How was trigonometry used to define this racing line
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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:
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.
trigonometry circle
edited Nov 10 at 12:34
Blue
46.7k870147
asked Nov 8 at 22:39
Oussama Safi
11
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show 1 more comment
up vote
0
down vote
favorite
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:
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.
trigonometry circle
edited Nov 10 at 12:34
Blue
46.7k870147
asked Nov 8 at 22:39
Oussama Safi
11
1
It's just trigonometry.
– Sean Roberson
Nov 8 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 8 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 9 at 1:48
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 9 at 8:22
1
@Blue Thanks very much, it couldn't have been clearer. I greatly appreciate it Mr. Blue
– Oussama Safi
Nov 10 at 14:11
|
show 1 more comment
up vote
0
down vote
favorite
up vote
0
down vote
favorite
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:
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.
trigonometry circle
edited Nov 10 at 12:34
Blue
46.7k870147
asked Nov 8 at 22:39
Oussama Safi
11
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:
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.
trigonometry circle
trigonometry circle
edited Nov 10 at 12:34
Blue
46.7k870147
asked Nov 8 at 22:39
Oussama Safi
11
edited Nov 10 at 12:34
Blue
46.7k870147
asked Nov 8 at 22:39
Oussama Safi
11
edited Nov 10 at 12:34
Blue
46.7k870147
edited Nov 10 at 12:34
Blue
46.7k870147
edited Nov 10 at 12:34
Blue
46.7k870147
46.7k870147
asked Nov 8 at 22:39
Oussama Safi
11
asked Nov 8 at 22:39
Oussama Safi
11
asked Nov 8 at 22:39
Oussama Safi
11
11
1
It's just trigonometry.
– Sean Roberson
Nov 8 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 8 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 9 at 1:48
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 9 at 8:22
1
@Blue Thanks very much, it couldn't have been clearer. I greatly appreciate it Mr. Blue
– Oussama Safi
Nov 10 at 14:11
|
show 1 more comment
1
It's just trigonometry.
– Sean Roberson
Nov 8 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 8 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 9 at 1:48
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 9 at 8:22
1
@Blue Thanks very much, it couldn't have been clearer. I greatly appreciate it Mr. Blue
– Oussama Safi
Nov 10 at 14:11
1
1
It's just trigonometry.
– Sean Roberson
Nov 8 at 22:42
It's just trigonometry.
– Sean Roberson
Nov 8 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 8 at 23:25
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 8 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 9 at 1:48
See Beckman’s old “Physics of Racing” papers for this and other fun stuff. Part 5 in particular covers this.
– amd
Nov 9 at 1:48
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 9 at 8:22
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 9 at 8:22
1
1
@Blue Thanks very much, it couldn't have been clearer. I greatly appreciate it Mr. Blue
– Oussama Safi
Nov 10 at 14:11
@Blue Thanks very much, it couldn't have been clearer. I greatly appreciate it Mr. Blue
– Oussama Safi
Nov 10 at 14:11
|
show 1 more comment
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1
It's just trigonometry.
– Sean Roberson
Nov 8 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 8 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 9 at 1:48
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 9 at 8:22
1
@Blue Thanks very much, it couldn't have been clearer. I greatly appreciate it Mr. Blue
– Oussama Safi
Nov 10 at 14:11