Adding Longitude and Latitude Lines to a map

Adding Longitude and Latitude Lines to a map

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.78).

#find North, #GPS, #navigation, #off grid, #adding, #longitude, #latitude, #coordinate, #lines, #map,

Adding Longitude and Latitude Lines to a map.

Locating where you are using the internet is great but there are times when you have no mean to connect to the internet and you have to use GPS for positioning without any assistance via the internet. Such a situation may arise when you have no internet coverage or when going hiking.

If you want to use your GPS off-grid with any map, you need to draw on top of the map an accurate system of regularly spaced longitude and latitude coordinate lines.

This posting shows how to add the lines.

1. Making a map graduated with Longitude and Latitude Lines.

1. Choose a map with your required resolution and range. The resolution differs for different application: For city street maps resolution should be better than 2m, for country town maps, resolurion only need to be better than 5m as houses are widely separated, for touring, exploring maps, resolution can be upto the (1/10) of the visual range, etc…

2. Make sure that the top of the map points to true North. (In some countries, maps are deliberately oriented at angle to true North, probably for security reasons.)

Figure: Openstreetmap for Melbourne with 3 airport landmarks. Map is used under Open License from Open Street Map, the data are owned by Open Street Map Contributors.

3. On that map, find some unmistakable features such as a well known Airport or Helipad, a Light House, a TV Transmission Tower, a Town Hall, Churches, Schools, Cottages in a forrest, sharply defined mountain peaks, trail intersections… with known longitudes and latitudes. Their coordinates are usually given on the Internet or or easily extracted from Google Map or Navigating Apps.
Find two to four such fearures located near the four extreme corners of your map. They will be used as land marks.

Ecample:

The 3 landmarks that can be used here are:

a. Melbourne Tullamarine airport, Elevation AMSL 434 ft / 132 m, Coordinates 37°40′24″S 144°50′36″E

b. Melbourne Moorabin airport, Elevation AMSL 50 ft / 15 m, Coordinates 37°58′33″S 145°06′08″E

c. Melbourne Essendon airport, Elevation AMSL 282 ft / 86 m, Coordinates 37°43′41″S 144°54′07″E

4. On a separate fresh sheet of paper make a coordinate grid of longitude and latitude covering your range.
On this sheet with grid but no map, mark the coordinates of your land marks.

Figure: Melbourne Tullamarine and Moorabin airports on a grid map.

5. Check that the shape of the figures formed by the land marks are similar in both the grid sheet and the map. You may have to stretch or shrink the grid vertically and then horizontally to have a fit. The figures should be similar if no mistakes have been made. If the shapes are similar you can proceed to the next step.

6a, If the map and grid are both digital, they can be superimposed in the computer to produce the following map with added coordinate lines:

Figure: Openstreetmap for Melbourne with added cooodinates. Map has been modified from original map used under Open License from Open Street Map, the data are owned by Open Street Map Contributors.

The added lines are on round figure coordinates and are 2 minutes of arc apart. The intersection nearest to the NW of Tullamarine airport has coordinate (144°50′E, 37°40′S ).

6b. If you are using printed map: Join two distant landmarks on the coordinate sheet and notice where the lines of “minute of longititude” and of “minute of latitude” intersect it

7. If you are using printed map: Reproduce that line, with all its intersecting points, on the actual paper map.

8. If you are using printed map: From these intersecting points project corresponding vertical lines to make the “minute of longititude” lines and horizontal lines to make “minute of latitude” lines.

9. The map is now graduated with longitude and laritude lines.

10. Its grid can now be used as a base to draw finer grids for detail maps with higher resolutions.

2. Using GPS with maps.

You can download a (preferably topological) map of your area to practice drawing the coordinate lines, the constant altitude lines and learn about the accuracy of the values of longitude, latitude and altitude given by your GPS apps.

It is preferable to use topographic maps with old fashioned land marks (such as churches, tall towers …). Topographic maps give the additional constant ground altitude contours (relative to some mean sea level surface). Constant altitude curves are the faint brown curves on the map illustrated here. The height of each contour is given by a small number. The altitude values of 20m and 10m have been highlighted in this example map by two red circles.

Figure: Opentopomap for the area in my test. Map is used under Open License from Open Street Map, the data are owned by Open Street Map Contributors.

References

[1]. tonytran2015, Using GPS in off-grid situations., posted December 6, 2016

[2]. tonytran2015, Measuring angles and distances for outdoor survival, survivaltricks.wordpress.com,

https://survivaltricks.wordpress.com/2016/06/29/measuring-angles-and-distances-for-outdoor-survival/, posted 29/6/2016.

[3]. tonytran2015, Selecting and using magnetic compasses, survivaltricks.wordpress.com,

https://survivaltricks.wordpress.com/2016/07/09/selecting-and-using-magnetic-compasses/, posted 09/7/2016.

[4]. , BBC News, UK radio disturbance caused by satellite network bug, http://www.bbc.com/news/technology-35463347, 2 February 2016.

Added after 2018 Nov 26:

The Thors’ son urged people travelling to remote locations without mobile coverage to download a GPS application to their phones ahead of their journey, as well as an offline map for their destination.

[5]. https://mobile.abc.net.au/news/2018-11-26/german-tourists-died-central-australia-walked-17km-heat-stress/10554408

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Navigating with an AM MW radio receiver

Navigating with an AM MW radio receiver

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.48).

#AM, #broadcast, #emergency, #radio, #radio direction finding, #find North, #Medium Wave, #radio navigation.

Every natural disaster emergency kit is recommended by authorities to include a battery operated Amplitude Modulation Medium Wave (AM MW, also called AM Broadcast) radio receiver to receive critical information and instructions.

The radio receiver can actually do much more than receiving information and instructions. It can find the direction to nearby AM broadcasting stations and even find your location on any map showing the stations.

Figure: Map of Melbourne with 2 nearby AM broadcasting stations shown as red dots. Map has been modified from original map used under Open License from Open Street Map, the data are owned by Open Street Map Contributors.

The technique is applicable when there are nearby (closer than 100km) AM broadcast stations. It is useful to regions near the terrestrial magnetic poles where magnetic compasses do not work well, to desert crossing and to coastal boat travel when visibility is very poor and other modes of navigation are not available (such as when in bad or extreme weather, during volcanic emergency and without any working magnetic compass).

1. Basis of Radio-direction-finding.

An AM broadcasting station in Medium Wave sends electromagnetic waves out from its antenna at the speed of light. The invisible EM waves propagate outwards from the broadcast station’s vertical antenna. The antenna continuously releases consecutive, expanding circular magnetic lines of alternating (clockwise then anti-clockwise) orientations. The circles spread out in all directions. When a receiver receives the signal, the alternating magnetic field is at right angle to both the spreading (propagation) direction and the alternating electrical field which is almost in the direction of the broadcasting antenna.

Most AM radio receiving Medium Waves (0.5MHz to 1.6MHz) use ferrite rod antennas to capture these magnetic field lines. The ferrite rod of an AM MW receiver is usually placed inside and along the top edge of the (usually flat) receiver. Figure 4 shows the ferrite rod antenna inside a Sony radio of a common design.

sharp radio

Figure 1: A battery operated multi-band AM radio that can be used in emergency. This battery operated multi-band AM radio with a fair sized signal strength indicator in a small window on the left of the dial was made in the 1960’s. Its pulled out rod antenna is only for Short Wave reception, an internal long ferrite rod antenna is used for Medium Wave reception.

radiosony

Figure 2: A compact radio receiver WITH an AM internal ferrite rod antenna that can be best for emergency use. This compact AM/FM receiver has an internal ferrite rod antenna for AM MW reception and can properly receive AM signals even without using any earphone.

When an AM MW (also called broadcast band) radio receiver has been tuned to a station, you can notice the signal strength varies when its ferrite rod antenna is rotated on the horizontal plane: The received signal is weakest when either end of the rod is pointed directly at the transmitting station, and it is strongest when the rod is at right angle to the line of sight to the station. The technique has been widely used for ships until the advent of low cost GPS. Reference [1] gives a really interesting long list with pictures of AM radio receivers specially built for the application of this technique on ships.

Figure 3: A 3 band Sony transistor radio with a retractable short wave rod antenna (radio model 838, assembled in South Vietnam in 1970, under license from SONY, as shown on the label on the back of the radio).

direction by ferrite rod antenna

Figure 4: The interior of the Sony transistor radio showing a long ferrite rod antenna of grey colour on the top and parallel to the top edge. (Sony radio model 838, assembled in South Vietnam in 1970, under license from SONY, as shown on the label on the back of the radio.)

CAUTION: Many compact AM MW radio receivers do NOT have ferrite rod antennas, they use their earphone wires to receive the electrical component of the broadcast waves. This method of finding directions does NOT work with such receivers.

2. Finding direction by a radio.

Rotate the top edge (with the ferrite antenna) of the receiver by a full horizontal turn and notice the two opposite directions where signal receptions are weakest. When this happens, one of the ends of the ferrite rod is pointing exactly at the station and the station lies on the line through the top edge of the receiver. Additional information from somewhere else is needed to tell in which of the opposite directions the station may lie.

Figure: Openstreetmap for Melbourne with added cooodinates and the locations of Delahey and Lower Plenty. Map has been modified from original map used under Open License from Open Street Map, the data are owned by Open Street Map Contributor.

Examples:

a. “ABC Radio Melbourne ‘s 774 kHz transmitter is located in Delahey (the left red dot in the map), 20 km north-west of Melbourne’s central business district. … at a power of 50,000 watts,… one of two transmitters using the callsign 3LO” [2].

When an AM radio is tuned to 3LO on 774kHz it receives the broadcast with call sign 3LO. When its ferrite antenna is pointed at the left red dot on the map, the signal will be weakest and the reception most noisy.

b. ABC NEWS on radio ABC NEWS on radio Frequency 1026 AM Callsign 3PB Sound Mode Mono Polarisation Vertical Broadcast Pattern OmniDirectional Transmitter Location Bonds Road LOWER PLENTY (the right red dot on the map)” [3].

When an AM radio is tuned to 3PB on 1026kHz it receives the broadcast with call sign 3PB. When its ferrite antenna is pointed at the right red dot on the map, the signal will be weakest and the reception most noisy.

You may be able to find the frequencies and transmitter locations of the AM broadcasts for your area from the useful sites [4] www.dxing.info, [5] wiki List of European medium wave transmitters

3. Finding location by a line through the station.

If the direction of the top edge of the receiver relative to true North is known, the locus of the receiver on the map is a straight line through the broadcasting station.

Your location can be found using the intersection of two such locus lines through two broadcasting stations shown on a map. (The intersection R of the lines RS1 and RS2).

4. Finding location by a circle through two stations.

If two stations S1 and S2 are shown on a map and A is a directed (signed) angle from the line to S1 to the line to S2 then the locus of the radio receiver is the circle through S1 and S2 bearing that directed angle A.

For example, if the angle from R-S1 to R-S2 is 40 degrees (an example value) in the anti-clockwise direction, the receiver must be on the red circle drawn through S1 and S2 on the map. The example circle is called the circle bearing the angle of 40 degree in the anti-clockwise direction for viewing the (direcred) line segment S1-S2.

5. Finding location by three circles through three stations shown on a map.

arc bearing

Figure 1: Finding your location using intersecting angle bearing circles.

Any map showing the locations of the broadcasting stations S1, S2, S3,… can be used to locate the position R of the radio receiver. Any receiver with the angle from R-S1 to R-S2 being 40 degrees clockwise (an example value) in the clockwise direction must be on the circle drawn through S1 and S2 for that example value of 40 degrees. The example circle is called the circle bearing the angle of 40 degree in the clockwise direction for viewing the line S1-S2.

If three stations S1, S2 and S3 are shown on a map as in the figure of the last section and the directed (signed) angles between the directions to S1, S2, S3 are all known, the receiver is on the intersection of all three circles through each pair of S1, S2 and S3 bearing the respective directed angles between them. Usually, only two circles are needed to draw the intersection point, which is the location of the radio receiver R.

6. Limitation of the method.

a. The method works well if there are non-interfering AM broadcast stations within 100km of the navigator and the terrain is nearly flat.

b. When there are high atmospheric electrical activities it may be hard to find the direction for weakest reception by the ferrite rod of the broadcasting signals.

c. Many compact AM MW radio receivers do NOT have ferrite rod antennas, they use their earphone wires to receive the electrical component of the broadcast waves. This method of finding directions does NOT work with such receivers.

d. The method does NOT work with Shortwaves as shortwave signals are not received through ferrite rod antennas.

e. Note that Philips from Holland had a famous radio model, L4X00T, with a fold up/fold down rectangular antenna loop for shortwaves, which can also be used to find out the direction of the incoming shortwaves in the same way as described in preceding sections. However shortwaves bounce and they do not accurately show the directions to the stations.

f. For the method to be useful after an Electro-Magnetic-Pulse event, the receiver and the broadcasting stations should all survive the event. You may have to wrap your radio receiver in many layers of Aluminium foils and the broadcasting stations must know how to protect themselves against EMP events.

Reference.

[1]. Radio Direction Finders, angelfire.com, http://www.angelfire.com/space/proto57/rdf.html, accessed 06 Feb 2017.

[2]. https://en.m.wikipedia.org/wiki/ABC_Radio_Melbourne

[3]. http://www2b.abc.net.au/reception/frequencyfinder/asp/details.asp?transmissionid=2956.

[4]. http://www.dxing.info/lists/

[5]. https://en.m.wikipedia.org/wiki/List_of_European_medium_wave_transmitters

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Using GPS in off-grid situations.

Using GPS in off-grid situations

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.36).

#find North, #tine #GPS, #GPS altitude, #GPS coordinates, #GPS navigation, #off grid, #topographic map, #longitude, #latitude,
Locating where you are using the internet is great but there are times when you have no mean to connect to the internet and you have to use GPS for positioning without any assistance via the internet.

Such a situation may arise when you have no internet coverage such as when going hiking.

This posting shows how to do it with minimum battery use.

1. Requirements:

a. A phone with GPS hardware preferably with back up battery or re-charger.

b. A procedure to minimize battery usage.

c. A map with longitude and latitude coordinates printed on paper or stored in the phone (Section 8 will show how to draw those lines on any paper map).

d. An optional software to display your position on the map.

Map with Coordinates

Figure: Openstreetmap for Melbourne with added cooodinates. Map has been modified from original map used under Open License from Open Street Map, the data are owned by Open Street Map Contributors.

2. Selecting a phone with good off-grid GPS capability.

I would choose one that can quickly obtain an accurate GPS value from cold start. Different phoneMarkingsand GPS apps have different sensitivities, algorithms and accuracy.

Compass app and barometer app are highly desirable additions on such a phone.

Compass app using magnetic sensors gives you the direction without having to move at speed to obtain the deduced True North.(GPS apps obtain True North using solely the tiny increments from GPS coordinates). You should know how to calibrate a magnetic compass app by the figure 8 motion.

Barometer app gives your accurate altitude change if you need that value for working out your position using angles and changes in altitude. Barometer app can also warn you of developing severe weather.

3. Two different pieces of hardware can give out two different GPS readings.

The following are the readings from two different smart phones placed in one place. The readings have differences of about 4m in distances in both longitude and latitude directions. (Each minute of latitude angle is one nautical mile, and each second of latitude distance is about 3m in length).

Fig 1&2: Readings from the first smart phone.

Fig 3&4: Readings from the second smart phone running the same app at the same place!

The hardware is guaranteed to give you only some accuracy. My two smart phones seem to have horizontal accuracy values of no better than 4m. Their vertical accuracy values are not better than 10m.

4. A single point may correspond to different latitude and altitude values depending on the different base surfaces used for mean sea level.

Remember that the earth is not a perfect sphere. Its rotation and non-uniform interior density creates its non-spherical surface at sea level. Vertical lines do NOT converge at the center of the earth but are only the lines at right angle to the local sea surface. The latitude and longitude of a point as determined by sextants only give the direction of its vertical line, not the intercept between the non-spherical surface and a line from the center of the earth pointing in that direction!

With that idea in mind, it is clear that a single point in space may have different latitude and altitude values depending on different type of non-spherical surface used for mean sea level.
So you should choose apps with a widely accepted base surface (such as WGS84) so that their latitude and altitude values are readily interchangeable.

Figure 5,6: Reading from GPS Test (1.3.2).

Fig 7: Reading from GPS Status (5.3.112) on the same smart phone. The two apps give matching readings.

5. When communicating your coordinates with others, you may have to mention the name and version number of your GPS app or the type of base surface in use!

For the same reason, the 3D coordinates from your GPS apps may be inconsistent with the published coordinates of international airports or the land marks on your trips.

Any map with GPS capability such as Googlemap should be already compatible with its GPS in use.

6. Using AGPS updates to save battery.

The phone app can only listen to one GPS satellite at a time. There are many of them and only four clearest transmissions are useful (The others are either out of view or do not provide positional precision). To listen to every transmission and select the clearest four takes time. Then starting from the far off position will take a lot of time for the calculation algorithm to arrive at the correct GPS position.

Remember that the more time you have to wait for a GPS fix the more you run down your battery.

AGPS (Assisted GPS) provides the app with the list of the best transmissions to listen to (from your approximate position) and the algorithm will begin from your approximate position. You will save a lot of time and battery. Choose a GPS app with off-line AGPS update as your principal GPS app.

7. Procedures to use GPS apps

a/- Beware of the high battery usage by GPS hardware.

b/- Run your magnetic compass calibration apps if you think that compass directions may be required.

c/- Run your principal GPS app (with off-line AGPS update capability). Once a fix has been obtained update its AGPS immediately; this saves battery on future fixes.

d/- Run any other GPS apps with your desired features (such as inclination, altitude, magnetic heading, light meter, etc…) immediately after the principal one. The hardware can continue from the values previously obtained by your principal GPS app.

e/- TURN OFF the GPS hardware.

f/- Relate your GPS position to the coordinates (longitude and latitude and possibly with altitude) on the printed map or the map stored in your phone.

g/- Know the horizontal and vertical error of each fix to know your PROBABLE position.

h/- Turn off the phone or put it in stand-by mode to save battery.

8. Making a map graduated with Longitude and Latitude Lines.

1. Choose a map with your required resolution and range. The resolution differs for different application: For city street maps resolution should be better than 2m, for country town maps, resolurion only need to be better than 5m as houses are widely separated, for touring, exploring maps, resolution can be upto the (1/10) of the visual range, etc…

Figure: Openstreetmap for Melbourne with 3 airport landmarks. Map is used under Open License from Open Street Map, the data are owned by Open Street Map Contributors.

2. On that map, find some unmistakable features such as a well known Airport or Helipad, a Light House, a TV Transmission Tower, a Town Hall, Churches, Schools, Cottages in a forrest, sharply defined mountain peaks, trail intersections… with known longitudes and latitudes. Their coordinates are usually given on the Internet or or easily extracted from Google Map or Navigating Apps.
Find four such fearures located near the four extreme corners of your map. They will be used as your four land marks.

Ecample:

The 3 landmarks in use here are:

a. Melbourne Tullamarine airport, Elevation AMSL 434 ft / 132 m, Coordinates 37°40′24″S 144°50′36″E

b. Melbourne Moorabin airport, Elevation AMSL 50 ft / 15 m, Coordinates 37°58′33″S 145°06′08″E

c. Melbourne Essendon airport, Elevation AMSL 282 ft / 86 m, Coordinates 37°43′41″S 144°54′07″E

3. On a separate fresh sheet of paper make a coordinate grid of longitude and latitude covering your range.
On this sheet with grid but no map, mark the coordinates of your four land marks.

Figure: Melbourne Tullamarine and Moorabin airports on a grid map.

4. Check that the shape of the quadrilaleral formed by the four land marks is similar in both the grid sheet and the map. You map have to stretch or shrink the grid vertically and then horizontally to have a fit. The quadrilaterals should be similar if no mistakes have been made. If the shapes are similar you can proceed to the next step.

5a, If the map and grid are both digital, they can be superimposed to produce the final map:

Figure: Openstreetmap for Melbourne with added cooodinates. Map has been modified from original map used under Open License from Open Street Map, the data are owned by Open Street Map Contributors.

5b. If you are using printed map: Join two distant landmarks on the coordinate sheet and notice where the lines of “second of longititude” and of “second of latitude” intersect it

6. Reproduce that line, with all its intersecting points, on the actual map.

7. From these intersecting points project corresponding vertical lines to make the “second of longititude” lines and horizontal lines to make “second of latitude” lines.

8. Your map is now graduated with longitude and laritude lines.

9. Using GPS with maps.

I prefer to use topographic maps with old fashioned land marks (such as churches, tall towers …). Topographic maps give the additional constant ground altitude contours (relative to some mean sea level surface). Constant altitude curves are the faint brown curves on the map illustrated here. The height of each contour is given by a small number. The altitude values of 20m and 10m have been highlighted in this example map by two red circles.

Figure: Opentopomap for the area in my test. Map is used under Open License from Open Street Map, the data are owned by Open Street Map Contributors.

If you want to use your GPS with any map, you need to draw on top of it an accurate system of regularly spaced longitude and latitude coordinate lines as instructed in Section 8.

You can download a topological map of your area to practice drawing the coordinate lines, the constant altitude lines and learn about the accuracy of the values of longitude, latitude and altitude given by your GPS apps.

10. Integrated GPS and map apps.

GoogleMap is one such app. It automatically supply you with a map and works out your position from its included GPS. It is great when you are connected. Some old versions of Googlemap allow you to store a map of an area of about 30kmX30km for off-grid use. I don’t know if you can store maps for much larger areas.

I would keep a printed map with coordinates for back up when going off-grid since I would not put everything into one smart phone.

11. Error from GPS is rare but not impossible.

As with anything, continuity (or consistency) of readings must always be applied to check for any sudden error arising. It has been reported by BBC news that during the decommission of the GPS satellite SVN23, “some GPS positioning would have been thrown off by nearly 4km.”.

References

[1]. tonytran2015, Measuring angles and distances for outdoor survival, survivaltricks.wordpress.com,

https://survivaltricks.wordpress.com/2016/06/29/measuring-angles-and-distances-for-outdoor-survival/, posted 29/6/2016.

[2]. tonytran2015, Selecting and using magnetic compasses, survivaltricks.wordpress.com,

https://survivaltricks.wordpress.com/2016/07/09/selecting-and-using-magnetic-compasses/, posted 09/7/2016.

[3]. , BBC News, UK radio disturbance caused by satellite network bug,

http://www.bbc.com/news/technology-35463347, 2 February 2016.

Added after 2018 July 17:

[4]. https://irishinfosecnews.wordpress.com/2018/07/17/how-to-spoof-someones-gps-navigation-to-send-them-the-wrong-way/

Added after 2018 Nov 26:

The Thors’ son urged people travelling to remote locations without mobile coverage to download a GPS application to their phones ahead of their journey, as well as an offline map for their destination.

[5]. https://mobile.abc.net.au/news/2018-11-26/german-tourists-died-central-australia-walked-17km-heat-stress/10554408

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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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Beware of perilous flips by magnetic compasses

Beware of perilous flips by magnetic compasses

by tonytran2015 (Melbourne, Australia).

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#compass, #flip, #reversal, #compass reversal, #compass flip, #re-magnetize, #navigation, #survival, #find North, #finding North,

There has been warning by a Mountaineering expert that many people got into perilous situation when their compasses unexpectedly flipped direction prior to critical use. The Mountaineering Council of Scotland has issued warning on this danger.

This posting gives a method to re-magnetize and set at will the direction of any compass needle. The basic steps in guarding against unexpected flipping of magnetic compasses are also shown.

One possible cause of flips by magnetic compasses.

When a magnetic compass is stored its needle can not swing or cannot swing fast enough to follow the change in magnetic field.

If a strong magnetic field is forced through the needle from one end to the other, the needle will be magnetized by this strong field.

Therefore when your compass is stored in your bag and a strong magnet approaches it faster than the needle can rotate to adapt to change, the new field may be able to force a magnetic flux from one end of the needle to the other end and re-magnetize the needle. This occurrence is not rare.

Proof and applications.

compassflipMEDIUM

Figure: The reverse-magnetized needle of the compass with clear case

The first pictures shows that the needle of the clear based compass is pointing in the opposite direction to that given by the reference, metal cased compass. The needle has been magnetized into the flipped condition.

Re-magnetize the needle again

compassRestoredMEDIUM.jpg

Figure: The re-magnetized needle of the compass with clear case.

The compass needle was then successfully re-magnetized back into normal condition. It again points in the normal direction.

So I have been able to re-magnetize (in any direction of choice) the needle of a compass (the clear based compass with a mirror) as shown in the first two pictures. The magnet I used costs me under $0.30USD and is shown in the third, composite picture.

Re-magnetizing the needle of any compass

CompassToolsMEDIUM

Figure: Tools for Re-magnetizing the needle of any compass.

1/- To re-magnetize a compass, it is preferable to have a single pole P of a strong magnet far away from its other poles. Lay the compass up-side-down. Find out the end A of the needle that is repulsed by P. Push that pole P to the center of the needle, then move P towards that end A. When P has reached the end A and attracted that end, the needle has been re-magnetized.

It is even better if you can supply another single pole Q of opposite polarity to also touch the other end B of the needle. Otherwise, just use the compass just re-magnetized by the single pole P.

2/- The above re-magnetization shows that it is preferable to have long, observable needles for compasses.

3/- If you carry any strong magnets make sure that they are closed by closing irons to keep their magnetic lines within the vicinity of the magnets and the lines do not affect your compass.

The magnet I used is a fridge magnet of the rare earth type, it costs under $0.30 USD.

Avoidance and detection of flipping of a magnetic compass.

On acquisition of a compass, you should

1/- inspect it for any damage,

2/- count the swing, roll, and pitching vibration frequencies of its needle and make a written record,

3/- check the pitching of the needle and make a written record.

Before packing the compass for each field travel, you should

1/- inspect it for any damage,

2/- compare its swing, roll, and pitching vibrations of its needle with the written record made on acquisition,

3/- check the pitching of the needle and compare against the written record made on acquisition.

4/- have the polarities of the strong magnets on your phone case marked on a sketch (showing which magnets attract which ends of the needle). A copy of the sketch should be carried with the compass.

Before each field use, you should

1/- inspect your compass for any damage,

2/- carefully check the pitching of the needle (If a flip has occurred, the pitching also changes as the North pointing end usually balanced to point horizontal. If the North end pitches in any other way, the needle may have flipped.),

3/- slightly and slowly move the compass towards the phone case to see if the attraction pattern is still the same.

4/- If the vibration patterns are noticeably different the compass may have been damaged or may be in a stronger or weaker than normal (abnormal) magnetic field. You need to think about possible causes and effects.

5/- The above steps only help to detect any unexpected flipping, you still has to carry out all other procedures recommended by the maker of the compass.

Your compass usage should be more reliable with these extra precautionary steps.

Reference.

[1]. Heather Morning, Calling ALL Hill Walkers,The Mountaineering Council of Scotland, http://www.mcofs.org.uk/navigation-reversed-polarity.asp, posted on April 2013.

Related SURVIVAL blogs:

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

Compass-Magnetic

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

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