Olympic Triathlon

8061 /www/nrich/html/content/id/8061/ 1 0000-00-00T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><mdo:image src="Tri_swim_bike_run.jpg" style="float: right;"></mdo:image> In a triathlon, competitors take part in three disciplines: swimming, cycling and running. The Olympic triathlon consists of a 1.5km swim, a 40km cycle, and a 10km run, completed in sequence. The first person to finish wins. Do you think the triathlon will be won by someone who is very strong in one event and average in the other two, or someone who is strong in all three disciplines? Take a look at this <a class="spreadsheetlink" href="/content/id/8061/TriathlonResults2008Men.xls">spreadsheet</a> showing the results from the 2008 Beijing Olympics Men's Triathlon. What do you notice? You may find it helpful to sort the results in various ways, work out averages and measures of spread, or plot some graphs to test correlations between times for individual events and overall finishing positions. Can you come up with any explanations for what you have noticed? This <a class="spreadsheetlink" href="/content/id/8061/TriathlonResults.xls">spreadsheet</a> contains results from male and female Olympic Triathlons since the introduction of the event in 2000. Do the results from the other years mirror what you noticed about the 2008 Men's Triathlon? Are your explanations for the 2008 results plausible for the results from other years too? Are there any events with unexpected results, or outliers? Send us anything interesting that you notice, together with graphs or statistics that highlight what you have noticed and your suggested explanations. <div class="framework">Notes and Background Triathlon swimming, and in particular cycling, is affected by a phenomenon called drafting. Click below to read more about drafting. Does it help to explain the spread of times in the different events? <div class="toggle">Drafting is a technique where moving objects align in a group to suffer less aerodynamic drag, by exploiting the lead object's slipstream. Essentially, those objects who move behind other objects will have to do less work. In sport, this effect is most commonly seen in cycling due to the high speeds involved, and is also significant in swimming due to the thick medium (water compared to air). It is less prominent in running, because the primary work in running is not to battle air resistance, but still has a small effect. In cycling, the majority of the work done at racing speeds will be to battle air resistance. This means that drafting has a large effect: a rider in a peloton (a large cluster of cyclists) can use over 30% less energy to move at the same speed as a cyclist riding alone. Drafting can be both co-operative and competitive: a small group of cyclists can work together to maintain a high speed in a paceline, rotating the lead position (who must work hardest) between them; alternatively, a lone rider can try to sit on the wheel of a competitor, allowing them to do the harder work and conserving energy for later. To try and get ahead of a peloton is called a break or a breakaway, and is difficult for the lone rider. This makes teamwork a very important part of cycling. Drafting also has an effect on swimming, because the main work is done against the drag from the water. Because of the much lower speeds involved, the slipstream of each swimmer is more spread out. This means that to draft in swimming, one can be adjacent and slightly back from the swimmer in front, instead of directly behind as in cycling. In swimming events without lanes, such as the triathlon, competitors frequently form groups and lines just like pelotons and pacelines. </div> If you have access to YouTube, you can try to observe the effects of drafting in the following videos from the 2008 Beijing Olympics: <a href="http://www.youtube.com/watch?v=8mpWpaiXWo4">Men's Triathlon</a> and <a href="http://www.youtube.com/watch?v=MHey0LuDH1k">Women's Triathlon.</a> </div> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Not many responses to this one - this was a tough problem! Let's have a look at what we got. Adam and Eva, at Ratoath Senior School, made a comparison of the various spreadsheets of data for men's and women's events since 2000: We figured out that the first 3 winning countries did not always have the highest score in any certain task. We also figured out the the overall winners in the men's events are very often Germany, Canada and New Zealand, and in the women's events from 2000 till 2008, Australia always comes within the top three. The Pythagoreans Club at All Saints Catholic School, on the other hand, commented on the men's results in 2008 in more detail: Firstly, we sorted the data in terms of the swimming results. We found out that none of the top three medallists was the fastest at swimming; in fact the gold medallist came 16th. Therefore we think that the swimming does not have a major impact on the final positions. For example the fastest swimmer actually finished 34th overall. Secondly, we resorted the data in terms of fastest cycling times. We noticed that the cycling also did not have a big impact on the final positions as the gold medallist came 33rd. Also the person who came 1st in swimming actually came last in cycling. Lastly, we found out that the running time was the most important result, as the ranking in the running event was almost the same as the eventual ranking with only a few changes. So whatever position you place after running really determines where you will place overall. We plotted a scatter graph of the running time against the total time. We wanted to find out whether these two variables were related, and they turned out to be very closely related. To conclude we would say that in order to have the best total time, you have to be good at running. If you want to be an Olympic gold medallist, you don’t have to get on swimmingly or get on your bike but you do have to be Forrest Gump. Great! Thanks for all your responses.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><h3>Why do this problem?</h3> <a href="http://nrich.maths.org/8061">This problem</a> offers a context to analyse some real world data and invites students to use their knowledge of sport to explain what they notice. <h3>Possible approach</h3> "The triathlon consists of a 1.5km swim, a 40km cycle and a 10km run. Do you think the triathlon will be won by someone who is very strong in one event and average in the other two, or someone who is strong in all three disciplines?" Give students some time to share their ideas. Display the <a class="spreadsheetlink" href="/content/id/8061/TriathlonResults2008Men.xls">spreadsheet</a>. "We have some data showing the times for each leg and the overall times from the Men's 2008 Olympics. What are you going to look for in the data to see if you are right about what makes a good triathlete?" Give students time to plan what analysis they will carry out. Suggestions might include scatter graphs to look for correlation between individual event times (or rank) and overall time (or rank), or an investigation of the average and spread of times for each leg. If a computer room is available, students could work in pairs with the <a class="spreadsheetlink" href="/content/id/8061/TriathlonResults2008Men.xls">spreadsheet</a>. If no computers are available, the data is on this <a class="pdflink" href="/content/id/8061/Triathlon.pdf">worksheet</a>. Finally, invite students to share what they found in the data, including any unexpected results, together with their explanations drawn from their knowledge of swimming, cycling and running. If time allows, further work could be done with the results on the second <a class="spreadsheetlink" href="/content/id/8061/TriathlonResults.xls">spreadsheet</a>, so that comparisons can be made with the Triathlons that took place in previous years. <h3>Key questions</h3> How well do each of the individual event times correlate with the overall times? Your explanations might want to take into account the following: How long do athletes spend on each leg of the Triathlon? How might the order of the events in the Triathlon affect the final times? What are the advantages of staying with other athletes over breaking away early? How do the energy requirements differ for each leg of the Triathlon? <h3> </h3> <h3>Possible extension</h3> <a href="/7360">David and Goliath</a> invites students to look for correlations and explain what they find in the data in the context of the men's shot put. <h3>Possible support</h3> <a href="/7367">Who's the Best?</a> offers a simpler context for exploring Olympic data.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Sort the data according to times for the swimming leg, cycling leg, and running leg. How well do each of the individual event times correlate with the overall times? Here are some ideas to consider when trying to explain what you notice: How long do athletes spend on each leg of the Triathlon? How might the order of the events in the Triathlon affect the final times? What are the advantages of staying with other athletes over breaking away early? How do the energy requirements differ for each leg of the Triathlon? </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <table style="width: 500px;border-spacing:1px;" border="1"> <tbody> <tr> <td>2008 Men's Triathlon</td> <td style="text-align: center;padding:1px;">Swimming</td> <td style="text-align: center;padding:1px;">Cycling</td> <td style="text-align: center;padding:1px;">Running</td> </tr> <tr> <td>Fastest</td> <td style="text-align: center;padding:1px;">00:18:00</td> <td style="text-align: center;padding:1px;">00:57:48</td> <td style="text-align: center;padding:1px;">00:30:46</td> </tr> <tr> <td>Lower quartile</td> <td style="text-align: center;padding:1px;">00:18:11</td> <td style="text-align: center;padding:1px;">00:58:49</td> <td style="text-align: center;padding:1px;">00:32:19</td> </tr> <tr> <td>Median</td> <td style="text-align: center;padding:1px;">00:18:21</td> <td style="text-align: center;padding:1px;">00:58:56</td> <td style="text-align: center;padding:1px;">00:33:23</td> </tr> <tr> <td>Upper quartile</td> <td style="text-align: center;padding:1px;">00:18:26</td> <td style="text-align: center;padding:1px;">00:59:06</td> <td style="text-align: center;padding:1px;">00:35:00</td> </tr> <tr> <td>Slowest</td> <td style="text-align: center;padding:1px;">00:18:56</td> <td style="text-align: center;padding:1px;">00:59:19</td> <td style="text-align: center;padding:1px;">00:38:39</td> </tr> </tbody> </table> Things to use: 2008 Olympics results: (drafting allowed, running dominates) http://en.wikipedia.org/wiki/Triathlon_at_the_2008_Summer_Olympics_%E2%80%93_Men%27s 2004 Olympics results: (drafting allowed, cycling dominates - leading breakaway about 1 and a half minutes ahead. Weird, since running dominates in 2000 and 2008) http://en.wikipedia.org/wiki/Triathlon_at_the_2004_Summer_Olympics The effect is less obvious in womens events, and much stronger in recent events. Considering that it was only introduced in 2000, perhaps development of strategy? Results to compare with: These are more amateur events A triathlon you can do in any order: http://www.racingunderground.com/mywaytriway/results.html Specific ideas to look at: Teamwork: Look at the German mens competitors: Unger was 1s in front of Frodeno by the end of the cycling, suggesting he probably used more effort to go at the same speed! Countries enter either 2 or 3 competitors. Look at some other countries, and see whether their team worked together or not. Breakaways: Look at the swimming results for 2008 women. The breakaway lead failed to keep her lead in the cycling, as she had to ride as an individual while a rotating peloton behind her had it much easier. Suggests that it's not worth breaking away in the swim in elite triathlon. A similar thing happened to the breakaway pair in the cycling in the mens event. Year-on-year difference: breakaways in 2000 and 2004 fared much better. How could this be? (possible differences in course shape and geography) Trying to find a draft-illegal event to compare, but these tend to be more amateur. Videos to demonstrate drafting: Womens: http://www.youtube.com/watch?v=MHey0LuDH1k Mens: http://www.youtube.com/watch?v=8mpWpaiXWo4 Swimming from 0:25 in both, particularly 0:33 in second diagonal line. http://www.youtube.com/watch?v=noji2m4AuR4 Cycling 0.55-1.07 Further references: http://www.swimsmooth.com/triathlon.html http://en.wikipedia.org/wiki/Drafting_(aerodynamics) http://digitalcommons.wku.edu/cgi/viewcontent.cgi?article=1022&context=ijes ORIGINAL PROBLEM A triathlon is an event that involves swimming, cycling and running. An Olympic triathlon consists of a 1.5km swim, a 40km cycle, and a 10km run, completed in sequence - the first person to finish wins. <a href="/content/id/8061/TriathlonResults2008Men.xls">Here</a> is a spreadsheet of the results from the 2008 Beijing Olympics Men's event. Looking at the results, do you notice anything interesting? Compare the correlation between overall position and each individual event, as well as the distribution of times within each event. Can you give a few different hypotheses to explain any trends you see? You may find it helpful to sort the results in various ways, plot some graphs, as well as apply any statistical techniques that you know. Charlie says: "I sorted the data based on the running time. The top runners tend to be the overall winners. I think the ratios of the events is biased towards running." Alison says: "I made the same observation, but I disagree, I think the reason is because running is the last event of the three and the weaker competitors fail to keep up." Do you have any other ideas of why this trend could be? How might you find out if each of your hypotheses were true? Here is another spreadsheet, this time containing all of the Triathlon events from the past three Olympics, starting from the introduction of the event in 2000: <a href="/content/id/8061/TriathlonResults.xls">TriathlonResults.xls</a> Do these results support your hypotheses? Can you come up with any new ones? How would your initial ideas have been different if you had started with a different set of results? Are there any factors which could affect the results which differ between the competitions? Click here to learn about a phenomenon called "drafting" which affects swimming and cycling: <div class="toggle">Drafting is a technique where moving objects align in a group to suffer less aerodynamic drag, by exploiting the lead object's slipstream. Essentially, those objects who move behind other objects will have to do less work. In sport, this effect is most commonly seen in cycling due to the high speeds involved, and is also significant in swimming due to the thick medium (water compared to air). It is less prominent in running, because the primary work in running is not to battle air resistance, but still has a small effect. In cycling, the majority of the work done at racing speeds will be to battle air resistance. This means that drafting has a large effect: a rider in a peloton (a large cluster of cyclists) can use over 30% less energy to move at the same speed as a cyclist riding alone. Drafting can be both co-operative and competitive: a small group of cyclists can work together to maintain a high speed in a paceline, rotating the lead position (who must work hardest) between them; alternatively, a lone rider can try to sit on the wheel of a competitor, allowing them do the harder work and conserving energy for later. To try and get ahead of a peloton is called a break or a breakaway, and is difficult for the lone rider. This makes teamwork a very important part of cycling. Drafting also has an effect on swimming, because the main work is done against the drag from the water. Because of the much lower speeds involved, the slipstream of each swimmer is more spread out. This means that to draft in swimming, one can be adjacent and slightly back from the swimmer in front, instead of directly behind as in cycling. In swimming events without lanes, such as the triathlon, competitors frequently form groups and lines just like pelotons and pacelines. </div> If you have access to Youtube, you can try to observe the effects of drafting in the following videos from the 2008 Beijing Olympics: <a href="http://www.youtube.com/watch?v=8mpWpaiXWo4">Mens Triathlon</a> and <a href="http://MHey0LuDH1k">Women's Triathlon</a>. What effects did this phenomenon have on these results? In some triathlon events, drafting is forbidden in the cycling segment. How do you think the results would have been different if this rule had been used? Which version, if either, do you think is more fair? (If you're interested in cycling, you might like to think about the difference between a road race and an individual time trial). Can you find some noteworthy individuals or teams, and describe their story based on their data? Look for examples of competition and teamwork, and successful/unsuccessful breakaways. You can try and confirm your stories with videos of the event.</mdoxml> 2 3 0 0 0 1 0 Olympic Triathlon Is it the fastest swimmer, the fastest runner or the fastest cyclist who wins the Olympic Triathlon? Applications sport Handling, Processing and Representing Data Interpreting data Handling, Processing and Representing Data Processing and representing data Handling, Processing and Representing Data Comparing data Handling, Processing and Representing Data Correlation