Physics of Sports Video

In nearly every action taken in sports, fundamental principles of physics are at work. Whether it’s shooting a three-pointer in basketball, executing a forehand flick in ultimate frisbee, or delivering an attack hit in volleyball, physics plays a crucial role. Our group—comprised of Huitzil, Dylan, and myself—had been tasked with exploring how physics is integrated into these sports movements and how it can be used to enhance performance. We decided to highlight the popular sport of American football and the action of a tackle, as it is a very defined moment in a game.

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Evidence of Work:

On the left is the script we used to make sure we recorded everything we needed to. Below is a storyboard showing what was initially meant to be shown in what order. The script wasn't entirely used and more of guidance to what should be mentioned and the wording was greatly changed.

Scene/Script Summary:

Video:

ScreenRecording_10-30-2024 22-56-22_1.mov

Football Tackle

Video Creation Roles:

Editing - Arnav

Cameraman - Arnav

Calculations - Arnav + Huitzil

Voice Overs - Arnav + Dylan + Huitzil

Acting - Dylan + Huitzil + Matthew(momentarily).

Planning and Script - Arnav + Dylan + Huitzil

Work Log

On the left are two images of the work log we used during the project. We had a total of 10 class days to work on this project spread out over 2+ weeks. The roles for each item are also shown in more detail.

Physics Calculations (Click >>>)

Below is all of the work done for the calculations we used to calculate the various physics principles shown/mentioned in the video.

Values Calculated

Distance Between Players: 2.44 m (8 ft)

Total Change in Time: 2.7 s

Vx of Tackler: 1.71 m/s (3.83 mph)

Mass of Tackler: 74.8 kg (164 lbs)

Mass of Victim: 59 kg (130 lbs)

Fimpact: 38.2 N (8.58 lbs of force)

Air Resistance: 1.21 N (0.27 lbs of force)

Vy of Victim: 1.53 m/s (3.42 mph)

Vtotal: 2.29 m/s (5.12 mph)

Momentum of Tackler: 61.83 kgm/s (similar to the momentum of a car going at very slow speed)

Angle of Tackler during impact: -20°

Angle of Victim during impact: +11° (when being lifted by tackler)

Momentum drops by 84.1%

On impact the tackler decelerated by 0.65 m/s^2

Taking these amounts into account, if done correctly, the collision will be elastic. Both players will bounce off each other, with the player who has more mass and is moving at a higher speed continuing in the initial direction for a brief period.

The success rate also goes up from 40% to 85-90% (based on real data in freshman, varsity, and college-level tackles).

Forces(click)

Unit: N or lbf (lbf=N/4.452) Use(in these calculations): Force of impact(Fimpact) and the force of air resistance.

Air Resistance is how much the air pushes back on the person as they run(+) or propelling them(-), it depends mainly on air density, area of the person, and the speed of the person.

Equation: Fd = 0.5 * ρ * v^2 * Cd * A

Fd = Air Resistance (unknown, for now)

ρ = density of air/fluid (can be calculated with this: ρ = p / (R * T). p= absolute pressure, R= gas constant, T = absolute temperature) - (ρ = 1.21)

v = velocity of the object (1.71 m/s)

Cd = drag coefficient (0.9)

A = Area of the person (0.72 m^2)

Which gives me 1.21N or 0.27 lbf

The amount of Force one object inflicts onto another while they collide is called the force of impact(Fimpact), usually during a short time. In the world of sports, this is usually a block or hit. While the two people stay together for a long period and this is called impulse, Fimpact is a more understandable variable.

Fimpact(t) = m * v

Fimpact = Force of impact (unknown, for now)

m = mass of object (74.8kg)

v = velocity of object (1.71 m/s)

t = time of collision in real-time (3.3 s)

Giving us 38.2N or around 8.6 lbf.

Velocities(click)

Horizontal Velocity (Vx): How fast something moves side to side or forward and backward. It usually stays the same unless something pushes or pulls on it.

Equation- Vx=dx/t

Calculations in Video- Vx= 2m/0.85s -> Vx= 1.71 m/s

Vertical Velocity (Vy): This is the speed at which an object goes up or down. It changes all the time because it depends on gravity but in our video, it depends on how much force the tackler applies to the victim as he lifts them.

Equation- Vy=dy/t

Calculations in Video- Vy= 1.65m/0.92s -> Vy= 1.53 m/s

Total Velocity: This is the combined speed of an object when you look at its Vertical and Horizontal Velocities.

Equation- Vtotal²=Vx²+Vy²

Calculations in Video- Vtotal²=(1.71m/s)²+ (1.53m/s)² -> Vtotal=2.29 m/s

Conservation of Momentum(click)

The Conservation of Momentum means that the total momentum an object has before it hits something is the same as the momentum it has after the collision. Momentum ends up dropping by 84.1% due to the tackler contacting the victim. Momentum is not conserved.

Angels(click)

The tackler's angle is negative because they go from standing straight to bending their back in an arch, which is about -20 degrees (I figured this out using a protractor while watching the video). On the other hand, the victim has a positive angle compared to the tackler since they also arch their back but are facing the other way. These angles can change with each tackle, and except for carry tackles, they aren't really necessary.

Labeled Diagram

Here is a physics diagram with most of the physics concepts discussed, if all of these are used and modified to match the scenario, a football tackle can get really good.

Reflection

2C's Positive(click)

Communication - I believe that my communication with the group was effective and balanced, as I made a conscious effort not to dominate the conversation or take control of the tasks at hand. Instead of simply taking charge and completing the work on my own, I focused on providing valuable guidance and sharing insights on how to approach various tasks. Such as for some of the calculations I did them myself then explained and taught them to my group. This collaborative approach allowed everyone to engage and learn, fostering a more inclusive environment where each member felt empowered to contribute.

Conscientious Learner - I not only offered my insights and suggestions, but I also embraced the guidance provided by others. Once we completed the rough draft of the video, my team pointed out that some sections were overly lengthy and that the sound was really quiet. Rather than defending my choices, I welcomed their feedback and promptly made the necessary adjustments to enhance the overall presentation. Additionally, I took advice to deepen my understanding of how a tackle functions, which enabled me to explain the concept more effectively in the video.

2C's Im-positive(click)

Collaboration - You might think that I didn't play a significant role in the project, but the truth is that I was quite engaged. This is where the problem arose. Instead of distributing tasks evenly among the team, I ended up shouldering most of the responsibilities. I had a specific vision for the video that was difficult to express, which led me to take control of many production elements. Additionally, I neglected to record all the voiceovers, forcing me to redo the recordings that were initially assigned to another team member. As we neared the final week of the project, I made a deliberate effort to balance the workload more fairly. This wasn't necessarily bad but wasn't good either.

Critical Thinking - In my usual project approach, I typically take the time to weigh my options before proceeding. However, with this specific project, I found myself straying from that habit. Rather than systematically tackling challenges as they arose, I often opted to overlook them entirely. At first, this seemed manageable and even somewhat effective, but it ultimately resulted in a considerable amount of extra work during the video editing phase. I came to realize that by delaying the resolution of various issues—especially those concerning content quality and clarity of explanations—I had made the final task much more challenging for myself.

Summary

Overall I feel like this was a more fun project and the action we picked was pretty difficult as there was a lot of physics involved in a short moment. Next time I would make the script more easy to follow and plan out voice-overs earlier on. I also would get mroe inspiration for the video and have a more structured plan.

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