Two years ago, our friends at the Harvard Sports Analysis Collective applied their usual rigorous statistical scrutiny to a series of basketball movies. We pick up the idea again with this analysis of Hercules, by Anthony Zonfrelli and Dmitri Ilushin.
Disney's Hercules: the classic tale of the clumsy boy blessed with superhuman strength who fights to become a hero to rejoin his family on Mount Olympus. With the help of his goat-man trainer, Philoctetes, Hercules learns to use his incredible gift to "Go the Distance," performing all kinds of outrageous physical feats.
In order to give Hercules his due—and to judge Disney's ability to follow the rules of the known universe—we looked into the physics behind these feats to better appreciate how otherworldly his strength really was. We don't care if we're watching a movie with shape-shifters and talking tornados—we want to see some consistency.
We see Hercules's first truly impressive feat of strength during his teenage years, when he is sprinting down a barren road with a cart loaded with an incredible amount of hay bound for the marketplace. Eager to help out, Hercules lifts the entire haystack, but his father tells him to wait by the cart while he haggles with the local hay-mongers. A chastened Hercules then drops the haystack back onto the cart, causing the cart to launch his father's donkey, Penelope, into the sky. With a few assumptions and basic kinematic equations, we can dig a little deeper into Penelope's wild ride through the clouds.
Poor Penelope was in the air for 7.7 seconds of screen time. With this measurement alone, we can deduce that she reached a maximum height of 73 meters, meaning she went on a ride higher than the eighth-tallest roller coaster in the world without so much as a seatbelt. Furthermore, we estimate that the g-force required to catch Penelope—a task Hercules managed with little to no stress—exceeds 19 g. Keep in mind that anything over 25 g is likely to result in serious injury or death to a human (and probably a donkey). At Penelope's speed, the force of the catch is equivalent to her crashing into a telephone pole at 84 mph.
To propel an average-sized donkey that high, the mass of the haystacks must have totaled 12,864 kg (28,360 lbs), which didn't seem to faze Hercules, who managed its weight with one arm. What's less clear is how Hercules's father expected Penelope to lug over 14 tons of hay into town. Donkey rights have come a long way.
We fast-forward past a strenuous Danny DeVito training program, and Hercules takes his first pass at being a hero. Two boys are trapped in a rock quarry, begging someone to "call IX-I-I." Hercules sees his big chance and hefts the enormous boulder off of the boys, presses it up over his head, and saves the day.
From a screenshot, we estimate that the boulder has a radius of approximately five times Hercules's height (6'5", according to legend). Using this measurement and Wolfram Alpha's estimate of the average density of rock, we find that the gargantuan boulder weighs nearly 23 million pounds. In non-rock terms, this is equivalent to the weight of 575 Greyhound buses or nearly 2,400 African elephants. Had this task been conducted in an official competitive setting, Hercules would have shoulder-pressed 44,000 times the world-record weight.
Soon after achieving hero status, Herc engages in that other favored pursuit of teenage males: chasing tail. After wooing the beautiful Megara, Hercules apparently gets a boost of testosterone from falling in love and goes straight to the stadium to lift weights with his flying horse pal, Pegasus. In a fit of youthful exuberance, Hercules jumps off the high bar and deep into the night sky, achieving an absurd hang time of 30.1 seconds—long enough for evil demons Pain and Panic to capture Pegasus by shape-shifting into a sexy Pegaslut (complete with tramp stamp) and luring him into their clutches.
Using the same method we used to calculate Penelope's height, and taking into account the standard height of a high bar, we find that Hercules took off with an incredible velocity of 147.6 m/s (330 mph) and reached a towering height of 1,113.7 meters (3,654 feet). Let's put that into perspective—the Empire State Building is 1,250 feet tall, the Willis Tower is 1,450 feet tall, and the tallest building in the world, the Burj Khalifa in Dubai, U.A.E., is 2,722 feet tall.
To figure out what kind of view our hero enjoyed from that height, we'll need a lesson in geometry. We only need two pieces of information: Hercules's maximum height and the radius of the Earth. Knowing that the line of Herc's vision will be tangent to Earth's surface, we can make a right triangle with this point on the horizon, Herc's viewpoint, and the Earth's very core. Taking the inverse cosine of the ratio of R/(R+h), we can figure out angle x. Then using tan(x), we can find d.
This calculation shows that Herc's spectacular view is over 74 miles in any direction, nearly twice as far as one's view from the top of the Eiffel Tower. Assuming his training area is located in the center of Thebes, he can see well past all of Athens and into the Aegean Sea.
The evil Hades greets Hercules upon his return to Earth, and in exchange for Megara's promised safety and Pegasus's release, Hercules agrees to give up his strength for 24 hours while Hades unleashes the Titans in an attempt to overthrow Zeus and take control of Mount Olympus. The deal is confirmed with a dramatic handshake that sucks the power right from Hercules's body. But there's only one problem with it—they shake with their left hands. In what universe is that deal legal and binding? Hercules might as well have just crossed his fingers behind his back if this is what constituted a legitimate, godly contract in Ancient Greece.
After a brief interlude involving a tender love scene and the recovery of his strength, Hercules chases down Hades and joins the gods in the war against the Titans, where he performs his final, absolutely ridiculous feat of strength. Hercules grabs the tornado Titan, Stratos, and swings him around until he has sucked up all of the bad guys, and, in super slow motion, hurls them all into outer space. Where they explode. This feat exhibits incalculable strength, and the explosion in space breaks all kinds of laws of physics. I cannot even begin to understand, let alone explain, how it all transpired.
The rest is (ancient) history. Hercules takes a dip in the underworld, revives Meg, and restores order to Mount Olympus. Take it away, Hades.