Mathematics HL Exploration: Estimating The Productivity In Cycling Mathematically

Mathematics HL Exploration

Under the supervision of Devrim Ozata

Issue: Cycling

Candidate Info:

Research Question: Can we estimate the productivity in cycling mathematically?

TABLE OF CONTENTS

Introduction 1

Background Information 2 Cycling and its equipment 2

Roadmap 7

Estimating Variables 5

Calculations 5 Independent variable: Road Independent variable: speed Independent variable: Slope

Conclusion and Evaluation 12 Limitations 13 Evaluation 13

Bibliography 14

INTRODUCTION

Even though it is not the case in Turkey, in most of the European countries most of the transportation is handled by bikes. Especially in the Netherlands, it is apparent that each household holds as much bike as the people living in the house.

Like how does the effort I am giving changes accordingly to the road type. Obviously, it is harder while you are going uphill so how can the level of difficulty be reduced? Then I searched for different tyre types and gear levels. The thing is we would be able to reach a clear conclusion as an evaluation of this exploration instead of a concrete statement like “you should cycle that way otherwise it is going to be very hard.” In which is apparently not true because there are too many other aspects in the efficiency while cycling as your heart rate and how warmed up you are, the way you cycle, and other personal aspects relating our body shape. These will also be explored in a short way on this

However, even though we have increased the coefficient 8 times the amount did not increased 8 times as the former one this suggests that there should be some another psychological explanation behind the thought that we think it is harder to cycle on some different tracks. When the speed increases however the amount of power needed also increases accordingly. As seen on the graph next to the 25 km/h speed when the speed increases the line on the power speed graph becomes more straight. With less speed the graph had suggested that if we keep on going the power would increase but the speed would kept the same. This suggests using lower speed but making the distance longer actually makes our input energy rise. Finally, the grade, on in other words slope, changes. This actually is an exploration of making the road up hill. When the slope rises the road becomes uphill. In this case on the second condition when we look at the y scale we come across to very high numbers which suggest when compared to other graph even though it seems as on the other graph at some point the speed stays still and the power goes up it probably will never reach as high power amounts as in the second graph. So if you want to use more power you have rise the