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Reply to "Turnarounds"

Final Answer:  Prize for best solution goes to Mark Neal who caught the minus sign that should have been a plus.  Everything worked fine after that.  He came up with an Excel Goal Seeker routine that gets the right answer to 5 places in the blink of an eye.  My “copycat” Basic routine took about 20 seconds for higher angles. 

  Dr. Coleman says he does not like to “let practical considerations get in the way of interesting math” but pointed out you can:

Draw the problem with the curve represented by the radius from –r,0 to –r, r.

  1. Subtract 2 * r from the distance needed. This is the hypotenuse of a right triangle with a height ALWAYS = to half the street width – 1 or Y.
  2. X for this triangle is the square root of the hypotenuse squared minus height squared.

 Example:  Need = 100’  more   Street = 20’ wide   Curb radius = 2’   Ride radius = 3

 100’ –  (2 * 3) = 94.   Then    94 / 2 = 47  Next  x = sqrt(47^2 – 9^2) =   46.13

This is from a point 1 foot W of curb line so out 45.13 feet.  This is exact at “no extra distance needed.  For very long distances, this is never more than 1.30 feet short.  

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