关于D.I.Y.的近似包括空气阻力的水火箭动力学
On the approximation of D.I.Y. water rocket dynamics including air drag
摘要：
如果你想准确预测水和空气推动的D.I.Y火箭的运动，忽略空气阻力是不可能的。但是，包括空气阻力的理论分析导致只能用数值方法求解的微分方程组。我们提出了一个近似的工作原理，简单地通过一个定积分的估计，这甚至是可行的本科物理课程。结果仅略微偏离参考数据（通过Runge-Kutta方法接收）。运动被分为几个飞行阶段，分别讨论和所得的方程求解的解析和数值方法。从飞行阶段收集不同的结果，并进行了比较，已取得的数据进行了很好的解释和记录的实验。此外，我们还从理论上估算了火箭的阻力系数。风洞实验结果证实了这一结论。
英文摘要：
If you want to get accurate predictions for the motion of water and air propelled D.I.Y rockets, neglecting air resistance is not an option. But the theoretical analysis including air drag leads to a system of differential equations which can only be solved numerically. We propose an approximation which simply works by the estimate of a definite integral and which is even feasible for undergraduate physics courses. The results only slightly deviate from the reference data (received by the Runge-Kutta method). The motion is divided into several flight phases that are discussed separately and the resulting equations are solved by analytic and numeric methods. The different results from the flight phases are collected and are compared to data that has been achieved by well explained and documented experiments. Furthermore, we theoretically estimate the rocket's drag coefficient. The result is confirmed by a wind tunnel experiment.
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