Baseball physics questions: pitching

Factual Questions
1

A few questions concerning the physics of pitching:

  1. What’s the slowest speed possible to throw a strike (without throwing underhanded)?

  2. How much does the pitcher’s mass affect the pitch? That is, what’s the difference between a 90mph pitch thrown by a 150lb pitcher and one thrown by a 175lb pitcher?

  3. Finish this analogy: being hit by a 5.5oz baseball thrown at 90mph from 60ft: being hit by a ______ oz _______ at 10ft?

2
  1. Don’t know
  2. Once the ball has left the pitcher’s hand and it’s travelling 90 mph, does it matter how big the pitcher was? The pitcher has done his work. He’s propelled the ball through the air. 90 mph is 90 mph, isn’t it?
  3. Depends where you’re hit
3

The leading shoulder (left if you’re right-handed, etc).

4

You’re basically asking an impossible question. The batter’s body dimensions and the umpire’s judgement determine the strike zone.

But to try and answer your question, the maximum travel distance for a projectile (in this case, baseball) will be acheived when the projectile’s initial trajectory is ca. 45deg from the horizontal. Given that the mound is 60 ft from home plate and slightly higher than home plate (I’m sure a baseball doper can fill us in on the details), you want to know the minimum initial velocity of a baseball thrown from (the vicinity of) the mound that will result in an arc that intersects the imaginary plane formed by the hypothetical batter’s knees. This velocity will vary considerably based on the height of the pitcher and batter, as well as the umpire’s proclivity to call strikes on urealistically slow, looping pitches.

5

Without accounting for air resistance, the slowest possible speed to throw a ball 60 ft is (by my calculation, unchecked because really it’s not that important now is it?) about 28 mph. You’d throw it up at a 45 degree angle.

The ball would be falling at 45 degrees just at the height of the pitcher’s arm.
Now the strike zone is slightly below that, so subtract a couple mph for that.

But then air resistance would have a significant effect, so add a few more mph to how fast you’d have to throw it (though it would be moving slower than 28 mph by the end).

At any rate, I’m not sure if it would be a legal pitch, or treated as a legal pitch by the umpire.

6

The answer to question 1 would probably involve the “Eephus pitch”. On this message board, someone reported that Bob Tewksbury threw one for a strike at 29 MPH. Orlando Hernandez threw one at 48 MPH acording to this article in Sports Illustrated, and a column reporting on that event quotes Dave LaRouche as saying that his was once clocked at 34 MPH.

7

I don’t see anything illegal with that pitch as described. You don’t have to throw the ball hard or straight. You just have to have one foot on the rubber to start off, more or less.

Most likely a pitch would be released from about 55 feet or shorter since the pitcher strides forward to the plate before releasing the ball.

8
  1. The ball would not slow down due to air resistance very much over its journey - whatever the difference was could be accounted for by making the ball slightly lighter in the “feels like when hit” department.
9

Certainly was the eephus pitch, though I question whether the current ones really deserve the name.

In the ‘Neyer/James Book of Pitchers’ that was released this year (I’m reading it now) they define the original eephus pitch as sailing up to 40 feet high before beginning its descent to the strike zone. They also note that it average about 40 mph, but obviously I don’t know how they determined that number.