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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