2022 meisai question a idea sharing

Topic translation ：

2022 MCM

Problem A: Bicycle An athlete's ability The amount features

      There are many types of cycling road races . Including standard events 、 Team time trial and individual time trial . Cyclists in these competitions may have a better chance of winning Different . Depending on On The type of event 、 Routes and the ability of cyclists . In personal time In the game , Every cyclist should ride a fixed route alone , The winner completed the cycling route in the minimum time since Drivers .

      Individual cyclists can produce different results in different periods of time level Energy output . and And On their own vehicle Athletes can produce energy and Given energy The duration of is Bicycle There is a big difference between sending and mobilizing The house is different . Bicycle Athlete's energy The curve shows Bicycle An athlete can produce a given energy The length of time . let me put it another way . Yes On A specific length of time , energy The curve provides the amount of time that a cyclist can maintain for a given period of time most Big power . Usually . Bicycle Athlete generated energy The more , On their own vehicle Athletes stay Reduce energy and To restore energy Keep this before energy The less time you have . Bicycle Athletes can Can choose to temporarily exceed the limit of its energy segment curve . but Bicycle The athlete then needs additional time to Energy level To restore . Besides . Athletes Before Of energy The output is very important , With the game In the process of , Athletes will get more and more tired .

      Bicycle Athletes Always want to try Reduce the driving setting distance Time required . According to the Bicycle Athlete's energy curve , Given a specific Cyclists Of Ability . The cyclist stay Through a given timing " How to apply Power ? Besides , Many types of cyclists may participate in individual time trials , For example, time trial athletes 、 Climbers 、 Sprinter 、 An all-around athlete or an accelerator , also Each type On your own vehicle Athletes have different energy curve .

requirement

Development One A model . This model Sure Apply to any type of bicycle to send mobilization . To determine the position of the cyclist on the track and the energy The relationship between . please remember . On their own vehicle The total amount that the athlete can consume in the whole process energy Limited . Include Before Consume and exceed energy The amount The limitation of curve accumulation .

Your model development and reporting should include Next Content ：

• Define two types of cyclists energy curve . Your One A cyclist should be a time trial athlete , another One position Is a different type of self vehicle shipment Mobilize . You should also consider the personal situation of cyclists of different genders .

. Apply your model to For each A time trial . Such as Next List the matches . Include at least what you defined above Bicycle exercise member energy features .

2021 year Japan This Tokyo Olympic accounting time .

2021 UCI World Championship time trial , Held in Flanders, Belgium

At least one route you designed yourself . Including at least four sharp turns and at least One individual important The gradient of the road . The end of the race should be near the starting point .

• determine The weather Conditions of the potential influence , Include Wind direction and strength To make sure your results are correct God Sensitivity to small differences between air and environment Degree of .

• indeed The result is right Bicycle The athlete deviated from his goal energy The sensitivity of the distribution . Bicycle Athletes are unlikely to follow Not Often miss out on detailed plans Energy goals . Cyclists and team leaders will have an understanding of the possible range of expected segment times for key parts of a given route .

• Discuss how to extend your model , To include each Fleet The best time trial for a team of six drivers energy Use . The time of the team is the fourth place Driver Determine when crossing the finish line .

As a solution One part . For the team Lord Prepare a two page guide to the far mobilization competition . The competition guidance of cyclists should Focusing on the One Name yourself vehicle Athletes and One The result of the time trial . It should contain an overview of the cyclist's direction . It should also include your Model A broad summary of . But it is suitable for instructors and bicycle drivers who have no math background .

Your total number of pages does not exceed 25 page PDF The solution should include ：

• One page Summary table .

• Catalog .

• Your complete solution .

• Fleet The director's two page bike send mobilization guide .

• Reference list .

Be careful ：MCM competition Yes 25 Page restrictions . You submitted all The contents are included in 25 Page restrictions （ Abstract 、 Catalog 、 Refer to the list and any appendices ）. You must quote your ideas 、 Source of any other material used in images and reports .

glossary

Criterium: stay Closed circuit bicycles match . The length can be specified by a fixed number of turns or the maximum number of turns in a predetermined period of time .

Directeur Sportif： Team leader , Responsible for the management of cyclists and work Working personnel . Make a game decision , And determine the... Of a particular game vehicle Team composition .

Individual Time Trial: On their own vehicle A race in which an athlete crosses a predetermined route . Cyclists must not One Ride or get close to each other . For each Bicycle The time required for the athlete to record the riding route . The shorter the time , On their own vehicle The better the final result of the athlete .（ Individual time trial ）

Power Curve: It's white Cyclists At a particular time Long Within degrees can To keep the maximum energy The embodiment of .

Glossary of cyclist types

Climber ： specially The door grows many times distance Climbing race Bicycle Athletes .

Puncheur: specially Door practice includes many short and steep Of a hill climb or many races with sharp acceleration Bicycle Athletes .

Rouleur: One Bit polyhedron hand , Can do well in all kinds of terrain .

Sprinter: specially door stay In a short time High energy On your own vehicle Athletes . These athletes usually focus on In Win at the end of the race or during the middle sprint （ If there is a middle sprint in the game ）

Time Trial Specialist: special be engaged in Individual time trial's own vehicle Athletes .

Thought analysis ：

1、 Read the questions

   This question asks us to give a strategic analysis of the bicycle in the course of the race , The factors that need to be taken into account are ： The reason for the weather , The energy difference of athletes （ Including gender 、 Total energy 、 Energy curve ）, The difference in the race path （ flat ground 、 Climbing 、 Turn a corner ....） under such conditions , The conclusion we want to reach is ： Given the competition path and the athlete's energy is certain , How to allocate physical strength （ Speed ） To minimize the total time .

2、 Preparatory work （ Analysis of influencing factors ）：

The reason for the weather ： Here we can mainly consider the wind direction and the size of the wind , The influence of wind direction is mainly the state of upwind and downwind , So it boils down to the effect of wind on the resistance during the movement . You can refer to the following answer . Under the condition of flat land and slope , The influence of wind force on resistance . The power consumption caused by wind resistance is roughly proportional to the cube of speed , Therefore, the influence of wind resistance in high-speed section will become more and more important .

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