Starts With A Bang!

What if Superman played Baseball?

Sometimes I read The Straight Dope, which is usually full of interesting questions and (relatively) well-researched answers. But the message board is another story. Sometimes you get good questions with no good answers, like this one:

How far could Superman hit a baseball?

Let’s assume, for the purposes of answering this question, that Superman basically has unlimited strength and speed, but is limited instead by the following things:

• He has to use a regulation wooden bat.
• He cannot break either the bat or the ball.
• No using superbreath, laser beams from his eyes, or any other superpowers to interfere.
• He’s still Superman, but the ball is still subject to the normal laws of physics.

So given all of these things, how far should Superman be able to hit a baseball?

Let’s start with the guy who researches the physics of baseball (right). We can immediately learn some wonderful things that are independent of Superman’s abilities. First off, the typical major league bat has a mass of about 0.9 kg, although they can be as massive as about 1.5 kg. The ball is between 142 and 149 grams, as per MLB regulations. Second, the difference in speed between the ball and the bat, in the end, is determined by the speed of the pitch, not the speed of the bat. For a baseball pitched at 90 miles per hour (40 meters/second), the difference between the final speeds of the ball and bat will be 0.55 times the difference between the initial speeds of the ball and bat. And for a normal human being (at least, a normal major league power hitter), there’s already been a study done where they’ve not only derived a formula for the final speed of the ball dependent on the initial speeds of the bat and ball:

But they’ve also determined what the optimal bat weight and swing is for someone who can make contact with a baseball, whose sole concern is how fast they can hit that baseball. Take a look at the graph:

And now, let’s come to the fun part. We’re not dealing with a Sammy Sosa here. We’re dealing with Superman. If a normal human can deform a baseball like this:

then it stands to reason that Superman will have to hold off, or the bat (and ball, for that matter) will be destroyed by the incredible forces. An important piece of information is that the contact time between the ball and bat is typically only 0.0007 seconds, and let’s assume that for Superman, it’s the same. The average force on the ball & bat? That just mass*change in velocity/contact time. The peak force? Twice that. So, if we can figure out how much force will destroy a bat or ball, and require that Superman swings no stronger than that, we can determine how quickly he launches that sucker.

White ash, the material that baseball bats are made out of, will rupture if you apply more than 15,000 pounds of force per square inch against it. Given that a baseball has a surface area of 26.4 square inches, and as you can see from this slow-motion camera shot of a struck baseball (right), about one-sixth of the ball comes in contact with the bat (and that’s being slightly generous), that means the bat can exert a maximum of 66,000 pounds of force on the ball without breaking, or 295,000 Newtons. This means we can get an average force out of about half that, or a maximum change in the ball’s speed of 712 meters/second.

This assumes that Superman hits the ball perfectly, dead center in the sweet spot of the bat. (And why not, really; after all, he is Superman.) That means the speed at which the ball leaves the bat is, maximally, about 672 meters/second, or around Mach 2. You know, the same as the maximum speed of the Concorde.

At these speeds, air resistance is definitely important, since the terminal velocity of a baseball is only about 33 meters/second. Without air resistance, the ball can travel about 46 kilometers before coming down to Earth, a truly amazing feat. However, air resistance slows this thing down pretty quickly, as you can find out for yourself by playing with this projectile motion launcher *with* air resistance! The ball comes down after about 50 seconds, and lands “only” about 900 meters away from where it started, or about 3,000 feet if you launch it at 45 degrees. Because of air resistance, though, smaller angles do better. By lowering the angle to only about 10-15 degrees, you can get the ball to go a little further, about 1,300 meters away, or close to a mile.

So take that, Superman! You can’t even hit the ball one stinking lousy mile! Umm… but I still want you on my team.