Dead reckoning, piloting

John Huth

Topics

• Measuring speed of boat

• Currents

• Leeway

• Errors from dead reckoning

• Piloting– Curvature of the earth– Landfall

Forces on boat

• Wind

• Resistance on hull

• Current

• Lee-way (wind on sailing vessel)

Wind

Direction of motion

Drag

Lateral force from keel

Leeway

Forces on a sailboat, and resultant motion

Steering direction

A big factor in hull resistanceis caused by the bow wave and stern wave, creating a wake.

The number of wavelengthsbetween the bow-wave and stern-wave partly determinesresistance.

A good navigator can estimatehull speed from the shapes ofthe bow wave and stern wave.

Estimating speed relative to water

Boat length L

Piece of flotsam in water

Start counting now

Stop counting now

Speed is L/time

Ships log (or chip log)

The log gets thrown overthe stern of the vessel – asthe line gets played out, sailors count the numberof knots that pass the stern for a fixed periodof time. (where theterm “knot” for “nautical mile” comes from).

This can be easily improvised.

Initial position

Position after drift

Current direction

Initial bearing

Final bearing

How Polynesians estimated currents

Estimating leeway

“Slick” of calmer water

Water piles up higher on bow

Wake is tilted

Leeway

Current

Desired heading

Direction of travel

Compensating for leeway and current

Actual motion

Example: compensating for current in a blind crossing

Desired heading

Current draining bay = 1 knot

Speed = 4 knots

Heading we chose

error -12o

error +12o

Desired heading

Errors (uncertainties) in position in dead reckoning

Uncertainty in speed

Uncertainty in heading

Uncertainties in speed and heading are typically a fixed percentage – so, as a journey progresses, the numericaluncertainty in position gets larger as time goes on

Expanding the target of landfall

Color of the sea

Birds

Clouds

Mountains

Color of the sea

• Deep sea is typically a dark blue– Reflects the color of the sky, plus absorption– Depends, in part on content of algae

• Color in shallower waters are a combination of factors– Color of the water itself– Color of the bottom (sand, rock, etc)

• Examples– Tropical waters can be azure

Importance of local knowledge: satellite photoof Black sea and Mediterranean

hHD

Range formula for objects

Curvature of the earth causes objects to be hiddenby the horizon

D = distance of object in nautical milesH=height of object in feeth= height of observer in feet

D

Ship hull down – in the distance

Sequence: approaching an island

Far distance – deep blue color

Sixty miles out – spot non-pelagic birds,steer toward land

Forty miles out – color of sea changes

Thirty miles out: clouds appear over land

Twenty miles out – two islands?

Ten miles out – one island