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Originally Posted by BigUmp56
Since you insist.
For years batters swore that some pitchers could throw a rising fastball. The laws of physics say this is impossible. Instead, it's an illusion caused when the pitcher throws a faster pitch than the batter has seen. In bottom figure b, the batter watches the ball for the first part of its flight and calculates its drop. Then he looks down at the bat and the ball appears to have jumped because it's higher than where his mental model predicted it would be, based on earlier, slower pitches as shown in the top illustration. (Graphic by Alison Habel)
By Ed Stiles
February 18, 2000
Baseball is numbers to Terry Bahill, as well - but of a different kind. The University of Arizona professor of systems and industrial engineering has used numbers, graphs and mathematical analysis to investigate some of baseball's more intriguing questions, most of which center around that half second between the time a pitcher releases the ball and the moment the batter hits it.
The Rising Fastball —
For years batters swore that some pitchers could throw a rising fastball that would "jump" a half foot as it crossed the plate, making it hop over the bat. But this isn't possible, Bahill says. Even the greatest pitchers can't violate the laws of physics. Once a ball is thrown, it follows a smooth trajectory. Physics simply doesn't allow abrupt jumps in that trajectory.
So what's happening? "The batter is using the wrong mental model," Bahill says.
Batters divide a pitch into thirds. The first third is sensory gathering, the second is computing, and the third is swinging. So a pitcher throws several 90-mph fastballs and the batter develops a mental model and reaction to this speed, Bahill says.
Then the pitcher slips in a 95-mph fastball. During the sensory gathering segment of the pitch, the batter doesn't see anything different. He calculates where the 90-mph fastball would go and swings at that spot. But the 95-mph fastball has a flatter trajectory. It doesn't drop quite as much from the pitcher to plate because it's going faster.
"When the batter starts to swing, he takes his eye off the ball to look at the predicted bat-ball collision point," Bahill says. "When the ball comes back into his view, it is higher than his mental model predicted and he sees it 'jump' higher than where he calculated that it would be."
Tim. |
In your illustration, the trajectory of the ball for the first 20 feet would take the ball just below the neck of the batter, yet the pitch finishes waist high.
What speed would this pitch be for that amount of drop? Assuming it is a fastball and assuming a normal sized man that would be about a 16 to 18" drop from the initial trajectory.
I'm guessing that's about a 50-60 mile an hour gasser.
I can't count the number of 12 yr old games I've done where the kid was bringing 55 mph heat, the ball was dropping 16" and everyone in the crowd was gasping WOW did you see that ball jump.
If a pitch is released at 5' above home plate with an initial trajectory that plots out to 3' above home plate, after drag and gravity and all that other good stuff, at what heighth will a 100 mph fastball be when it crosses the plate? How about a 90 and 85mph ball?