COOL FOOTY MATHS: THE LONGEST KICK

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The following maths is suitable for Year 9+

but can be presented to lower grades just to show

maths is cool!

And the tic tic toc of the HYPERBOLA CLOCK

You will find everything you want to know about  HYPERBOLAS HERE.

10. You can out run a lava flow … USA UNITS

This is a rework of a previous post with full calcs.

Every volcano disaster movie from Volcano (1997) with Tommy Lee Jones to Dante’s Peak (1997) with Pierce Brosnan someone somewhere tries to out run a lava flow. Is this possible?

The answer is maybe. You will find everything you want to know about lava flows here.

On January 10,1977, at Nyiragongo lava sprang from the sides of the volcano moving at speeds up to 40 miles per hour. About 70 people were killed.

 

 Measuring the temperature of lava. Photograph by R.L. Christiansen, U.S. Geological Survey, January 9, 1973.

The fastest Lava flows recorded were in Hawaiiin 1950 when Mauna Loa erupted. The lava traveled at 6 miles per hour through thick forest. But once the lava flows became established and good channels developed, the lava in the channels was flowing at up to 60 mph.

Speed of average sprinter = 10 – 15 mph

Can you out run a lava flow?

 You would be scorched in 33 seconds!!!

10. You can out run a lava flow … METRIC

This is a rework of a previous post with full calcs.

Every volcano disaster movie from Volcano (1997) with Tommy Lee Jones to Dante’s Peak (1997) withPierce Brosnan someone somewhere tries to out run a lava flow. Is this possible?

The answer is maybe. You will find everything you want to know about lava flows here.

On January 10,1977, at Nyiragongo lava sprang from the sides of the volcano moving at speeds up to 40 miles per hour (60 km/hr). About 70 people were killed.

 Measuring the temperature of lava. Photograph by R.L. Christiansen, U.S. Geological Survey, January 9, 1973.
The fastest Lava flows recorded were in Hawaiiin 1950 when Mauna Loa erupted. The lava traveled at 10 kilometers per hour through thick forest. But once the lava flows became established and good channels developed, the lava in the channels was flowing at up to 97 kph.

Speed of average sprinter = 16 – 24 kph

 

Can you out run a lava flow?

You would be scorched after 3 minutes!!!! 

What do the Sydney Opera House and Freddie Mercury have in common?

Freddie Mercury is back in the news with the release of the new biopic BOHEMIAN RHAPSOSDY. ( Mathspig gives it ⭐⭐⭐⭐⭐. But I’m a Freddie fan. ) So Freddie and the Opera House? What do they have in common?

NOTE: Uncanny likeness of biopic actors to the real Queen!

According to intmath The Sydney Opera House is a very unusual design based on slices out of a ball. Many differential equations (one type of integration) were solved in the design of this building.

You will never see a better parody of Queen’s ICONIC song BOHEMIAN RHAPSODY than Calculus Rhapsody By Phil Kirk & Mike Gospel (below).

And if you need to be reminded of the maths you will find links to texts here.

Simple Equation For Calculating Skyscraper Sway in an Earthquake

Skyscrapers swaying during earthquake in Japan from woahdude

A major and disasterous earthquake has just hit Indonesia. It is the job of engineers to calculate and incorporate – as far as possible- safety margins into the structures of buildings, dams, power plants and even pipe lines. Observers have noted that the skyscrapers in Fukushima wobbled during the recent 8.9 magnitude earthquake in Japan.

This is intentional, as rigid structures can snap in strong winds or during earthquakes.

But the maths used to calculate SKYSCRAPER SWAY is straightforward.

The Earthquake Engineering website offers a simple explanation.

Short, rigid buildings are damaged in earthquakes because they shake very fast. 10 story buildings have a period of oscillation of about 1 second the same as the earthquake pulse. This is VERY dangerous.

Tall, flexible buildings can withstand an earthquake because they can sway. They are like a very large, slow moving tuning fork. If they are TOO RIGID they snap. If they are too flexible the people on the 100th floor would be throw all over the place.

The 59-story steel-construction Citicorp Centre, NY (pictured) has an oscillation time of 6.7 seconds. Details Google Books.

The 102-story brick clad Empire State Empire Building sways about 8cm ( 3 inches) whereas the 110-story steel -mesh World Trades Centre Towers, NY, before they collapsed swayed over 1 m ( 3 ft 5 inches).

One more thing. You want buildings to have springy foundations so they don’t snap at the base and fall over.

Earthquake Engineering

The idea is not to strengthen the building, but to reduce the earthquake generated seismic forces acting upon it. This can be done in 3 ways.

1. Base Isolation. Rubber pads or Rollers. Are used so the base does not feel the full shake or jump off foundations.

Details Base Isolation Specialists

2. Shock absorbers or dampers are added to the structure to dissipate the seismic shock.

Details Damper Supplier

 

3. Active Tuned Mass Dampers use a computer controlled counter moving weight to actively move against the building sway.

The 508m (1,667-foot) Taipei 101 Tower would sway back and forth up to 60cm (2 feet) each way within five seconds. This according to Wired magazine is highly vomit inducing (barfomatic?).

The Taipei 101 engineers included a 662 tonne (730-ton) counter giant pendulum to act as a counter weight.Some buildings use a big block of concrete.

It is pushed in the opposite direction to the building sway to dampen the oscillation.

Earthquake Engineering Maths

Take 1:

Wired magazine includes the equation for Skyscraper Sway acceleration (See definition of terms @ Wired link):

But I’m going to use a student friendly equation from Wind Engineering for Large Structures.

Calculus Equation here.

Mathspigs, you can just look at this equation and see how to change it to make a building EARTHQUAKE SAFE. Keep in mind that k, the stiffness constant actually decreases for taller buildings.

Imagine you are designing a building to withstand the 8.9 magnitude earthquake. You have already added base isolation. Now you have three options to work with: building mass (m), damping constant (c) and stiffness constant (k). Remember the earthquake force is constant. If you change just the stiffness of the building (k) what happens to the distance of sway(x)?

Engineers have to come up with the optimum design for the strongest structure with least acceleration (but enough building mass for strength), greatest damping and least sway at the lowest cost.

How far does the tallest buidling in the world SWAY in an earthquake?

Earthquake Engineering Maths

Take 2:

Structural Engineer Ron Klemencic explained on the Discover News that a simple rule of thumb for calculating skyscraper sway was to simply divide the buildings height in by 500 because the building codes demand the building fit a 1:500 sway ratio.

The tallest building in the world at 2,716 feet (828m), the Burj Khalifa, Dubai, would sway back and forth about 5.5 feet or 1.7 m.

Ahhhhhhhhh!  But you would have to drag Mathspig onto the 168th floor screaming.

But mathspigs you can work out the sway on the top ten tall buildings in the world.