Tag: navigation

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Phillosoph

Survival Library: Chapter 2, Bushcraft 101

Continuing my suggestions for a survival library.
Today I will look at a title that is relatively new to me. Some other reviewers consider it a “must have”.
The book is “Bushcraft 101” by Dave Canterbury.
Cover of Bushcraft 101
I quite liked this book.
The early section on safe and effective ways to use your knife and other tools is particularly good, and possibly worth the price alone.
It is a good book for rending topics down to a simply grasped form.
An interesting aide memoire Canterbury uses is “the Five Cs”: Cutting, Cover, Combustion, Containers and Cordage. Personally, I would advise adding “Consumables” and “Compass” to that list.
Another useful aide memoire is the “Four Ws”, used for selecting a good campsite: Wood, Water, Wind and Widowmakers.
To the advice given in the book, I will remind the reader that water sources often come with biting insects, so a camp should not be too near. Under the same category, one should consider watercourses. If you camp in a dried river bed or runoff, a storm miles away may result in your camp literally being washed away.
A third handy memory aid is “LURD”, used to determine the direction viewed by star movement. I recommend memorizing it as “LURD:NESW”. If a star is moving upward, you are looking east, and so on.
Determine direction of facking by star movement
The section on maps and compass is much more straight forward than in some publications:
“The most important reason to carry a compass is so that we can walk a straight line over distance.”
• Here I will insert a useful tip not given in this book. To walk in a straight line, align three objects. Tree trunks in a forest are ideal.
As you reach the first object, align the next two objects with a fourth, and keep repeating this process as necessary.
While applying a calculation to compensated for difference between magnetic and grid north is mentioned in Bushcraft 101, the actual method (LARS) is not detailed.
Perhaps it was felt that in a survival situation the difference is not significant, only a general orientation of the map being adequate. A similar approach is taken in the SAS Survival Handbook.
In some parts of the world, or for more general navigation, magnetic declination may be significant.
I would recommend regarding the navigation section of Bushcraft 101 as a useful primer and follow it with some more detailed reading on the topic.
The above brings me to one of the shortcomings of Bushcraft 101.
The book is very much written for a North American audience, and mainly geared for travel or emergencies in woodland.
If you frequent the prairies or deserts, you may wish the book had mentioned some tent poles to rig the suggested tarp. Similarly, some of the advice given may not be so valid for other parts of the world.
That said, my impressions of this book are very positive.
Once you have the suggested titles by Kephart, Greenbank and Wiseman (and my own books, of course!), Bushcraft 101 is worth considering as a useful addition. 

 

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Phillosoph

Sun-Compass

Yesterday’s topic logically brings me onto today’s, and another ancient but useful navigation device.
If you have even just glanced through a survival manual, you will most likely have seen the shadow-stick method.
I have previously described this in the context of navigating by the moon. Like the sun, the moon and stars also rise in the east and set in the west.
The more usual context for the shadow-stick is using the sun.
The method is simple.
Place a stick or similar in the ground so that it casts a shadow. Mark the end of the shadow.
Wait for at least twenty minutes.
The tip of the shadow will have moved. Mark this new position. The first marker will be west of the second.
Draw a line between the two markers, then run a line perpendicular to this and back towards the base of your stick (gnomon).
This second line will be true north-south. The greater the distance/longer the time between marker placement, the more accurate will be your determination of north-south.
Logically, we will get a more accurate estimate if we take several hours and place a number of markers.
If we do this we will observe that the shadow is longest in the morning and evening, and shortest when the sun is directly overhead.
The arc plotted on the ground will be flattened rather than constant, unlike some illustrations of this method!
When the shadow is at its shortest, it is on the north-south line, and the time will be local midday. The shadow will be shortest at local apparent noon (LAN), which is midway between sun-up and sun-down, so may differ from 1200 hrs.
As well as determining distance, you have also made yourself a crude sundial. This can be useful in determining true local time.
Some countries on the same longitude use different times. China spans several time zones but uses one official time for the whole country!
The principle is simple enough, but it can get confusing which end of the north-south line is north. In the northern hemisphere the sun (or moon) rises in the east and travels west, passing through the south. In the southern hemisphere it goes through the north.
  • In the northern hemisphere the shadow always points in a northerly direction. At midday the shadow will point due north.
  • In the southern hemisphere the shadow always points in a southerly direction. At midday the shadow will point due south.
Memorize that and solar navigation becomes much less confusing.
In the movies, air-crash survivors usually undertake an epic journey back to safety.
In the real world, your prudent strategy is to stay near the crash site if practical.
Setting up a shadow stick is a practical way to spend the time, and establishing the bearings of visible landmarks may be useful later on.
Suppose, for whatever reason, you need to travel. This decision should never be made lightly.
Thanks to your shadow-stick, you know what bearing you are heading out on, and that of some of the local features.
But we cannot take our compass/sundial with us!
With a few modifications, we can make a portable variant.
If you have ever read about the early days of the SAS or of the Long Range Desert Group (LRDG), you will most probably have encountered to references to sun-compasses on their vehicles.
In those days, trying to use a magnetic compass while riding in a large lump of steel was problematic. The solution was the sun-compass.

Descriptions of how the sun-compass was used used to be hard to find. Thankfully, this is changing.

The sun-compass is an ancient device, and was used by the Vikings, among others. A version was also used by some Apollo missions on the moon.

As you can see, some sun-compasses are very complicated or sophisticated, so not really something you can improvise.
I am going to describe a less accurate variant that can be easily constructed.
In the previous blog, I described how a circle of 57 mm radius had a circumference of c.360 mm. (The person who taught me this trick had 5 mm and 57 mm marked on the zipper of her jacket. I notched my penknife handle).
Create such a circle on a piece of paper, back of a notebook, etc.
An alternate name for a sun-compass is “shadow board”, which reminds us it can be made with a piece of plank or other flat material.
A folded piece of paper will help us mark off the 45, 90 and even 22.5 degree points.
Each 1.5 cm of the circumference is 15 degrees.
The radius of a circle can be measured twelve times along its edge using a drawing compass, or an improvisation of one.
By folding the marked points together the circle can be divided further into 24 parts, or the drawing compass can be used further.
A nail or pin can be used as the gnomon, but a sliver of wood is more likely. In fact, you do not have to mount the gnomon, just place a shadow-casting object in the centre of the circle whenever you take a reading.

All we have to do now is mark off the circle. This will be a 24 hour clockface so mark off every 15 degrees with an hour.

Remember that the shadow will point due north at midday in the northern hemisphere, so mark 1200 hrs as North/0 degrees (In the south, 1200 will be South/180).

Fill in the rest of the face. You might get something that looks like this:

Using this simple sun-compass is simple.
Hold it level and rotate it until the gnomon shadow is over the current time. If the clocks are adjusted for daylight saving/BST or similar you will have to account for this.
Remember, “spring forward, fall back”, so the shadow will be on the north-south line at 1300hs, not 1200, so you will have to subtract an hour from local time to get the time to read on the dial.
Once you have your sun-compass orientated, use the dial to find the bearing you want. Your portable sun-compass should agree with your base-camp shadow stick.
Pick out a landmark, put away your sun-compass and walk towards the landmark. 
An alternate method is to do the same as you did with a shadow-stick. Erect a little gnomon on a board or sheet of paper and plot the tip of the shadow over the course of a day.
Draw a line from the base of the gnomon across the curve where it is at its closest.
To use this version you do not need to know the time.
Rotate the sun-compass until the tip of the shadow meets the curve. The line you drew will point north (or south if you made your sun-compass in the southern hemisphere).
You must use the same height gnomon for each reading, so mount this permanently.
The Ottomani version is suspended from three or four points by cord to ensure that it is level.
You may have realized that if you know the bearing of something, your sun-compass can be used as a crude sundial.
Related to the methods described above is using a watch directly to navigate by the sun.
Remember to adjust time for BST/DST. Substitute “1 mark” for “12 mark” in the above instructions.
If your watch is digital, or you are using your phone clock, use your imagination.
If you become confused as to which end of the north-south (N-S) line is north, check the local shadows.
Hold a blade of grass over the watch-face and see if it casts a shadow. The one direction a shadow cannot point in the north is south.
Useful to recall is “the north gets up around 3 o'clock, goes to bed around 9”.
In other words, the north end of the N-S line will be in the small numbers in the morning, the higher numbers in the afternoon. (In the southern hemisphere replace the word north with south and the motto still works.)
Remember, sometimes shadows are still visible even when you cannot see the sun directly. 
The basic watch method is easy to remember: midpoint between “12(/1)” and the hour hand.
The specifics for each hemisphere can be difficult to remember.
It may help to think that “N” for north-hemisphere looks like a “H” for “hour-hand” and that this should be pointed at the sun. A cast shadow will point in the opposite direction to the hour hand.
For the southern-hemisphere, the 2 in “12” looks a little like an “S” so the 12 should be pointed at the sun. A cast shadow should point towards “6”.
Hopefully that will help you use this method.
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Phillosoph

Magnetic Declination

Methods for finding direction without a compass give you true north.
Strictly speaking, a map shows “grid north”, which may differ from true north, particularly on older maps.
Since we generally use a compass with a map, the difference between true north and grid north isn’t usually a worry.

A compass does not point to true nor grid north, it points at magnetic north.

Magnetic north is somewhere up in Canada, but currently seems intent on defecting to Siberia. The difference between magnetic north and true/grid north is known as the “magnetic declination” or “G-M angle”.

This map of the world shows magnetic declination in different parts of the Earth’s surface. Since magnetic north is moving, this map will be out of date when you read it.
Note that declination has very little correlation with longitude.
The green line shows the agonic line. If on this line a compass will point towards true north.
On the isogonic lines, declination may be more than 20° in the northern hemisphere and even greater values as we travel south. Easterly declinations are in red. Westerly declination are in blue and given as a negative number.
So what effect does magnetic declination have on navigation?
Suppose I am in an area where the declination is 2° west. I’m facing a direction the compass tells me is north, 0°.
I notice something of interest ahead of me and try to locate it on my map. Rather than being on the north-south line the point of interest will actually be at a bearing of 358° from my position on the map. 0° is the same as 360° so 2° west gives 358°.
In another part of the world. I might face towards magnetic north but in fact be facing at a bearing of 13° east, a significant difference.
Magnetic declination will probably be marked in the margin of your map. Some maps have a declination in each corner of the map. Use the value closest to your position on the map. If you are midway or in the centre average the relevant values.
Note that the declination diagram is not drawn to scale. Don’t try to measure it with your protractor, use the values given in the text.
To make our life more interesting, magnetic north moves over time. The magnetic declination information will include an annual rate of change so you can calculate how much the declination has changed since the map was printed.
An old map I have of London tells me the magnetic declination for June 1989 was 6°W and that this was expected to change by 9'E every year.  
In 2001 it would therefore be expected to be 4.2°W.  
In 2016 this map predicts magnetic north will have shifted by 243' from what it was in 1989. There are 60' in a degree so 243' is 4° 3' and predicts magnetic declination in London would be 1° 57' west by 2016.
This website gives the magnetic declination in London in 2016 as actually being 2° 10' west.
In practice, declination is rounded to the nearest half degree/30' or 10 mils. so we would treat both 1° 57' and 2° 10' as 2°.
The difference does illustrate that not only does magnetic declination change over time, but the rate of change may also vary.
If using old maps. it is important to get up-to-date information.

Once you have an up-to-date magnetic declination, what do you do with it?

This is where a lot of people get confused.

Declination, or G-M angle, is the difference between grid north (GN) and magnetic north (MN). The magnetic north line may have half an arrowhead or a barb. The declination diagram may also include true north, often marked with a star (★).

When do you add it, when do you subtract it? Some maps will give you this information, relevant for the area covered in the map. Where present, follow these instructions.

When a  map lacks this information, there are lots of rhymes and aide memoires that have been created to teach you what to do. Some of these, however, are only “true” in certain parts of the world.
Many readers will have been taught use the acronyms “MUGS” and “GUMA”. These stand for “Magnetic Unto Grid: Subtract” and “Grid Unto Magnetic: Add”.
A related rhyme is “Magnetic to Grid, get rid” and “Grid to Mag, Add”. Another acronym pair is “MUCA” and “CUMS”. The “M” stands for map and the “C” for compass in this case, but when stressed you might confuse these with “magnetic” and “chart”, so I find MUGS and GUMA safer, and LARS even better.
 
What MUGS means is that if you have a magnetic bearing, taken with your compass, you must subtract the magnetic declination before plotting the angle on your map. In our example above the magnetic bearing of 0°/360° has the declination of 2° subtracted from it to give the actual bearing of 358°.
When converting a bearing on the “grid” to a magnetic bearing you add the declination (GUMA).
I suspect that the MUGS/GUMA acronyms are probably British Army in origin, since they tend to favour a westward declination and could be used in the UK and most of Western Europe.
To make MUGS/GUMA global in application, we needed to learn one more thing: “West is Best, East is Least”.
“West is Best, East is Least” tells us to treat a west declination as positive and an easterly one as negative.
As you should know, subtracting a negative number adds the value of the number to the total. Adding a negative number subtracts the value.
Hence, from the above examples:
0°/360°(magnetic) – 2°W = 360°-2° = 358° grid (MUGS)
0°/360°(magnetic) – 13°E = 360°- (-13°) = 0°+ 13°= 13° grid (MUGS)

(It is possibly more logical to treat a westward declination as negative, giving us the rather nice acronyms of “MUGA” and “GUMS”. MUGS and GUMA are very well established, however.)

Another disadvantage of MUGS and GUMA is that the movement of magnetic north is changing the magnetic declination of the British Isles and parts of Western Europe to easterly.
As I update this article in February 2024, magnetic declination in London is now 1°51' East.
Yet another system, which is probably more useful in the future, is “LARS” = “Left: Add/ Right: Subtract”.
This uses the declination diagram on the map. You need to move right/clockwise to get from a westerly magnetic north line to the grid north line, so you subtract the G-M angle to convert from magnetic to grid azimuth. From the grid line to magnetic north is left/anticlockwise, so add the difference for calculating magnetic from grid.
For an easterly declination, the grid line will be to the left/anticlockwise of magnetic north, hence magnetic to grid adds the G-M angle and grid to magnetic (right/clockwise) subtracts in this case.
I recommend that you learn and use the LARS method.
Treat the G-M angle as an absolute value (always positive) and follow LARS: Left Add, Right Subtract.

The method in the illustration above will be familiar to many compass users.
Rather than aligning the needle with the “N” arrow on the face it is possible to compensate for magnetic declination by holding the needle pointing at the declination value on the dial.
Hence if the local declination is “10°W”, you hold the compass so the needle points to the “350°” mark on the bezel rather than “0°”.
You may use LARS to calculate the offset (the value the needle should point at).
You are making a magnetic bearing into a grid one.
MAGMGA: Magnetic Azimuth +/- G-M Angle = Grid Azimuth.
For a easterly declination (East/Left Add) add the G-M angle to 0.
For an westerly (West/Right Subtract) , subtract the G-M angle from 360°/6400 mils.
As a check, the needle and the north mark should resemble the declination diagram. In other words, if the G-M angle is easterly, the needle should be to the right/clockwise of the north mark.
This is useful when walking to a bearing, although you are better walking towards a landmark rather than walking staring at your compass (or phone!) all the time.
When sighting with a compass, the values you will get will still need conversion.
Remember that metal objects on your person or in your surroundings may affect a compass reading. Overhead power cables may influence the needle from as far as 55 metres away!
“West is Best, East is Least”
MUGS
GUMA
LARS
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Phillosoph

Duodecimal Finger Counting: Counting to 60 on One Hand.

Currently I am reading “The Last and First Men” by Olaf Stapledon.
I’ve just reached the section on the third species of mankind. The third species have six fingers on each hand and Stapledon notes that they have a duodecimal mathematical system.
By a manifestation of synchronicity. I was watching “QI” that very night and a base- twelve finger counting system they attributed to the Babylonians was featured. Using this system it was possible to count up to or display numbers of up to 60.
Investigating the topic further, I came across a number of websites averring that the Babylonians in fact had a base-60 numerical system. Looking at their numeral system, however, seems to suggest a decimal system. Which of these is true is out of the scope of this blog.
I thought it would be handy (pun intended) for readers of this blog to know about a hand signal system that can represent relatively high numbers. Many measurement systems are based on dozens, 24 or 60, after all.

The system is very simple. There are four fingers on your hand and each has three joints and three bones. The joint or bone of the first finger nearest the wrist is “1”. The join of the little finger nearest its tip is “12”.
By pointing at a joint with the thumb of your other hand you can indicate any number from 1 to 12. If you point with your index finger instead of your thumb the joints are designated 13 to 24. And so the progression goes on up to 60, which would be the tip of your little finger pointing to the last joint of the other little finger.
Counting in dozens makes this technique even easier. For example, a count of “three dozen and two” can be easily converted to 38.  
The illustration above is labelled in “dozenal” notation so the upside down 2 (↊) is “ten” and the inverted 3 (↋) is “eleven” in base-10.
Twelve and 60-based counting has obvious applications to navigation using degrees, minutes and seconds, or calculations of time using hours, minutes and seconds.
That is the system. Perhaps you may find it of use sometime.

Update

You can actually count to 156 on your hands! Use the tip of your thumb of your same hand to touch the finger bones between the joints rather than the joints.
You may find it more logical to start with the little finger for the lower numbers.
For each dozen you count off, you touch the corresponding bone on your other hand with the thumb of that hand. 12 x 12 =144.
You other hand can actually represent any number from 0 to 12, hence this system can count up to 156 (12×12 + 12).
You can also do quick additions using this method. Shifting your thumb from a finger bone to the equivalent fingerbone on the next finger adds three, two fingers adds six and three fingers adds nine. Using the other hand, skipping a finger adds 36/three-dozen. For more on dozenal counting see here.
Using this method you can use your hands as a simple abacus in either base twelve or base ten. For the latter you just ignore the first two sections of your last finger.
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Phillosoph

Direction Finding by the Moon

The other night I was looking at the crescent moon.
Many readers of this blog are doubtless familiar with how to find direction from the moon, but some will not be, so indulge me for a moment.
By drawing an imaginary line between the horns of the crescent and extending it down to the horizon, the approximate position of south can be estimated if in the northern hemisphere, or north if you are in the southern hemisphere.
Idly, I wondered if the angle of this line had any relationship to the latitude of the observer. I recalled there was something about navigating by the moon in the Japanese Manual of Night Movements:
“Although it is difficult to determine direction by the position of the moon, the latter has the advantage of being recognizable even on nights when all the stars cannot be seen. The moon crosses the meridian about noon on the first lunar day, and it moves about fifty minutes behind the sun every day. Therefore, if the age of the moon be known, the approximate passing of the meridian can be easily computed. Its approximate age can be computed from the shape of its bright portion.”
Not really that helpful!
Something may have been lost in the translation.
Most websites I looked at had no answer but eventually I found this interesting paper and found the answer is “no”.
I later confirmed my latitude was 51 degrees so an angle of either 51 or 39 would have been expected if the hypothesis had been correct.
The range of angles the terminator can be at as it approaches and passes meridian will vary with latitude, however, but this has very little application to practical emergency navigation.
An alternate method for direction finding by the moon involves remembering that the sun sets in the west and rises in the east.
If the moon is up in the early part of the night, or in the evening before the sun has gone down, the illuminated side will be the western.
If the moon is observed in the latter part of the night or in the morning, then the eastern side will be illuminated.
In this context “latter” and “early part” of the night are defined in relation to the median point of the night, also known as Solar Midnight.
In other words, the middle of the period of darkness rather than the chronological “midnight”, 12:00am or 0000hrs on the clock.
This is more of a secondary method since if you can see the light and dark parts of the moon you can use the terminator method to find north or south. I suppose you could make a crude estimate of the time by establishing where south or north is located and then observing which side of the moon was illuminated.
You can also estimate direction from the moon using the shadow tip method.
This is often illustrated using the sun but the principle is exactly the same using the moon.
Place an object such as a stick in the ground so that it casts a shadow.
Mark the tip of the shadow.
Wait for at least fifteen minutes so the shadow has time to move.
Mark the tip of the shadow’s new position.
A line drawn between these two points will run east-west.
The first point you marked will always be west, the second east.
Easy for me to remember since my name is “West” so “West comes first!” 
Both the moon and the sun move from east to west and in the northern hemisphere they are always in the southern half of the sky, so shadows cast have varying degrees of northward orientation.
A line perpendicular to the east-west line will be north-south and the shadow will be in the direction of the pole of the hemisphere that you are in.
The advantage of the shadow tip method is that you can use it when there is a full moon and you could not use the terminator method.
In the daytime you can use the shadow tip method when the exact position of the sun cannot be seen because of clouds, so long as there is enough light to throw a shadow.