第七次作业课后题2.19

摘要

Baseball is a sport of great interest for physics for its appropriately complexity of combining the elastic dynamics of bats, fluid dynamics of the ball and so on. In the report a discussion of the backspin of the baseball is presented .
棒球运动是一项十分受欢迎的运动，原因是棒球击出来的球的轨迹难以预测，使得棒球是一项非常吸引人的运动。给棒球加上不同的自旋，棒球的运动轨迹变得多种多样。

背景

2.19：Model the effect of backspin on the range of a batted ball. Assume an angular velocity of 2000 rpm.
Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738.This principle is often demonstrated as the following equation
$p+{1\over 2}ρV^2+ρgh=const$
But we should be careful since this equation is based on the conseravtion of mechanical energy, thus is valid only when fluid of interest is inviscid and uncompressable.
Now we consider a special case of such principle, a spinning in a fluid.

正文

程序代码

In the code we treat the air drag coefficient as a function of velocity and compare the effect with that without backspin. Under the initial condition given (a velocity of 45 m/s and shooting angle of 45 degrees), the baseball with backspin has a higher maximum height and a longer range.

总结

回旋球会使棒球往上飘，相对于无旋球射程变得更远了。可以看出加上回旋后，棒球飞行得更高更远了。可以想象，给棒球加上不同的旋可以打出各式各样的曲线来。

致谢

王世兴同学的代码和周辉同学的提示。