Sunday, 29 July 2012

My Olympic Predictions

Over at Plus Magazine, I came up with a predicted medal tally for the London 2012 Olympics. Check out my Mapping the medals article if you are interested in the maths behind it.

My top 20 predicted countries (ordered by total number of medals) are:

2012 Predicted Position2012 Predicted Medals
United States1112
Great Britain279
South Korea832

And check out my interactive world map, where my predicted top 20 countries are coloured. If you click on each country, you will see results from previous games, a (semi-regularly) updated 2012 medal count, and some occasional comments.

Wednesday, 25 July 2012

Broadcasting on ABC Riverina

I have recently been doing a science segment with Chris Coleman on the morning show of ABC Riverina. If you are interested in listening to what we had to say, check out the following links:
We also done a couple of Olympics shows, which will be online soon. Listen in at about 9.45 am each Monday.

Saturday, 21 July 2012

Visualising Runs

Inspired by a recent post from Kasey Clark in which he plotted all his runkeeper runs (tracked via GPS) on a single map, I thought I'd explore my own running from the last few years and see how it might be visualised in an interesting manner.

Using his method, I exported all my runs as one big zip file of gpx files (found under your profile) then imported them all into Google Earth. Here is an image of all my runs around Sydney's inner west over the last few years. Most of the time I run along the Cooks River.

I also had a bit more fun with it, and for this you will need the Google Earth plugin for your browser - if you can see the following images you already have it, and if not then there should be a link for you to get it.

The city2surf is one of the world's biggest fun runs and I have done it the last few years. By creating a Google Earth tour, you can create an animation of your runs. I tweeked the gpx code in a text editor (and Excel) to make my 2010 and 2011 runs start at the same time, and then by using the tour gadget, you can embed the animation on your website. Perhaps over time I will add further year's runs to this animation. You'll need somewhere to host the exported kml files from Google Earth. There is a small lag at the start of the video and if it doesn't work, see the video on youtube. I'm looking to knock off that 2011 time this year in a few weeks! Edit 1: I have added a friend from 2010 and 2011.
The next tour doesn't look so great but it would look great in San Francisco or New York City. Google Earth has 3D buildings built in, and by turning these on, you can visualise your runs in 3D. The following shows my Bridge Runs across the Sydney Harbour Bridge and finishing at the Opera House. Runkeeper doesn't quite get the elevation of the bridge correct so it looks like I'm running across water. As mentioned, in cities where there are lots of rendered 3D buildings, this would look great. I haven't bothered yet to tweek the start times for each of the races to all be exactly the same as it's a bit fiddly, but you get the point. Again there is a small lag and if it doesn't work, see the video on youtube.
If you can't see the above videos, and the Google gadget seems really buggy, I have uploaded them to youtube and there you can see city2surf and bridge runs videos.

Tuesday, 17 July 2012

Swimming - technique, drag and strength

The 2012 Olympics are now only days away. I put together this article for Plus Magazine - check out the original article on Plus for full coverage, and follow Plus closely during the Olympics as they will be running regular sporting articles - see their package on maths and sport.

The men's and women's 100 metre freestyle swimming races are set to be two of the most glamorous events of the London 2012 Olympic Games. Much has been made of the swimming events for London 2012 because the previous 2008 Beijing Olympics saw an unprecedented number of new world records, due to the use of controversial swimsuits. Sixty-six Olympic records were broken during the 2008 Games – indeed, in some races the first five finishers beat the old Olympic mark – and 70 world swimming records were broken in total throughout the year 2008.

The controversial swimsuits have now been banned, but the records they set have not been revoked, so the 2012 Olympics are unlikely to see many new records. This does not mean, however, that the events will be any less competitive, and indeed if records are broken, the performances will likely be exceptional.

Pumping iron or beating drag?

Broadly speaking, records in all sports are determined by two factors: the physical and mental performance of the athlete and technological influence. Pure physical performance tends to improve over time as our understanding of the scientific aspects of sport lead to improved training techniques, diets and race tactics. Technological factors, such as a more supportive shoe, aerodynamic bike or faster car can also lead to quicker times. Some sports such as Formula One car racing have an obvious reliance on technology – notwithstanding the incredible physical and mental toughness required to withstand the cockpit of the F1 car. Other sports such as long distance running may have very little to do with technology, with famous examples of Kenyan runners winning major world events bare foot.

Although at first impression swimming seems to rely little on technology, there are many factors outside a swimmer's control that influence their final time. The type of pool has a considerable influence — the first four Olympics Games were not held in pools, but in open water (1896 in the Mediterranean Sea, 1900 in the Seine River, 1904 in an artificial lake). The 1908 Games were held in a 100 metre pool, whilst the 1912 Games were held in Stockholm harbour. The 1924 Olympics were the first to use a 50 metre pool with marked lanes, and the 1936 Games saw the introduction of diving blocks. Before the 1940s male swimmers wore full body suits that were heavy and caused a lot of drag. Pool designs have also changed with pool and lane width modified to eliminate currents, and energy absorbing lane barriers used to stop waves from adjacent lanes. (See below for a chart of world records over the 100 metre freestyle event since 1904.)

There are, broadly speaking, two things you can do to reduce your swimming time:
  1. Increase your power
  2. Reduce your drag
The magnitude $F_ D$ of the drag force acting on a swimmer moving in a fluid is given by the following equation

\[ F_ D=\frac{1}{2}\rho v^2 C_ D A, \]
  • $\rho $ is the mass density of the fluid
  • $v$ is the speed of the swimmer relative to the fluid
  • $A$ is the swimmer's cross-sectional area, that is the area of your body as it is pushing through the water head on
  • $C_ D$ is the drag-coefficient, a number which depends on factors such as the exact shape of the swimmer and the hydrodynamic qualities of their skin and what they are wearing.
Although it may seem like going to the gym and pumping some iron might be the obvious thing to do, reducing your drag is actually a speedier route to a quick lap time. Your power $P$ is the rate at which your body uses its energy, and when you are swimming the power you exert is proportional to the cube of your speed $v$

\[ P=F_ D v = \frac{1}{2}\rho C_ D A v^3. \]

Now suppose you want to increase your speed by 10%, from $v$ to $v+0.1v$. To do this solely by increasing your power, you need to exert a new power $P_1$
\[ P_1 = \frac{1}{2}\rho C_ D A (v+0.1v)^3. \]

The percentage increase in the power required is given by

\[ Increase = 100 \times \frac{P_1-P}{P}= 100 \times (\frac{P_1}{P}-1). \]

\[ \frac{P_1}{P} = \frac{\frac{1}{2}\rho C_ D A (v+0.1v)^3}{\frac{1}{2}\rho C_ D A v^3}=(1.1)^3=1.331 \]

we have

\[  Increase =100 \times (1.331-1)\% =33.1\% . \]

So to increase your speed by 10% solely by increasing your power, you need to increase the power by 33.1%.

Reducing your drag is easier. From the equation for power above we see that the drag coefficient $C_ D$ is

\[ C_ D=\frac{2P}{\rho A v^3}. \]

Keeping your power output and cross-sectional area the same, increasing your speed by 10% requires a new drag coefficient $C_{D1}$ of

\[ C_{D1}=\frac{2P}{\rho A (v+0.1v)^3}. \]

The percentage decrease in drag coefficient is given by
\[ Decrease = 100 \times \frac{C_ D-C_{D1}}{C_ D}=100 \times (1-\frac{C_{D1}}{C_ D}) = 100 \times (1-\frac{1}{1.1^3})= 25\% . \]

So the 10% increase in speed requires a 25% reduction in the drag coefficient.

The exact same working can be used for cross-sectional area — a reduction of 25% will increase your speed by 10%. This is actually the key to the simplest method of reducing drag for most swimmers: improving your technique. Because human lungs are full of air, when we swim our upper body tends to rise and our lower body sinks, increasing cross-sectional area A. The drag force increases and you slow down. Keeping your feet nearer the surface is the easiest method of reducing drag for everyday swimmers.

Drugless doping

At the top end of competitive swimming nearly all swimmers already have very good techniques, so swimsuit technology comes into play. Materials have been developed that increase the swimmer's buoyancy, making it easier to keep their feet near the surface, and reduce the drag coefficient as the material glides through the water more easily than human skin does.

Full-length high-tech swimsuits were first introduced in 1999 before the 2000 Sydney Olympics, with the Speedo Fastskin suits containing V-shaped ridges, modelled on shark skin, to reduce drag. By 2008, the Speedo LZR Racer swimsuit was the most advanced. It was put through wind tunnel tests by NASA and mathematicians modelled water flow around it using a technique called computational fluid dynamics, which simulates how fluid flows around objects (see this article for more on modelling fluid flow). And this research all happened before real swimmers tested the suits in real pools. In Beijing, 89% of all swimming medals were won by swimmers wearing LZR Racer suits.
One of the ways the LZR Racer suits reduce drag is by having panels of a plastic called polyurethane on parts of the body that produce the highest drag. Other swimsuit manufacturers took note. Instead of being textile based with only patches of polyurethane, suits like the subsequent Arena X-Glide were made entirely of polyurethane. These suits were completely impermeable to water, so swimmers could conceivably complete their race without getting wet between their ankles and neck! Records continued to tumble. See more on the Speedo swimsuit technology in this article.

The governing body for swimming, FINA (Fédération Internationale de Natation – International Swimming Federation), took note of the plummeting records and the accusations of "technological doping". In March 2009 it put limits on the suits' thickness and buoyancy, affirming that "FINA wishes to recall the main and core principle that swimming is a sport essentially based on the physical performance of the athlete." They also stipulated that the suits should not cover the neck, shoulders and ankles.

This edict did not actually ban any of the new suits at the 2009 World Aquatics Championships (the "plastic games") — 38 meet records were broken. Subsequently all body-length swimsuits were banned. It was ruled that men's swimsuits may only cover the area from the waist to the knee, and women's from the shoulder to the knee. FINA also ruled that the fabric used must be a textile and not polyurethane. Despite these new rules, the records set by the now banned swimsuits were not revoked and still stand.

And as the term "textile" is not defined, and as scientists are pretty clever folk, the ambiguity of the new rules leaves open a large area for swimsuit development.

Record history

The progression of world records over the 100 metre freestyle event is shown below. Apart from some of the pool changes mentioned earlier, records have continued to drop as we increase our understanding of our physical abilities. Other innovations which have helped reduce times include the introduction of diving blocks in 1936 – previously swimmers had just dived from the wall – and the development of the tumble turn in the 1950s.


It is interesting to note that freestyle as we know it now has not always existed. By definition, in freestyle races you can pretty much swim however you like (with some exceptions), unlike breaststroke, butterfly or backstroke which have defined methods of swimming. During the 1840s, even though they were beaten by native North Americans swimming with a front crawl style, British gentleman swimmers (in an oh so British fashion) swam only breaststroke, considering the front crawl too splashy, barbaric and un-European. In the late 1800s, the quickest (British) freestyle was the Trudgen style, named after John Arthur Trudgen, whose stroke was a combination of side stroke and front crawl. The Australian Dick Cavill modified this style to something similar to what is seen today with his Australian crawl and set a new world record for 100 yards in 1902.

The figure below shows a close-up of times from the early 1980s. You can see the decline around 1999 when the first fast-suits came in, then the sharp decline in 2008. It is difficult to predict when the next dots on the curves will occur.

Zoom on times from 1980s

At the time of writing, Australians are the favourites for both the men's and women's 100 metre freestyle events, with James Magnussen and Matt Targett having recorded the quickest men's 100 metre times in 2012, and Melanie Schlanger the quickest women's time. The UK's Francesca Halsall is 5th so far this year in the women's event, however Simon Burnett in 39th would be doing well to make it past the heats in the men's.