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I was searching through the internet for an equation that defines the path followed by a racing line, when I came across the following formula on StackExchange posted by another user as a reply for another user. However, I could not understand what kind of maths is being used in the proof submitted by this user:

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I created this account, but couldn't comment on the user's proof, so I decided to post it as a question. I would appreciate it if someone was able to explain to me just what kind of maths was used to solve the problem.

I understand that it involves trigonometry, but I can't seem to figure out exactly how he used it to solve this problem and how he applied trigonometry to solve it, as I don't think I have advanced that far in maths.

I am not sure how I am supposed to apply trigonometry here because I honestly cannot understand how each he (or she) transitions from the first equation to the second and then to the third.

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Oussama Safi
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    It's just trigonometry. – Sean Roberson Nov 08 '18 at 22:42
  • It's geometry/trig in making the biggest radius from the outside of the roadway at the start of the turn, to the inside closest to the inside corner or apex, and back to the outside. – Phil H Nov 08 '18 at 23:25
  • See Beckman’s old “Physics of Racing” papers for this and other fun stuff. Part 5 in particular covers this. – amd Nov 09 '18 at 01:48
  • Thank you for replying, but I am not sure how I am supposed to apply trigonometry here because I honestly cannot understand how each he (or she) transitions from the first equation to the second and then to the third. – Oussama Safi Nov 09 '18 at 08:22
  • @OussamaSafi: I posted a new answer to the old question. Does it help clarify things? – Blue Nov 10 '18 at 14:00
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    @Blue Thanks very much, it couldn't have been clearer. I greatly appreciate it Mr. Blue – Oussama Safi Nov 10 '18 at 14:11
  • @OussamaSafi As a formality, I put in a vote to close because Blue answered your question on your linked answer. (This is not because anything is wrong with your question.) – Kyle Miller Nov 29 '18 at 07:50

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