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.

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

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.

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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