Get ready mathspigs. You need one Lego Man, Girl, Vampire or Alien each for this exercise. Now we are going to set out the Lego Olympics Athletics track.
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But this story of the Olympics begins with Carl Lewis, one of the greatest athletes of all time who won 9 Olympic Gold medals in 100m, 200m, relay and long jump.
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Carl Lewis
Mathspig needs to find out how big the Lego Olympics track would be. How? Easy.
Carl Lewis will be our standard Lego Man.
I chose Carl Lewis because he kindly gave me his autograph once when I sprinted in high heels across a ballroom floor at a sports dinner in Melbourne and beat all other journalists. It was my personal best in high heels, I think.
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This means everything at the Lego Olympics will be
1:50
of the real Olympics.
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The Lego Bird’s Nest Stadium @ Beijing will be 1/50th of the real Bird’s Nest Stadium. (Not the scale shown here). Pictures by Johor Bahru.
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The Lego Beijing Water Cube Swim Centre will be 1/50th of the Real Water Cube.
EXERCISE 1:
Now mathspiggies over to you. The first thing to do is calculate the Lego Olympic measurements (table below).
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EXERCISE 2:
Then mark out a Lego Olympics 100m sprint to scale and/or
draw a Lego Olympic track (in chalk, perhaps) and/or
step out a Lego Olympic marathon track and/or
make a pole vault pole to scale for your little Lego Man.
Here is the US Army Herald Trumpets playing a rousing fanfare:
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Marching Maths
Three nations are marching one after the other:
Pajamaramas (PJ Boy flag bearer),
The Crytomanians (Mummy’s Boy flag bearer)
and the Berserkers (Olag the Viking flag bearer).
But there is a problem.
They march around the Olympic Track, which is a 400m circuit (inside track).
Lego Olympic Track Circuit = 400/50 = 8 m
But the Pajamaramas, the Cryptomanians and the Beseerkers all walk at different speed. They could just bump into one another and end up in a big heap. So how much time should the officials allow between each country so they don’t collide on the track.
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Speed S1
PJ Boy is a really slow walker
Real life Really Slow walk = 3.0 kph = 3000 m/hr
……………………………………………….= 3000/60 = 50 m/min
Lego really slow walk= 50/50 = 1 m/min
Speed PJ Boy = S1 = 1m/min
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Speed S 2
Mummy’s Boy is a slow walker
Real Life Slow walk = 4.5 kph = 4500 m/hr
…………………………………. = 4500/60 = 75 m/min
Lego slow walk = 75/50 = 1.5 m/min
Speed Mummy’s Boy = S 2= 1.5 m/min
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Speed S3
Olag is a fast walker
Real life fast walk = 6 kph = 6000 m/hr
……………………………… = 6000/60 = 100 m/min
Lego really slow walk = 100/50 = 2 m/min
Speed Olag = S3 = 2m/min
Lego Track Circuit = 8m
Time on circuit (T) in mins:
T = d/S
T = 8.0 /S
The time each nation takes to finish marching around the track will be:
T1 = 8.0/S1 = 8.0/1 = 8 mins
T2 = 8.0/S2 = 8.0/1.5 = 5.3333 = 5 mins 20 secs
T3 = 8.0/S3 = 8.0/2.0 = 4 mins
If you started them all at once there’d be a real pile up.
March Time with 1 min gap between groups:
The Enforcer from the Constellation Obeymia will make sure each marching group leaves exactly on time. He will set the clock ticking at 0 mins then enforce a one minute gap between each group.
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Look at the times each nation finishes marching around the track now:
PJ Boy…………………………………………………………………………..
and the Pajamaramas ……………………………………………..8 mins,
Mummy’s Boy and the Crytomanians ………………. 6 mins 20 secs
and Olag and The Beserkers start 2 minutes after PJ Boy and Co and finish at …………………………………. 6 mins.
They will still collide on the track!!!!!
Here are the results for different gap times:
Nation
March Time
Gap time
0 min
March Time
Gap Time
1 min
March Time
Gap Time
2 min
March Time
Gap Time
3 min
PJ Boy + the Pajamaramas
8
8
8
8
Mummy’s Boy and the Crytomanians
5mins 20 secs
6 mins 20 secs
7mins 20 secs
8 mins 20 secs
Olag and The Beserkers
4
6
8
10
The 3 minute gap works!!!
I think we need a round of applause:
Why not ALGEBRA?
If you had to do this calculation for the entire 205 nations at the 2012 Olympic Games, you can see that your brain might explode.
Da-DA! We can use algebra.
Here is a formulae:
T = d/S + ntg
where
T = time (mins)
from beginning of ceremony.
d= track circuit distance = 8 m
S = speed m/min
n = nation march order number = 0,1,2,3,etc
tg = time gap between nations (mins) = 1, 2, 3, 4 etc
The closing ceremony is chaos. All the athletes crowd together.
There is one last lot of calculations, mathspigs.
Think about this.
% Gold Medal Winners:
At the 2012 London Olympics there will be 47 Gold medals awarded in athletics.
There will be 2,000 athletes competing for these medals. Now some athletes will win more than one Gold medal and some events eg. the relay race involve more than one athlete. Each member of the winning relay team wins a Gold Medal.
Approximately what % of athletes won’t win a Gold Medal at the London Olympics?
Ans: 97.65%
Probability of Winning a Gold Medal:
Ha-HA! Tricked ya! Such a calculation would be meaningless.
The core to all probability is, or should be, RANDOM SELECTION.
Lottery balls fall randomly into the tube. But the Olympic athletes represent a BIASED SAMPLE. Athletes are selected for the games. They must qualify for an event. They train. The chance of one athlete winning is quite different from that of another.
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Eight numbered 100m-sprint athletes is a Biased Sample.
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Eight numbered lottery balls in last nights draw make up a random sample.
This brings us to the end of the Lego Olympics.
We will finish with this end song by Lego Rock Band and some Lego fireworks.
It’s BACK TO SCHOOL TIME in Australia. All the little mathspiggies are shaking sand out of their ears and putting hot little feet into sensible school shoes……….
We are doing the BIG MATHS SELL this year. No more Mr Boring Maths Guy. We’re goin’ into the classroom armed with plenty of cool reasons to do maths … You don’t have to actually do the maths. Just show the mathspiggies, any level, that this is how maths is used in really cool jobs.
Watch this video of Harry Potter and the Half Blood Prince: Death Eater Attack.
You can click on the link here or below (Video will only play on You Tube site):
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A recent article in The Guardian, UK, explained the link between Harry Potter and Maths:
‘(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.”
Fluid Dynamics is the study of fluid flow. You can look at this picture (below) and see the similarity to the Death Eaters water-flowy appearance.
Here is a experiment showing lamina Vs turbulent flow in water. Mathspig did experiments like this at university in Chemical Engineering. Equations can be scary, mathspigs, but not necessarily.
Here is a water flow equation for a sharp edged weir with a V notch out let from AQUATEXT:
Q = 0.266 x cB x (2g)0.5 x H1.5
where;
Q = water flow rate, m3/sec
B = width of the weir at the flowing rate
c = discharge coefficient, average 0.62
g = gravitational constant, 9.81
H = Height of the water over the weir, measured behind the weir edge, m
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Here is a real flood caused when water was released from a real weir or dam.
In 2011 operators of the Wivenhoe Dam in Queensland (above) had to release water to stop the dam collapsing during severe floods. 8,000 properties were flooded.
In a recent article in The Guardian, UK Ian Wright, the chief engineer for vehicle dynamics with the Mercedes AMG Petronas Formula One team, said: “There’s definitely a shortage of the right people. What we’ve found is that somebody spot on in terms of the maths can’t do the software; if they’re spot on in terms of the software, they can’t do the maths.”
Knowledge of Catia V5, suspension systems, vehicle dynamics, hydraulic systems and composites would be an advantage. Flexibility in hours and approach is required, along with a positive ‘can do’ attitude and the skill to communicate effectively. The ability to work unsupervised and with a very high degree of drive and self-responsibility is essential.
Well, of course, mathspigs, you need a high level of drive to work in a Formula 1 team, but you also need maths. SeeCan a Formula 1 Car drive Upside Down?
There is a lot of maths in designing F1 racing cars.
The following video gives a very good insight into Formula One Car Design and Aerodynamics
Formula One Design Maths
Here is a grab of Formula One Design Maths from Formula1 Website:
The Bernoulli principle has a big role in the operation of the aerodynamic surfaces of an F1 car. The Bernoulli principle is expressed by an equation, which states that for a given volume of fluid, the total energy remains constant. This means that when a fluid is in relative motion, the energy is split into the ‘parts’. The sum of these parts will not exceed a certain value, which will remain constant as long as the external conditions do not change.
The three parts of the total energy are:
1) The pressure energy within the fluid.
2) The movement of the air (kinetic energy)
3) The potential energy of the air (in this case, elevation)
This can be written as:
p + 1/2 r v2+ rgh = some constant
p = Pressure
r = Density of fluid
v = Velocity of fluid
g = Acceleration due to Gravity
h = Height of fluid above some reference point
Your average track is fairly level, so a race car will not have enough change in elevation to make the potential energy a variable, so we take this potential energy as a ‘constant’and therefore are able to remove it from the equation. This leaves us with:
p + 1/2 r v2 = some (other) constant
We can rewrite this as:
p + q = H
p = static Pressure
q = 1/2 rv2 = dynamic pressure
H = some (other) constant
This basically means that if the dynamic pressure increases, the static pressure has to decrease and if the dynamic pressure decreases, the static pressure will increase. This means that if we speed up a fluid, the pressure will fall.
They (hopefully) calculate stresses and loads on structures BEFORE the building, bridge, airport is built.
Not only do you need maths, mathspigs, to ‘virtually’ destroy the Millenium Bridge in a Harry Potter film, you need maths, obviously, to build the real bridge. Unfortunately, the engineers made a big Boo Boo! They didn’t allow for pedestrian feedback causing sway or wobble. See 10 Biggest Maths Disasters in the World
Here’s a little grab of the maths showing the pedestrian feedback loop causes wobble.
‘ we see that phase of the pedestrians’ feedback force is leading the output displacement of the bridge deck by an angle which becomes exactly at the resonant frequency . This of course is what we expect for a negative damping force.’
Lego engineers need maths.
Lego bridges can be VERY strong.
This is a LEGO MILLENIUM BRIDGE.
But this is NOT a suspension bridge. It is just a model. Here is a FANTASTIC site @ EXPLAIN THAT STUFF showing how bridges work.
A REAL Lego suspension bridge can hold a very heavy load. Here is a Lego suspension bridge built at LegoWorld 2005. The break load for this Lego bridge was 40kg (88 lb). This bridge could support a kid.
Here are two other Lego Bridges. The break load for the next bridge was 76 kg (167 lb). The break load for the third bridge was > 100 kg (220 lb). These bridges could support an average sized adult.
A Neat Lego (Suspension) Bridge on You Tube. *
* Observe neat bridge Vs Unmade bed!
But here is Mathspigs FAV Lego bridge.
Not exactly a suspension bridge but very strong. And this was a kid experiment!!!!!!
Break load = 30.3 kg ( 66.8 lb)
See the next post for some fabulous Lego Maths. In the meantime, if you are going to build a bridge, perhaps, you should do it with maths not love. This is a truly spooky video from Cher and co. Wait for the chorus.
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Ha-HA! Tricked ya! Such a calculation would be meaningless.
‘(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.’
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More @ News Limited 
