The Physics of Movies and StuntsIn our modern day of action-comedies and superhero movies, stunts are an integral part of what makes these movies so exciting and fun to watch. However, in order to make these stunts happen, we need to guarantee safety for the stuntmen and ensure they can look/be filmed as cleanly as possible.
|
Motion and Forces: Spider-Man
To better understand the physics of stunts, let's take a look a stunt from Spider-Man: Far From Home by Tom Holland (video at the bottom). Although he is attached to a harness and these jumps have different physics rules than "normal" jumps, we can still use some physics concepts to analyze this stunt. Looking at parkour stunts, the object of our system is the stuntman and, as they jump, the only force that affects them is the force of gravity. This is explained by inertia and Newton's first law. The stuntman would stay in motion with the same exact initial speed, however, they are affected by an outside force (in this case the force of gravity), which brings Holland to the earth even with the harness as he tries to make these otherwise physically impossible jumps. Gravity, like any other force, makes the object accelerate and, in this case, makes Holland pick up velocity as he plummets to the platforms. Assuming superheroes are still affected by gravity, (with higher strength/speed) they start off with a higher initial velocity, but the force of gravity affects them relatively the same as a stuntman/normal human. Holland is undergoing projectile motion here, as the force of gravity accelerates him vertically but he stays at a constant horizontal velocity. Projectile motion is this idea of motion happening in a curved parabolic path and is affected by vector components. Looking at a WIRED article that discusses about the physics of this stunt, Rhett Allain says this proves how the real Spider-Man moves according to normal physics rules. Allain found Holland's vertical acceleration for the first jump by using the kinematic equation of y(t) = 1/2*a*t^2 + Yi * t + y0 and a video analysis tool (similar to our experiments), and, after plugging in the known variables (from video analysis), found that the vertical acceleration is -4.192 m/s^2. This is not equal to -9.8 m/s^2, showing how the force of gravity that affects Holland is not equal to that of Earth due to the harness. Allain says it's why the video has this "weird floaty affect". However, to account for this unrealistic acceleration, post-production alters the frame-rate of the stunt (the "t"/time) to ensure Holland's movement is affected by -9.8 m/s^2, the force of gravity of earth, and make Spider-Man feel like he's in our world. As shown by the video below, Holland moves quicker in the post-editing video, but more realistically than the actual stunt, similar to how we would expect a real-life superhero to move. Article about the Physics of the Stunt + Original Video: https://www.wired.com/story/spider-man-stunt-physics-tom-holland-projectile-motion/ Holland's Stunt Post-Editing: https://www.youtube.com/watch?v=k4QYXoNKWkA&t=6s |
Circular Motion, Energy and Momentum: Fury Road
To pull off the Oscar-winning spectacle of Mad Max: Fury Road, choreographers and stuntmen worked hard to create visually incredible stunts. Circular motion, energy transfer, and momentum play a huge role in how the movement of cars in stunts.
Circular Motion:
Understanding circular motion specifically would be important for shooting scenes on mountains. When a car travels over a hill, it's moving in a circular path. For example, let's say Fury Road's stunt coordinator, Guy Norris, wants to have the War Rig 1,200kg drive up a 15m high hill at a speed that allows it to leave the ground and soar in the air for a cool shot . Below, knowing the rules of circular motion, I set up the equation that the centripetal force would be equal to the normal force minus the force of gravity. Since, after the maximum velocity is reached, there would be no normal force (because the Rig would no longer be on the ground), so I solved for the velocity by plugging in 0 for the normal force and the other given variables (work/diagram shown below.
This means the War Rig would need to reach a velocity of 12.12 m/s before the peak of the hill in order to lose contact with the ground and create this "flying" effect. Additionally, if cinematographer John Seale wanted to employ a tracking shot on the side of the War Rig, we would need to do the same circular motion calculations, but with a different mass and probably aim to move faster than the War Rig for the shot.
Circular Motion:
Understanding circular motion specifically would be important for shooting scenes on mountains. When a car travels over a hill, it's moving in a circular path. For example, let's say Fury Road's stunt coordinator, Guy Norris, wants to have the War Rig 1,200kg drive up a 15m high hill at a speed that allows it to leave the ground and soar in the air for a cool shot . Below, knowing the rules of circular motion, I set up the equation that the centripetal force would be equal to the normal force minus the force of gravity. Since, after the maximum velocity is reached, there would be no normal force (because the Rig would no longer be on the ground), so I solved for the velocity by plugging in 0 for the normal force and the other given variables (work/diagram shown below.
This means the War Rig would need to reach a velocity of 12.12 m/s before the peak of the hill in order to lose contact with the ground and create this "flying" effect. Additionally, if cinematographer John Seale wanted to employ a tracking shot on the side of the War Rig, we would need to do the same circular motion calculations, but with a different mass and probably aim to move faster than the War Rig for the shot.
Energy and Energy Transfer:
Guy Norris and John Seale likely utilized concepts of energy transfer to perform stunts. For example, if they wanted to film Rockriders pursuing the War Rig down the mountain with their dirt bikes (pictured to the right), our knowledge of energy transfer can be used to better film the scene. One Rockrider has a 100 kg and is moving at a certain speed 15m up in the air. How fast does this motorcyclist need to move when he is 15m up in the if he's moving 35 m/s when he hits the ground. T
o solve this, I created a diagram and LOL chart to reflect the situation, signifying the energy transferred from a combination of potential and kinetic energy to just kinetic energy. I found the car would have to move at about 30.51 m/s when 15 meter is the air in order to be moving at 35 m/s when it hits the ground (work shown below). While Norris and Steele probably didn't create bar charts or create a conservation of energy equation, they still had to have basic understanding of how kinetic energy and, as a result, velocity increases as the bike travelled down the mountain.
Guy Norris and John Seale likely utilized concepts of energy transfer to perform stunts. For example, if they wanted to film Rockriders pursuing the War Rig down the mountain with their dirt bikes (pictured to the right), our knowledge of energy transfer can be used to better film the scene. One Rockrider has a 100 kg and is moving at a certain speed 15m up in the air. How fast does this motorcyclist need to move when he is 15m up in the if he's moving 35 m/s when he hits the ground. T
o solve this, I created a diagram and LOL chart to reflect the situation, signifying the energy transferred from a combination of potential and kinetic energy to just kinetic energy. I found the car would have to move at about 30.51 m/s when 15 meter is the air in order to be moving at 35 m/s when it hits the ground (work shown below). While Norris and Steele probably didn't create bar charts or create a conservation of energy equation, they still had to have basic understanding of how kinetic energy and, as a result, velocity increases as the bike travelled down the mountain.
Momentum:
Mad Max: Fury Road (and several other action movies) would not be the same without its spectacular car collisions and road chaos. In order to better film these crashes, momentum concepts and a conservation of momentum equation can be used to precisely find the final velocity of the cars involved. Knowing the final velocities/direction of the final mass(es) can help the director and cinematographer in filming the crash, as, now, they accurately know where/how fast the masses move after the crash.
At the end of the climatic car chase where Max, Furiosa, and company take the War Rig back on the Fury Road, Nux, a War Boy who turned on Immortan Joe, purposefully crashes the War Rig to create a blockade and destroy Immortan Joe's truck in pursuit. This was shot in real life (as shown by the video below), so momentum can help contribute to our understanding the final velocities/reaction of the crash between the 1200 kg Rig and 600kg truck. Roughly estimating, let's say the Rig was moving at a slow 5 m/s before Nux flips over and the Truck is speeding towards it at 35 m/s. I found, if they were to collide at this point and Immortan Joe's truck stopped completely upon impact, the War Rig be pushed at a velocity of 22.5 m/s. This is important, because Nux/Nux's stunt driver is trying to flip over the car so it is pushed by the truck into the nearby mountain, which would create a blockade. Thus, if the stunt driver/coordinators know that the War Rig will be pushed at about 22.5 m/s until it comes into contact with the force of the mountain, then they can more easily estimate when to flip the car. Additionally, this will help Steale better film this climatic scene since he knows when/where the War Rig will be.
Raw Footage of Stunt: https://www.youtube.com/watch?v=5WDmLCmixeE
V
Mad Max: Fury Road (and several other action movies) would not be the same without its spectacular car collisions and road chaos. In order to better film these crashes, momentum concepts and a conservation of momentum equation can be used to precisely find the final velocity of the cars involved. Knowing the final velocities/direction of the final mass(es) can help the director and cinematographer in filming the crash, as, now, they accurately know where/how fast the masses move after the crash.
At the end of the climatic car chase where Max, Furiosa, and company take the War Rig back on the Fury Road, Nux, a War Boy who turned on Immortan Joe, purposefully crashes the War Rig to create a blockade and destroy Immortan Joe's truck in pursuit. This was shot in real life (as shown by the video below), so momentum can help contribute to our understanding the final velocities/reaction of the crash between the 1200 kg Rig and 600kg truck. Roughly estimating, let's say the Rig was moving at a slow 5 m/s before Nux flips over and the Truck is speeding towards it at 35 m/s. I found, if they were to collide at this point and Immortan Joe's truck stopped completely upon impact, the War Rig be pushed at a velocity of 22.5 m/s. This is important, because Nux/Nux's stunt driver is trying to flip over the car so it is pushed by the truck into the nearby mountain, which would create a blockade. Thus, if the stunt driver/coordinators know that the War Rig will be pushed at about 22.5 m/s until it comes into contact with the force of the mountain, then they can more easily estimate when to flip the car. Additionally, this will help Steale better film this climatic scene since he knows when/where the War Rig will be.
Raw Footage of Stunt: https://www.youtube.com/watch?v=5WDmLCmixeE
V
Rotation in Movies: Indiana Jones
While this first one may not be a stunt, the iconic opening scene from Indiana Jones features Indy running away from a giant rolling boulder after stealing a golden idol from a temple. Due to a lack of technology at the time, this scene used entirely practical effects, therefore, Harrison Ford (or his stunt double) actually had to run away from this boulder. Since the boulder is entirely real, it rotates and follows the physics of rotational motion. Spielberg and his crew can use rotational motion and new equations to find important information about the boulder's movement to make it easier to film. Let's assume the boulder starts from rest, is 200kg with a radius of .5 m, and faces a rotational inertia of 0.5 kg * m^2. It is rolling down a 5m incline at an angle of 10 degrees. I can set up an equation that sets the potential energy of the boulder equal to the translational kinetic energy and rotational kinetic energy. Then, using a r*omega= v equation, and, after solving for v (it's 4.122 m/s), plug the velocity into a rotational kinematic equation and find that it takes 2.426 seconds for the boulder to go down this incline. This is important during the filming and editing process, as it allows the cinematographers/editors to know exactly how long it takes for the boulder to travel certain distances. |
Rotation (cont): Even a simple flip involves rotational physics concepts and stunt performers need to have a solid grasp on how changing their distribution of mass affects their motion. For example, if Tom Holland were to attempt a few flips down a ledge, assuming rotational momentum is conserved, he would need to make his mass larger by moving his legs/body around in order to rotate slower. If he were to make his mass smaller, rotational inertia would be able to less easily stop his movement and he would rotate faster and his rotational velocity would increase. This is why we see professional stunt doubles and gymnasts/divers move their bodies during flips and stunts, as it allows them to control their rotation velocity: something very important when executing carefully-planned stunts.