Transcript Distances and Dead Reckoning

Distances and Dead Reckoning
• Simplest and most common means of
navigation
– Land
– Sea
– Sky
• Use of maps or memory
• Must have an initial point of reference
– Called a “fix”
Dead reckoning - land
• Need to know a fix (present position)
• Need to know direction of travel
– Compass
• Magnetic compass
• Natural compasses
– Natural means
– Other
• Need to know speed (we’ll calibrate pace)
– How many paces
– Length of time traveling
– Terrain, weather
• If you don’t have a map, draw on a piece of paper
• Use memory
Considerations
• Heading – direction you are moving toward
• Bearing – direction to an object
• Walking
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Know your pace under different conditions – mine:
Fastest – 4 miles per hour
On rough terrain 2 mph
With a backpack on, on rough terrain with my brother-in-law: 1.2
mph
– With a backpack on, racing my nephews – 3.5 mph
– At altitude with a pack on 0.7 mph or less
– Detours
• Directions
– Pick a distant landmark for direction (found using a compass or
other means), walk to it, then pick another landmark
If you use a magnetic compass
• Use the compass to identify a distant object for
heading, walk toward that.
– Don’t walk staring at the compass
• Take into account declination or variation
(preferred term – declination also refers to the
sun)
– Caused by difference of magnetic fields, which do not
align with true north/south (see map)
– Going from map to land – add variation
– Going from land to map – subtract variation
• Compasses can lie (deviation)
– Iron in glasses, on the ground, in your pack
Natural Compasses
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Stars
Sun
Moon
Wind
Waves or swells
Planets
Jet contrails
Dividing up the azimuth
• Azimuth = horizontal angle from north, going
clockwise
• North/East/South/West – easy
• If using natural signs, can divide the azimuth into
8 directions reliably – add northeast, southeast,
southwest, northwest
• Most cultures have a minimum of 8 points
• Some as large as 32 points (rare)
• 360 degrees for modern compasses
Example – Viking sun compass
Angles refer to
rising and setting
angles of the sun
at different times
of summer months
(voyaging season)
Example: Carolinian sidereal compass
Azimuth of rising and
setting stars in the sky
Habits in dead reckoning
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Be absolutely certain of fix before moving
– Memorize landmarks and bearings to landmarks at time of fix.
“We should have kept track of our outward bearings.” Robert Falcon Scott (in his
death diary, deleted before it was published)
– Remember time of fix.
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Determine your heading
Try to use natural compass to find a landmark or way to steer (e.g. wind in
ocean) on your heading.
– Move in this direction. Line up further landmark if possible.
– When you reach the landmark, note the time and distance of travel, recheck
heading and find a new landmark
– Repeat, keeping track of estimated distance traveled
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When changing direction, create a new fix based on direction of travel, time
of travel (or number of paces).
Use a map, if available, write on a piece of paper, if available, remember all
legs of the journey, and significant landmarks, and bearings to them.
Proceed deliberately, taking time.
Even if you don’t have a map, use a piece of paper
Keep track of the number of paces or length of time
on each segment
End 326m, 39o from start
Go north
132m
Turn
Go 266m at 73o
Start
Detouring around an obstacle
If you can see the far side (e.g.
swamp or lake), pick a prominent
object on your heading and use
right angles to keep track of
distance covered.
If you cannot see the far side (e.g.
a cliff) make a detour using right
angles and dead reckoning
Use deliberate compass “error” to hit a target
(typically can’t hold a path to better than 10o)
Most direct path
Path with deliberate
error to hit land
Target position
Use natural bearings to get a fix
An exercise to try
• Find a spot in the woods that’s “random”
(i.e. difficult to distinguish)
• Make a mark on the ground
• Walk away on a known heading for some
number of paces or amount of time
– Far enough to be out of sight
• Backtrack to your original point and try to
find the mark on the ground
Considerations for DR on sea/air
• On the ocean, there are more
considerations
– Leeway – the amount that a ship gets blown
sideways by the force of the wind
– Currents – partly unknown, but can be
deduced by observations
• Polynesians – waves, “standing off”
– Wind strength – again can be estimated
• In the air – similar issues
Estimating distances
• If you have a map, use a piece of string to lay
out a path, and use the legend or scale to
estimate distance (can snake around the path,
too)
• If you see a distant object, and know how large it
is (e.g. a lighthouse), use the angle it subtends
to estimate distance.
• If you can barely distinguish certain
characteristics visually, this can help you
estimate distance.
Path laid out with a string
Distance checked against scale
Small angle approximation
angles measured in radians
π radians = 180o , 1 radian = 57.3o, 1 degree = 0.1745 rad
sin   tan   
At 20o, 6% error or less
cos   1
R
 R

R
Using the hand at the end of an outstretched
arm as a way of measuring angles
sine
cosine
From pinky to outstretched thumb is typically
20 degrees – for angles larger than this the
“small angle approximation” begins to break down
Winking off distances
For most people,
the distance between
the eyes is 1/10th the
distance to an outstretched
finger.
By looking at and object
of a known width (or height)
with one eye closed and then
the other, you can use this
factor of 10 (similar triangles)
to estimate the distance.
You can also use the distances between
stars in constellations to calibrate your
fingers.
100 feet at 1 mile “subtends” 1o
“All lighthouses are 100 feet tall” – J. Huth
(do you believe this?)
Judging distances
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50 yards – mouth and eyes can be distinguished
100 yards – eyes look like dots
200 yards – details of clothing can be distinguished
300 yards – faces can be seen
500 yards –colors of clothing can be distinguised
800 yards – a person looks like a post
1 mile – trunks of large trees can be seen
2.5 miles –chimneys and windows can bee distinguished
6 miles – large structures can be recognized
9 miles – very tall structures – water towers, church
steeples can be recognized (curvature of the earth
becomes significant)
Caveats
• Objects look closer when
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Up or down a hill
Light is shining on it
Looking across a flat, featureless surface
Air is clear
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Lighting is bad (e.g. sun behind them, dark)
Color blends in with background
The object is at the end of a tunnel (e.g. trees)
Ground varies between you and object
Air is hazy, foggy etc.
50 meters – Mouth and eyes of a person can clearly be distinguished
100 meters – Eye appear as dots
200 meters - General details of clothing can be distinguished
300 meters – Faces can be seen
800 (0.5 miles) meters – A person looks like a post
At 2.5 miles, windows and chimneys on
houses can just barely be recognized
Example: house is 1.8 miles away
Example: structure on Egg Rock is 6.5 miles away