Blog image of Contents of Survival sub-page

These are the contents of SURVIVAL sub-page re-organized in book order for coherent reading.

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NAVIGATION (Celestial).

The Sun, the Moon and identifiable stars are used to work out North direction and time in this section.

divider43.jpg

Finding accurate directions by a watch .. Posted on May 12, 2015.. This is my novel technique.

WatchCompass_22NL

Finding accurate directions using a watch, posted on May 19, 2015 . This is my novel technique to replace the horizontal watch method.

DirectionBySun_12N

Caution in finding North by bisector line of a horizontal watch. Posted on October 28, 2015: The commonly known “Scout method” using a horizontal watch may give directional errors of up to 180 degrees in some circumstances.

wpid-bisectorns2c.jpg
, posted on 2018 July 10

Find North By Fingers
, posted on May 06, 2015 . <<<—This is my MOST USEFUL novel technique.

wpid-dividermwp3e2c2.jpg

find North by the Sun

CloudyL

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

image

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

image

Finding North direction and time using the Moon surface features. Posted on July 1, 2015. This is a useful technique.

image

, posted on

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

Sky map Northern 3/4 sphere

Sky map Southern 3/4 sphere

Finding North and time with unclear sky. Posted on October 17, 2015. This includes my novel method for finding North and with unclear sky.

image

image

posted on October 21, 2016

ariessmallc30.jpg

. Posted on May 25, 2016

mercator8gc30.jpg

. Posted on April 05, 2018

star map mercatorx1p6

. Posted on April 12, 2018

. Posted on May 13, 2018

. Posted on September 16, 2018

Find North with Orion Equatorial stars

, posted November 3, 2016

slide-sky-disk

Slide Sky-Map for displaying tropical stars, posted on October 7, 2016

photo

, posted July 22, 2016

DirectionTimeByStars

Finding time to Sunset with bare hands. Posted on November 11, 2015 .This is my novel improvement for improved accuracy.

wpid-sunset2.jpg

Finding time to Sunrise with star maps, Posted on January 9, 2016 . This is a novel application for star-maps.

sunrise

Finding direction, distance and navigating to a distant base by stars (Part 1). Posted on January 27, 2016 . This is a novel application for direction of stars in the sky.

Sky map Northern 3/4 sphere

Sky map Southern 3/4 sphere

Finding direction, distance and navigating to a distant base by stars, fine reading of latitude (Part 2).. Posted on February 6, 2016. This is a novel way of accurately arriving at any chosen destination latitude using no instrument.

BStarsN20Vega8C2.jpg

NAVIGATION using only constellations.

The Orion constellation., posted December 26, 2016

The Scorpius constellation, posted on January 8, 2017

The Southern Cross Pointer stars, posted February 26, 2018

NAVIGATION (Terrestrial).

Measuring angles and distances for outdoor survival, posted on June 29, 2016

DistPole

NAVIGATION (Instrumental).

Finding North with a lensatic compass, posted on August 21, 2017

Compass-Magnetic

Determining local magnetic declination by a magnetic compass, posted on March 31, 2016

Compass-Magnetic

, posted on June 14, 2016

compass Reversal

Selecting and using magnetic compasses, posted on July 9, 2016

Compass Lensatic Jap

Shadow stick navigation and graph of solar paths, posted August 19, 2016

ShadowStick

Using GPS in off-grid situations, posted December 06, 2016

Adding longitude and latitude lines to a map, posted August 23, 2017

Map w Coordinates

Navigating with an AM MW radio receiver, posted January 17, 2017

radio sony

Finding North direction and time using geological features, plants and animals, posted August 04, 2017

FIRE MAKING.

Making fire and lighting cigarettes with sunlight. Posted on February 27, 2016

StormWatchDiagram

Quick fire making using sunlight, posted on January 4, 2017

20161222_131508gballfirec60.jpg

Mirror for making fire using sunlight., posted on April 13, 2016

20160105_143215C

Predicting-the-temperature-of-a-habitat, posted on August 31, 2017

compass thermometer

, posted October 23, 2018

Pushing away

FOOD

Rice as emergency food., posted December 24, 2016

20161230_192839ricegrains2c60.jpg

Dried-sweet-fruits-as-energy-food, posted December 24, 2017

Air-grown-mung-bean-sprouts-for-food, posted March 07, 2016

MISCELLANEOUS

Old maps:

Interesting maps of old Saigon , posted on March 20, 2016 .

SaigonThanhQuy

Detecting Counterfeit Currency

Detecting Counterfeit Currency, US dollars, posted on July 15, 2016

Hologram

, posted on November 15, 2016

polymer 5 dollars transparent stripe

Cashless bartering

Cashless-bartering-for-survival, posted on February 20, 2017

crystalball2c70.jpg

Other languages:

Survival-topics-available-in-other-languages , posted on june 18, 2017 .

click to go to polymeraust100dollarsMONEY , 20160105_145215CHOW TO , 20160105_145215CSOCIAL ISSUES , 20160105_145215CLIVING sub-pages

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Identifying moderately bright navigational stars.

Identifying moderately bright navigational stars

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. 27).

#find north, #navigation, #survival, #moderate stars, #bright star, #Antares, #Fomalhaut, #direction, #distance, #great circle, #navigation, #stars, #neighbour stars, #sky map

Introduction.

Some navigational stars are only moderately bright although they are in the top 20 brightest stars. Antares and Fomalhaut are two such stars. They are used for navigation from September to November but are not easy to identify among their nearly as bright neighbours. The method for identifying them is to relate them to brighter neighbours which have been identified in previous periods of the year.
(GPS navigation cannot be relied on during periods of uncertainty. Traditional methods of navigation is still a necessary skill.)

Using an identifying map.
Knowing the date or even only the month of a star help locating parts of the sky where it may be found. The map giving distances and angles to its more distinctive neighbours then help its identification.

The maps are to be held such that its shown Celestial pole is pointing close to that actual Celestial pole whether it is in the sky or below the ground. The map is thus to be held in the star direction but oriented either upright or up-side-down.

Examples:

Figure 1: Antares in Scorpii with its neighbours. The centering mark is the Southern Celestial pole.

Figure 2: Fomalhaut with Alpha, Beta Grus and their neighbours. The centering mark is the Southern Celestial pole.

ariessmallc30.jpg

Figure 3: Hamal in Aries and its brighter neighbours. The tail of the inverted Little Dipper in the North is the North pole.

The first two maps make easy the confusing identification process of these two Southern navigational stars for October.

The third map makes easy the identification process of the dim Northern star Hamal in Aries for November.

References.

[1]. tonytran2015, Finding North and time by stars in the tropics, survivaltricks.wordpress.com, https://survivaltricks.wordpress.com/2016/05/25/finding-north-and-time-by-stars-in-the-tropics/, posted on May 25, 2016

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

RELEVANT SURVIVAL blogs (Added after February, 2017)

, posted on May 06, 2015 .

wpid-dividermwp3e2c2.jpg

find North by the Sun

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

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

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

wpid-wp-1439376905855.jpeg

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

wpid-wp-1435755781395.jpeg

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

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

wpid-bstarsn20b.jpg

, posted July 22, 2016

NorthByKnownStar

RELATED SURVIVAL blogs

Navigating with an AM MW radio receiver, posted January 17, 2017, The Scorpius constellation, posted January 8, 2017, The Orion constellation., posted December 26, 2016, Rice as emergency food., Using GPS in off-grid situations, Slide Sky-Disks with grid masks showing azimuths and altitudes, Slide Sky-Map for displaying tropical stars.

Click here for my other blogs on divider43.jpgSURVIVAL

Click here for my other blogs on divider43.jpgSURVIVAL

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Measuring angles and distances for outdoor survival

Measuring angles and distances for outdoor survival

by tonytran2015 (Melbourne, Australia).

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

#angle, #distance, #estimate, #measure, #bare hands, #parallax, #slope, #survival

Measuring angles and distances for outdoor survival (Blog No. 21).

When you are outdoor, you often need to work out the distances to various objects around you so that you can plan your activities and know exactly where you are on your map to be in control of your trip, to make your plan to get back to safety, or to inform your rescuers of your exact position. However the challenge arises you have to make angle and distance measurements but neither can nor should employ any instrument, such as when hiking, when riding a motor-bike, or when on a touring bus. In such cases measuring angles with bare hands is the only method left. (Accurate measurement of angles allows determination of distances in survival situations.)

The method is described here and it uses the edges of the index and middle fingers as parallel guide lines for measuring angles. (Measuring posture must be correct to keep the viewing angles separating them nearly constant.)

1. Frontal measurement of angular separation at eyes level (Basic posture).

BasicVert

Figure: Basic arm posture for angle measurement. The two outer edges of the measuring fingers form the marks on a scale of 0 to 10 for measuring vertical angular separations. The fraction of (10/200)rad in this figure is only for an angle of 3 degrees, the denominator will be different for other values of the angle.

This measurement uses the basic posture for angle measurements.

User has his face and chest facing the object to be measured. His shoulders are kept level, one of his arms stretched out, to have its measuring fingers precisely in front and on the symmetry plane of the torso.

The index and middle fingers of that hand are curled. The two outermost joints of each of these fingers are kept horizontal, straight and at right angle to his line of view. The edges of those finger extremities form three regularly spaced parallel guide lines to make a scale for measuring angles. The two outer edges are separated by an unchanged angle depending only on the bone structure of the user. This angle is constant over a long time for each individual and can be used to measure any angular separation. It can be easily measured by comparing it with the diameter of the Moon. It is usually between 2 and 5 degrees (which is 4 to 10 diameters of the Moon; each diameter sustains half a degree). The user must know how to find out the value for his own body structure:

1 finger has nearly 1.5 degree width in frontal measurement (for most people),

2 adjacent fingers have nearly 3 degree width in frontal measurement (for most people).

User can also have those index and middle fingers pointing in any direction from 1 to 7 o’clock to measure any non-vertical angular separation.

When the object in view is not level with eye level, the user can raise or lower his stretched arm, tilt his head and bend his upper torso to keep the distance from the measuring hand to the eyes constant. By raising and lowering the arm, the aiming line can reach an elevation of 80 degrees and a depression of 90 degrees.

Measurement of overhead angles is more difficult and has reduced distance from eyes to hand. The resulting angle must consequently be increased by some percentage to compensate for that.

To have consistent results, all other measuring postures should be immediately alternated with the basic posture to check for the constancy of the distance from eyes to hand.

2. Conversion of the angle into fractions of radian or mil.

BasicHor

Figure 1: The two outer edges of the measuring fingers form the marks at 0, 5 and 10 on a scale of 0 to 10 for measuring angular separations; the scale is oriented horizontally in this illustration. The fraction of (10/200)rad in this illustration is only for an angle of 3 degrees, the denominator will be different from 200 when the angle is not 3 degree.

Angle7C30

Figure 2: The two outer edges of the measuring fingers form the marks at 0, 5 and 10 on a scale of 0 to 10 for measuring angular separations; the scale is oriented vertically in this illustration. The fraction of (10/200)rad in this illustration is only for an angle of 3 degrees between the two outer edges of the two fingers, the denominator will be different from 200 when that angle between the two outer edges is different from 3 degrees.

The angle between the outer edges of the two fingers is next converted into a gradient (or slope) value which is more useful.

3 degrees is nearly equal to a slope of 0.0523 (= tan (3 degree) = 3*0.01745) which is next written as 1/19.12 = 10/191.2 # 10/200 (You can use 10/191 but rounding the ratio to 10/200 make field calculations much faster.).

The separation angle of 3 degree has thus been converted into an angle of (10/200) radian (see the step on Units for angle measurement).

Similarly, the separation angle of 4 degree is converted into an angle of (10/150) radian.

Each user has to determine the value for his own individual angle which is determined by his body structure, convert it into a fraction of one radian with a nominator of 10 and remember his own denominator value. The denominator may be any rounded numbers between 100 and 400.

The two outer edges of the measuring fingers thus form a scale from 0 to 10 for measuring angles. Angles are measured against the nominator of the fraction for the angle between the outer edges of the two fingers.

Readers may skip to Units for measuring angles on first reading.

3. Measurement over the shoulder.

This is used when it is not practical to assume the basic posture, such as when standing on a tight spot.
User has one of his shoulder facing the object to be measured, his two shoulders in line with the object , the arm nearer to the object fully stretched out, its index and middle fingers placed between his eyes and the object. This is for measuring angle over the shoulder. The parallel guide lines formed by the fingers are now separated by a smaller angle. The angular separation of the guide lines is now reduced by about 25%.

4. Measurement at 45 degrees to your shoulder line.

This is used when it is not practical to assume the basic posture, such as when standing on a tight spot.
User has his measuring arm stretched out, pointing to the object. The user can raise or lower his stretched arm and tilt his head and upper torso to keep the distance from the measuring hand to the eyes constant. By raising and lowering the arm, the aiming line can be reach elevation of 60 degrees and depression of 90 degrees. The angular separation of the guide lines is now reduced by about 20%.

5. Units for angle measurement.

Figure: A full circle is designated to be 360 degree. This is given on most compasses.

The angle for a full circle is divided into 360 degrees, or 2X(3.14159) radians. As it is not convenient to use any compass scale in radians, the US military compasses use their scales in mils. A full circle is divided into 6400mils, so

6400mil = 360degree = 2*3.14rad,

1 rad = 1019mil # 1000mil (This is a convenient conversion formula).

Quick reference values for angle measurement:

An equilateral triangle has 3 equal angles of 60°.

1 degree angle is equal to (2*3.14159/360)rad # (1/60)rad # a slope of (1/60).

6 degree angle is equal to (2*3.14159/60)rad # (1/10)rad # a slope of (1/10).

10 degree angle is equal to (2*3.14159/36)rad # (1/6)rad # a slope of (1/6).

The diameter of the Moon varies between 0.5degree and 0.55degree. It can be taken to be 1/2 degree and is used to conveniently calibrate the angular spacing of your index and middle fingers.

Note: The mils on Chinese compasses are NOT US mils; 6400 US mils are equal to 6000 Chinese mils.

6. Application 1- Estimating distance to an object of known size on the ground.

LandMark

Figure: A distinctive building with known dimension can be used to estimate your distance to it.

Objects of known sizes such as your companion and his survival walking stick or of standardized sizes such as train track widths, street signs, car lengths or of very similar sizes such as fully grown plants and animals can be used to estimate your distances to their nearby objects. Your distance to it is given by the simple formula:

(inverse of angle in radian) * (size of object) = (distance to object).

A numerical example will be given in Application 6.

7. Application 2- Estimating distance to an intersection along a road of constant width.

DistIntersection

Figure: A straight road of constant width. The arrows on the right correspond to the distance to the intersection, 1/2 and 1/4 of it.

(Estimating distance to an intersection along a straight road of constant width.)

The width of the road must be constant in this application. You first find an observation point higher than the surface of the road to observe the width of the road with SAFETY and ease.

Measure the angular width of the road at the intersection. The point on the road where the angular width is double that is at half the distance. The point on the road where the angular width is double that new width is again at half of that new distance. Use the method repeatedly to obtain 1/2, 1/4, 1/8, 1/16 of the unknown distance, until the last one in the sequences can be accurately estimated by any other method such as comparison to your height. Note that suitable adjustment should be made for the height of your observation point.

8. Application 3- Estimating distance to a point along a straight line on the ground.

DistLine

Figure: A straight yellow line to an object of unknown distance, which is placed at the smallest arrow on the line. Your observation point is at the center of the bottom edge of the figure. The arrows on the right correspond to the distance to the object, 1/2 and 1/4 of it.

You should choose an observation point on one side and away from the line. Imagine a parallel hand rail at your eye level on top of that line. The hand rail runs from your eye to the intersection of that line and the horizon. Use the method of the preceding section to repeatedly divide the distance into half until the last one so obtained can be accurately estimated by any other method such as comparison to your height.

9. Application 4- Measuring distance to a ground object by traversing horizontally.

DistPole

Figure 1: A pole of unknown distance from the observer who is at the short base of the triangle drawn by the dotted line. Top inset: The pole seems to move against the distant background when the observer moves at right angle to the line of view.

PoleMovement

Figure 2: On the scale 0-5-10 formed by the edges of your two measuring finger, the pole seems to move by a value of 17.

DistOblique

Figure 3: A movement at an oblique angle can be made and the traverse is obtained from the projection of this angle onto the normal to the line of view.

Measuring distance to a ground object by traversing horizontally is also known as measurement by parallax angle.

Notice the position of the object on the distant (far) skyline (or low clouds). Traverse 10 parade paces (7.5m) in a direction at right angle to the line of view. Observe the relative horizontal displacement of the impression of the object on the distant sky line and measure this angular displacement. (If at night, observe the relative horizontal displacement of the object against the low elevation stars and measure this angular displacement.)

(inverse of angle in radian) * (traverse) = (distance to object).

When it is not practical to move at right angle to the line of view, a movement at an oblique angle can be made and the traverse is obtained from the projection of this angle onto the normal to the line of view.

(The result will be more accurate when the traverse and the angle are determined more accurately such as when using a tape measure and an accurate sighting compass.)

Example:

1. The distance to a transmission tower may be known if the you can walk around it in a circle and measure the length of the circle.

Distance = (Length of circle)/(2*3.14)

When the whole circle cannot be made, part of it (a circular arc) can be used instead and the distance is given by

Distance = (Length of arc)*(360degrees/(angle of arc in degrees))/(2*3.14)

or

Distance = (Length of arc)*(6.28318radians/(angle of arc in radians))/(2*3.14)

or

Distance = (Length of arc)*(1radian/(angle of arc in radians))

2. If the direction to the transmission tower changes by 5 degrees (=5*0.0174 radian) after you have traversed 7.5m, as in Figure 1, the distance will be

(1/(5*0.0174))*(7.5m) = 86m.

The value of 5 degrees was supposed to be obtained by an accurate measuring device and is equal to the angle of the arc. The value of 5 degrees is only an example, you have to use whatever value given by your angle measuring device.

3. Since the transmission tower appears to move against the distant skyline when you traverse 7.5m, as in Figure 1, the angle of this movement relative to the distant skyline can also be used to work out your distance to the tower without using any measurement device as in the following.

We first assume the ratio measuring the angle between the outer edges of your two measuring fingers to be 10/200 (This is the ratio for most people). On the scale of 0-5-10 formed by the edges of your two measuring fingers, the transmission tower seems to move by a value of 17 units (which is a rough value of 5degrees (=0.087radian) read on a scale of (1/200)radian per unit) against the distance skyline (Figure 2). With this reading of 17, the distance to the tower can be worked out to be

(1/(200/17))*(7.5m) = 88m,

So, the distance has been worked out in a simple way with an error of about 5%, using only your bare hands.

4. If you are on moving along a track at 30° angle to the line of view, you don’t have to leave it only to make a traverse at right angle to the line of view. Just keep moving along the track for about 15m, the transmission tower will move against the sky line by some angle. The traverse distance is now

15m*cos(90°-30°)=7.5m.

Other calculations remain the same.

10. Application 5- Measuring distance to a ground object by traversing vertically.

DistTree

Figure: A tree of unknown distance to observer. Inset: The horizon seems to follow the observer and moves against the tree when he stands up and crouches down.

Measuring distance to a ground object by traversing vertically.

Notice the position of the object on the distant (far) skyline (or low clouds). Crouch down and stand up to move your eyes at right angle to the line of view. Crouching reduce your eye level by half your height. Observe the relative vertical displacement of the impression of the object on the distant sky line and measure this angular displacement.

(inverse of angle in radian) * (change in height) = (distance to object).

11. Application 6- Locating your position on a map relative to a tall land mark.

LandMarkNightView

Figure 1: The tall, distinctive building of step 6 is used as a landmark for navigation around the city.

LandMarkMap

Figure 2: The location of the landmark on a map with distance scales. Notes on the map: The map data are used under Open License from Open Street Map, the data are owned by Open Street Map Contributors.

Use the known size of the distinguishable parts of the landmark for estimating of its distance (as given in preceding section). The direction of the landmark from the observation point gives the direction of the observation point relative to the landmark.

Example:

The landmark building is observed to be in the direction of 0° to 10° (North) of the observation point.

Measurement of the top segment of the landmark building by using the scale 0-10 of the method in step 1 gives a value of 6. The angle thus is (6/10)*(10/200)rad = (6/200)rad.

The top segment (from the helipad to the top) of this building has a height of 71m (from data provided on the internet). Therefore its distance from the observation point is

(200/6)*71m = 2400m (10% accuracy).

The observation point is thus on the thick faint red arc drawn on the map and in the direction 180°-190° (South) of the landmark.

So the observation point should be somewhere close to the Southern end of a bridge on the map.

This method for positioning is found to be quite good for this example as the actual observation point is right on the South end of that bridge.

12. Estimating distance by the speed of sound.

At the moment of seeing the cause, such as a firework, an explosion, you should start counting “one thousand and one, one thousand and two, one thousand and three, . .” . Your “one” , “two”, “three” will correspond to 1second, 2seconds, 3seconds after the flashing. The sound will come against the your counting to give the time for the sound to come to you. It gives your distance from the source of the sound.

1 second corresponds to 340m, 2 second, 680m, 3 second, 1020m, . . .10 second, 3400m.

Estimating distances to thunder storms.

When you are outdoor in the wilderness, it is vital to avoid lightning strikes. Lightning strikes occurs when there is discharge to the ground by electrically highly charged clouds. Highly charged clouds usually discharge among themselves creating lightning flash. At the moment of flashing you should start counting “one thousand and one, one thousand and two, one thousand and three, . . ” to determine your distance to the lightning discharge.

When the lightning strikes is closer than 2000m (that is when any thunder arrives within 6 seconds of its flash) you should think about your safety and your plan to avoid lightning strikes.

RELATED SURVIVAL blogs
, posted on

Finding North with a lensatic compass, posted on August 21, 2017

Compass-Magnetic

Selecting and using magnetic compasses, posted on July 9, 2016

JapLensatic

Shadow stick navigation and graph of solar paths, posted August 19, 2016

ShadowStick

Navigating with an AM MW radio receiver, posted January 17, 2017, The Scorpius constellation, posted January 8, 2017, The Orion constellation., posted December 26, 2016, Rice as emergency food., Using GPS in off-grid situations, Slide Sky-Disks with grid masks showing azimuths and altitudes, Slide Sky-Map for displaying tropical stars.

Click here for my other blogs on divider43.jpgSURVIVAL

divider43.jpg

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Finding direction, distance and navigating to a distant base by stars, fine reading of latitude (Part 2).

Finding direction, distance and navigating to a distant base by stars, fine reading of latitude (Part 2)

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, #star, #sky map, #sky disk, #declination, #right ascension, #fine reading, #celestial, #distance, #find, #latitude, #navigation, #no instrument, #polynesian, #zenith,
This is applicable to navigation in an ocean or in a large desert with clear, flat horizontal skyline. It uses the complementary stars touching the horizon instead of stars traveling directly over the zenith of the navigator. It is more suitable for sea travel with readily available horizon but unsteady travel platform. It is a useful trick to return to a base (e.g. a Polynesian island) when having no measuring instrument.

Step 1: Basis of the method.

BStarsN20Vega8C

wpid-30naugplrnc-.jpg.jpeg

wpid-30naugplrsc.jpg

Figure: The trajectory of the complementary star touches or nearly touches the horizon. Figures: Horizon for an example latitude of 30degrees North projected onto North and South Celestial hemispheres respectively.

Stars travel along constant declination circles drawn on the Celestial sphere. If the base city is at latitude L then the constant declination circle of 90°-L on its same (North or South) hemisphere will be seen touching the horizon and the lowest position of the complementary star will be right on the horizon and in the principal Northern/Southern direction. When the (complementary) stars of declination 90°-L is at its lowest point near the horizon, unaided human eyes can easily tell its elevation accurate to 1/4 Moon’s diameter (1/8 of a degree).

If bright complementary stars are unavailable for any latitude, users of this method have to identify some constellations having dim complementary stars for that latitude and use these stars instead.

Step 2: Preparation at base for this method.

BrightStars0b

polrnorthqrefc60.jpg

polrsouthq3c60.jpg

Figures: 20 brightest stars and their positions in the sky represented in Northern and Southern 3/4 spheres. Dimmer stars beyond this list may have to be used by this method for traveling to any arbitrarily given latitude.

1. Work out the latitude of the chosen city.
2. Work out the complementary angle for that latitude.
3. Use a list of bright stars (in reverse order of brightness) to choose a star or stars having declinations being equal or greater than the complementary angle by less than 2 degrees (the difference is less than 2degrees or 4 Moon’s diameters). The less bright stars may have their declinations closer to required values but their poor visibility may make them unsuitable. The chosen star may slightly dive under the horizon but its neighbouring stars can indicate how far it has dived.
4. Practice identifying the complementary stars in all imaginable conditions.

Step 3: Field application

5. Travel North or South until the lowest position of the complementary star touching or slightly above the horizon by the so determined adjustment of less than 4 diameters of the Moon.
6. On attaining that latitude, only travel along a parallel circle to maintain the latitude.

Step 4: Examples.

BStarsN20Vega8C2.jpg

Figure: The trajectory of the complementary star for London touches or nearly touches the horizon when viewed at the latitude of London.

London is at (0°5′ longitude, 51°32′ latitude), choose Vega (18hr 37 RA, +38.8deg declination). Around midnight of Dec. 25th, the star Vega travels to its lowest point on a circle glancing the horizon. Its distance from horizon is 51°32 + 38.8° – 90° = 0.3°.
This angle is half the diameter of the Moon and can be judged accurately by unaided eyes.

Berlin is at (13°25′ longitude, 52°30 latitude), choose Vega (18hr 37 RA, +38.8deg declination). Around midnight of Dec. 25th, the star Vega travels to its lowest point on a circle glancing the horizon. Its distance from horizon is 52°32 + 38.8° – 90° = 1.3°.
This angle is 3 diameters of the Moon and can be judged accurately by unaided eyes.
Manila (120°57′ longitude, 14°35′ latitude), choose a dim star Beta Ursae Minoris, (Kochab, 14hr51RA, +74.3deg declination). Around midnight of Nov. 07th, the star Kochab travels to its lowest point on a circle glancing the horizon. Its distance from horizon is 14°35 + 74.21° – 90° = -1.3° (under the horizon by 1.3degrees. This angle is 3 diameters of the Moon and cannot be seen but its visible neighbouring stars in the Ursa Minoris group can indicate how far this star is below the horizon.).
Mecca(39°45 longitude, 21°29 latitude) choose Gamma Ursae Minoris (Pherkad Major, 15hr 21RA, +71.8° declination). Around midnight of Nov. 16th, the star Kochab travels to its lowest point on a circle glancing the horizon. Its distance from horizon is 21°29 + 71.8° – 90° = +3.3°. This angle is 7 diameters of the Moon and can be judged accurately by unaided eyes using fingerwidths on a stretched arm.

Tonga Capital city is Nukuʻalofa (175°12′W = 184°48′ longitude, 21°08′S latitude). Choose the star Beta Carinae (Miaplacidus 09hr 13 RA -69.7decl). Navigators may have to identify the constellation Carina containing the bright star Canopus in order to identify a not quite bright Beta Carinae. Around midnight of Aug. 10th, the star Beta Carinae travels to its lowest point on a circle glancing the horizon. Its distance from horizon is 21°08′ + 69.7° – 90° = +0.8°. This angle is 1 and 1/2 diameters of the Moon and can be judged accurately by unaided eyes.

The Northern tip of Iceland is at 66°30′ (see the map from viking ships , [2]). Choose the Sun at its June 21st solstice. Around midnight of Jun. 21st, the center of the Sun travels to its lowest point on a circle glancing the horizon. Its center is exactly on the horizon when the navigator is on the latitude of the Northern tip of Iceland. The upper rim of the Sun is just touching the horizon on Jun. 21st when the navigator is on the latitude of Northern Iceland. Keeping this latitude brings the navigator to Iceland on a journey of 900km from Norway.

Step 5: Notes on terminal homing of journeys.

Near to the end of his journey, an ocean navigator may release island spotting birds.
If the birds can attain a height of 800m, they can spot land (even without using cloud features) at distance of 110km away (60 nautical miles, or 1 degree of arc or 2 Moon’s diameters).
If the birds can attain a height of 250m, they can spot land (even without using cloud features) at distance of 55km away (30 nautical miles, or 0.5 degree of arc or 1 Moon’s diameter).
If the birds can attain a height of 62m, they can spot land (even without using cloud features) at distance of 28km away (15 nautical miles, or 0.25 degree of arc or 0.5 Moon’s diameter).

Alternatively the navigator may note the presence of nautical birds from the island ( viking ships , [2]). The navigator can also use currents, winds and even smells in this phase.
The error of this navigation method is thus well within the operational range provided by the spotting birds.

References

[1]. tonytran2015, Finding direction, distance and navigating to a distant base by stars (Part 1). Additional Survival tricks, wordpress.com,
Posted on January 27, 2016.

[2]. viking ships , http://www.hurstwic.org, http://www.hurstwic.org/history/articles/manufacturing/text/norse_ships.htm

Added after 2018 July 20:

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

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Finding direction, distance and navigating to a distant base by stars (Part 1)

Finding direction, distance and navigating to a distant base by stars (Part 1)

by tonytran2015 (Melbourne, Australia).

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#find North, #finding North, #direction, #time, #star, #sky map, #sky disk, #declination, #right ascension, #celestial, #distance, #find, #latitude, #navigation, #no instrument, #polynesian, #zenith

polrnorthqrefc60.jpg

Figure: The sky map for use in Northern hemisphere.

The method here uses stars for finding base city at a distance between 1000km to 9000km and for traveling to that base using constant latitude for final path.
It uses the stars passing overhead the base city and accurate time to tell those moments. Direction and distance to that city are directly observed from the stars. If no current longitudinal information is available and longer travel distance is acceptable then the user can also use this method to aim for base city on the final constant latitude part of the travel.
This is a back up or emergency method for people who may need to find out their direction to base and how to arrive there even when having no landmarks for current position. This is the case for:
A. People who are lost in the ocean or in a large desert with no reliable landmark. They need some method of orientation using minimal number of tools.
B. People drifted to an isolated island in the ocean after a tsunami !
C. Installers of long distance or satellite communication antennas wishing to aim their devices when not having any map.
Required information:
1. Selected star(s) for the chosen base city with the target point(s) underneath the star(s) reasonably close to the base city.
2. Longitude of the base city and time signal announcing GMT time to show the time at base city. The time signal may come from Broadcast or Marine Band Weather Radio.
3. or an accurate watch that allows determination of the true (not zonal) time of base city (Each minute earlier or later than intended time may cause a longitudinal error of 0.25 degree that is about 27km near the equator.).

Step 1: Preparation before expedition

polrsouthq3c60.jpg

Figure: The sky map for use in Southern hemisphere.
1. Search from the list of brightest stars (in descending order) for the brightest identifiable star that can closely pass overhead the base city (with acceptable error distance) and the approximate date for it to be seen in at midnight.
Examples:
London is at (0°5′ longitude, 51°32′ latitude). In June, choose Eltanin (Gamma Draconis, 17hr 57′, +51.5° declination) target point underneath the star is 0km from base.
Berlin is at (13°25′ longitude, 52°30 latitude). In June, choose Eltanin (Gamma Draconis, 17hr 57′, +51.5°declination), target point underneath the star is nearly 110km South of the city while the zenith of the city is 2 Moon’s diameter from the star and toward the Celestial North . In December choose Gamma Persei (03hr05RA +53.5degrees declination, app magn 2.91) target point underneath the star is nearly 110km North of the city while the zenith of the city is 2 Moon’s diameter from the star and toward the Celestial South.
Mecca(39°45 longitude, 21°29 latitude) choose ArcturusBoote (213.9RA, 19.2° declination) nearby location underneath the star is 230km South of the city while the zenith of the city is 4 Moon’s diameter from the star and toward the Celestial North.
Manila (120°57′ longitude, 14°35′ latitude) choose Regulus, (Alpha Leonis, 10hr08’RA +12.0°declination) nearby location underneath the star is 280km South of the city while the zenith of the city is 5 Moon’s diameter from the star and toward the Celestial North.
2. Work out the day for the star to be highest at midnight. The day is the same for all locations. It is almost Sep23rd plus the RA of the star multiplied by (365.25days/360°).
Example:
Gamma Persei is nearly overhead at midnight of
Sep23 + 3hr05*(365.25days/24hr) =
Sep23 + 46.92days = Oct23 + 17d = Nov 09.
3. Learn by heart how to identify in the sky the stars associated with the base city. The accuracy and speed of this ability is essential to avoid mistakes under adversed circumstances. Users should not confuse between stars near the ecliptic and wandering planets nearby.
4. Practice determining the time when the star passes the vertical North-South plane at the base city on that date. It is midnight minus the local advance on GMT, which is equal to longitude multiplied by (24hr/360°).
Example:
Gamma Persei passes near Berlin (longitude 13°24′) on that date ahead of mid – night GMT by (13°24′)/(15°/hr) = 0.89hr, that is at
24hrGMT – 0.89hr = 23.11hrGMT = 23hr07GMT.
5. Every day later/earlier than that date, the star passes the location (60minx24/365.25) = 3.942 min of time earlier/later. This earliness is observable at all locations including your current one. When observing the star on another day, the earliness adjustment is needed.
6. If the Sun crosses the North-South vertical plane earlier/later than at base, the chosen star also crosses the North-South vertical plane earlier/later than at base by the same amount of time.
Step 2: Field application

BrightStars0b

List of 20 brightest stars. Additional, dimmer stars are also needed to travel closer to any arbitrarily given latitudes.

7. Identify the star and obtain the time signal from GMT. Work out the instant the star is overhead the base. (Alternatively, the moment the chosen star passes overhead the base can also be determined with an accurate watch from the time it passes the North-South vertical plane of current location and the advancement or retardment of local Noon relative to Noon at base.)
8. At that moment, the star is above the nearby spot close to the base. Every degree from your zenith is 111km distance from you. The direction to the star projected onto the ground gives direction to the chosen nearby location. To obtain more accurate direction to your base when the star does not pass its zenith, you can imagine another star at some diameters of the Moon on either North or South side of the RA circle from the chosen star and use it instead. Alternatively you can add some adjustment based on the differentials on a spherical surface to obtain the exact direction to your base.
Step 3: Navigating by only stars.
9. To travel to the target location, aim for a location on the same latitude but more in the North-South direction of the current point. This makes the travel distance longer but ensures that the target is not missed in the final part of the travel. When arriving at that target latitude, aim at the target location. Keeping the selected star on the East West line when it has highest altitude will ensure that the traveler does not miss the target.
This method suggests a possible way used by desert travelers and an alternative for refinement of Polynesian method of navigation.

4. How to find the zenith point.

The navigator has to hang a long plumbing line from a point higher than his eye level, stand away from it and look at the projection of the line onto the sky. The projection is a great circle arc through the zenith.

Looking at the plumbing line from many directions gives many great circle arcs intersecting at the zenith point in the sky. The navigator may have to note its relative distances to familiar stars and draw it and the stars on a piece of paper for future reference and cross checking.

This method requires a steady plumbing line and is suitable for ground travelers when resting at night.

5. How to locate any chosen bright star in the sky.
1. Find out its position relative to the 20 brightest stars by plotting it on the star maps here from its RA and declination.
2. Work out steps starting from identifiable top 10 brightest stars to positively identify it through progressively nearer, easily identifiable, bright neighbours .
3. Use the sky maps here to practice finding it in the sky.
4. Examples.
4.1 Locating Eltanin:
Eltanin is found from star charts and the sky maps here as the brightest star near to the point of one third of the way from Vega to Dubhe (There is no brighter star in the vicinity.).
4.2 Locating Regulus:
The broom shaped group of stars (Sirius, Canopa, Orion-Rigel, Betelgueuse, Procyon) identifies their elements. Betelgueuse-Pollux forms the hypotenus of the isoceles right triangle (Procyon, Betelgueuse, Pollux, Procyon, counter-clockwise) with Procyon at the right angle. Regulus is then one distant vertex of the rhombus (Procyon, Betelgueuse, Pollux. Regulus, Procyon, counter-clockwise).

6. Notes.
1. The local true time at the base city has the Sun crossing the North-South vertical plane at 12am. The zonal time (broadcasted by local radio and TV stations in the winter) is the true time advanced or retarded so that it differs from GMT by a whole number of hours.
2. The Sun crosses the North-South vertical plane before or after 12am zonal time by the difference between the local true time and zonal time. This amount is due to the excess or shortage of longitude to the nearest multitude of 15 degrees chosen for zonal time.
3. With an accurate watch still showing the zonal time at the base city, the longitudinal increment from that of base city can be worked out by the increment in the earliness of the crossing of the North-South vertical plane by the Sun. Each increment of 15 degrees in longitude corresponds to 60 minutes advancement in noon time.
4. Near to the end of the journeys, overland navigators may apply terminal homing using mega-features such as familiar city silhouettes, mountain peaks, rivers, rock and soil formation, permanent cloud formations, existing or ancient tracks, vegetation boundaries or even smell from plants. Some traditional land travelers may even release trained eagles to home on prairies while some traditional ocean travelers may release islands spotting birds to home on islands.
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Click here for my other blogs on divider43.jpgSURVIVAL

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

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