# Speed of a Rogue Bludger: Harry Potter

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## Abstract

The purpose of this analysis is to determine the average speed of the rogue bludger Quidditch ball in the movie *Harry Potter and the Chamber of Secrets* (2002).

## Introduction

Quidditch is the popular wizard sport played in the Harry Potter books and movies. It is often played in an oval shaped stadium with four balls -- one quaffle, two bludgers, and the golden snitch. There are two teams of seven whose goal is to score the most points. The game ends when the seeker of one team catches the golden snitch and earns an extra 150 points. Usually, this team wins. There are three players on each team whose job is to score 10 points by throwing the quaffle pass the keeper into one of the three goals. There are two other players whose job is to hit the two bludgers away from their teammates to try to knock the other team off. The bludgers are two heavy balls that fly around trying to knock random players off their broomsticks. The perimeter of the quidditch stadium in Hogwarts consists of connecting colored sections representing the four different houses. During the quidditch match of Gryffindor vs. Slytherin in the movie, Harry was attacked by a rogue bludger jinxed by the house elf Dobby to get Harry injured enough to go home. So, just how was fast was Dobby's rogue bludger? How much faster did Harry need to fly to avoid getting knocked off his broom? Speed is the rate of motion, or rate of change of position with respect to time. The formula for average speed is change of distance over the change of time, v = Δs/ Δt where s is distance and t is time.

## Diagram/Screen Captures

Plan from Wikipedia | Screen Captures from the DVD |

## Procedure

- Play the movie in Media Player Classic and find a scene where the bludger is traveling in a relatively straight path. We chose Chapter 15, "The Rogue Bludger".
- Count the number of different colored sections there are that represents the four houses surrounding the quidditch pitch.
- Using Windows Media Player Classic, count the number of frames there are per second. Accomplish this by pressing pause and using the right arrow key. Count the number of frames it takes for one second to pass.
- Count the number of frames it takes for the bludger to travel one section of the pitch in the scene chosen.

## Analysis

Using the formula for the circumference of an oval

C ≈ 2π√(a^{2} + b^{2})/2

we found the perimeter of the quidditch pitch. According to Wikipedia, the quidditch pitch is 55 m wide and 152 m long. To find the circumference of an oval, a is half the length and b is half the width so therefore a is 76 m and b is 27.5 m. After plugging in the numbers, the calculated circumference of the quidditch pitch is approximately 360 m. Since there are 18 differently colored but equal sections surrounding the circumference of the pitch, each section is 20 m.

Pausing the movie, we counted 27 frames played per second. We selected a scene where the bludger was traveling in a straight path along one colored section of the circumference. It took the bludger 20 frames to travel the whole length. We divided one second by 27 frames to find the time for one frame which is about 0.037 s/frame. To find the time it takes for the bludger to travel that one section, we multiplied 20 frames by 0.037 s/frame so the time was 0.74 s. Since velocity is distance divided by time

v = Δs/Δt = 20 m/0.74 s

## Conclusion

The average speed of the Rogue Bludger is approximately 27 m/s or 60.4 mph.

## Sources of Error

- We estimated the length of the colored sections by replacing the larger goal ends with two sections each.
- The bludger wasn't traveling completely parallel to the colored section so the distance estimated was a minimum. The actual distance would be the hypotenuse of a triangle.

Eunice Huang, Ting Ting Luo, Collin Tam -- 2005

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