1. 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”

2. 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

3. 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

4. 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

6. Natural Compasses Stars Sun Moon Wind Waves or swells Planets
Jet contrails

7. 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

8. Example – Viking sun compass
Angles refer to
rising and setting
angles of the sun
at different times
of summer months
(voyaging season)

9. Example: Carolinian sidereal compass
Azimuth of rising and
setting stars in the sky

10. 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.

11. 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

12. 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

13. 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

14. Use natural bearings to get a fix

15. 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

16. 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

17. 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.

18. Path laid out with a string

19. Distance checked against scale

20. Small angle approximation angles measured in radians
π radians = 180o , 1 radian = 57.3o, 1 degree = rad
At 20o, 6% error or less

21. Using the hand at the end of an outstretched
arm as a way of measuring angles

22. sine
cosine

23. From pinky to outstretched thumb is typically
20 degrees – for angles larger than this the
“small angle approximation” begins to break down

24. 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.

25. You can also use the distances between
stars in constellations to calibrate your
fingers.

26. 100 feet at 1 mile “subtends” 1o
“All lighthouses are 100 feet tall” – J. Huth
(do you believe this?)

27. 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)

28. Caveats Objects look closer when Objects look further 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.

29. 50 meters – Mouth and eyes of a person can clearly be distinguished

30. 100 meters – Eye appear as dots

31. 200 meters - General details of clothing can be distinguished
300 meters – Faces can be seen

32. 800 (0.5 miles) meters – A person looks like a post

33. At 2.5 miles, windows and chimneys on
houses can just barely be recognized

34. Example: house is 1.8 miles away

35. Example: structure on Egg Rock is 6.5 miles away