Aerodynamic Effects on a Baseball

Procedure:A baseball was made as the end of the pendulum. As it was swinging, its motion was simultaneously captured on camera from three perpendicular directions.

At first, trials were confined to 2-D motion. Later, the string was twisted so that as the pendulum was swinging, the baseball was spinning, simulating the forces on a curveball.

Or HERE is the link

Hand CalculationsHand Calculations

- Using energy conservation, the max velocity = approximately 10 mph

- The Moment of Inertia can be assumed to equal mr2 so:

Period = approximately 2π(r/g)1/2

= 2.13 secondsFBD!!!

Fdrag eθ

W(-j)

Ner

Finduced i

eθer

k

j

-mgrsin(θ)=Iθ

θ+(g/r)sin(θ)=0

i

Experimental ResultsAvg. Height Reached vs. # Swings

00.10.20.30.40.50.60.70.80.9

1

0 5 10 15 20

# of Swings

Hei

ght (

met

ers)

No Spin

W/ Spin

Total Average θ due only to the spin (θf-θ0)= .0378 rad/s

Total Average due only to the spin θ = (θf-θ0)= .00182 rad/s2

Theta Double Dot for each oscillation

-0.25-0.2

-0.15-0.1

-0.050

0.050.1

0.150.2

0.25

0 5 10 15 20

# of Swings

d^2θ

/(dt)^

2 (r

ad/s

^2)

First Trial

Second Trial

Third Trial

x

Summary

• Using Angular Momentum: H2=H1+AI and

assuming the Force from the spin is constant, F=3.3*10-4 Newtons.

• This may not seem like much but the baseball only weighs .142 kg, and the drag force can be modeled to increase exponentially with respect to velocity. This is the force for less than 10 mph, so with 80 to 100 mph, the accelerations on the baseball will be in m/s.