单板滑雪场设计.doc

Control#10493 Model the snowboard course to help you fly higherAbstractSnowboarding is the leading trend in todays world of sports, it not only requires athletes excellent skills, but the accurate and precise designing of the snowboarding are essential as well. Snowboarding for a good athlete, a good venue is in the race reached its maximum vertical vacated, and play an important guarantee optimum levels. To ensure the athletes will reach the maximum vertical air, we build a model of the snowboarding track. We first built a simple model, and then we redesigned and changed more detailed aspects of the model to optimize the model. Finally we came out with a safe and practical model project.Firstly, to find out the main factor affecting the Vertical air, we analyzed and studied the movement of the athletes on the U-shaped track, and concluded that the kinetic energy which an athlete needs during while vacating is transferred from gravity. According to this finding, we built a simple semi-circular cylinder. We found the friction and resistance were always the same and the whole movement consists of the movement along the boarding track and the movement perpendicular to the track, and established multiple differential equations. We gained the work done by resistance forces during these two processes. prepare between two actions, we built a circular smooth glide in the middle of the semi-circle, and this the U-shaped model is improved. Athletes in the slide area should keep a constant state of motion . According to the data we got from the previous model, we calculated the sliding velocity of the athlete at the bottom of the U-shaped track. We obtained the designing requirements for the bottom of the U-shaped track according to the reaction time of the athletes.The last step is to ensure that the athletes will be able to complete the rotation, flipping and other difficult movement, we use the worlds most skilled and difficult movement of Shoun White as an example to build approximate parabolic model of the movement in the air. Based on theoretical calculations and practical experiments, we came up with the glide length. Together with the U-shaped track model, we had the final U-shaped model, and the relationship between Vertical air and the designing requirements of boarding track. We built a simulated model by using MATLAB. The final best designing proposal was completed after analyzing the data.Finally, We made objective evaluation of the model and predictions of the improvement of the model.Contents1 Introduction22 Problem Assumptions23 Problem Setup33.1 The main factors which affect the Vertical air33.2Requirements of the course by repeatedly vacated players33.3Requirements of course by competition difficulty44 Models44.1 Basic Model44.2 Improved Mode74.3 Flight Model85 Results105.1 MATLAB on the basic model used for simulation105.2 MATLAB on the improved model used for simulation105.3MATLAB on the flight model used for simulation115.4 MATLAB on the final model used for simulation126 Feasibility test137 Strengths And Weaknesses157.1 Strengths157.2 Weaknesses158 Future Work159 Reference151 IntroductionSnowboarding is a current trend event, both free and exciting. Athlete make a separate, twist, flip, grabbing the board and other activities in the air, through the movement of body and the control of the direction and speed. The higher athletes fly, the more time allows athletes to complete a wonderful and complicated action. So that the height of the athlete fly restricts the difficulty, diversity, quality of the action completed. The technology of the athlete determines his wonderful performance, but the standard of the snowboard course objectively impact the level that an athlete can play. International regulations on the scope of the indicators, but because half-pipe snowboarding is a new current event and the balance of the indicators is not enough in the mostly snowboard course, resulting in the perfect athlete cannot show their talent. Currently, there are many studies on the snowboarding: Skiing mechanics analysis based on a multi-rigid-body system model1, Discussion on the exchange area and rotary technique theory of competitive alpine skiing2, Analyses of mechanical characteristics for alpine ski3. On this basis, we build models to get the relation between indicators and the vertical air, using MATLAB to optimize model and ultimately obtain the optimal design.2 Problem AssumptionsLook the athletes and skateboarding as a whole;Skilled players can control the direction of glide skateboards;Game players need to complete five movements;Snow ski the same quality and uniform, sliding friction coefficient is constant, skateboarding and snow is always a positive contact;The earth of slide in the region is level.Variable Meaning the length of the course the width of the course the radius of the circle the inclination of the course the resistance of I direction the friction of I direction the air resistance of I direction the work done by the resistance of I direction the air resistance coefficient the coefficient of resistance on snow Atmospheric pressure Sign function3 Problem Setup3.1 The main factors which affect the Vertical airBy analyzing the whole course of the athletes from whereabouts to taking off the first time we know that the kinetic energy athletes need to fly out of orbit is transformed by the gravitational energy. In connection with the function relation between Vertical air athletes vacated and space a the main indicators of the design to create a simple model of half cylinder. During exercise, air resistance and friction are constantly changing, but their direction is always the same, and in the opposite direction with speed. The process in the model can be decomposed into the movement along the orbital plane perpendicular to the orbital plane direction and the direction of movement analysis, Establishment of differential equations, obtain the work done by the resistance. Then obtain a function of Vertical air and space length, width, depth and angle by using functional principles. The followed several times of movement similar with the first can be obtained by analogy.3.2Requirements of the course by repeatedly vacated playersCompetition include several times of take-off to complete the action, as between the two actions (declining phase of landing and taking off over stage) ,the athletes need some time and distances to adjust the state of motion to prepare for the next take-off, which requires to set a smooth flat area for the athletes. The state of the athletes in this flat area does not change and should be the basic, which can be considered as uniform linear motion. On this condition, according to the motion analysis of title 3.1 to infer the speed of athletes at the bottom, according to the preparation time and speed of sliding to obtain distance in the flat, then get the relevant data about the flat by trigonometric function.3.3Requirements of course by competition difficulty As referee will score the athletes according to the difficulty and quality of their Vacated action, to ensure that players in the competition can make a variety of difficult actions accordingly to adjust and optimize the design of course before, so that Competition course is more practical .There is no harm in setting Shoun White completed the worlds highest Difficulty (1280 degree air rotation) as an example, establish the air movement phase to an approximate parabolic model. Estimated by theoretical calculations and practical tests get the same sliding length, combined with the overall model of U-shaped to get the final model of U-shaped site and find the Vertical air and site index as a function of the design. By using MATLAB to simulate the model and analyzing the data, we can draw the best U-shaped ski design.4 Models4.1 Basic ModelIn this model, we do not consider the athlete have to do the movements in the air displacement, and create the establishment of semi-circular cylinder model. The process in the model can be decomposed into the movement along the orbital plane perpendicular to the orbital plane direction and the direction of movement analysis, the work done by friction will be obtained.Orbital plane in the direction perpendicular to the movement of objects can be approximated by the movement along the circular orbitStress analysis as shown in the following figure.Figure1: Semi-circular cylinder modelFigure2: Section stress analysis 4，Direction along the sub-orbital plane movement is linear motion,Figure3: Orbital plane modelAccording to the proportion , we know:，So in the whole course of the campaign, athletes increase the kinetic energy provided by the potential energy, according to known functional relationships, we knowTherefore, ，In the next four jump, the kinetic energy of the athletes have already meet their vertical air then the gravitational potential energy and friction work into each other only to meetGet the length of each ，Therefore, the total length of snowboard course is4.2 Improved ModeTaking into account the athletes between the two actions will take some time to adjust themselves, competition include several times of take-off to complete the action, as between the two actions (declining phase of landing and taking off over stage) ,the athletes need some time and distances to adjust the state of motion to prepare for the next take-off, which requires to set a smooth flat area for the athletes.Figure4 : Improved cylinder modelFigure4:Flat stress analysisFigure4:Flat stress analysisdiscuss the movement in the flat regionSince athletes do uniform motion within the flat, it does not change its kinetic energy. Because the increase of the gravitational potential energy and the resistance acting are equal, we haveAngle of the orbit to the ground is In the previous model, we can figure out, the speed t of the athletes at the lowest point is . Getting access to the relevant information by the adjustment time of athletes is about ,Therefore, the width of the flat should be .On this basis, you can get the total athlete Sliding length of in the flat region Then 4.3 Flight Model Taking into account the athletes need to complete the twist in the air, there is no harm in setting Shoun White completed the worlds highest Difficulty (1280 degree air rotation) as an example, establish the air movement phase to an approximate parabolic model.Figure6: Approximate projectile modelAthletes during exercise by gravity and air resistance, taking into account the player can control the speed of a certain groove and into the slot, and the rotation itself is also need to cause some loss of speed, players using the physics knowledge is flying out of orbit by the to fall back to the track length of track required at least. In order to ensure athletes are able to play all the actions the highest level, we should be designed for each track length vacated action. Therefore need to extend the total track.We also observed Shoun White race through the Internet, by making use of the visual estimation method, we get the estimation distance of their movements in the orbital plane. The following data arelineLength of line/mDistance/mA0.717b0.818C0.818average7.7The results show that the model results are consistent with the actual visual result.So the total length of snowboard course Summing up the above three models, we can get the final shape of Vertical air parameters in the relationship between snowboard course，；The width of the snowboard course The depth snowboard course 5 Results5.1 MATLAB on the basic model used for simulationget the following figure:5.2 MATLAB on the improved model used for simulation get the following figure:5.3MATLAB on the flight model used for simulationget the following figure:5.4 MATLAB on the final model used for simulationget the following figure:Simulation results, draw under certain conditions, , l, , as a function of the image. From the graph, the optimal solution can be directly elected as follows:RWLhBasic modle81660.897.04614.99Imprive modle516144.910.817.98Flight modle416114.95.68217.913.516120.95.74518Figure7: .U-shaped model6 Feasibility testAccess to information obtained,the parameters of the snowboard course are in the following tabletMinimumRecommendmaximumpitch 141618length100120140width141618Depth33.54.5Recommended data based on model checking, Known And then using the model test the accuracy of the modelAthletes from the first drop to vacate the entire movement ,based on the basic modle,takeadvantage of MATLAB, Length and the athletes are a function of displacement in the imageThe following chart:Obtained from the table: Therefore, the model has some validity and feasibility, it can be guide the construction of snowboard course under certain conditions, .7 Strengths And Weaknesses7.1 Strengths(1) Around the Vertical air ,set up the direct and effective model and seize the main influencing factors, so that the shape of the snowboard course relationship with