Authored by Alan Nathan of the University of Illinois, Lloyd Smith and Warren Faber of Washington State University, and Daniel Russell of Kettering University in Flint, Mich., “Corked bats, juiced balls, and humidors: The physics of cheating in baseball,” just appeared in the journal of the American Association of Physics Teachers.

The researchers set out to investigate, from a physics perspective, three “questions of relevance to Major League Baseball”: “Can a baseball be hit further with a corked bat?” “Is there evidence that the baseball is more lively today than in earlier years?”, and “Can storing baseballs in a temperature- or humidity-controlled environment significantly affect home-run production?” Their experiments took place in the bat-ball test facility at the Sports Science Laboratory at Washington State University.

The first question under consideration was whether a baseball can be hit farther with a corked bat. The researchers note that in 2003 Sammy Sosa of the Chicago Cubs was caught using an illegally corked bat: a wooden bat that has been drilled out lengthwise and filled with a lightweight inert material.

The theory behind corking is that, because the bat is lighter, players can swing it faster and therefore hit the ball farther. But the counter-argument is that a lighter-weight bat imparts less energy to the ball on impact. So…does a corked bat work?

To find out, the researchers fired a baseball from an air cannon at 110 mph onto a solid wooden bat, then on the same bat with a hollow interior, and then with the interior filled with cork. (They’d intended to try the experiment with the bat filled with superball material, too, but the bat broke.)

They measured the speed at which the ball hit the bat, and the speed at which it rebounded, using those measurements to calculate the coefficient of restitution, or COR, the ratio of the outgoing velocity of the ball to its incoming velocity. They found that the COR was identical, no matter what they did to the bat.

What about the swing speed? The effect of swinging a lighter bat faster versus a heavier bat slower, when both have the same COR, can be calculated mathematically, and the calculations were clear: the higher swing speed wouldn’t do the batter any good. In fact, a corked bat will usually hit the ball a shorter distance, not a longer one. The only advantage that a corked bat might give is allowing the batter to react faster.

The next question was whether today’s baseballs are livelier than those of the past, a question that pops up (rather like an overworked metaphor) whenever there’s a spate of home runs.

By good fortune finding several unopened boxes of baseballs from the late 1970s, the researchers were able to compare 35-year-old balls to modern ones, firing both against both flat surfaces and bats at speeds ranging from 60 to 125 mph. Again, they found no significant difference between the old balls and the new balls (although of course that says nothing about balls from even older eras, as the researchers are the first to admit).

Finally, the researchers set out to see if the Colorado Rockies’ practice of storing their baseballs in a humidor with a constant temperature of 70 degrees and a constant relative humidity of 50 percent, to counteract the effect of the lower air density in Denver, could account for the decrease in offensive statistics at Coors Field since 2002.

Sure enough, they found that the COR fell by 4.5 percent when the relative humidity at which the ball was stored increased from 30 to 50 percent. They estimate in an actual game the humidified balls would fly 14 feet less on average than regular ones, which could cut home runs by a quarter.

They also found you could cut home runs even more with cold baseballs: the COR fell by 3.3 percent when the storage temperature was decreased from 70 to 35 degrees F, translating to an average 10-foot reduction in flight distance, and a 19-percent reduction in home runs.

So the answers to the three questions? No, no and yes, respectively.

In baseball terms, that’s batting .333. In science terms, that’s batting a thousand.

(The photo: Toronto at bat against Baltimore, in Toronto, summer 2008.)

Yeah, I know, I said it seems improbable to me now. Nevertheless, I can’t help but feel a stronger relation to other people named Willett than I suspect your average Smith does to other Smiths: there just aren’t as many of us as there are of them.

And so, just for fun, I’m launching a new Hassenfeature: the Willett of the Day. (Not that there’ll be a new Willett here every day, but most days, I hope.)

And who better to start with than Robert Edgar Willett, better known as–you guessed it!–Ed Willett.

Born March 7, 1884, Ed Willett was a Major League pitcher. He played with the Detroit Tigers of the American League (1906 – 1913) and the St. Louis Terriers of the Federal League (1914 – 1915).

You can read all about him on Wikipedia–and here’s his baseball card!

Is there a family resemblance? I’ll leave that to you to judge.

Yeah, I know, I said it seems improbable to me now. Nevertheless, I can’t help but feel a stronger relation to other people named Willett than I suspect your average Smith does to other Smiths: there just aren’t as many of us as there are of them.

And so, just for fun, I’m launching a new Hassenfeature: the Willett of the Day. (Not that there’ll be a new Willett here every day, but most days, I hope.)

And who better to start with than Robert Edgar Willett, better known as–you guessed it!–Ed Willett.

Born March 7, 1884, Ed Willett was a Major League pitcher. He played with the Detroit Tigers of the American League (1906 – 1913) and the St. Louis Terriers of the Federal League (1914 – 1915).

You can read all about him on Wikipedia–and here’s his baseball card!

Is there a family resemblance? I’ll leave that to you to judge.

So this week I was pleased to discover that there are solid scientific grounds for missing easy pop flies, and they have nothing…well, very little…to do with a complete lack of skill and/or depth perception on my part.

A team of researchers led by Alan Nathan at the University of Illinois, Urbana-Champaign, and Terry Bahill at the University of Arizona, Tucson, will soon be publishing a “pop-up paper” in the American Journal of Physics that explains it all.

Normally, a ball that’s been hit follows a parabolic path, which is pretty easy to figure out. But when a ball is popped up, its path is influenced by the backspin it gets from the top of the bat. This backspin generates a rotating layer of air around the ball, which makes it curve (something known as the Magnus effect).

Sometimes this curve is enough to cause a ball that originally flew forwards at a steep angle to begin climbing vertically, and then actually loop back on itself.

The researchers used a computer simulation to calculate all the various trajectories a pop-up could take. They also simulated a fielder, who reacted to the pop-up just like a real fielder: it moved back and forth in a kind of dance as it attempted to position itself under the ball.

With baseball soon to get underway even here in late-blooming Saskatchewan, the study is a reminder that there’s a lot of physics at play in the game…which may be why a lot of physicists like to study it.

Just last December, two physicists at the University of Colorado at Boulder, Edward Meyer and John Bohn, decided to find out if the Colorado Rockies baseball team’s practice of keeping game balls in a high-humidity chamber for several months prior to their use would actually achieve its stated goal of making the balls more “sluggish,” the better to counteract their propensity to fly up to six meters farther in Denver’s high-altitude air than they do in other parks.

It turned out that in their experiments, keeping a baseball in humidity of 30 to 50 pecent for two months actually had the opposite effect. At first that seems counterintuitive: after all, humidifying the balls increased their diameters by an average of 0.24 percent and their mass by 1.6 percent, making them both squishier and more subject to air resistance.

However, the balls’ slower speed off the bat is more than made up for by their increased mass, which means they take longer to decelerate. Not only that, moist balls curve less than dry balls, making them easier for batters to hit.

And speaking of curves, I could never hit those, either. Turns out that, once again, it’s not really my fault. Rather, it’s the fault of our evolutionary history, according to Cathy Craig, a psychologist at Queen’s University in Belfast.

Craig was investigating soccer, not baseball, but the principle is the same. She decided to see if experienced players could follow the trajectories of balls with side spin. She had them watch simulated shots with a spin of 600 rpm, and asked them to decide whether the balls would end up in the goal or not–and discovered that even professional soccer players couldn’t predict the results accurately.

The reason? Until recently, there was no reason why humans needed to be able to judge the trajectory of a side-spinning sphere travelling through the air. We know how gravity affects objects moving through the air, because that’s been important in evolution, Craig told New Scientist magazine. “But spinning balls don’t occur naturally. Why would nature bother having a visual system that’s adapted to them?”

My point exactly. Which means that I, who am unable to accurately judge the trajectory of spheroids hurtling through the air, am the normal one, and all of you good ball players are freakish mutants.

I feel much better now.

More photos here.

Baseball is essentially a battle between the pitcher and the batter, and scientifically, it’s a battle the batter should never win.

It takes a 90-mph fastball (since this is baseball, I’m not going to bother with metric conversions) about 400 milliseconds to cross the plate. It takes 100 milliseconds for the eye of the batter to even see the ball and send the image to the brain, 75 milliseconds for the brain to process the information and judge the ball’s speed and location, 25 milliseconds to decide whether or not to swing, 100 milliseconds to choose a swing pattern, and 150 milliseconds to swing. That adds up to 450 milliseconds–50 more milliseconds than the batter actually has. This means either that hitting a baseball is impossible–obviously not the case–or, more realistically, that hitters swing by instinct, before their brains have really had time to calculate where the ball is going to be.

To get a hit, the batter’s bat must intersect the ball at precisely the right millisecond, no more than an eighth of an inch from the ball’s centre. If a righthanded batter is even seven milliseconds late or early, the ball will go foul.

The construction of that ball hasn’t changed in decades. Since 1872, the rules have stated that the baseball must weigh 5.1 ounces and have a 9.1-inch circumference. All major league baseballs are manufactured by Rawlings. From the outside in, they consist of a cowhide cover, three layers of wool windings, and finally the core, or “pill,” made of compressed cork covered with two different types of rubber.

An extraordinary number of home runs earlier this season led to tests to see if, somehow, this year’s balls were livelier than last year’s.

A “livelier” ball, in scientific terms, has a higher coefficient of restitution: the speed at which a ball bounces off of a solid surface divided by the speed at which the ball was thrown against that surface. The coefficient of restitution should fall between .514 and .578–in other words, the ball should bounce off of a wall at roughly half the speed at which it hits it.

Alas for the overly suspicious, the tests showed that, if anything, the 1999 balls were slightly livelier than the 2000 ones. This year’s spate of home runs seems to be part of a long-term increase in home runs, probably the result of several factors, including bigger ball players and smaller ball parks.

This year, batters had a new type of bat with which to experiment. Although baseball bats have traditionally been made out of ash, major league baseball has now approved bats made out of maple, which, fittingly enough, were born right here in Canada. Ottawa-area carpenter and baseball aficionado Sam Holman began making them after Colorado Rockies scouting supervisor Bill MacKenzie mentioned to him that too many bats were being broken: on average, 100 per player per year.

Holman’s Sam Bat is made of sugar maple, a denser and therefore tougher wood than ash. Whereas few ash bats last longer than a week, maple bats can last a month. Players can even risk using the same bat they’re going to use in a game during batting practice.

Maple has a more variable grain than ash, so careful selection of lumber is vital. Maple’s density is also more variable, which can result in otherwise identical bats having different weighs, so Holman has developed a device for testing the wood’s density.

Currently, Holman is turning out 200 bats a week in a workshop behind his home. He hopes to soon move into a larger facility. He’ll likely need it: proof of the growing popularity of the maple bat is that Louisville Slugger is now making them, too.

Although tests show no distance advantage to maple bats, their increased use could dramatically decrease the number of broken bats. Mike Piazza and Roger Clemons, I’m sure, would agree that’s a good thing.

I remember it like it was yesterday. The smell of the grass, the roar of the crowd, as I made my way to the mound to start for the Detroit Tigers…

What’s that? I’m too young to have pitched in the 1909 World Series? Well, I dare you to look it up. 1909. Detroit Tigers. Ed Willett.

See? I’m older than I look.

The game has changed a lot since then, but it’s still a duel between pitcher and batter, a duel the pitcher usually wins (which is why a .333 batting average–meaning the player failed two out of three times at bat!–is considered pretty good).

Something else that hasn’t changed is that nothing gets the crowd on its feet like a home run. That’s because they’re so excited by the fascinating physics involved–physics outlined in an article by Noel Wanner that I came across on the World Wide Web site of San Francisco’s Exploratorium, the granddaddy of all science centres.

Here’s the gist of it:

Several factors determine the outcome of a hit. One is the air density. To travel through the air, a ball has to push air molecules out of the way. That takes energy. (In a vacuum, a 400-foot home run would travel twice as far.) The more densely packed those molecules, the more energy it takes.

Air density changes with temperature, air pressure and humidity. Hot air is less dense than cold air: 36-degree Celsius air is 12 percent less dense than zero-degree air. Air pressure varies with altitude, dropping about three percent for every thousand feet of elevation–which means a baseball hit in Denver experiences 15 percent less drag than a baseball hit in Boston. And humid air is less dense than dry air, because the water molecules in it weigh less than the oxygen and nitrogen molecules they displace. Air at 80 percent humidity is one percent less dense than dry air. Even one percent is significant, because just a five percent difference in drag can change a fly ball into a home run–or vice versa.

Another factor in the outcome of a hit is where the ball hits the bat. Every bat has a “center of percussion” (better known as the “sweet spot”), generally located around the maker’s label. If you hit the ball there, you don’t feel any wobbling or twisting of the bat. Miss the sweet spot, and you’re more likely to have a weak hit.

The angle at which the bat hits the ball is also important. A dead-center hit produces a line drive. If the bat hits the ball a few millimeters above center, it drives the ball down, if it hits a few millimeters below center, the ball will fly up. That could produce a home run or just an an easily caught fly. The difference between the two is distance, which is largely determined by how fast the ball travels after it’s hit.

Both the bat and the ball have momentum, calculated by multiplying mass times speed. The more momentum an moving object has, the more energy it takes to change its direction. The 30-ounce bat has more momentum than the five-ounce ball, so when the two hit, the bat continues on its way, while the ball stops, then accelerates away in an entirely new direction.

Theoretically, a heavy bat should send the ball faster and farther. However, a heavy bat takes longer to get up to speed, and therefore requires not only greater strength but faster reflexes on the part of the batter. Many hitters prefer lighter bats, which they can swing faster.

How fast the ball was pitched also figures into the outcome. Baseballs are very elastic: in scientific terms, they have a high “coefficient of restitution.” That means that after they’re squashed on impact, they spring back into shape, using most of the energy imparted by the pitcher to zip off in an entirely new direction. (A little energy is lost as heat.)

With so many factors having to be just right, it’s amazing there are as many home runs as there are. Baseball fans should be grateful that baseball changed the ball in 1920 to make it livelier and encourage more power hitting.

It makes it harder on the pitcher, though. Sure am glad I retired in 1915.

So to write this column about the science of pitching, I turned to an expert: Robert K. Adair, Sterling Professor of Physics at Yale University, whose 1990 book The Physics of Baseball provided all the information I needed. If you’re a serious baseball fan (or a serious physics fan), I highly recommend it.

As every batter knows, the baseball does not follow a perfectly straight line between the pitcher and the plate (more’s the pity). In fact, the pitcher has a number of weapons in his arsenal, all designed to confuse the batter, beginning with the curve ball.

Curve balls are thrown with a spin, which means one side of the ball spins against the flow of air, and one side with it. Air resistance is higher on the side spinning into the wind, and that pushes the ball in the other direction. This is called the Magnus Effect.

A “typical” wide-breaking curve ball might be thrown at 70 miles per hour, spinning at 1600 rpm, and would cross the plate about six-tenths of a second later at about 61 mph. Although the path of the ball is actually a smooth curve, like a small piece of a much larger circle, to the batter it appears to “break” because halfway to the plate it’s only 3.4 inches away from the initial, straight path, but by the time it gets to the plate it’s curved 14.4 inches–the distance from the inside corner to the outside corner.

Most curve balls wouldn’t actually be thrown like that, because major league pitchers are more interested in making the ball curve downward than to the side. There is, however, a kind of fast curve ball with its direction of spin parallel to the ground. Because it’s fast, it doesn’t curve as much (because there’s not as much time for the Magnus Effect to act on it), and all of that curve is to the side. It’s known as the slider.

The screwball is a reverse curve thrown by a right-handed pitcher to break away from a left-handed batter. (Or, presumably, vice versa.)

An even more confusing pitch, for everyone concerned, is the knuckle ball, which, though it curves, is quite different from the curve ball. Whereas a curve ball’s curve is generated by its spin, the knuckle ball (usually thrown off the fingertips, not the knuckles) is thrown with almost no spin: maybe just a half-turn between pitcher and batter.

Its trajectory is therefore influenced most by the difference in air resistance between the stitched and smooth parts of the ball. The slow rotation of the ball moves that area of drag around, so the ball can be pushed in more than one direction. One simulated knuckle ball in a wind-tunnel had moved a full 11 inches off-centre when it was only 20 feet from the plate–then ducked back in to pass right through the strike zone. A batter would relax long before that ball turned into a strike, and a catcher would gather himself to chase a wild pitch. The trouble is, tiny changes in the initial ball orientation give wildly different results at the plate, which makes the knuckle ball very hard to control.

Of course, the key baseball pitch is the fastball, which sizzles across the plate at between 90 and 100 mph. Since the ball loses about one mile per hour every seven feet due to air resistance, it’s actually leaving the pitcher’s hand at well over 100 mph.

Gravity insists that a fastball drop about three feet in the 56 feet it travels from pitcher to batter, which means the pitcher actually has to throw the ball at an upward angle. To the batter, however, a perfectly thrown fastball will appear to travel in a straight line, because the upward angle the pitcher applies and the gravitational effect cancel each other out. The pitcher can also put a “hop” on the ball by throwing it with a backspin, which increases air resistance on the bottom of the ball and forces it up four or five inches.

The “split-finger” fastball, which is legal, has a lot in common with the spitball, which isn’t. Both are delivered with very little spin (the spit, or other lubricant, allows the ball to slip smoothly out of the pitcher’s hand), which means they travel slower and arrive lower than a regular fastball–but the pitcher throws them just as hard, which means the batter is expecting a regular fastball, and is likely to swing too soon and too high.

Scuffing the ball (which is also illegal) can increase drag on one side and cause the ball to move in that direction. It takes a skilled pitcher to make effective use of scuffing, since the effect is small, but even a small effect can be the difference between a home run and a pop fly. That’s because baseball truly is a game of inches–and that, by the way, is why I didn’t use metric measurements in this column.

Whoever heard baseball called a game of centimetres?

So to write this column about the science of pitching, I turned to an expert: Robert K. Adair, Sterling Professor of Physics at Yale University, whose 1990 book The Physics of Baseball provided all the information I needed. If you’re a serious baseball fan (or a serious physics fan), I highly recommend it.

As every batter knows, the baseball does not follow a perfectly straight line between the pitcher and the plate (more’s the pity). In fact, the pitcher has a number of weapons in his arsenal, all designed to confuse the batter, beginning with the curve ball.

Curve balls are thrown with a spin, which means one side of the ball spins against the flow of air, and one side with it. Air resistance is higher on the side spinning into the wind, and that pushes the ball in the other direction. This is called the Magnus Effect.

A “typical” wide-breaking curve ball might be thrown at 70 miles per hour, spinning at 1600 rpm, and would cross the plate about six-tenths of a second later at about 61 mph. Although the path of the ball is actually a smooth curve, like a small piece of a much larger circle, to the batter it appears to “break” because halfway to the plate it’s only 3.4 inches away from the initial, straight path, but by the time it gets to the plate it’s curved 14.4 inches–the distance from the inside corner to the outside corner.

Most curve balls wouldn’t actually be thrown like that, because major league pitchers are more interested in making the ball curve downward than to the side. There is, however, a kind of fast curve ball with its direction of spin parallel to the ground. Because it’s fast, it doesn’t curve as much (because there’s not as much time for the Magnus Effect to act on it), and all of that curve is to the side. It’s known as the slider.

The screwball is a reverse curve thrown by a right-handed pitcher to break away from a left-handed batter. (Or, presumably, vice versa.)

An even more confusing pitch, for everyone concerned, is the knuckle ball, which, though it curves, is quite different from the curve ball. Whereas a curve ball’s curve is generated by its spin, the knuckle ball (usually thrown off the fingertips, not the knuckles) is thrown with almost no spin: maybe just a half-turn between pitcher and batter.

Its trajectory is therefore influenced most by the difference in air resistance between the stitched and smooth parts of the ball. The slow rotation of the ball moves that area of drag around, so the ball can be pushed in more than one direction. One simulated knuckle ball in a wind-tunnel had moved a full 11 inches off-centre when it was only 20 feet from the plate–then ducked back in to pass right through the strike zone. A batter would relax long before that ball turned into a strike, and a catcher would gather himself to chase a wild pitch. The trouble is, tiny changes in the initial ball orientation give wildly different results at the plate, which makes the knuckle ball very hard to control.

Of course, the key baseball pitch is the fastball, which sizzles across the plate at between 90 and 100 mph. Since the ball loses about one mile per hour every seven feet due to air resistance, it’s actually leaving the pitcher’s hand at well over 100 mph.

Gravity insists that a fastball drop about three feet in the 56 feet it travels from pitcher to batter, which means the pitcher actually has to throw the ball at an upward angle. To the batter, however, a perfectly thrown fastball will appear to travel in a straight line, because the upward angle the pitcher applies and the gravitational effect cancel each other out. The pitcher can also put a “hop” on the ball by throwing it with a backspin, which increases air resistance on the bottom of the ball and forces it up four or five inches.

The “split-finger” fastball, which is legal, has a lot in common with the spitball, which isn’t. Both are delivered with very little spin (the spit, or other lubricant, allows the ball to slip smoothly out of the pitcher’s hand), which means they travel slower and arrive lower than a regular fastball–but the pitcher throws them just as hard, which means the batter is expecting a regular fastball, and is likely to swing too soon and too high.

Scuffing the ball (which is also illegal) can increase drag on one side and cause the ball to move in that direction. It takes a skilled pitcher to make effective use of scuffing, since the effect is small, but even a small effect can be the difference between a home run and a pop fly. That’s because baseball truly is a game of inches–and that, by the way, is why I didn’t use metric measurements in this column.

Whoever heard baseball called a game of centimetres?