K = Coefficient of Exposure = 0.5 (Engineers use standard tables for K)

v = Wind velocity = 72 kph = 20 m/sec

A = area of X-section exposed to the wind

Now, we’re going to be tricky. A 1 kg weight (eg. a litre of milk) exerts a force of 9.8 N or 1 kgf = 9.8 N on your hand. If we divide the above formulae by 10 we end up with a unit we know …. kgf.

F = Kv^{2}A/10 kgf

If the wind force is 9,560 kgf in a storm it can easily pick up a 600kg duck. In fact, if you do the calcs, it is only in a normal wind ( 20 kph or 5 m/sec) that the duck would stay put (F = 597 kgf).

So WATCH OUT!!!!!

If that duck is not tethered to a building or pontoon it could take off and it could easily take out a school!!!!!

The UK supermarket chain, Asda, is currently trailing 3D in-store printing of mini-me figurines. Cost: £ 40 (€ 47 or $Aus 67 or $USA 64)

Customers can buy 3D coloured versions of any person or object including the family car or dog (if Trixy can keep still for 2 mins) scaled down to an 8-inch figure.

Now you too can play games with yourself. (Warning: Avoid wording involving ‘play with’ and ‘yourself’.)

It takes two minutes using a hand-held scanner to create the 3D image and 6 – 8 hours for the 3D printer to produce the figure.

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The Virtual You

3D body scanning already exists so you can create a 1:1 scale avatar (A Mevatar, perhaps?) of youself for online shopping. By combining this technology with 3D printing the scaled-down Mini Me concept was born.

YOu can walk your personal exact-scale Avatar into an online shop and try on clothes!

3D PRINTING: THE MATHS

Maths is involved at every stage of the Mini Me production to produce the scanner, the scanner program, the printer and the printer program.

It is the scale that is intriguing.

The scale used by the 3D printer is approx 1:10 ratio.

What?

According to the BBC average man in England is 5ft 9in (175.3cm) tall and weighed 13.16 stone (83.6kg) and woman is 11 stone (70.2kg) and 5ft 3in tall (161.6cm).

3D printers use materials from brass to silver to ceramics so figurines can be quite heavy. Assuming the ceramic material has a similar density to the human body, the 1:10 scale male figurine would weight over 1 stone (8 kg) and a female 1 stone plus (7 kg)!

Will shoppers be staggering home in York carrying 7kg figurines?????

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Wait a minute:

1:10 scale along each axis produces an overall scale of 1:1,000

Mini Me Mathspig is just 1/1,000 of Big Mathspig

or one little cube in the pack of 1,000.

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The supermarket figurine @ 1:1,000 scale by volume (and, assuming, weight too) would weight 83 gm ( 3 ounces) for men and 70 gm (2.5 ounces) for women. That’s more like it. The figurines will be, in fact, a little heavier as customers will be scanned wearing clothes and shoes, we hope, or the scanning sessions at the supermarket will be really weird.

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

The Lydbov ORLOVA in action.

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 quofataferant.com

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.

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

Radar BASICS:

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)

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.

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).

It’s caused by too much nitrogen dissolving in the blood under pressure.

At 50 m (165 ft) Slowed response. Laughter.

AT 66 m (217 ft) oxygen toxicity kicks in.

At 70 m (230 ft) Flawed judgment. Hallucinations.

At 90 m stupefaction.

But if you surface too quickly the nitrogen bubbles out in your blood and gives you the bends so called because it is soooo painful.

Ahhhhhh!

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Introducing the Crabster CR 200

According to Gizmodo, one problem with conventional ROVs – Remotely Controlled Vehicles – is their propellers kick up silt from the sea floor, and their engines struggle in strong currents. But this new underwater explorer sidesteps both of these problems by skittering around the sea floor like a crab.

CRABSTER CR 200, developed by a team at the Korean Institute of Ocean Science and Technology (KIOST), can survey shipwrecks and collect data for research. It has 4 pilots. One for the walking and posture. One for the manipulators, cameras and lights. One for the sonar and other scanning equipment. One navigator. This is some creepy crab.

Producers, writers and presenters of TV science and health docos need maths. But did you know mathematicians are also involved in drama and comedy shows from Numb3rs to The Big Bang Theory to The Simpsons.

Mathspig wrote for an Australian comedy Show in the 80s called The Comedy Company.

What’s the connection between Maths and TV Comedy you ask? The Crazy Bit.

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The Big Bang Theory Maths

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The Big Bang Theory is a comedy based on the lives of house-mate physicists Sheldon and Leonard. But the science has to be right for the humour to work as not only do maths nerds star in the show, maths nerds watch it too.

According to Wired magazine, David Satlzberg a physics professor who teaches at UCLA is ‘working on his fifth season as the science consultant for The Big Bang Theory’

He makes sure the science on the show is right.

Here’s what a fact checker does:

‘For example, the script I’m reading right now I changed one letter. They had mentioned an ‘anti-photon’ but that doesn’t make any sense because there is no such thing. So I suggested changing it to ‘anti-proton.’

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The Simpsons Maths

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Simon Singh recently explained in The Guardian that an amazing number of Maths Geeks are writers for The Simpsons.

eg. ‘Al Jean, who worked on the first series and is now executive producer, went to Harvard University to study mathematics at the age of just 16.’

The maths geeks entertain themselves by dropping hidden maths references into the TV series.

eg. The screen displays three multiple choice options; 8,128, 8,208 and 8,191. These digits might seem arbitrary and innocuous, but in fact they represent a perfect number, a narcissistic number and a Mersenne prime.

Fortunately, Simon goes on to explain these and many more Maths references in The Simpsons in his book: The Simpsons and their Mathematical Secrets.

32 people died when the Costa Concordia ran aground in a protected marine park off the coast of Italy. The $US800 million salvage operation to remove the Costa Concordia needs lots of maths.

It is the biggest salvage operation ever undertaken in seafaring history.

THIS IS THE PROBLEM. It is a one off project and the engineers have to hope they get the maths right.

Here’s the plan:

Here are the maths problems:

Problem 1:

The ship, which is 290 meters (951 feet) long and 36 meters (118 feet) wide, is on its side and full of seawater. It has a displacement of 50,000 metric tons plus the weight of the water inside that, at a guess, could weight 30,000 metric ton. This is a BIG problem. Normal salvage methods cannot be used.To give you an idea of the scale:

50,000 metric ton = 50,000,000 kg

1 London Double Decker Bus = 8,000 kg (Empty) or 12,000 kg full

Now add the water.The salvage operation must lift the equivalent, maybe, of 8,000 London Buses.

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Problem 2:

The ship is resting on a seabed that slopes at an angle of 20^{0}.

Simply winching the ship upright would have it roll down the slope. A horizontal platform must be built that can take the 50,000 metric ton plus load.

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Problem 3:

The platform has to be built underwater. This will take 111 salvage divers working around the clock to secure the platform and attach cables to the ship.This steel platform weighs three times as much as the Eiffel Tower.

The weight of the salvage platform = 26,000,000 kg

or 2,600 London Buses.

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Problem 4:

The Costa Concordia must be winched onto the platform slowly. Too quickly it might topple off the platform.

As the 50,000 metric ton ship (plus the weight of trapped seawater) is winched upright the load on the winches decreases (See simplified diag below.) Think of picking up a chair off the floor. As you rotate the chair upwards the load decreases to zero …. when the CENTRE OF GRAVITY lies directly above the PIVOT POINT then gravity works with you and the chair drops with a thud to the floor. Engineers cannot allow 50,000 plus metric ton to drop with a thud. Winches must be carefully controlled. The winching operation took 19 hours.

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Problem 5:

The Costa Concordia was winched upright on 17 Sept 2013. Floats must now be welded onto the damaged side of the ship. Once the ship is refloated it will be towed away to be broken it up for scrap metal. This will take 2 years.

UPDATE:

The costa Concordia is floating again. On 27 July 2014 the crippled cruise ship arrived in Genoa, it’s final destination, where it will be broken up for scrap metal. The complex engineering feat to refloat the vessel proved successful.

Here is the current Math 10270 syllabus for architecture students at Notre Dame University, Indiana

Illus: Opera House, Sydney

The related mathematics is drawn from today’s Euclidean geometry, trigonometry, the properties of vectors, coordinate geometry in two and three dimensions, and calculus.

CGI of Death Eaters in Harry Potter and the Half-blood Prince

An article in The Guardian, UK, explained the link between Harry Potter and the Maths of fluid dynamics or flow (See pic below):

‘

‘(Alex)Hope, managing director of the visual effects firm Double Negative said:

“In Harry Potter [and the Half Blood Prince],

the opening sequence has Death Eaters flying across the river Thames, destroying the (Millennium) Bridge between St Paul’s and the Tate Modern.’

“The way you create that is people who understand computational fluid dynamics, they know how water moves. They take the physics that’s used in modelling rivers and the flow of water and apply that in our world. People doing it need an artistic sensibility as well.

An understanding of maths and science

is fundamental to many of the

disciplines in our industry.”

Now there is motivation, mathpiggies. To create Computer Generated Images for movies you need maths!!!!!!

For helicopters the lift comes from the rotor props.

But the lift is greater for the prop moving into the flight path than the prop moving away from the flight path.

To overcome this problem the rotor props change pitch (blade angle) during each 360 degree rotation.

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Here are the specifications for the hotelicopter:

………………………………………………………………………………… * Dimensions Length: 42 m (137 ft) * Height: 14m (45 ft) * Maximum Takeoff Weight: 105850 kg (232,870 lb) * Maximum speed: 255 km/h (137 kt) (158 miles/h) * Cruising speed: 237 km/h (127 kt) (147 miles/h) * Original Mi Range: 515 km (320 mi) * Our augmented Mi Range – 1,030 km (640 mi)

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Pretty amazing, eh?

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Not if you do the maths.

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Problem No. 1:

It has the capacity for 18 – 36 passengers plus crew.

Here are some google glasses that actually look cool.

Here’s what Google Glasses can do.

Instead of using the Google Maps on your phone the Google Glasses put the map onto the glass lense so you can see where to go and where you are going. Theoretically.

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The Maths

Google Maps uses GPS or Global Positioning System satellites and simple maths of TRIANGULATION or, in the case of the 3D model, 3D TRILATERATION to accurately locate your position on earth.

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You will find excellent explanations of how GPS works at the Nova Scotia Dept of Education website and by Diana Cooksey MSU GPS Laboratory website.

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Simple Explanation:

GPS satellites broadcast two signals which allows the GPS program in your phone or device to calculate your distance from the satellite. GPS needs data from 3 satellites to locate your position on earth.

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2D Model:

Let’s assume your phone can calculate how far you are from a radio tower.

Tower 1:

Your phone can calculate how far your are from the tower but you could be anywhere on the first circle.

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Tower 1& 2:

Your phone can calculate your distance from two towers and locate you at one of two points where the circles intersect.

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Tower 1, 2 & 3:

Now you phone can accurately find your position at the intersection of 3 circles.

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3D Model:

Your phone can calculate how far you are from a satellite.

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Satellite 1:

You could be anywhere on the first sphere.

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Satellite 1 & 2:

You could be anywhere at the intersection of the two spheres. These spheres intersect along a circle.

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Satellite 1, 2 & 3:

The 3rd sphere will cross that circle at 2 points. As one position is not on earth it can be discarded.

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Error Alert:

All measurements have an inbuilt uncertainty (scientists call it an error) because the accuracy of instruments is limited. Measuring across such long distances makes for significant errors. One problem for GPS is signal interference.

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New Techno Frontiers in the Maths Classroom

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1. If you teach maths wearing Google glasses you can INSTANTLY record students bad behaviour in class on your computer. Wow! Evidence. THE FORCE BE WITH YOU, Mathspiggies.

OR

2. You can record a maths lesson using Google Glasses. It is already happening, my Sweeties. Have a look at this.