Question

There is a myth in baseball that a pitcher can throw a “rising fastball” meaning that if the ball is thrown horizontal, the Magnus Force created from backspin will overcome gravity and the ball will literally rise in the air. This assignment is to be done individually. 95 speed of the baseball in mph. a. Calculate the rpm that is needed to generate enough Magnus Force to overcome the force of gravity. Note: Be careful with units and show all calculations clearly! b. Interpret your result. Is this a realistic value?

Answer 1

The mass of baseball ball is around 145 gram.

The radius is 0.12 feet.

So the Magnus force is given by F = S (w × v)

where S = air resistance coefficient of baseball

w = rpm of ball

v = velocity of air around it

for it to overcome gravitation force = mg.

we have S*w*v = m*g

v = 95 mph = 42.46 metre/second

S = drag coefficient for sphere = 0.5 but baseball is not sphere and it's Re = 2.2 x 10^5 so we take drag coefficient as = 0.3.

Hence w = (m*g/S*v) = .145*10/0.3*42.46 = 0.113 radian/second = 1.07rpm

so this value is achievable but due to many factors like air resistance the spin and velocity will reduce and hence magnus force will decrease and ball will di down.