Distances and Dead Reckoning

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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

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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 (well calibrate pace)
• How many paces
• Length of time traveling
• Terrain, weather
• If you dont have a map, draw on a piece of paper
• Use memory

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Considerations

• Heading direction you are moving toward
• Bearing direction to an object
• Walking
• 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

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If you use a magnetic compass

• Use the compass to identify a distant object for
  heading, walk toward that.
• Dont 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

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Natural Compasses

• Stars
• Sun
• Moon
• Wind
• Waves or swells
• Planets
• Jet contrails

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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

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Example Viking sun compass
Angles refer to rising and setting angles of the
sun at different times of summer months (voyaging
season)
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Example Carolinian sidereal compass
Azimuth of rising and setting stars in the sky
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Habits in dead reckoning

• 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.
• 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
• 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.

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Even if you dont 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
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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
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Use deliberate compass error to hit a
target (typically cant hold a path to better
than 10o)
Most direct path
Path with deliberate error to hit land
Target position
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Use natural bearings to get a fix
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An exercise to try

• Find a spot in the woods thats 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

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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

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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.

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Path laid out with a string
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Distance checked against scale
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Small angle approximation angles measured in
radians
p radians 180o , 1 radian 57.3o, 1 degree
0.1745 rad
At 20o, 6 error or less
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Using the hand at the end of an outstretched arm
as a way of measuring angles
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sine
cosine
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From pinky to outstretched thumb is typically 20
degrees for angles larger than this the small
angle approximation begins to break down
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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.
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You can also use the distances between stars in
constellations to calibrate your fingers.
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100 feet at 1 mile subtends 1o
All lighthouses are 100 feet tall J. Huth (do
you believe this?)
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Judging distances

• 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)

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Caveats

• Objects look closer when
• Up or down a hill
• Light is shining on it
• Looking across a flat, featureless surface
• Air is clear
• Objects look further when
• 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.

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50 meters Mouth and eyes of a person can
clearly be distinguished
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100 meters Eye appear as dots
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200 meters - General details of clothing can be
distinguished 300 meters Faces can be seen
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800 (0.5 miles) meters A person looks like a
post
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At 2.5 miles, windows and chimneys on houses can
just barely be recognized
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Example house is 1.8 miles away
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Example structure on Egg Rock is 6.5 miles away