Baseball Musings: Check My Math

March 20, 2007

Check My Math

Dan Larson writes:

Buster Olney linked this weekend to a Hal McCoy article in the Dayton Daily News that discusses minor leaguer Jerry Gil being able to throw a ball four hundred feet, even over most centerfield fences from behind home plate. This brings to my mind a question about velocity. Since I have no understanding of physics beyond the most basic principles, I'd like to know if there are other factors involved in the distance of a throw than the speed (like, for instance, force ??). Like, for instance, if Jerry Gil can throw 400 feet, does that mean he's throwing 100 mph? Or am I wrong to assume Joel Zumaya could make the same throw only because he can hit 102 over 60 feet? I've always assumed pitchers turned position players, like Rick Ankiel who hit 95-96, must have the strongest arms in the league but am wondering if there's a factor I don't understand once distance is involved.
So I guess my assumption has been: whoever throws fastest also throws farthest (and the reverse, of course--Jerry Gil must be throwing 100 over 60 feet if he can outthrow the rest of the league)? Is this true?

My response that the two things that matter are the initial speed of the ball and the angle of launch. Since a 45 degree angle gives you the most distance for a particular initial velocity, I figured out the minimum speed it would require to get a ball 400 ft (133 meters). It worked out to 36 meters per second, or 80 MPH, neglecting air resistance. My guess is that a 90 MPH throw launched at a 45 degree angle will clear the fence no problem. Maybe a physics wizard can confirm that.

Posted by David Pinto at 03:30 PM | Baseball | TrackBack (0)

Comments

I think the actual optimum angle is less than 45, probably closer to 42 or so. Plus, you have to take into account the rotation of the ball along with the velocity and angle.

Posted by: sabernar at March 20, 2007 03:52 PM

I found this, too:

"Actually, this estimate is somewhat altered by the presence of air resistance. In fact, the optimal launch angle is 35 degrees to 40 degrees to the horizontal, the ball travels less far, and it spends less time in the air. Air resistance is negligible for pitching, but not in hitting; nor for throwing balls from the outfield."

It is here:

http://www.iit.edu/~johnsonp/baseball.html

Posted by: sabernar at March 20, 2007 03:54 PM

This won't help solve the problem, but as an aside, Rob Dibble once threw a ball from the infield into the outfield "bleachers" at Riverfront Stadium in a fit of rage after giving up a pair of runs to the Cubs. Dibble regularly hit the high 90's when pitching, so this anecdotally supports the idea that folks with strong arms can throw far.

...Dibble hit a fan, bruising her arm badly, and as I recall ultimately had to go to anger management classes over the incident. :)
http://query.nytimes.com/gst/fullpage.html?res=9D0CE5D61F3FF933A05757C0A967958260
-j

Posted by: JinAZ at March 20, 2007 04:35 PM

Also, correct me if I'm wrong, but pitchers get a bit of extra velocity from their arm angle and from pitching off a lump of dirt - so there probably isn't a 1:1 correlation between how fast a pitcher can throw (presumably from the mound) to how far they can throw.

Posted by: scaught at March 20, 2007 05:26 PM

The spin of the baseball has a decent effect on how far it will travel. A four seam fastball will travel farther than a two seam fastball with the same initial velocity. The optimum launch angle is less than 45 degrees, around 35-38 because of the lift force from the spin. See Adair's "The Physics of Baseball".

Posted by: Jeff Mc. at March 20, 2007 06:18 PM

A couple of quick factors:

- 45 degrees is the optimum angle if there is no air resistance. As mentioned above, the optimum angle is closer to 35 degrees (I could calculate it but I'm lazy right now and don't want to look up the drag coefficient for a baseball)
- As noted, arm angle and release point also influences velocity. It is easier to throw 100 mph downhill (at a slightly negative angle) than at a 45 degree angle (since you have to release the ball before using all of the potential muscular power)
- Not mentioned yet is the effect that spin can have on a baseball's velocity and trajectory. A baseball with backspin will fly farther than one with a forespin or sidespin (this is why outfielders intuitively throw with a two seam fastball grip because of the high backspin you can achieve)

So the conclusion is that pitchers don't necessarily have the strongest arms in the maximum distance competition depending on how much of their velocity derives from the extra arm motion they can get (on the mound vs this contest) and how much spin they can put on the ball (as compared to another player who might have stronger wrists)

Posted by: Matt at March 20, 2007 06:21 PM

Gil gets a running start from the backstop, so he gets about a 10-15 mph boost from that vs what he could get from a standing position on the flat (depending on how far back the backstop is). Must still be very close to that advantage compared to a pitcher on a mound.

Posted by: JoeArthur at March 20, 2007 08:37 PM

JinAZ,
A Yankee pitcher (Dave Righetti?) did that once (except for the hitting a fan thing), 1980s IIRC -- earning the wrath of Steinbrenner, who wanted him to pitch better. Sorry my memory is a bit hazy, but I did see it.

Posted by: rbj at March 21, 2007 08:25 AM

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