Vampires are a favorite TV and film monster, ranging from the very serious and scary Nosferatu (1922) and Bram Stoker’s Dracula (1992) to the campy and amusing Buffy the Vampire Slayer. To get an idea of the enduring popularity of the vampire, I ran a search on the Internet Movie Database. Since the 1930s, more than 350 movies, television shows, and video games have come out with vampire as part of the title. (This includes episodes of some TV shows, and a number of foreign films, but that’s a lot of undead, nonetheless.) Stephenie Meyer’s novel Twilight moves the genre into teen romance, and the recent film adaptation had a record-setting opening weekend. Given the popularity of the books and the film with middle and high school age girls, discussing the physics in the movie may help science teachers connect with female students.
Twilight is the story of Bella Swan (played by Kristin Stewart), a high school junior who moves from Phoenix, Arizona, to Forks, Washington. As she tries to settle into a new high school, Bella meets Edward Cullen (Robert Patinson), her pale biology lab partner. Their conversation over onion root-tip slides heightens Bella’s initial attraction. Edward is one of a family of five foster children who recently moved from Alaska and travel as a pack around the high school. Bella falls for Edward and, through some sleuthing, deduces that the Cullens are vampires. The film follows Bella’s attempts to reconcile this human/vampire relationship. For an excellent analysis of the antifeminist messages in the Bella/Edward storyline, see Lucy Mangan’s review.
Every author of vampire literature emphasizes particular weaknesses and strengths of the undead, and there are quite a few to choose from. Meyer’s vampires avoid direct sunlight, but appear unaffected by crosses as one is prominent in the Cullen’s home. They are very strong, very fast, and have a heightened sense of smell. It’s interesting to think about what the consequences of these abilities would be if actual physics were taken into account. Perhaps the best opportunity to do this in Twilight is when Bella joins the Cullens for that most American of pastimes, a game of baseball.
In vampire baseball, you have to wait for a thunderstorm to get out the bat and glove. You might wonder why the Cullens prefer rainy days on the field, aside from the protection from sunlight. While the pitches look relatively normal, vampire batters hit the ball so hard that they generate sonic booms, which would attract unwanted attention if not for the covering noise of the thunder. Sonic booms are created when objects go faster than the speed of sound, so this got me thinking about just how much faster vampire line drives are than those hit by humans. A quick internet search turned up a typical top-end speed for a batted baseball of about 125 miles per hour. In more physics-friendly units that is about 55 meters per second (m/s). The speed of sound is roughly 343 m/s, so vampires are able to hit the ball at least six times faster than human batters. That’s pretty impressive, and it left me with a few questions:
- How far would one of these supersonic line drives go? This is not a trivial question to answer since wind resistance increases with velocity, but I think we can get a ballpark figure (pun intended).
- How long would the ball be in the air?
- How much force is put on the ball when struck by the bat?
The exact distance of the longest home run ever hit is subject to a great deal of debate in baseball history, but it is probably between 500 and 600 feet (150 to 200 meters). The stadium tends to get in the way when you’re trying to measure from home plate to where the ball landed, and eyewitness are not always sure of that location in any event. I took advantage of a baseball home run simulator to do some extrapolation. An initial ball speed of 140 mph (225 km/hour) and launch angle of 20 degrees produces a 550 foot (168 m) home run. The simulator does not allow initial speeds over 140 mph, but I used increments of 20 mph from 80 to 140 and extrapolated out to the speed of sound and obtained a distance of more than 3000 feet (nearly 1 km). In traveling that far, the ball would also be in the air for more than 30 seconds. That’s quite a hit. I suspect that both of these numbers are a bit too large, as the simulator isn’t designed for such high initial velocities, and wind resistance increases with the square of velocity.
In my review of The Dark Knight, I brought up the relationship between impulse and momentum, and this relationship is useful in answering my third question about the force on a batted ball. In the collision between bat and baseball, the ball experiences a very large change in momentum: it was coming toward the batter at about 45 m/s, and in a fraction of a second the bat causes it to change direction and fly away from the batter at 55 m/s. Because velocity is a vector quantity, that is a net change (Δv) of 100 m/s. We can rearrange the impulse-momentum equation FΔt = Δmv to get F = Δmv/Δt, and because the mass does not change, F = mΔv/Δt.
Using the mass of a baseball (0.145 kg) and the time of contact between the bat and ball (0.0007 s), we can calculate the average force on a ball batted by a human (about 20,000 Newtons) or a vampire (about 80,000 Newtons). The difference is the Δv for the vampire is 390 m/s instead of 100 m/s. Note the peak force is approximately twice as large, and 160,000 Newtons is about 18 tons of force. I’m not sure that either a bat or ball could withstand that kind of impact.
There are a few other moments in Twilight physics students might be interested in examining: Edward saves Bella from a sliding van by simply putting up his hand to stop it. How much force does it take to stop a sliding minivan? Later, Edward runs up a tree with Bella on his back, and I was curious how his feet and hands could stick to the trunk of a mossy tree. How much friction would it take for someone to be able to climb a tree in that way?
For those looking to delve further into the physics of baseball, here are a few resources: Robert Adair’s The Physics of Baseball; an investigation of the ball/bat collision, and a nice collection of web resources.
Jacob Clark Blickenstaff is Assistant Professor of Physics and Assistant Director of the Center for Science and Mathematics Education at the University of Southern Mississippi. He can be reached at email@example.com.
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