Minipost
You've probably heard about softball pitcher Jennie Finch striking out major league baseball players.
She's standing about 43 feet from the batter rather than the 60.5 feet seen in major league baseball. Her fastest pitch is about 70 miles per hour giving a 0.42 second flight time for the ball. What's interesting is human reflexes aren't fast enough to allow even the best batter a hit. He's not thinking about it, but all of those year playing baseball taught him to read the pitcher and some clues. Clues up until the time the ball is released and perhaps a very short time afterwards.
The fastest fastballs travel about 145 feet per second (apologies to those who use sane units. Most of the readers here are American). Human reaction times range run between 0.25 and 0.35 seconds with most of us a tad below 0.30 seconds.1 Even with superhuman reflexes a the ball has traveled more than halfway to the plate before the batter notes it has left the pitcher's hand. Real time adjustments are hopeless as Jennie Finch has demonstrated.
That brings up an interesting question. If you're designing a ball a stick game - a game where a ball is thrown and hit by a stick or an arm - is there a characteristic time of flight that tests the best athletes? Another way of putting it is "is there an optimal distance for the ball to travel?"
For baseball, using 95 mph, we get 60.5 feet/140 feet per second for men .. that's about 0.42 seconds. For women the shorter path length and ball speed give the same number.
In tennis the maximum length used, neglecting the vertical component, is the diagonal of a 27 by 78 foot court - about 82.5 feet. The fastest reliably measured serve in the men's game is about 140 mph or 205 feet per second - about 0.40 seconds.2
Venturing into cricket we have a pitch that is 66 feet long. The fastest bowlers are a bit over 100mph - apparently a bit faster than baseball. The batsman generally stands about three feet in front of the wicket so we have 63/150 or about 0.42 seconds.3
Beach volleyball works out much the same for men... around 0.4 seconds flight time for the fastest serves.
four tenths of a second
That's the interesting number for all of these sports and perhaps it tells us something about human capabilities. When you subtract reaction time it emphasizes the importance of reading the other player.
Experiments have been made where baseballs are pitched from 50 feet. Now flight times are under 0.35 seconds and the game is unplayable. Once the pitches slow down playability returns. The numbers here ignore quite a bit, but are probably good to five percent or so. Some of these games are at the edge of playability and that makes them interesting.
A comment on beach volleyball. The women's court is the same size as the men's only the net is lower. A fast serve is useful, but like the other sports there is much more going on. The slower ball speed allows for more strategic play. About a month ago Kareem Abdul-Jabbar, writing in The Guardian, said:
One of the most significant contributors to the sport’s growing popularity is the dynamic play of the women. Although their games are generally not as explosive as the men’s, they play with greater technique, variety of shots, and chess-like thinking, often making their matches more compelling.
It makes one wonder about interesting physical limits and sweet spots in other sports.
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1 Curiously enough MLB players have average reflexes and some of the greats are slower than average. You can easily test your reaction time with a ruler and a friend.
2 note that I'm ignoring air resistance.. that will add a couple hundredths of a second in tennis and a bit less in baseball. In tennis the bounce adds a few small amount.
3 the ball bounces off the ground once, but the collision is highly elastic.. many a couple hundreds of a second are lost.
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