Archive for the ‘Area’ Category

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7. You can safely jump from a burning skyscraper/bridge/aircraft into water.

December 13, 2018

Angels and Demons (2009) Tom Hanks character, Robert Langdon, hero of Dan Brown’s jumps from a helicopter and falls thousands of feet into Rome’s Tiber River and survives, of course.

Ahhhh! Look up. It’s raining Tom Hanks!!!!!The Hulk (2003) The Hulk hops from the Golden Gate bridge onto a jet fighter, whose pilot tries to get rid of him at high altitude. The Hulk falls off and plummets many thousands of feet into the bay. He survives.

There are 2 factors we must consider when jumping or diving from a great height:

1. Surface Impact

2.Water depth 

1. Surface Impact

According to the Free Fall website falling into water is not a good survival strategy. 

‘Someone falling without a parachute from more than 2,000 feet or so would be falling quite a bit faster than 100 miles per hour (161 kph) The folks who have survived falls into water have had streaming parachutes above them, which probably slowed their falls to the 60 mph range (97 kph). Having a streaming parachute helps in another way because it aligns the body in a position where the feet enter the water first.’

The website goes on to explain that water is an INCOMPRESSIBLE FLUID. It’s like landing on concrete. Landing in mud, on snow, on trees, on circus tents etc helps break the fall. Moreover, jumping off a bridge into turbulent sea may be safer than jumping into calm water.

On 24th Oct 1930, Vincent Kelly, 31, while working on the Sydney Harbour Bridge fell 170 ft (52 m) into Sydney Harbour and survived.

A champion diver he did several summersaults and landed feet first. He broke a couple of ribs as he did not enter the water at a perfect RIGHT ANGLE but rather a few degrees off perpendicular..

2. Water Depth

The next issue is, if you are going to dive or jump into water from a great height and, miraculously, survive the impact, how deep should the water  be?

Olympic divers often practice their dives in a bubble pools (like a spa). This reduces the impact for a bad dive but the water must be much deeper. Sports Smart Canada recommends a water depth of double the height of the drop. But is this realistic if, say, you are jumping or diving from the top of a waterfall into aerated water.

You can work out approximate depths needed if you were jumping into calm water from heights such as below:

How deep do you plunge? The answer is surprising because, in fact, you decelerate really fast in water.

See REd Bull Jump Science here

Thanks to Rod Vance  for the Fluid Engineering Calcs (done by hand … not by computer program) for calculating the depth of water when your feet stop moving. That is the minimum depth of water needed for the jump (See graph below)

NOTE: Even with this fancy maths assumptions must be made about the transition epoch-half in/half out of the water.

 Assuming you survive the impact and you breath out through your nose – to stop water going up your nostrils really fast- then you will not go any deeper than approx 4 m or 13 ft from a platform of 20 m (65 ft) or less.

If you’re diving into water from, say, a helicopter as in the Demons & Angels movie you don’t need extremely deep water. Assume Langdon was at 100m (328 ft) or the height of The Statue of Liberty(above) or a 33 story building  when he jumped, then extrapolating the graph (above), maybe, a depth of 5m (16 ft) would do.

If you want to see what looking down from a 58.8 m (193 ft) platform looks like check out thisWorld Record Jump by Laso Schaller.

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9. A single match or candle will light a room the size of a football stadium.

November 21, 2018

 

This is the rework of a previous post.

Action heroes such as Indiana Jones or even film kids like Tom Sawyer or The Goonies who go into a cave, anabandoned house, a crypt or a catacomb light the entire place with one match, one candle, a lighter or a cellphoneIndiana jones 1tm sawyer.

Is this real?

 

Now mathspigs, if you are interested in a career in stage/film lighting or even architecture you will need this maths.light globe_tns

 

60Watt light globe tells us how much power it uses. But some 60W globes are brighter than others. Light is measured with weird units.

candle_tnsUSA uses Foot-candles. Can you imagine the pickup line ‘You brighten up my world like a footcandle’? A foot-candle is the brightness of a candle 1 foot away. Now think of a bubble around the candle. Brightness is mostly measured using one square foot or one square metre of that bubble:

1 LUMEN = 1 Footcandle/ft squared

1 LUX = 1 footcandle/m squared

Don’t get too hassled by these units.  As a rough rule:

1 candle = 1 LUX

candle 1 Correction

candle 2 Correction

candle 3 Correction

From graph you can see by 3m a Birthday Cake is not very bright even in a haunted house or crypt.

Challenge: Draw a graph of the brightness of your own Birthday Cake!

Big Challenge:Draw a graph of your Teacher’s Birthday Cake!!!!!! Ahhhh!!!!

We know:

1 candle = 1 LUX

Now compare the brightness of 1 candle to the brightness of other sources of light:

If you want sufficient light to live your everyday life you’d need:

80 candles just to go to the toilet!!!!!!

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WINTER OLYMPICS: How ski Jumpers Use Math to Increase their Jump Length

February 16, 2018

While air resistance has little impact on aerial skiers it is a significant factor used by ski jumpers to increase their jump distance.

The significant maths for ski jumpers is therefore X-section area.

Here is the jump at Pyeong Chang, 2018. Just imagine going down that at top speed!!!

              A ski jumper is set to jump in Pyeongchang.

                   Casey Larson USA Pyeong chang 2018

Ski jumpers increase their speed going down the ramp by reducing their X-section area:

Lindsey Van, USA, practicing in a wind tunnel

           Lindsey Van, USA, practicing in a wind tunnel

Once they leave the ramp, ski jumpers try to increase their X-section area like Ski Divers to slow their vertical fall. But they have to land safely so they keep their skis at a minimum  angle.

Abby Hughes, USA, practicing in a wind tunnel.

Abby Hughes, USA, practicing in a wind tunnel.

Abby Hughes, USA, in the air

          Abby Hughes, USA, in the air

Here are the X-section areas for Abby Hughes*:

Abby Hughes X-section

Here is the formula for Air Resistance of Drag:

D = ½CApv2

Where C is the drag coefficient or constant, which depends on the shape and spin of an object. It is found by testing the object in a wind tunnel.

A is the X-section Area,

p is the density of the air and

v the velocity of the object.

More here.

As Abby Hughes has tripled here X-section area in the air she will have tripled the vertical drag during her jump. This will slow here decent.

*Mathspig calculated the X-section area by the old fashioned method of counting squares and rounding off the final count. Mathspig sized the two pics of Abby Huges so that her head was the same size in both pictures.

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1a. The WORLD POPULATION as ONE BIG CROWD … METRIC

December 9, 2017

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1b. The WORLD POPULATION as ONE BIG CROWD … USA Units

December 8, 2017

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2a. If all the cars in the world were parked together what area would they cover? Metric Units

November 28, 2017

*For the year 2015 by Statista here.

Area by Country

Area by State USA
…………………

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2b. If all the cars in the world were parked together what area would they cover? USA UNITS

November 28, 2017

*For the year 2015 by Statista here.

Area by Country

Area by State USA

………………….

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Maths Mystery Box 4: FUNNY THAT

March 3, 2015

Maths Mystery BOX 4

1 BArt Simpson Death Wish

 Quadratic Equation  joke MathspigGraffiti pic found @ imfunny blog.

Maths is full-on full of humour.

Can you die laughing, sir?

Try these weird death stats.

Or, how about some maths jokes?

Or, how about a Maths Scavenger hunt.

Funny that!

Many maths teachers come up with great ideas so middle school students have fun with maths. Here are a few:

Human Graphs, Charts and Diagrams

Ellies Active Maths

2 line-graph   Ellie's graphs activemaths

 

How about a human bar graph?

3 human bar graph stenhouse  pinterest

Or a student linear graph?

4 human graph  bigpic     thecolab

Find more @ the colab

 

Or explore geometry through, well, dance?

6 Geometry dance

These students are showing supplementary angles

7 Geometry dance

These students are acting out the concept of complementary angles.

Tricia Appel; Middle School Math

Or, how about the geometry of yoga?

Mathspig groaning pig pose

Can you get your leg or knee to make a perfect right angle?

Or how about a Venn Diagram using Hola Hoops?

9 student venn diag

More info at Howard’s Happy Campers

Or you can measure length using bodies.

How many Smoots long is your football field?

Another Smoot, Oliver Smoot, is used to measure the length of the bridge in 1962.

Oliver Smoot is used as a unit of measure in 1962. 

Or try measuring the area of your school hallway in bodies!!!!

10 y4 rainbow school bradford uk

More info @ Rainbow school, Bradford, UK.

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3. How maths rules ski jumping

January 23, 2014

While air resistance has little impact on aerial skiers (above) it is a significant factor used by ski jumpers to increase their jump distance.

The significant maths for ski jumpers is therefore X-section area.

Here is the jump at Sochi. Just imagine going down that at top speed!!!

Sochi Ski Jump 2014 by blogger Melbourneer

Sochi Ski Jump 2014 by blogger Melbourneer

Ski jumpers increase their speed going down the ramp by reducing their X-section area:

Lindsey Van, USA, practicing in a wind tunnel

Lindsey Van, USA, practicing in a wind tunnel

Once they leave the ramp, ski jumpers try to increase their X-section area like Ski Divers to slow their vertical fall. But they have to land safely so they keep their skis at a minimum  angle.

Abby Hughes going down jump:

Abby Hughes, USA, practicing in a wind tunnel.

Abby Hughes, USA, practicing in a wind tunnel.

Abby Hughes, USA, in the air

Abby Hughes, USA, in the air

Here are the X-section areas for Abby Hughes*:

Abby Hughes X-section

Here is the formula for Air Resistance of Drag:

D = ½CApv2

Where C is the drag coefficient or constant, which depends on the shape and spin of an object. It is found by testing the object in a wind tunnel.

A is the X-section Area,

p is the density of the air and

v the velocity of the object.

More here.

As Abby Hughes has tripled here X-section area in the air she will

have tripled the vertical drag during her jump. This will slow here decent.

*Mathspig calculated the X-section area by the old fashioned method of counting squares and rounding off the final count. Mathspig sized the two pics of Abby Huges so that her head was the same size in both pictures.

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1. Design a Monster Duck

November 7, 2013

Dutch conceptual artist Florentijn Hofman has entertained millions around the world with his Monster Rubber Ducks.

pic 1 duck Rubber-Duck-Florentijin-Hofman-21-537x357

Different sized ducks have appeared in Amsterdam, Lommel (Belgium), Osaka, Sydney, Sao Paulo, Hong Kong and Pittsburgh.

pic 2 duck

Each duck is constructed using 3D and Computer computer generated models.

More here. 

pic 3 Hofman duck construction

pic 4 rubber duck beak

The Duck that appeared in Darling Harbour, Sydney in 2013 measured approx 15 m x 15 m.

It was FIVE STORIES high.

The largest duck, which appeared in Saint Nazaire, France measured approx 25 m high or 82 ft and weighed almost 600kg or 1300 lbs.

This mega duck is over 8 stories high!!!!!

BUT how does an artist stop the wind picking up an 8 story duck and dumping it on your head?

He – Florentijn is a he – does his maths.

Here is a simple wind load formula for stormy conditions.

F = Kv2A

F  = Wind Force (Newton)

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

Pic 5

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 = Kv2A/10   kgf

pic 7

 

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!!!!!

pic 8