by Tom Rogers
For Americans, December 7, 1941, is an “if-only” kind of date. If only the American aircraft hadn’t been parked in easily bombed clusters and had gotten in the air. If only the American military had heeded the signs of an impending attack and stood ready at their guns. If only the DVD had existed, Americans could have corrupted the physics knowledge of the Japanese with Hollywood movies, thereby ruining the aim of their high-level bombers and causing their torpedoes to be harmlessly dropped in the mud.
Such are the thoughts of Monday-morning generals and armchair admirals. Unfortunately, using Hollywood fantasy to counteract physics knowledge is worse than using a knife in a gun fight; it’s like using a water balloon in a gun fight.When it comes to real-world tasks, even a small amount of physics knowledge held by a few individuals can overpower a flood of filmmaker foolishness.
BOMB-LIKE JUMPS
Bogus bombing physics isn’t limited to just WWII aircraft depictions. From the standpoint of physics, the terrorist who motorcycles off the top of a skyscraper in True Lies [PGP-13] (1994) is a falling bomb. In the movie, the motorcycle-riding terrorist (the same bad guy who jumped through the window described in Chapter 5) roars through the lobby of a classy hotel to escape the relentless pursuit of Arnold Schwarzenegger. Admittedly, it’s a fantasy far better than running with scissors. Roaring around indoors on a motorcycle vicariously slams all the indoor rules set forth by mommies and grade school teachers everywhere. What satisfaction!
Then Hollywood logic takes over. To escape a pursuer, what should one do? Naturally, go to the highest point in any nearby structure, preferably a perilous place where there is no chance of hiding or escaping. Dutifully, the terrorist rides his cycle into an elevator and pushes the top floor’s button.
At the top, he suddenly realizes there’s no place to hide or reasonable means of escape. What a surprise. In desperation, he revs up his machine and races over the side. At this point he has a horizontal velocity and a downward acceleration just like the previously described bomb. Like a bomb, his horizontal velocity has no influence over his downward acceleration caused by gravity. By the same token, the downward force of gravity has no influence on his horizontal velocity. Only air resistance can exert a horizontal force. Put the horizontal velocity and ever-increasing downward velocity together and, just like a bomb, the cyclist will travel in a downward-sloping parabolic path.
After going over the side, the bad guy remains airborne for roughly 7.5 seconds. He lands with a slightly downward angle in a swimming pool on top of a shorter building, a considerable distance from where he jumped.The impact does nothing more than get him soaking wet. He walks away without so much as a limp.
A falling motorcyclist is definitely not as aerodynamic as a bomb, but then he is not going as fast. Considering that the terrorist only had about a 66-foot (20 m) runway, his horizontal speed could have been no more than twenty-five miles per hour (40 kph) before his take off, as compared to 225 miles per hour (362 kph) for the previously discussed WWII bomb when first dropped. Poor aerodynamics makes air resistance higher, but lower velocity makes air resistance lower. As a rule of thumb, air resistance goes up by a factor of 4 when velocity is doubled. Low speed would tend to compensate for poor aerodynamics, so it’s still possible to evaluate the jump using a simple calculation and ignoring air resistance altogether.
TRUE LIES MOTORCYCLE JUMP CALCULATIONS
We can estimate the height (dy) of the fall by using the same bomb drop equation derived in the Pearl Harbor example:
In other words, the bad guy fell a distance of 904 feet, or roughly 74 stories. His final vertical velocity would have been:
The terrorist’s horizontal velocity can be estimated using the distance equation again to estimate his acceleration as follows:
Rearranging yields:
As depicted in the movie, the motorcycle’s acceleration on the roof took 4 seconds and occurred in a distance estimated to be 20 meters.
The velocity is found as follows:
Allowing for some possible inaccuracy in the distance estimate, his horizontal velocity would have been, at most, 25 miles per hour (40 kph or 11.2 m/s). The vertical and horizontal velocities can be combined as follows:
Terminal velocity is the highest velocity a falling object reaches and occurs when an object’s downward weight force is exactly equal to its upward air-resistance force. Increasing an object’s weight or making it more aerodynamic gives an object a higher terminal velocity. Terminal velocity for a human falling with outstretched arms and legs is around 124 miles per hour (200 kph). If the person folds into a ball, the terminal velocity increases to 200 miles per hour (322 kph). Adding the motorcycle’s weight to the terrorist would increase the terminal velocity above 124 miles per hour, and so the 166 miles per hour final speed of the cyclist looks reasonable. Using the slowest conceivable velocity of 124 miles per hour, the height would have been overestimated by only 34 percent. In other words, the motorcyclist would still have fallen about forty-nine stories.
The horizontal distance the motorcycle would have traveled, assuming it had an initial horizontal velocity of 25 miles per hour, would be calculated as follows:
Based on the analysis and calculations, the terrorist would have fallen seventy-four stories and landed in the swimming pool at about 166 miles per hour (267 kph). When it hit the water, the motorcycle would have slowed abruptly, causing the bad guy’s torso to pivot at the waist and violently slam his head forward. He would have ended up wearing a shiny new handlebar mustache in the middle of his face, courtesy of the motorcycle.
It’s easy to see that this was not a jump he was likely to walk away from. Furthermore, he would have experienced all the problems a bombardier faces when trying to accurately place a bomb. Even a small error in speed, or aim, could easily have caused him to completely miss the rather small target of a distant swimming pool. To make matters worse, the terrorist had no bombsight. In fact, he would not have even been able to see the pool until he was close to the edge of the building and it was too late to correct his aim.
Aiming issues aside, the motorcycle would probably have fallen far short of the swimming pool. In the 7.5-second jump it would have traveled only 92 yards (84 meters) in the horizontal direction. Judging from the tiny appearance of the people around the pool, the horizontal distance was farther than the 100-yard length of a football field.
If the terrorist actually did fall seventy-four stories, the Marriott Hotel he jumped off would have had to be eighty or more stories high for him to land on top of another building. Keep in mind that the observation deck of the Empire State Building is only eighty-six stories high.Yet, even this height would have been inadequate to give the jumper enough time in the air to travel the horizontal distance needed for reaching the pool.
While True Lies does serve up some motorcycle-jumping silliness, at least it does so with a sense of humor. Not to be outdone by a motorcycle-riding terrorist, Arnie, who’s riding a horse, attempts the same jump. Unlike the terrorist, the animal has horse sense and stops short, sending Arnie over the side. He’s left dangling on the end of the reins. In a parody of old cowboy flicks from the fifties, Arnie finally convinces his not-so-trusty steed to back up and rescue him from certain destruction.
THE POWER OF DIRECTORS
So, why does Hollywood give us these bogus bomb scenes? The answer is a combination of box office savvy and physics ignorance. The director of Speed (see Chapter 1) was driving down the highway and saw an overpass bridge with a missing section. Being an imaginative guy in the process of making a movie, he immediately visualized a scene in which his movie’s bus would be compelled to jump such a gap. He had no idea if the jump could actually be done, nor did he care. He wanted to do something big for boosting box-office appeal, and his intuition told him this was it. The writers were less than enthusiastic, but that mattered little. On the set the director speaks with the voice of a god.
There were, naturally, problems. As described in Chapter
1, the bridge was flat in the area where the jump was to take place, not to mention that the gap was created on film by carefully erasing the bridge’s image. Had there been a real gap, as soon as the bus went off the end it would have, from a physics standpoint, become a falling bomb. The fact that it was moving forward would have in no way stopped or slowed the falling action. As stated in Chapter 1, the bus’s wheels would have fallen at least 3.8 feet (1.16 m) below the roadway, causing the bus’s front end to slam into the edge when it reached the gap’s far side (assuming the bus had reached the unlikely high velocity of 70 mph or 113 kph before arriving at the gap). In the movie, this problem was solved with the distraction of dramatic music, screaming actors, and rapid camera cuts to prevent viewers from focusing on the flatness of the bridge.
Ironically, a real bus jump was also filmed and artfully edited into the movie to give the scene realism. So it’s understandable that the reader described in Chapter 1 completely missed the fact that this bus could not possibly have been jumping the gap depicted in the movie. The highly modified bus used in the actual jump drove up a specially made ramp at over sixty miles per hour (97 kph) and traveled over twice as far as the length of the 50-foot gap before slamming into the ground, blowing out its front tires, and destroying its oil pan. Afterward, the bus was undrivable. To the horror of the moviemakers, the bus also traveled so far that it wiped out all but one of the cameras placed in its path. The last camera did get the shot, but it was improperly framed, although eventually used in the movie. All of this could have been prevented if the moviemakers had just made the right calculations. Even more ironically, had the moviemakers spent more time making calculations and studying the physics of the jump, they could have designed a jump in which the bus actually traveled across a 50-foot gap and remained drivable, but that’s a subject for the next chapter.
Summary of Movie Physics Rating Rubrics
The following is a summary of the key points discussed in this chapter that affect a movie’s physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best.
[–] [–] Bombs that fall straight down.
[–] [–] Jumps in which a person falls like a bomb for several seconds and walks away uninjured.
[–] [–] Impossible vehicle jumps.
[+] Any of the above that are presented tongue-in-check or with a sense of humor.
CHAPTER 9
LEAPING LOGIC:
Why Moviemakers Say “How High” When the Director Says Jump
JUMPING BUSES
The passengers scream and the driver ducks as the bus hurls towards the edge of disaster. Suddenly, within inches of the gap in the freeway bridge, the front of the bus miraculously flips upward, having hit a short ramp just seconds from oblivion, restoring hope for survival. But when the back wheels approach, the ramp fails. It seems to have disappeared. Instead of being projected upwards like the front, the back wheels go over the edge and fall below it—ending all hope of survival.
The camera angle changes rapidly as the bus drifts across the chasm. When the bus reaches the far side of the gap, are its back wheels even further below the edge? Does it smash into it and explode? Why, no! The back wheels touch down on the roadway. It’s a miracle! The columns holding up the bridge have shrunk in height, dropping the roadbed to a lower level.
Yes, the moviemakers did film an actual bus jump of sorts in Speed that was then skillfully edited into the film. However, the jump was not made across a gap in a flat section of an overpass bridge as depicted in the movie.
The bus drove at a speed of about sixty miles per hour (97 kph) up a special ramp built on a ground-level section of unused highway. A small additional ramp, called a kicker plate, was positioned at the top and did indeed flip the front of the bus sharply upward as the front wheels drove over it. The kicker then fell out of the way so that it had no effect on the back wheels.
Had the bus merely gone over the ramp, the back wheels would not have immediately fallen below the edge of the ramp. The kicker plate caused the bus to rotate around its center of mass with the front moving higher and the back lower than normal. Since the top of the ramp was about 12 feet (3 m) above the level of impact on the roadbed below, the bus flew horizontally over 100 feet before its rear wheels slammed into the ground, followed by the front wheels slamming downward even more violently. Such a landing left the bus undrivable, a condition that would have doomed the passengers to die in a fiery blast (assuming they were still alive).
To prevent serious injury during the landing, the stunt driver was suspended in a special shock absorbing restraint. Had the stunt driver driven the bus in the normal manner, he would have almost certainly broken his back—an occupational hazard for stunt drivers before the invention of the shock absorbing restraint. As it was, he forgot to wear his mouth guard during the jump and accidentally bit his tongue.
Needless to say, the bus was not an off-the-shelf variety. It was specially modified with driving controls located halfway between the front and back of the bus—a section where normally only passengers sit. This was done to help the driver line up the bus with the ramp as well as put the driver in a less vulnerable position. If the bus went out of control, the front was the most likely part to get smashed in. Everything that could be removed from the bus was taken out to reduce the bus’s weight.
SIMPLIFIED BUS JUMP CALCULATIONS
Traditional projectile-motion equations, which ignore air resistance, work well for modeling compact objects such as balls projected off ramps. While ignoring air resistance is not a big source of error for calculating the length of a bus jump, there are other possible errors. When the front wheel goes over the edge, the bus’s center of mass is still well behind the edge but is no longer supported by the bus’s front wheel. The center of mass essentially has to cross a larger gap than the front wheels. If the bus is not moving fast enough, the bottom of the bus can actually scrape the edge of the ramp.
With the front wheels over the end of the ramp, the back wheels will still be in contact with the ramp and create an upward normal force. This force will tend to rotate the front of the bus downward. On the other hand, the torque applied to the back wheels by the engine will tend to rotate the front of the bus upward. For motorcycle-jump-length calculations, these differences are not a big problem, since the length of the cycle is fairly short. A bus, however, is a lot longer, and making a precise jump length calculation for it would require a computer simulation. Still it’s possible, even with a simple equation, to make a reasonable approximation for a bus jump in order to determine if the jump is at all possible.
To start, let’s assume that the bus’s center of mass is located about half a bus length behind the bus’s front tire at the moment the wheel goes beyond the edge of the ramp. When the bus reaches a similar elevation on the other side as it lands, the bus’s center of mass will be about half a bus length in front of the gap. So let’s model the gap as though it were the length of the actual gap plus the length of the bus. Even when ignoring rotation caused by the normal force on the back wheels and counterrotation from engine torque, this length should yield a conservative estimate of whether or not the jump is possible.
The simple projectile-motion equation for horizontal displacement or range of a jump is as follows:
Where:
dx = the range or length of the jump
v = velocity of the bus up the ramp or takeoff velocity
g = the downward acceleration due to gravity, 9.8 m/s2
ß = the ramp angle above the horizontal
Note that the bus’s mass does not appear anywhere in the equation. The jump depends only on ramp angle and speed.
Could the jump have been achieved under more realistic conditions, and could the bus have remained drivable? The
answer: yes, but with some qualifications. It would have required matching ramps on both sides of the gap and a precise bus speed. Surprisingly, the ramps’ angles needed to be no more than 11 degrees and the bus’s speed roughly sixty miles per hour (97 kph) in order to make it across the 50-foot gap. Having a landing ramp at the same angle as the takeoff ramp allows the bus to gently touch down, because the bus’s net velocity will be nearly parallel to the ramp. This lets the bus roll down the ramp rather than collide with it.
Ramps act like velocity splitters. The takeoff ramp converts part of the bus’s horizontal velocity into a vertical velocity component that moves the bus upward and a horizontal component that moves the bus forward. The gravitational force acts in only the vertical dimension and slowly reduces the vertical velocity component until it is zero at the top of the trajectory. At the top, the gravitational force then increases the bus’s vertical velocity component in the downward direction. The bus has to be up in the air above the takeoff ramp long enough for its horizontal velocity to carry it across the gap.
