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Summary What is the fastest time a swimmer can take for 50m Butterfly?

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This is a Mathematics document for IBDP Maths Analysis and Approaches

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Modeling the Fastest Time for 50m Butterfly Swimming
ResearchQuestion:
What is the fastest time a swimmer can take for 50m Butterfly?




1

,TABLE OF CONTENTS
Introduction 3
The Dive 3
The Underwater Kicks 12
The Swim 17
Combining the three components of the full swim 18
Conclusion 19




2

, Introduction
My favorite sport has been swimming since I joined high school three years ago. Of all the four swimming
strokes, the butterfly has been the hardest for almost every swimmer that I have met. This is due to its
complexities and the multiple resistive forces that arise when swimming butterflies. I was however curious
about mastering the technique and it later became my favourite. However, the butterfly Olympics world records
for the 50m long course between 2015-2022 have been stagnating at just about 22s to Caleb Dressel’s 2022
record of 22.27s (FINA, 2022), which led me to question whether the stagnating is because the time is
approaching the peak, or it is the maximum possible time, or it is just a trend and will keep on improving. To
answer this question, I decided to model the optimal achievable time for the 50m butterfly technique. Therefore,
the aim of the exploration is to model the optimal fastest time a swimmer can take in butterfly swimming
technique in a long course 50m swimming pool.
I therefore focused my exploration on a male swimmer. An Olympic long course swim can be divided into three
categories, the dive, the underwater dolphin kicks, and the swim, which is how I grouped the sections. After
modeling the optimal times for the three categories, I will then sum them up to get the total optimal time a
swimmer can take in a 50m butterfly-long course swim. Finally, I will discuss the assumptions made and the
possible improvements that could be made.




The Dive
For the dive, two times are needed, the reaction time, which is the time the swimmer takes to react to the
starting ‘beep’ of the referee, and the time of the dive itself, from the diving block to the water.. To do that, I
will need to calculate the diving time of the swimmer. Therefore, I will use the physics kinematic equations and
laws of mechanics, since there will be a number of forces acting on the swimmer while he is standing on the
starting block ready to dive. In this step, I will be modeling the optimal time a swimmer can take to dive,
considering the forces acting on him, and the reaction time, which, in this case, will be assumed to be the same
for Olympic swimmers because of the uniform starting conditions of the Olympic swimming pools. Again,
since I am modeling the fastest time a swimmer can take during the dive, I will also assume that the swimmer is
an Olympic swimmer. For Olympic swimmers, the average reaction time is 0.685 seconds, which is the value I
will be using for the reaction time (Mering, 2020). Although the reaction time is negligible, it is essential to
include it in the exploration to achieve the best results. The first step in calculating the time it will take the
swimmer to dive off the starting block to the water surface is to get the forces acting on the swimmer. These


3

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