"Maritime Maths" is a Mathematics Talk that Colin Wright gives. It's still
evolving and changing as a result of audience responses, but some
of the aspects touched are:
The tragedy on October 22nd, 1707
Admiral Sir Clowdisley Shovell
Computing your position from bearings
Using bearings from North
Including error allowances
Using relative bearings between multiple points
Generalisation of Thales' Theorem
Thales was about 600BC
Doesn't work over the horizon
What shape is the Earth?
Shadows during Lunar Eclipses show it's a sphere
Eratosthenes of Cyrene measured the circumference of the Earth
Summer Solstice (not necessary)
Reflected in a deep well => Sun overhead - no shadow
7.2 degree shadow in Alexandria, some distance north
Divide by 2*pi to get the Radius of the Earth
Eratosthenes also invented Latitude and Longitude
How far is the horizon?
"Mountain" 5 metres high
How far to get to that point?
Uses Pythagoras - about 550BC
Pythagoras of Samos - student of Thales
Wouldn't accept Irrational Numbers
Add answers for total distance
Out of sight of land
Measure Latitude with a Sextant or an Octant
How does that work?
Dead reckoning
Log / Knots
7 fathoms in 30 seconds = 5040ft/hour
47'3" in 28 seconds = 6075ft/hour
How do we measure Longitude?
That is the £6m question
Prize offered in 1714 - 6 million pounds in today's money
Many methods suggested
wounded dogs
Anchored ships with flares and cannons
Measuring the Moon against a fixed star map
Parallax
Distance to the Moon?
Acceleration due to gravity - value of g?
Regular dropping - two ticks per second
Pendulum timing
Clocks
Existing clocks were out by minutes per day
Robert Hooke had a clock in the late 1600s
Required sub-second error
John Harrison, 1693-1776
H1 - still can be seen in the Worshipful company of Clockmakers Guild Museum
H4 - Met the requirement
Never given the prize
K1 carried by James Cook on his second and third voyages
not on his first to Tahiti for the transit of Venus
Galileo Galilei
Acceleration is a time squared thingy
Analysed the pendulum
Or was that Isaac Newton?
CPA / Closest Point Of Approach
Intercept Problem
Isaac Newton (1643-1727)
Royal Mint / Royal Society
Inverse square law of gravity
Acceleration due to gravity
Reflecting telescope
GPS / Global Positioning System
Speed of light
1638 Galileo Galilei
Lanterns
1676 Ole Roemer
Eclipses of moons of Jupiter
Galilean Moons
1728 James Bradley
Stellar Aberration (1/200 degrees)
Other topics:
Newtons Cannon
Orbital Velocity
Orbital Period
Contents
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