For thousands of years, the Marshall Islanders of Micronesia have been finding their way around a broadly dispersed group of low-lying islands, navigating apparently without effort from one atoll to another one far beyond the horizon. They had no maps or magnetic compass, no clocks, no weather forecasts and certainly no GPS or SatNav equipment … Continue reading The Navigational Skills of the Marshall Islanders
Tag: Navigation
From a Wide Wake to the Width of the World
The finite angular width of a ship's turbulent wake at the horizon enables the Earth's radius to be estimated. By ignoring evidence, Flat-Earthers remain secure in their delusions. The rest of us benefit greatly from accurate geodesy. Satellite communications, GPS navigation, large-scale surveying and cartography all require precise knowledge of the shape and form of the … Continue reading From a Wide Wake to the Width of the World
Geodesics on the Spheroidal Earth-II
Geodesy is the study of the shape and size of the Earth, and of variations in its gravitational field. The Earth was originally believed to be flat, but many clues, such as the manner in which ships appear and disappear at the horizon, and the changed perspective from an elevated vantage point, as well as … Continue reading Geodesics on the Spheroidal Earth-II
Geodesics on the Spheroidal Earth – I
Both Quito in Ecuador and Singapore are on the Equator. One can fly due eastward from Singapore and reach Quito in due course. However, this is not the shortest route. The equatorial trans-Pacific route from Singapore to Quito is not a geodesic on Earth! Why not? The General Equation for Geodesics Open a typical text … Continue reading Geodesics on the Spheroidal Earth – I
From Sailing on a Rhumb to Flying on a Geodesic
If you fly 14,500 km due westward from New York you will come to Beijing. The two cities are on the fortieth parallel of latitude. However, by flying a great circle route over the Arctic, you can reach Beijing in 11,000 km, saving 3,500 km and much time and aviation fuel. [TM124 or search for … Continue reading From Sailing on a Rhumb to Flying on a Geodesic
Geometry in and out of this World
Hyperbolic geometry is the topic of the That’s Maths column in the Irish Times this week (TM031 or click Irish Times and search for “thatsmaths”). Living on a Sphere The shortest distance between two points is a straight line. This is one of the basic principles of Euclidean geometry. But we live on a spherical … Continue reading Geometry in and out of this World
Where in the World?
Here's a conundrum: You buy a watch in Anchorage, Alaska (61°N). It keeps excellent time. Then you move to Singapore, on the Equator. Does the watch go fast or slow? For the answer to this puzzle, read on. The Global Positioning System In the Irish Times column this week ( TM009 ), we look at … Continue reading Where in the World?
Shackleton’s spectacular boat-trip
A little mathematics goes a long, long way; in the adventure recounted below, elementary geometry brought an intrepid band of six men 800 sea miles across the treacherous Southern Ocean, and led to the saving of 28 lives. Endurance For eight months, Ernest Shackleton's expedition ship Endurance was carried along, ice-bound, until it was finally … Continue reading Shackleton’s spectacular boat-trip
ThatsMaths 