“飞越北极”的时间节省模型

Mathematical Model of Time-saved Flight Course

通过采用计算机模型绘出的飞机飞行航线 ,建立了 2个数学模型 ;并且通过对模型的分析 ,采用MATLAB编程计算球面距离 .对于模型 1,采用立体几何知识求球面距离的方法 ,得出从北京直接到底特律的时间为 10 8734h ,而按飞机的原航线则至少需14 7793h ,所以至少节省时间为 3 90 5 9h .对于模型 2 ,采用参数方程得出纬度与经度之间的函数关系 ,然后用积分方法求得球面距离 ,最后求出节省时间为 4 2 891h .因此 ,通过对飞行航线和球体的分析可证明“飞越北极 ,可节省时间为 4小时”的命题 .

By analyzing the flight course and spheroid,the term imitates a flight course drawing by computer,and establishes a mathematical model to prove that A hours could be savedin flying in the new flight course.By analyzing the model,we calculate the spherical distance in MATLAB programming method.As to Model 1,we work out the spherical distance in solid geometry,it turns out that it only costs 10 8734 hours to fly from Beijing to Detroit,while 14 7793 hours by the original flight course,and at least 3 9095 hours is saved.As to Model 2,the spherical distance by integral is worked out,finally it concludes that it saves 4 29891 hours.