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

– 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

• 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 torising and settingangles of the sunat different timesof summer months(voyaging season)

Example: Carolinian sidereal compass

Azimuth of rising andsetting stars in the sky

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.

StartGo 266m at 73o

Turn

Go north132m

End 326m, 39o from start

Even if you don’t have a map, use a piece of paperKeep track of the number of paces or length of timeon each segment

Detouring around an obstacle

If you can see the far side (e.g.swamp or lake), pick a prominentobject 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 rightangles and dead reckoning

Use deliberate compass “error” to hit a target(typically can’t hold a path to better than 10o)

Target position

Most direct path

Path with deliberate

error to hit land

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

tansin

R

1cos

Small angle approximationangles measured in radians

π radians = 180o , 1 radian = 57.3o, 1 degree = 0.1745 rad

R

At 20o, 6% error or less

R

Using the hand at the end of an outstretchedarm as a way of measuring angles

sine

cosine

From pinky to outstretched thumb is typically20 degrees – for angles larger than this the“small angle approximation” begins to break down

Winking off distances

For most people,the distance betweenthe eyes is 1/10th thedistance to an outstretchedfinger.

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 yourfingers.

100 feet at 1 mile “subtends” 1o

“All lighthouses are 100 feet tall” – J. Huth(do you believe this?)

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)

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.

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 distinguished300 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