Every action hero gets into a fistfight. James Bond, Jason Bourne, Indiana Jones. Then there are all the stars known for their fight scenes. Sylvester Stallone ( Rocky), Arnold Schwarzenegger (True Lies), Jackie Chan (Any movie), Bruce Willis (Die Hard 1,2, 3 etc), Mel Gibson (Lethal Weapon I, II, III etc), Jean Claude Van Damm (Blood Sport, Street Fighter), Brad Pitt (Fight Club), Fast & Furious 1,2,3 and so on.
But can the human body take this punishment?
We can work it out. Measurements taken at The University of Manchester have shown that local boxing hero Ricky ‘The Hitman’ Hatton really does live up to his name. (DailyScience)
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 cellphone.
Is this real?
Now mathspigs, if you are interested in a career in stage/film lighting or even architecture you will need this maths.
60Watt light globe tells us how much power it uses. But some 60W globes are brighter than others. Light is measured with weird units.
USA 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
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:
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 flowshere.
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.
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 Nyiragongolava 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.
The main concern when jumping out off a building is that the airbag (cardboard boxes) cover the drop zone.
The maths calculations involved in jumping off a building are straightforward. You might like to check out How Maths Solved a real murder.
Jump Height that Kills
It doesn’t take much of a fall to cause damage. Sean Hughes, professor of surgery at Imperial College, London. Says “From a height of 3m you could fracture your spine,” he says. “At around 10m, you’re looking at very serious injuries.” (The Guardian, 20 MAY 2014)
Stunt Jump from building from standing start
As this jump – as in most base jumps – involves a standing start:
Star Stuntman Monte Perin (pictured) has involved many films, including “Spider-Man,” “Star Trek, “Indiana Jones and the Kingdom of the Crystal Skull” and portraying Arnold Schwarzenegger’s stunt double in “Terminator 3: Rise of the Machines.”
Perhaps his most difficult stunt was landing his Harley in an open boxcar of a moving train for Disney’s 2008 Adam Sandler movie “Bedtime Stories”. In a career of over 25 years Perin has broken “almost everything” including both his arms, legs, knees, feet, ankles, several ribs, his back and his pelvis. See Confessions of a stuntman
Veteran stuntman Evel Knievel (1938 – 2007) was the pioneer of many stunt jumps. Here he is jumping 10 cars and 3 vans in 1973.
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.
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. DetailsGoogle 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.
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 toWiredmagazine 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:
Wiredmagazine includes the equation for Skyscraper Sway acceleration (See definition of terms @ Wired link):
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.
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