Posts Tagged ‘Real World Trigonometry’


3. Find a Ghost Ship

October 14, 2013

The Ghost Ship, Orlova, disappeared on 4 FEB, 2013 while being towed off the coast of Canada and has not been seen since. The 1,500 tonne 110 passenger Russian vessel is drifting somewhere in the Atlantic Ocean. Missing, Richard Fisher, New Scientist, 5 Oct 2013

Orlova 2

The Lydbov ORLOVA in action. 

Orlova 3

The Lydbov ORLOVA as a Ghost Ship.

Despite 2 separate SOS broadcasts from Orlova life rafts in March,

it has not been found. These SOS signals are the last two ‘sightings’ shown on the map (below),

but an aerial search did not find the GHOST  SHIP.

Map from

Map from

The Problem:

Ghost ships, pirates and illegal fishing vessels do not want to be found. They do not give off radio signals or identify themselves in any way to other vessels. Ghosts ships, in particular, are dangerous because other ships can crash into them at night. Seven ghosts ships have been found since 2000 including an 80m tanker off the coast of Australia. 

GPS is not always accurate. (Scroll down to see error chart: 10. Design Cool Techno Stuff )

Ships must use radar to get instant readings of other vessels in the shipping lane. Can you find a GHOST SHIP Mathspiggies?

bae-radar used by BRitish Fleet



Radar, short for “Radio Detection And Ranging”, sends out short pulse microwave beams that either focus on a narrow area (eg. speed cameras) or scan an entire semi-circular dome (eg War ships). Radar measures the angle and time taken of the reflected echo. This gives the location and altitude (distance and angle) of the airplane or ship.

It is used to detect the location, speed and direction of weather fronts, cars, airplanes, ships and more.

The weather radar beam is typically reaches about 322km or 200 miles. Here is the current radar map produced by the Bureau of Meteorology at the Terry Hills unit north of Sydney (pictured below)


BOM radar 1  sydneyBureau of Met RADAR with protective dome

Bureau of Met RADAR
with protective dome


The Doppler Effect is used to calculate the speed of the ship. Every kid knows the Doppler Effect. eg.  sound of a racing car turning a corner. High pitch approaching, low pitch leaving as sound waves are shorted on approach and lengthened on departure. Today Doppler Radar is automated. This was not possible before computers. eg. World War 2

The Maths:

You are going to do some World War II Radar Operator maths.

To do RADAR MATHS you must THINK HARD and picture what is happening in your mind. All you see on the screen at any one time is YOUR SHIP’S POSITION (in the middle) and a BLIP showing the GHOST SHIP’S POSTION as the microwave beam scans the ocean.

You mark the GHOST SHIP POSITION on screen  and then do these calculations. But remember this …every time you see a blip you have moved too.

Radar Maths 1

 Radar Maths 2

Now we’re going to look at the sort of calculation needed if ships we’re heading on a collision course. You will find all the GHOST SHIP DATA under the RADAR screen (below).

RAdar Maths 3


Sharp Shooter Maths

May 14, 2010

Mathspig grew up on a police station in the small Australian country town of Kyneton, Victoria in the 1960s. Mum fed the prisoners. Dad’s car an old FC Holden, maroon and white with a pink door, was the police car. And the police phone sat in the kitchen.

Australia has a very strict gun laws today. Thank goodness. But such laws didn’t exist in the sixties. My Dad’s .22 rifle rested against the fridge in the kitchen – without it’s 6-bullet magazine – in case my dad was called out to some police emergency.

There were a number of gun incidents in my childhood. One time my mum was cleaning the house. She usually put paper rubbish in her apron pocket and threw it at the end of the day into our combustion (wood-fired) stove. She forgot she had three .22 bullets in her pocket. It took some time for the bulletsto heat up.

My parents were in bed when bullets started exploding in the kitchen. The explosion blew off the hot plate and blew the ash door open covering our kitchen in grey ash. And it nearly gave my dad a heart attack. This was a typical story of my childhood and why I became a humour writer.

My Dad the Sharp Shooter My dad stopped a stolen car with one bullet. This was considered legendary by his fellow cops. He didn’t shoot the tyres. He managed, by accident and possibly even though he was aiming at the tyres, to hit the electrical lead into the car’s  distributor cap. Phht! Car go no more.

This math post has been updated here:

Sharp Shooter Math …. USA units

Medals, Meglomaniacs and Sharp Shooters…….. The Math USA units