Finding accurate direction by a watch

Method for finding accurate directions by a common analogue watch.

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.120).

WatchCompass_22NL

#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.

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

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.

Red hand is the bisector of 0 hr direction and the hour hand; green hand is the reflection of red hand across the (6-12) axis.

In the southern hemisphere points the green hand instead of the red hand.
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.

Figure: Summary of finding North by a watch.

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When is Lunar New Year? (Khi nào là Tết Âm Lịch?)

 

When is Lunar New Year? (Khi nào là Tết Âm Lịch?)

by tonytran2015 (Melbourne, Australia).

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(Blog No.103).

#find North, #finding North, #Lunar calendar, #New Year, #Tết, #Âm Lịch, #Tết Nguyên Đán , #Tết Nguyên Tiêu,

When is Lunar New Year? (Khi nào là Tết Âm Lịch?)

To many Western and Vietnamese people, it is hard to tell when East Asian Lunar New Year (Tết Âm Lịch in Vietnamese) will come.

This blog gives an easy answer to that question.

1. The time for East Asian Lunar New Year.

The New Year begins with a New Moon. Each Lunar month span from one New Moon to the next one.

The month enclosing the December Solstice time (in December 21st) is defined to be the second last Lunar month of the year.

After that is one last month of the year and then comes the New Year Festival.

The rule gives people adequate time (more than one Lunar month) to prepare for the festival.

2. Example for 2018.

On the Solar New Year for 2018, the Moon was full. It was the 15th day of some Lunar month. Ten nights prior to that was the December Soltice (on December 21st). That night was the 5th night of that some Lunar month. That Lunar month is defined to be the second last (11th) month of the Lunar year. So the Solar New Year night was the 15th night of the 11th Lunar month.

Therefore the beginning of last Lunar month of the year is around Jan. 14th, while Lunar New Year is 29.5 days after that and is around Feb. 12th of 2018.

3. Tết Nguyên Đán and Tết Nguyên Tiêu.

The first New Moon in each Lunar year is called “Tết Nguyên Đán” in Vietnamese and the Full Moon following it is called “Tết Nguyên Tiêu”  (many Vienamese don’t know the words “Tết Nguyên Tiêu”), or more commonly “Lễ Hội Rằm Tháng Giêng”.

Ancient Chinese historical texts made many references to (yearly) First Full Moon Festivals but it is very hard to find any mention of (yearly) First New Moon Festivals.

So Chinese people have been celebrating the yearly Festivals of First Full Moon (with Moon lit nights). When and why the Festivals of First New Moon (with dark, stars lit nights) became more celebrated than the Festivals of First Full Moon is an interesting question.

It is seen in the following two figures that at Lunar New Year, the bright star Leo Regulus crosses the meridional plane near to midnight. At First Full Moon Festival, Leo Regulus crosses the meridional plane about 1 hour before midnight while the Full Moon crosses the meridional plane at midnight.

equatorial stars

Figure: Stars in tropical zone for beginners (Tropical zone). Click to enlarge figure.

Bright Stars 20 Plus 2

Figure 2: Table of 20 brightest +2 stars in order of appearance.

4. Neighbouring countries may have their Lunar New Years differing by one month.

a. Soltice time can be accurately determined by watching the direction of the setting (or rising) Sun. When the azimuth angle of the setting Sun is plotted for consecutive days near solstice time it shows an increase then decrease (or the other way around). The time for the turn-around is the accurately determined solstice time. Solstice time is a global event and is the same for all locations on Earth.

b. New Lunar month begins on the day preceeding the night with the first view of a thin crescent on the trailing side of the  Moon (an initial New Moon.). New Lunar Month is a local event. The beginnings of new Lunar months differ for different locations on different longitude of the Earth.

c. It is rare occasions but we can sometimes observe that one country A begins its New Moon just before solstice while its neighbour B on the next time zone begins its New Moon just after solstice.

Therefore for the next Lunar month, country A is still in Lunar month 11 while its neighbour B is on is already in Lunar month 12.

Consequently country B has its Lunar New Year one Lunar month ahead of country A.

d. The months in these two countries will get synchronized again when the astronomical event marking Lunar month 2 falls into the Lunar months of both countries.

Example: Vietnamese (time zone +7) Lunar New Year in 1984 was earlier than Chinese (time zone +8) New Year by one Lunar month.

5. Neighbouring countries may also have their Lunar New Years differing by one day.

New Lunar month begins on the day preceeding the night with the first view of a thin crescent on the trailing side of the  Moon (an initial New Moon.). New Lunar Month is a local event. The beginnings of new Lunar months differ for different locations on different longitude of the Earth.
It is rare occasions but we can sometimes observe that one country A see no Moon for the night while its neighbour B on the next time zone sees a New Moon just before Sunrise.
Therefore for the next whole Lunar month, country A is behind its neighbour B by one Lunar calendar day.

If this happens at the end of a Lunar year, the Lunar New Year day of country A will be behind the Lunar New Year day of country B by one day.

Example: Vietnamese (time zone +7) Lunar New Year in 2007 was earlier than Chinese (time zone +8) New Year by one day.

References.

[1]. tonytran2015, Simple-determination-of-east-asia-lunisolar-new-year , posted on 2017 January 19th.

[2]. http://www.bbc.com/vietnamese/vietnam/story/2006/07/printable/060704_lichvietnam.shtml

[3]. https://m.thanhnien.vn/van-hoa/vi-sao-nam-nay-viet-nam-an-tet-truoc-trung-quoc-mot-ngay-317188.html

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Time keeping without using watches

Time keeping without using watches

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.84).

#find North, #find time, #finding time, #time keeping, #timekeeping, #shadow stick, #star disk, #aiming rod, #equatorial mount, #sundial, #true North.

Time keeping without using watches.

Whenever an expedition camp is set up there is always a need for time keeping in the camp. Time keeping is required to get everyone back to base at the same time for meals or for camp activities. In the Eastern World, people had practiced reasonably accurate time keeping WITHOUT USING WATCHES since more than 2000 years ago. Their technique has been fairly accurate and is explained here so that it can be appreciated and be useful to modern campers when separated from their watches.

1. The vertical shadow stick for finding time and finding North.

In the old-time in Eastern World, each castle has a time-keeper. It is interesting to learn the tricks of such a timekeeper. His main instrument is the vertical shadow stick the operation of which is described here

shadow stick to tell time and find North

Figure: A shadow stick for finding North and time is drawn here in blue colour. The shadow of its tip always move WEST TO EAST along a conical curve C (drawn in red). The shadow of the whole stick is a straight line joining its base to the shadow of its tip on the curve C. The axis of symmetry of the curve C is the terrestrial North-South direction.

A. The timekeeper/navigator first sets up a rigid vertical rod firmly buried in a level ground. The movement of the shadow of its tip gives time as well as directional information. That is it tells both time and the North-South direction.

B. He then draws many concentric circles on the level ground around the base of the stick. He then marks the position of the shadow of the tip on the ground, joining them to make a curve (which can be shown by geometry to be a “conical curve”). The symmetry axis of this curve is the true North-South direction at the location and the point on the curve closest to the base of the vertical stick corresponds to Local Noon (which differs significantly from Zonal Noon due to difference in Longitude and the variable speed of the Sun on the Celestial Sphere, the effect of the latter is known as the effect of the Time Equation). The shadow of the tip always moves WEST TO EAST and does so accurately near to NOON. Near to noon the shadow of the tip moves Eastwards by a distance of 1/4 of its distance to the tip every hour.

The timekeeper/navigator gives daily instructions to camp inhabitants on the time to come back to camp for meals/activities. The time for coming back is selected by his predetermined ratio of the length of the vertical stick to that of its shadow. When leaving the base camp, each inhabitant has to make his own portable vertical stick to keep track of the approaching time for returning to base.

C. The vertical stick has a drawback that is the shadow of its tip travels at non-constant speed on a curve that changes slowly during the year.
One example of the disadvantages of the vertical shadow stick is that it cannot help dividing daylight duration into six intervals of equal duration for guard duties.

D. Equal intervals of time are determined from burning incense sticks, reciting prayers, filling containers with dripping water, boiling water pots, etc… Near to noon the shadow of the tip moves Eastwards by a distance of 1/4 of its distance to the tip every hour (During one hour the Sun moves along an arc which is nearly 15 degrees long and sin 15° is nearly 1/4.).

2. Star disk for time keeping at night.

Time keeping at night can be carried out accurately using the stars.

Any star-gazer (ancient timekeepers/navigators had to be star gazers) in temperate zones can easily see that all stars on the Celestial sphere rotate around the stationary Polar star (when observed from Northern hemisphere) or a stationary black point (from Southern hemisphere). It appears as if all circumpolar stars have been stuck on a heavenly disk pivoted on the Celestial pole in the sky and the disk rotates slowly during the night.

The stars have certainly been drawn on an Egyptian Senenmut star map since before 1473BC (https://en.m.wikipedia.org/wiki/Astronomical_ceiling_of_Senemut_Tomb)

220px-Senenmut

Figure: The double wall mural of the tomb of Senenmut, (https://en.m.wikipedia.org/wiki/File:Senenmut.jpg), the image has been released into Public Domain.

on China Suchow map about 1190BC, and on walls of tombs in the land of present China, wiki, Chinese star maps

Figure: Suchow map, from Wikipedia. Used under Common Creative License conditions.

The rotation of the disk can be used to tell time. The rotation seems to be at constant speed as equal angles of rotation seem to always correspond to the same duration of time for burning incense sticks, reciting prayers, filling containers with dripping water, boiling water pots, etc…

Figure: A circular disk with the drawing of bright Northern circumpolar stars as well as other bright stars visible in the sky.

To tell time accurately, the time-keeper can draw the bright circumpolar stars (including the Little and Big Dippers) on a paper disk, hold the paper disk in the direction of the Celestial pole in the sky and rotate the paper disk to align the drawing to the actual star. The slow rotation of the paper disk indicates the passage of time. The accuracy of the method depends on the size of the disk and the accuracy of its alignment to the real stars in the sky.

star disk alignment

Figure: Aligning the center of the paper star disk to the Celestial pole in the sky to determine its rotation during the night.

This method does not require the determination of meridional crossing of dim stars. Ancient time keepers may have used this method to keep accurate time at night using only bright stars..

3. Time divisions by meridional passing of selected stars.

A star makes a meridional passing when it passes the vertical plane in the North-South direction. That is when it is vertically on top of a wire strung in the North-South direction.

A time-keeper may use the meridional passings of selected stars as markers for division of time (into many known recorded unequal parts) during night-time.

Based on those markers a time-keeper can divide the night into nearly equal intervals.

4. Improved Star disk for time keeping at night.

A bigger disk can be aligned more accurately, its rotation can be more accurately measured, but is harder to be held up in the sky. Making a bigger disk mounted in air for improved accuracy is therefore an expensive design.

star disk for equatorial mount on ground

Figure: A star disk on equatorial mount on the ground, to be read from its upper surface.

A better design is presented here and it is to make a big star disk on equatorial mount so that it will be parallel to the paper disk in the air but is mounted on the ground like a tilted round table top, with an aiming rod mounted at its center pointing to the Celestial pole. The star map engraved on the big disk here is a mirror reflection of the image of stars in the sky. An imaginary observer underneath the disk would see through it the image of the stars in the sky. Markings will be drawn accurately on the rim of the big disk for the positions of the engraved stars (which are drawn for a designated night of the year). There will also be regularly spaced markings for measuring the rotation of the observed stars from their engraved standard positions. A time-keeper will only require access to the upper surface and the rim of this large star disk mounted on the ground.

star disk for mounting on the ground

Figure: A star disk for installing on an equatorial mount on the ground. The map here is a mirror reflection of the image in the sky. This disk is aligned for September Equinox.

With this type of large star disk and its central aiming rod, a time-keeper can tell where a star is relative to its position engraved on the disk. The disk is engraved with drawing of the stars on one designated night which may be either the spring equinox night or the winter solstice night.

The spring equinox night has the advantage of accuracy of date in the year, it is the night when the Sun rises and sets exactly in the East and West principal directions. The winter solstice night has the advantage of having the longest duration to observe stars.

On the designated date for the disk, the rotation of any star from its engraved position directly gives the time from midnight. On any other night an offset can be worked out using only a string placed along the perimeter of the circular disk. For every night subsequent to the designated night the stars move forward by nearly 1/365 of the perimeter.

5. Star disk for time keeping in the day.

The nights with partial Moon show that the Moon moves around the aiming rod at nearly the same speed as the stars. The days with partial Moon also show that the Moon and the Sun move around the aiming rod at nearly the same speed.
Therefore any time-keeper with an inclined star disk will find that the Sun, the Moon and the stars all move together around the aiming rod with nearly the same speed. This would lead to his use of the inclined star disk for time keeping, with the advantage that the shadow of the aiming pole moves on the rim of the inclined disk at constant speed! So the inclined star disk also work as an equatorial mounted sundial (meaning the sundial disk is parallel to the equatorial plane.).
(This knowledge has given rise to the description of Solar position in the Zodiac. The shifting of the Zodiac by precession shows that the association of solar position with the Zodiac has begun thousands of years ago.)

So far I had been able to find only equatorial mounted sundial with no engraving of stars. One such a sundial can be seen in Beijing. This disk has only time markings and can be read on both sides.

Figure: A sundial in the Forbidden City, or Imperial Palace, in Beijing. https://commons.wikimedia.org/wiki/File%3ABeijing_sundial.jpg, Date 26 February 2003, Author User: Sputnikcccp~commonswiki .Figure used under the Creative Commons Attribution-ShareAlike License.

During Winter months, a flat cardboard can be used to find the intersection of the shadow of the aiming stick and the rim of the large disk if it has no accessible lower surface.
Using the equatorial sundial during the days gives the advantage of fast determination of time with no required large seasonal adjustment. With the help of an equatorial mounted sundial, a time-keeper can divide time into any number of equal intervals and can also work out the ratio of a vertical stick to its shadow at any time of the day.

6. Timing wires used in remote areas.

Similar to the central rod of an equatorial mounted star disk, any taut wire strung parallel to the Celestial axis can be used to time intervals of 24 hour. The shadow of such a wire under a strong Sun comes back to its previous position after every 24 hours. Clock makers in the 1800’s, when radio receivers were not widely used, have been using this trick to time the clocks under their repairs .

7. Time keeping with an unclear sky.

Burning of incense is used to complement time keeping using star disk in days of poor visibility.

Time keepers have incense sticks for short-term timing or incense coils which last up to three days for long-term timing.

Time keepers also have other methods for timing, they are reciting prayers, filling containers by dripping water, boiling water pots.

On ancient ships, time keepers can count repetitive actions such as the rowing cycles of oars, the food items made by a kitchen, etc…

8. Announcing time to surrounding area.

The time-keeper may use drums or low pitch horns to announce the time to his surrounding area.

On receiving the signal for time, surrounding institutions such as nearby pagodas synchronize their own activities and then may sound their own gongs as secondary level time signals.

The population around the castle use these time signals to open their shops, prepare their predawn cooking etc…

The whole community relies on those signals to synchronize their interacting activities.

9. Natural time keepers.

There are natural time keepers, they are the animals and plants in the areas.

Certain types of birds tweets ar some fix time intervals before sunrise. Each type of tweets has its own fix interval before sunrise. The tweets by different types of birds follow one another in the same sequence every day.

Chickens’ roosting have been used as reliable time signal foe imminent sunrise.

Chameleons’ croaking have sometimes been used by some people in Vietnam as reliable Noon time signal.

There are some plant flowering at some certain time during the day. The Vietnamese plants “HOA MƯỜI GIỜ” (meaning “Ten o’ clock flowering plants”) flowers at a constant time near to 10 AM.

References.

[1]. tonytran2015, Shadow-stick-navigation-and-graph-of-solar-paths, posted on August 19, 2016.

[2]. wiki, Astronomical_ceiling_of_Senemut_Tomb.

[3]. Suchow map, http://www.adlerplanetarium.org/exhibits/planetary-machines.

[4]. wiki, Chinese_star_maps

[5]. tonytran2015, Finding directions and time using the Sun and a divider, survivaltricks.wordpress.com , Finding directions and time using the Sun and a divider., posted on May 6, 2015.

[6]. tonytran2015, Finding North direction and time using the hidden Sun via the Moon, survivaltricks.wordpress.com, Finding North direction and time using the hidden Sun via the Moon . Posted on July 6, 2015.

[7]. tonytran2015, Finding North direction and time by stars, survivaltricks.wordpress.com, Finding North and time by stars. Posted on August 28, 2015

[8]. tonytran2015, Finding accurate directions using a watch, posted on May 19, 2015 .

DirectionBySun_12N

.

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Shadow stick navigation and graph of Solar paths

Shadow stick navigation and graph of Solar paths

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, #shadow stick, #Sun shadow, #Solar declination, #graph, #Solar path,

Shadow stick navigation and graph of Solar paths.

In the 1950’s some maps have their graphs of Solar paths printed next to the compass roses. A graph of Solar paths helps the users of that map (for some certain small area) in orientating it correctly using only the direction of the Sun and the approximate time (month) in the year. It also help people visualize the direction of the Sun at each time of the year relative to a building. For some unknown reasons, graphs of Solar paths are all replaced by compass roses in modern maps. The roses take up nearly the same areas while give less information,.

A graph of Solar paths can also be used on its own with a vertical stick in the center to tell (local) time and direction. This application is suitable to day time navigation of vehicles as it relies only on the Sun and needs no battery. The application devices can be left on the vehicles as they are of very low-cost and are burglary resistant.

This posting shows how to construct and use a graph of Solar paths for your own map or for use on its own.

1. Description of the basic graph of Solar paths.

Solargraph10N

Figure: A typical graph of Solar path. This particular graph is made for 10 degrees North, for an example use in Saigon (around Tan Son Nhat International Airport).

The graph of Solar paths is a circular disc with concentric circles and radial lines bearing division marks to represent the elevation and azimuth angles of the Sun at different times of principal days.

The perimeter circle of the graph is graduated into 360 degrees to show the azimuth angle of the Sun from True North. It can also be used as a protractor for measuring angles. The concentric circles are the constant elevation circles.The radial lines are graduated 0 to 90 to show the angle from zenith to the Sun. The circle 90 degrees from the zenith represents the horizon in flat locations. The graduation can also be read from the horizon circle toward the center to show the elevation angle of the Sun.

All positions of the Sun at various time on an equinox day are plotted to make a Solar path for that day. The paths for the Sun on two solstice days are similarly plotted. The time for the each Solar position on a path is also given by time marks such as 6hr, 12hr and 18hr.

It is assumed here that the Sun attains its highest elevation at noon of local time everyday (the duration of the day is therefore slightly longer or shorter than 24hr, to discount any effect from the Equation of time).

2. Using a graph of Solar paths.

Be certain that the graph is for your current latitude! If it is printed on a map, it is for the latitude of that area.

The following steps show how to use the graph on an equinox day:

1/- Point your index to the Sun.

2/- Point your middle finger horizontally.

3/- Hold still the two fingers and measure the angle between them by placing those fingers along two radial lines of the Graph of Solar paths. Read the value of the angle. It is called the elevation angle of the Sun.

4/- Follow the Solar path for that day on the graph to its 2 points having that elevation value. The two intersection points give two times (one before and one after noon) and two positions of the Sun.

5/- Choose the one of those two points fitting your half day (either before or after noon-time).

6/- Lay the graph of Solar path horizontally. Rotate the graph until the line from the graph center to the chosen intersection point goes beneath the Sun.

7- The 0 degree azimuth line of the graph is now aligned along the direction of the true terrestrial North.

For any other day of the year, use the particular path for it. A graph supplies at least three paths: for summer solstice day (21 June for Northern Hemisphere), for equinox days (21 March and 23 September), and for winter solstice day (21 December for Northern Hemisphere). The path for any other day can be interpolated from these three.

3. Interpolation for any arbitrary day of the year.

wpid-divider10l.jpg

Figure: Solar declination for various days of the year.

The declination value for any day varies between the principal values for solstice and equinox days and its solar path varies similarly.

The rough graph here allows the estimation of how close the Solar path of any day is to its two neighbouring bounds for the equinox and solstice days.

4. Making a graph of Solar path for your latitude.

SunCelestSphere

Figure: The Celestial sphere directly above a circular disc of the same diameter.

The following steps show how to make your own graph of Solar paths for your arbitrarily chosen latitude.

1/-Draw 9 equidistant concentric circles and 12 (or 36) equally spaced radial lines as the frame for the planar polar coordinate system.

2/- Place this disc (as the frame) on a horizontal plane.

3/-Set the angle between 2 divider legs to be 90 degrees.

4/-Place the hinge of the divider exactly above the center of the disc. It should be at the center of the sphere in the figure.

5/- Hold the first leg of the divider pointing downward, inclined by latitude angle, in the 180 degree or 360 degree direction depending on your Lower Celestial pole being South or North Celestial pole. The first leg point downwards along the Celestial axis in the figure.

6/- The second leg will point at different directions to the Sun for different times of the day when the divider is rotated about the first leg. It uppermost position corresponds to mid-day.

7/- Looking downwards along the first leg of the divider gives the picture of a 24 hour clock with the second leg being the hour hand. The clock dial is clockwise when you are in Northern hemisphere and anticlockwise when Southern.

8a/- Looking at the second leg from the top of the disc gives azimuth angle of the Sun.

8b/- Looking at the second leg from its side gives elevation angle of the Sun.

9/- Record on the polar graph on the disc the direction of the second leg for 6hr, 12hr and 18hr.

10/- Join the curve by a smooth curve. (Additional points may be added for a more precise curve).

11/- The curve is the Solar path for equinox days.

12/- Set the angle between the divider legs to 90+23.5 degrees and repeat steps 4 to 10 to draw Solar path for summer solstice day.

13/- Set the angle between the divider legs to 90-23.5 degrees and repeat steps 4 to 10 to draw Solar path for winter solstice day.

The graph of Solar paths is now COMPLETE. It is usable with only 3 paths for equinox and solstice days. Paths for other days can be interpolated from them.

Manually drawn graphs are accurate enough for normal usage. If all steps are simulated with your computer, the graph will be very accurate.

If you live near to 20 degrees N latitude (20 degrees is only an example value) and need a graph for your personal use but don’t want to spend time drawing it, you can do a Google search for “graph solar path 20 degrees”. The search results will give many ready made graphs and you can select one of them for your own use.

5. Application 1: Shadow stick navigation for vehicles.

ShadowStick

Picture of Application 1: Shadow stick navigation for vehicles.

You can print your graph on a disc for use in your vehicle. You can use only one single disc if the vehicle does not travel more than 5 degrees = 300 nautical miles = 555km in latitude from your base.

Lay the rotatable disc horizontally with a vertical stick at its center. When the shadow of the stick is on the opposite side of the chosen point on the graph, the line of 0 degree points exactly at True North. This method of Solar navigation only needs the graph and a vertical stick and is immune to vehicle shocks and stray magnetism.

This method needs the above device and is less general than my other methods given in references [1, 2, 3] but may be easier for users to comprehend.

6. Application 2: As a North direction marker

DirectionMarker

Picture of Application 2: As a North direction marker

Figure: Map of an old citadel overlaid on a modern satellite based map. The graph of Solar paths is given on bottom left corner instead of the compass rose.

The illustration is the map of an old citadel overlaid on a modern satellite based map. The graph of Solar paths is given on bottom left corner instead of the compass rose. The graph of Solar paths gives more useful information than a compass rose occupying same area.

Notes on my composite map: The modern map data are used under Open License from Open Street Map, the data are owned by Open Street Map Contributors. The old area has adjusted and selected data from a 150 year old map with expired Copyright.

7. Additional observations.

The graph of step 1 shows that the Sun can travel on the other side of your zenith when you are in a tropical zone. This explains why the bisector method using a horizontal watch may give you an error of 180 degrees around summer solstice (see reference [2]).

The graph shows that the terrestrial direction (azimuth) angle of the Sun varies quickly with time when the Sun is close to the zenith point. This quick change in direction may be main the reason for the ancient custom of cross-country travelers to take their rest when the Sun is near to their zenith.

You can also use a graph for your EXACT latitude to calculate if and for how long a proposed neighbouring tall building may over-shadow your house. Architects have been using graph of Solar paths and physical sunlight simulator on their scale models even before 1914.

References.

[1]. tonytran2015, Finding directions and time using the Sun and a divider, survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2015/05/06/finding-directions-and-time-using-the-sun-and-a-dividing-compass/, posted on May 6, 2015.

find North by the Sun

[2]. tonytran2015, Finding accurate directions using a watch, survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2015/05/19/finding-accurate-directions-using-a-watch/, posted May 19, 2015

[3]. tonytran2015, Caution in finding North by bisector line of a horizontal watch, survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2015/10/28/caution-in-finding-north-by-bisector-line-of-a-horizontal-watch/, Posted on October 28, 2015.

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Finding time to Sunrise with star maps

Finding time to Sunrise with star maps

by tonytran2015 (Melbourne, Australia).

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

#determine, #find, #find North, #time, #Sunset, #Sunrise, #time to Sunrise, #time to Sunset, #sky disk, #star disk,
Finding time to Sunrise is needed for traveling across deserts as the travellers may want to be on time to avoid excessive heat and coldness. It is also needed by long distance traders and country people who have to schedule their peak activities around Sunrise time.
Finding time to Sunrise is harder than to Sunset because the Sun is not seen before Sunrise (for people in tropical and temprate zones)! This method relies on the symmetry between Sunset and Sunrise to work out the time to next Sunrise using a circular sky map.

1. Mark the direction to the setting Sun

sunrise1

Use two rocks or a stick lying on the ground to mark the direction of the setting Sun.

2. Start a stop-watch.
The interval from Sunset to alignment of star maps may be significant (See the note at the end of step 5.).

3. Aligning stars and the Sun to star map

sunrise2

sunrise3

sunrise

Figure 1: Aligning the sky map to the stars and Celestial axis OP. Figure 2: Constructing the half-plane containing the Celestial axis OP and the half-line pointing to Sunset position. Figure 3: The intersection between the sky map and the Sunset half-plane gives the radial line OC.

Accurately align one of the star maps (such as of this article) to the stars and align its axis to the Celestial axis so that it points to the upper Celestial pole P. Work out the half-plane of constant R.A. containing the Celestial axis and the Sunset direction half-line. This half-plane intersects the polar sky map along a radial line which is often non-horizontal. Use a paper clip to mark the intersection C of the rim of the star-map disk and the half-plane.

4. Stop the stop watch.

PolrNorthNC20const8

 

polrsouthp4

 

Figure 1: The sky map for use in Northern hemisphere. Figure 2: The sky map for use in Southern hemisphere.
Stop the stop watch and note the time from Sunset to time of alignment of the sky map. This time varies from 5 minutes in the tropic to nearly one hour in the cold temperate zones (See the note at the end of step 5.).

5. Adjustment of alignment of the Sun
Use the stop-watch reading to determine the small amount of time from Sunset to the successful alignment of the star map. The paper-clip on the rim should be moved to a new position toward the bottom of the sky map by an angle corresponding to the time interval given by the stop-watch.
The paper clip should now be on the R.A. half-plane containing the Celestial axis and the Sun. The Sun has moved further down under the horizon corresponding to the rotation of sky map since Sunset to alignment time.
The stop-watch of steps 2, 4 and 5 is not necessary if the rotation of the Celestial sphere during that time interval can be worked out by any other mean such as from the rotation of an early Moon which is visible both before and after Sunset.
6. Coarse time to Sunrise.
The rising Sun will be the left-right reflection image of the setting Sun through the true North-South plane . So are the two corresponding positions of the paper clip. The sky map will rotate during the night and the paper clip will move through the position for Sunrise. The time to Sunrise is the time for the sky map to rotate between its current position and Sunrise position. (One full circle is 24 hours).

7. Alternative coarse time to Sunrise by the late Moon.
A late Moon remains in the sky until Sunrise. The shape of the Moon indicates the direction of the out-of-view Sun. The Celestial axis can be determined from the declination of the Sun and the local latitude. So time for the Sun to reach the horizon can be estimated. This method has been given previously.
8. Fine time to Sunrise.

Sunrise5

Observe the identifiable stars near the 90 degree Eastern horizon. They always rise up at the same angles (along the constant declination lines) from the same terrestrial directions on the horizon. Before the stars fade at Sunrise, pay attention to those that have risen about 1 to 5 degree from their rising positions and take notes of their travel (at angle to the horizon, along the constant declination lines) from the initial rising positions on the horizon. The stars rise 1 additional degree early for each subsequent day and new stars will appear to take their role. Using these stars close to the Eastern horizon, the time to Sunrise on subsequent days are determined with better accuracy.
Notes.
1. The motion of a new or early Moon in the sky can be used to time the interval from Sunset to alignment of the star map (by checking its rotation with the sky map). A stop-watch is not required in such a case.
2. If a large sky map is drawn on a wheel mounted on its axis aligned along the Celestial axis then a time keeper only needs to align the sky map to the stars at night and the paper clip to the Sun during day time to read fairly accurate local time from the travel of the rim of the wheel. The paper clip will make one complete rotation everyday and its position on the sky map needs adjustment by only 1 degree each day.
References

[1]. tonytran2015, Finding North direction and time by stars, Additional Survival Tricks, http://www.survivaltricks.wordpress.com/, posted on Aug 28, 2015
[2]. tonytran2015, Finding North and time with unclear sky, Additional Survival Tricks, http://www.survivaltricks.wordpress.com/ , posted Oct 17, 2015.
[3]. tonytran2015, Finding time to Sunset with bare hands, Additional Survival Tricks, https://survivaltricks.wordpress.com/2015/11/11/finding-time-to-sunset-with-bare-hands/, posted Nov 11, 2015.

[4]. tonytran2015, Finding North direction and time using the hidden Sun via the Moon, Additional Survival Tricks, http://www.survivaltricks.wordpress.com/ , posted Jul 06, 2015.un/, posted May 24, 2017,

 

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Finding time to Sunset with bare hands

Finding time to Sunset with bare hands

by tonytran2015 (Melbourne, Australia).

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#bare hands, #determine, #find, #find North, #time, #Sunset, #Sunrise, #time to Sunrise, #time to Sunset.

Finding time to Sunset with bare hands (Blog No. 11).

There are times when you have no watch or when it is not practical to carry a watch (such as when going for a swim in the sea) and you need to know the time from Sunrise or to Sunset. This time can be determined reasonably accurately using only your bare hands.

1. Hand postures

image

Figure. Hand posture for determining time to Sunset in the Northern hemisphere.

Cup your hand as if about to hold water. Position the wrist to have the thumb on top with four fingers horizontal and close together. Then stretch your arm, keeping all fingers at right angle to the stretched arm. Stand with your chest facing the Sun but DO NOT LOOK INTO THE SUN. Interpose the bent fingers on your stretched arm between the Sun and your aiming eye on the same half of your body. Twist the stretched arm to have the bent fingers forming with the horizon an angle equal to the local latitude angle and the contact line between middle finger and ring finger being on the same plane with the Celestial axis (Tilting the fingers from the horizontal by an angle equal to latitude angle is close enough).
The Sun will travel at right angle to your fingers to its setting position on the horizon .
Count the finger widths from the Sun to its setting position. Each finger width is about 1.5 degrees distance and is equal to 1.5×4 = 6 minutes of time to setting on equinoxes or is equal to 6.6 minutes of time to setting on solstices.
(At solstices, the length of the trajectory of the Sun is only (6.24radius)x cos(23.5degrees), so each 1degree of length corresponds to 4.4minutes of time).
For example, four finger widths to setting point gives 4×1.5×4 minutes of time to setting at equinoxes or 4×1.5×4.4 minutes of time to setting at solstices.

2. Notes

1/- In the Northern hemisphere the Sun moves to the right (North) when setting.
2/- In the Southern hemisphere the Sun moves to the left (South) when setting.
3/- The Sun is between the middle and ring fingers if any small gap between them let through strong rays of light.
4/- Your finger width on your stretched arm may sustain an angle different from 1.5 degree. You need to check it against the diameter of 0.5 degree of the rising or setting Moon.
5/- In Northern hemisphere, the Sun rises to the right (South).
6/- In Southern hemisphere, the Sun rises to the left (North).

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Caution in finding North by bisector line of a horizontal watch.

Caution in finding North by bisector line of a horizontal watch

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, #bisector, #horizontal watch, #inclined watch, #limitation, #caution.

Caution in finding North by bisector line of a horizontal watch (blog No. 10).

There is currently wide advocating for the application of the method of finding North direction by “the bisector line of a horizontal watch”. There have even been proposals to use the method on the new and full Moon as the position of the Sun can be determined from the position of new or full Moon [1], [2]. However people should remember the basic limitations of the method and if they exceed its hard limitation perilous and catastrophic consequences (such as direction errors of 90 degrees or even direction reversal sending people astray) may result.

1. POSSIBLE PERILOUS SITUATIONS.

image

Figure: Limitations of finding North by the bisector of a horizontal watch. The picture in the title page shows the two applications to Southern (red direction line) and Northern(green direction line) hemispheres of the method of “bisector line of a horizontal watch”. The limitations for each case are clearly displayed in yellow.

Here are the few possible perilous situations:

a/- On any summer solstice day, at latitude +23.5 degrees, the Sun rises in ENE, travels to a point in the East direction, to the zenith, to a point in West direction, then sets in WNW.

b/- On any summer solstice day, at latitude +20 degrees, the Sun rises in ENE, travels to a point in North direction, then sets in WNW.

If the method of “bisector line of a horizontal watch” is used for case a, the error will be a flipping +/- 90 degrees near to noon while if it is used for case b, the error will be a devastating 180 degrees around noon time.

With such situations in mind, people using the method of “bisector line of a horizontal watch” should heed the warning to preserve its accuracy and NOT to use it during their summers in zones near to the equator, with less than 30 degrees latitude (low temperate and tropical zones).

Users of “bisector line of a horizontal watch” should be even more cautious when they guess the position of the Sun in the sky from the position of the Moon and then apply the method. A perilous situation may arise as illustrated in the following:

c/- On a summer solstice day, at latitude +26 degrees, the Sun rises in ENE, travels to a point in South direction at mid-day then sets in WNW. However at night the Moon rises in ENE, may travel to a point in North direction at mid-night then sets in WNW. Note here that the Moon may go to the North while the Sun goes to the South at their highest altitudes and the Moon does not necessarily retrace the path of the Sun 12 hour later, as the proponents of the extension had wished.

So users should be even more cautious when guessing the position of the Sun in the sky from the position of the Moon. They should heed the warning to preserve its accuracy and NOT guess the position of the Sun from the Moon to use the method in zones near to the equator, with less than 40 degrees latitude (temperate and tropical zones).

2. UPDATING TO A SAFER METHOD.

Figure: Summary of my new method of finding North by a watch.

 

image

Figure: My new method of finding North by a watch.

WatchCompassG

Figure: My new method of finding North by a watch.

For accuracy and safety, it is worthy for users to switch to my new method of “inclined bisector line of a tilted vertical watch” [3]. It has no latitude limttion and requires only the declination of the Sun and the simple knowledge that the Sun is rising or falling.

References

[1]. Unknown Author. Use the moon and a watch to find north, Boy’s Life magazine ,http://boyslife.org/video-audio/134162/use-the-moon-and-a-watch-to-find-North, 2011 Mar.

[2]. Frank Williams, Finding North By The Moon In The Southern Hemisphere, BushcraftNZ,http://bushcraft.org.nz/m/blogpost?id=5745113%3AB… 2011 Jul 24.

[3]. tonytran2015, Finding accurate directions using a watch, Additional survival tricks, wordpress.com, Finding accurate directions using a watch, https://survivaltricks.wordpress.com/2015/05/19/finding-accurate-directions-using-a-watch/, posted on May 19, 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).

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(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.

image

image

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

image

image

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.

image

image

image

image

image

image

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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image

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Finding accurate directions using a watch

Method for finding accurate directions by a common analogue watch.

by tonytran2015 (Melbourne, Australia).

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

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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).

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, #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).

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