mcm2001A Choosing a Bicycle Wheel 选择自行车车轮美国数学建模 - matlab数学建模

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标题：mcm2001A Choosing a Bicycle Wheel 选择自行车车轮美国数学建模
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所属分类: 数学建模资源类型：文档文件大小: 11.3 KB 上传时间: 2019-08-19 20:42:45 下载次数: 57 资源积分：1分提供者: jiqiren 20190819084357563

内容：
(MCM 2001A)

Cyclists have different types of wheels they can use on their bicycles. The two basic types of wheels are those constructed using wire spokes and those constructed of a solid disk (see Figure 1) The spoked wheels are lighter, but the solid wheels are more aerodynamic. A solid wheel is never used on the front for a road race but can be used on the rear of the bike.

Professional cyclists look at a racecourse and make an educated guess as to what kind of wheels should be used. The decision is based on the number and steepness of the hills, the weather, wind speed, the competition, and other considerations. The director sportif of your favorite team would like to have a better system in place and has asked your team for information to help determine what kind of wheel should be used for a given course.

Figure 1: A solid wheel is shown on the left and a spoked wheel is shown on the right. The director sportif needs specific information to help make a decision and has asked your team to accomplish the tasks listed below. For each of the tasks assume that the same spoked wheel will always be used on the front but there is a choice of wheels for the rear.

Task 1. Provide a table giving the wind speed at which the power required for a solid rear wheel is less than for a spoked rear wheel. The table should include the wind speeds for different road grades starting from zero percent to ten percent in one percent increments. (Road grade is defined to be the ratio of the total rise of a hill divided by the length of the road. If the hill is viewed as a triangle, the grade is the sine of the angle at the bottom of the hill.) A rider starts at the bottom of the hill at a speed of 45 kph, and the deceleration of the rider is proportional to the road grade. A rider will lose about 8 kph for a five percent grade over 100 meters.

Task 2. Provide an example of how the table could be used for a specific time trial course.

Task 3. Determine if the table is an adequate means for deciding on the wheel configuration and offer other suggestions as to how to make this decision.

选择自行车车轮(美国竞赛2001年A题)

有不同类型的车轮可以让自行车手们用在自己的自行车上。两种基本的车轮类型是分别用金属辐条和实体圆盘组装而成（见图1）。辐条车轮较轻，但实体车轮更符合空气动力学原理。对于一场公路竞赛，实体车轮从来不会用作自行车的前轮但可以用作后轮。

职业自行车手们审视竞赛路线，并且请一位识文断字的人推断应该使用哪种车轮。选择决定是根据沿途山丘的数量和陡度，天气，风速，竞赛本身以及其他考虑作出的。你所喜爱的参赛队的教练希望准备妥当一个较好的系统，并且对于给定的竞赛路线已经向你的参赛队索取有助于确定宜用哪种车轮的信息。

这位教练需要明确的信息来帮助作出决定，而且已经要求你的参赛队完成下面列出的各项任务。对于每项任务都假定，同样的辐条车轮将总是装在前面，而装在后面的车轮是可以选择的。

任务1. 提供一个给出风速的表格，在这种速度下实体后轮所需要的体能少于辐条后轮。这个表格应当包括相应于从百分之零到百分之十增量为百分之一的不同公路陡度的风速。（公路陡度定义为一座山丘的总升高除以公路长度。如果把山丘看作一个三角形，它的陡度是指山脚处倾角的正弦。）一位骑手以初始速度45kph从山脚出发，他的减速度与公路陡度成正比。对于百分之五的陡度，骑上100米车速要下降8kph左右。

任务2. 提供一个例证，说明这个表格怎样用于一条时间试验路线。

任务3. 请判明这个表格是不是一件决定车轮配置的适当工具，并且关于如何作出这个决定提出其他建议。

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