Math Extended Essay on Racing Lines?

[RLin]

I am really passionate about math and cars, so I decided to do my IA on racing lines and mathematical approximations of them. The trouble is, I am lost as to how to start. I don’t know how to approach this (should I start with a single corner and try to come up with a line for it?), and furthermore, I can’t prove that the line is the best/better; that would be physics. Should I switch topics or could I save this topic, as it really interests me?

[RLin]

I’ve created a very broad outline as follows:

Introduction

• Introduce racing lines, discuss “outside-inside-outside” geometric line that is typically used

Approximation of a 90° turn

• State assumptions regarding physics of car
• Give equations for turn, which will be modeled by two circular arcs 
• Use these assumptions to determine the ideal line that will result in the lowest time through that turn

Approximations of turns with angle θ

• Generalize formula for a turn with width w and angle θ

Conclusion

[kw0573]

In physics, rolling with slipping is when tangential speed is not speed of the center of mass. In more common terms, the object is moving at a different speed than its surface. In racing, this is evident from skid marks, that is wheels forcefully scratch against the track. I presume this and centripetal acceleration will be important in your EE. Rolling with slipping is also an interesting topic that could be explored in a stand-alone EE.

I am not sure how strong you are at physics but math-wise this topic is challenging because the differential equations are complex and not using Diff Eq (such as using arcs) are more of modelling shape. To me, it sounds like a complex version of modelling a trajectory, with some optimization thrown in. The trick to write an EE like this is to simplify the math to a right amount and starting from somewhat realistic assumptions about skid and acceleration of the car. I assume that's what you intended but using circular arcs could be distorting and incomplete. 

[somewhatfluffy]

On 5/30/2018 at 4:39 PM, RLin said:

I am really passionate about math and cars, so I decided to do my IA on racing lines and mathematical approximations of them. The trouble is, I am lost as to how to start. I don’t know how to approach this (should I start with a single corner and try to come up with a line for it?), and furthermore, I can’t prove that the line is the best/better; that would be physics. Should I switch topics or could I save this topic, as it really interests me?

Hey, would it be possible for you to share your EE with me? I'm doing an IA on a similar topic, so I'd appreciate the guidelines~

[stoots]

On 2/12/2021 at 7:53 PM, somewhatfluffy said:

Hey, would it be possible for you to share your EE with me? I'm doing an IA on a similar topic, so I'd appreciate the guidelines~

Hi, did you end up writing your IA about this? Because I'm also planning on doing a math IA on a similar topic but I'm quite lost so I would really really appreciate it if you could send it to me if you did it please.