Slide Me In St. Louis, or More Sliders Than at White Castle

When mathematicians meet baseball, you can expect that the numbers will add up when answering age-old questions. Questions like whether base runners will reach the bag faster by sliding feet-first or head-first, for instance. Long-time fans of Ricky Henderson--remember him?--will swear by head-first slides; long-time foes of Henderson will just swear.

But according to David Peters, a professor of engineering who specializes in aircraft and helicopter engineering at Washington University in St. Louis (clearly a Cardinal's fan who still sees in his mind's eye Lou Brock stealing bases), it's all a matter of the player's center of gravity. More specifically, Peters says that dynamics equations can determine which slide gets you there more quickly, and that there are three important mathematical issues at play:

• Momentum. The mass of the body x how fast the player is moving. Peters explains: "There's angular momentum (mass movement of inertia times the rotational rate). If it's feet-first and you're starting to slide, your feet are going out from you and you're rotating clockwise; if it's head-first, as your hands go down, you're rotating counterclockwise."
• Newton's Law. Force is mass times acceleration.
• Finally, moments of inertia x your angular acceleration.

Right, but answer the question--who gets there faster?

"It turns out your center of gravity is where the momentum is," Peters says. "This is found half way from the tips of your fingers to the tips of your toes. In the headfirst slide, the center of gravity is lower than halfway between your feet and hands, so your feet don't get there as fast. It's faster head-first." Right, but try telling that to my son's Little League coach.

Peters goes on to say that "mathematically, you might think there's an advantage, but leaving your feet is actually a detriment because you're no longer pulsing (pumping your legs) and you start to decelerate. When you're running, you get your feet out in front of the center of gravity, so you're getting maybe three or four steps of an advantage."

So there you have it. Ricky Henderson might actually have known what he was talking about.

-- Jonathan Erickson
jerickson@ddj.com

Posted by Jon Erickson at 12:38 PM  Permalink