the Moon surface features. Posted on July 1, 2015.

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, posted on

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

Sky map Northern 3/4 sphere

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

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, posted July 22, 2016

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Click here for my other blogs on divider43.jpgSURVIVAL

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polymeraust100dollars

Click here go to Divider63D400 Home Page (Navigation-Survival-How To-Money).

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