The Physics of the Pitcher’s Padded Cap

The history of head injuries to pitchers is pretty gruesome.  Despite this long record, it was not until recently that MLB approved optional padded cap for pitchers.  It isn’t rocket science, so it would not surprise me to learn that even our ancient simian relatives knew that padding reduces injuries.  However, the fundamental physics of padding wasn’t codified until Sir Isaac Newton unveiled his three Laws of Motion in 1687 in “Philosophiæ Naturalis Principia Mathematica” (The Mathematical Principles of Natural Philosophy).

Newton’s Second Law is a good place to begin to understand the new padded hats for pitchers.  If you can remember your high school physics…well, I guess that was a lot of ballgames and adult beverages ago.  So, let me remind you, you used to call this, F=ma.  The truth of the matter is the Sir Isaac never actually wrote it that way. He actually wrote something closer to,

equation

Since equations probably aren’t your favorite way to understand ideas, let me elaborate.  Even though Newton’s work predates the earliest references to baseball’s precursor, Rounders, he was trying to tell us the force exerted by a ball is equal to the change in momentum of the ball (∆p) divided by the time it takes to make the change (∆t).  If a moving ball comes to rest, it has the same change in momentum whether it comes to rest quickly or slows down gently.  If it slows rapidly, the time is short, so the force is large.  If it slows in a longer time, the force is smaller.

Newton’s Law applies to everything, not just baseballs.  Your car has many features that illustrate this trade off between time and force.  Airbags are an amazing invention.  Without them, an accident would result in a very short collision between your head and the steering wheel.  The short time of this collision results in large forces and serious injuries.  The airbag makes the collision time much longer thereby reducing the force on your noggin as well as minimizing the resulting damage.  The same reasoning explains why dashboards are padded and seatbelts are stretchy – yes stretchy.  You might have thought that seatbelts were made out of webbing for strength and comfort.  However, that isn’t the reason.  The webbing will stretch several inches during a collision thereby increasing the collision time and reducing the force the belts exert on you and, in turn your internal organs.

That car commercial was interesting and all, but let’s get back to the game.  While baseball doesn’t use padding to the extent the NFL does, it has its fair share.  The catcher’s chest protector, the foam inside the batting helmet, and the fielding glove itself are common examples.  In each case the padding elongates the collision time and thereby reduces the force.  Beyond padding, players instinctively know that the way to minimize pain and injury is to lengthen the time of collisions.  When sliding into a base they bend their knees once they hit the bag.  The best fielders are known to have “soft hands.”  A physicist would explain soft hands as the ability to gently slow down a hot grounder.   Think about your Little League coach reminding you to bend your elbow when catching the ball.  In every case, the trick is to keep the collision time as long as possible to reduce the force as much as you can.

Let’s spend an inning trying to make sense of the limited information available about the new pitcher’s hats.  The New York Times states, “The caps have more than a half-inch of padding in the front and an inch on the sides. The company said the new cap could withstand an impact of 90 m.p.h. in front and, near the temple, an impact of 85 m.p.h.”  Videos of these collisions can be found on YouTube.  IsoBlox describes their hats as using “dispersion and absorption techniques.”  You can see the “absorption” as the padding slows the ball down relatively gently and so reduces the force on the dummy’s skull.  Absorption has been what we’ve have been talking about.  Notice also the “dispersion” as the cap seems to distribute some of the force around the head.

Dispersion is the way a catcher’s mask works.  While I’m sure some days a catcher would prefer to have their face covered in padding, it will simply block their vision way too much.  So, a hardened steel grill covers their face.  When the ball collides with the grill, the time for the collision is very short and the force is quite large.  However, the force is dispersed around to the edges of the face where there is…you said it before I wrote it….padding.

Sir Isaac – you likely never knew the pleasure of an afternoon at the ballpark, but thanks for giving us a greater insight into the game as well as saving our pitchers from career ending injuries.

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Comments

  1. John Paschal said...

    Serious question here, David. And I need your answer to be rooted in empiricism and not in wild speculation: When my mother dropped me on my head so many years ago, was the collision time long or short?

  2. Charles Chen said...

    The padded cap is UGLY. Why not just make a cap that offers some protection and still look normal. It doesn’t have to protect you against an 85mph ball. It just has to be better then the normal wool cap and still look like a normal cap. 30mph protection is better then none , because no one is going to wear the ugly 85mph protection cap.

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