The Non-Centered Pill Baseball Drag Theory: Post 36

Here is an excerpt from the MLB Home Run Committee report from 2017.

The committee has not yet succeeded in definitively explaining the
cause of the decreased drag coefficient beginning in 2015. Various hypotheses have been proposed and tested, including gradual changes in
the manufacturing process affecting the centering of the pill within the
baseball or the deformation of the baseball while spinning. There is
an ongoing effort to develop more precise measurement techniques to
investigate these hypotheses.

The commissioner has mentioned this idea several times in 2019. This is a small part of the report, but the one he seems to remember the most.

Let me start by admitting that when I first heard the idea that a “wobbly baseball” could have different drag, I got pretty excited, because such things are really cool fluid dynamics, and I spent a lot of my grad school days investigating such phenomenon.

A sphere that is slightly squashed and is spinning should have an average drag similar to the unsquashed sphere, unless….

All bluff bodies, such as baseballs, shed vortices. For some time, aerodynamicists have sought to control flow over bluff bodies by stimulating these vortices (in one of many ways) at the same frequency that those they naturally shed. When this is done, even a very small perturbation can have a huge effect on the boundary layer and wake of the bluff body. This is called “Active Flow Control”. Since the perturbations do not need to be large, they can be accomplished in many ways. I would guess that a wobbly ball would introduce such a perturbation.

I’ve added an example of active flow control below. My friend Professor Lou Cattafesta of Florida State was kind enough to send it. In the video, a common airfoil (NACA0012) is at an angle of attack above stall, meaning the boundary layer has separated on the top. If you are in an airplane at this condition, you are in free fall. It is pretty unpleasant. Note two sets of vortices: 1) The separated boundary layer forms Kelvin-Helmholtz vortices (which I discussed as related to baseballs in Post 31) and 2) large vortices shed from the “bluff body” wake. Lou has inserted a “synthetic jet” actuator in the nose of the airfoil which allows him to rapidly blow and suck air from that location at a wide range of frequencies. When he runs the actuator at the frequency of either the Kelvin-Helmholtz vortices or the wake vortices, the flow reattaches and the drag goes down quite a bit.

NACA 0012 airfoil in stall. Perturbations are applied near the leading edge at the frequency of the Kelvin Helmholtz vortices in the shear layer or the shedding. In either case, the flow reattaches, and drag is reduced drastically. Video from Cattafesta, L., Tian, Y., and Mittal, R., “Adaptive Control of Post-Stall Separated Flow – Application to Heavy Vehicles,” The Aerodynamics of Heavy Vehicles II: Trucks, Buses, and Trains, Lecture Notes in Applied and Computational Mechanics, vol. 21, eds. Fred Browand, Rose McCallen, and James Ross, Springer, pp. 151-160, Dec. 2008.

The rate at which bluff bodies shed these vortices shed is reported using the Strouhal number, which allows us to compare flows in different fluids over different sized objects to each other. Strouhal number is St = f D/V where f is the shedding frequency, D is the diameter of the ball and V is the ball’s velocity. For a sphere (baseball) at about 90 mph, St = 0.2, so f = 122 Hz or 7300 rpm. Clearly this is much faster than a baseball ever spins, by a factor of 2 at least. Note that the frequency of any Kelvin-Helmholtz vortices on a baseball is even much larger.

Because of this, I am very skeptical that a wobbly ball (whether due to the location of the pill or a non-round ball) will lead to any change in drag of the ball.

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2 thoughts on “The Non-Centered Pill Baseball Drag Theory: Post 36

  1. I came to a similar conclusion, but through a series of calculations.

    By the material properties of the various components of a baseball, you can find that the displacement of the center of gravity (and thus the maximum surface displacement) would be less than 10% of the displacement of the rubber pill.

    Consider the flight of the baseball- the average launch velo and spin off the bat means a baseball will travel about 60 inches per revolution. Coupled with a **horrible** assumption of 0.5 in. displacement of the pill, we would expect that the surface of the baseball would be displaced by a maximum of less than one percent of an inch per revolution. For every five feet of flight, less than one percent of an inch of displacement at the surface because of a misplaced pill.

    I would expect ambient winds to absolutely dominate these tiny effects due to a misplaced pill, aerodynamically speaking. I wouldn’t be confident betting that the ambient wind in a dome wouldn’t crush the displaced pill effect.

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