THAT ANYONE CAN even hit a big-league pitch is a wonder in itself. That some can hit home runs is practically a miracle. On paper, at least, the feat seems impossible.

A pitcher starts his windup for each pitch at a distance of 60 feet six inches from home plate. But by the time he releases the ball, he’s about five feet closer to the plate. If he throws a 99-mph fastball, the ball is going to reach the batter in 395 milliseconds. By comparison, it takes 400 milliseconds to blink your eye completely.

A lot has to happen in those 395 milliseconds. It takes the first 100 just for the batter to see the ball in free flight and get an image of it to his brain. If a decision is made to swing, the batter generally has a grand total of 150 milliseconds to get the bat around and through the strike zone.

And those are only for the gross movements involved. There’s still some fine-tuning to do. If the batter is only seven milliseconds early or late in connecting with the ball, he’s going to send it foul. And even if his timing is perfect, he still has to put the “sweet spot” of the bat within an eighth of an inch of the correct spot on the ball. To give you an idea of the margin of error, the width of an average pencil is twice as big as the margin of error on a major league bat.

To top it off, the batter has to swing pretty hard. If he’s going to hit a home run, he has to swing very hard, and as every golfer, tennis player, and place-kicker knows, the harder you try to hit, the tougher it is to hit with accuracy.

If you told all of this to an alien freshly landed from Mars, he’d refuse to believe that anyone has ever hit a home run, except maybe by pure luck once every 25 years or so. And he’s never going to believe that Mickey Mantle hit a 565-foot bomb—at Griffith Stadium in Washington, D.C., on April 17, 1953. That shot remains baseball’s official record holder.

It’s natural to think about human limits. So what is the longest home run it’s possible to hit?

FIVE-HUNDRED-FOOT HOME RUNS are still extremely rare. But to predict exactly how much farther beyond 500 feet a homer can travel, we first need to know what kind of pitch produces the longest ball. Simple physics tells us that we want the fastest pitch possible, because the ball’s forward energy will be returned when it bounces off the face of the bat. To prove this to yourself, imagine throwing a ball against a wall: The harder you throw it, the faster it’s going to bounce back at you.

That would seem to complicate things a little, because in order to figure out the longest possible homer, we also have to figure out the fastest possible pitch. The good news here is that we don’t need to worry too much about that because, unlike many athletic skills, pitching seems to have a fairly definite outer limit.

According to Dr. Bassil Aish, chief medical advisor for the ESPN show Sport Science, the limiting factor is not muscle power or technique. It’s how hard a pitcher could throw without dislocating his shoulder or tearing a rotator cuff or pulling a tendon off a bone. Aish has calculated that an appropriately proportioned pitcher could get strong enough to throw well above 105 mph—the fastest pitch ever recorded in the major leagues—but that anything over 111 is almost sure to result in serious damage.

If you think serious injury as a result of throwing a hard pitch is just theoretical, just ask Tony Saunders of the Tampa Bay Devil Rays, who broke his humerus, the bone that runs from the shoulder to the elbow, on a 3–2 pitch to Juan Gonzalez of the Texas Rangers in 1999. Of course, Saunders and the other major leaguers who’ve suffered similar injuries weren’t throwing anywhere near 111 mph, which is what we’re going to use for the pitch that would produce the longest possible home run.

IT SEEMS SIMPLE now: Just launch a 111-mph missile and let the batter hit it with everything he’s got at an optimum launch angle. But it isn’t that simple, because there’s air friction involved. That’s going to slow the ball down, and while there’s not a lot we can do about that, there is a little. As long as we’re going to encounter friction, we might as well use it to our advantage. We do that by imparting some backspin to the ball when it’s hit, changing its trajectory in a way that will increase distance.

It’s not easy to hit a 111-mph pitch, but we’re not going to concern ourselves with that difficulty: After all, our guy has to hit it only once. All we care about is the type and speed of the pitch when it does get hit, and the pitch we want is a fastball.

There are other factors that come into play. For one thing, we want the driest ballpark possible, because the “springiness” of the ball decreases as the air gets more humid, resulting in less distance. Temperature counts, too. Cold air is denser and puts more drag on the ball. When the air temperature is 75 degrees or higher, about 4 percent of batted balls result in homers. When it’s colder, that number can drop to as low as 3.2 percent. To decrease air density even further, we want a stadium at high elevation. Wind speed enters the equation as well. But for our longest-ball prediction, we’re going to assume a windless day because we’re trying to calculate the ultimate human performance under repeatable conditions.

All we need now is the fastest possible bat speed.

THE EASIEST WAY to talk about what we’re looking for is to start with someone we know already who has one of the highest measured bat speeds in the game. That would be Derek Bell, an outfielder who had an 11-year major league career highlighted by his 1995 season, when he hit .334 for the Houston Astros. Bell was 6 foot 2 at 215 pounds in his playing days, and his highest recorded bat speed was an incredible 95 mph. Using this as a starting point, we’ll break the swing into its major components to analyze how that speed could be exceeded.

According to Dr. Aish, a batter’s hands, wrists, elbows, and shoulders form a “kinetic chain” enabling the linked sequence of motions that results in rotational acceleration of the upper extremities. At the “extreme of the extremities” there’s a baseball bat, a highly leveraged extension of the body. The purpose of all that rotating is to get the bat’s sweet spot moving through the air as fast as possible.

One way our ideal hitter could increase bat speed is simply by having longer arms. Swing a rock tied to a 1-foot string around your head at one rotation per second and the rock will move at about 4 mph. But make it a 2-foot string, and the same rotational speed will get the rock moving twice as fast. Similarly, for any given rpm, the farther you can get the bat from the center of rotation, which is the center of the batter’s body, the faster the sweet spot of the bat will be moving when it meets the ball. A player 6 feet 8 inches tall would have a swing arc about 15 percent longer than Derek Bell’s for the same given bat size. This translates to a bat speed of 109 mph based on arc size alone.

Of course, that extra speed is not free: You have to add more power in order to maintain the same rotational speed with longer arms and a longer bat. So the second thing we need to do is give our batter the power to increase the rotational speed of his upper extremities. An increase in muscle mass without counterproductive loss of flexibility would be about 20 percent over Derek Bell’s playing weight of 215 pounds and estimated body fat of 9 percent.

The lower body contributes torque to the upper body, and by Aish’s estimates, the right physique—with no performance-enhancing drugs allowed—would add 4 percent more power. He also believes that a quick, well-timed forward stride by a 6-foot-8 man can add up to 7 mph to bat speed, bringing us up to 120.6 mph.

While body rotation is doing all its work to get the bat accelerating to as high a speed as possible, there’s still one more opportunity to impart a last burst of power—the “snap of the wrists” that comes at the last instant before contact. That last snap can account for as much as 20 percent of the ultimate bat speed. In technical terms, the wrist slides from maximum radial deviation to maximum ulnar deviation, and because many athletes have unusually high radial/ulnar deviations, we’re going to assume that our ideal hitter has a maximum deviation of 115 degrees. (The structure of the bones precludes anything higher.) That gets 25 percent more power out of the wrist snap than Bell achieved. Twenty-five percent more of a 20 percent contribution to bat speed gets us an overall increase of 5 percent.

Final bat speed? Nearly 127 mph.

WE NOW HAVE everything we need to calculate the perfection point for the longest ball it’s possible for a human batter to hit. It’s not an easy calculation. It involves a series of differential equations developed by Robert Adair for his book The Physics of Baseball.

But imagine that 400 years from now, a slugger named Smith will step to the plate one warm day during a game at Coors Field in mile-high downtown Denver. Smith, who will stand 6 foot 8 and weigh 247 pounds, will be facing a rookie flamethrower fresh out of the bullpen. On the fifth pitch of the at-bat, the rookie will tilt back and unleash a 111-mph fastball over the heart of the plate.

No athlete uses more of his muscles at one time than a batter, and Smith will be able to feel his coming into perfectly orchestrated play as he starts the bat around, pours power into it, and keeps pouring it on through the entire arc of his swing.

The ball will have slowed to 100 mph by the time the bat, moving at 127, finally connects. The sound of impact will be like nothing anyone in the ballpark has ever heard. Even in the upper deck it will sound crisp and sharp, like a rifle shot or a dry log breaking cleanly in two.

The ball will leave the face of the bat at 194 mph and soar upward at a 35-degree angle. Backspin will cause it to rise sharply at first, and it will still be heading upward when it rises above roof level.

When the ball finally lands, 9.3 seconds after Smith hits it, it will strike a patch of dirt outside the stadium and leave a sharp indentation. After the game, measurements will be taken that show the ball traveled exactly 748 feet from home plate.

Will it happen? In reality, probably not. Because the danger to pitchers would be far too great, it’s likely that baseball’s rules or equipment would be changed before a ball ever flew that far. But it could.

From the book The Perfection Point by John Brenkus. ©2010 by John Brenkus. Reprinted by arrangement with Harper, a reprint of HarperCollins Publishers.