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# Need some help on this

Posted by treematt on March 25, 2012 at 12:47 amGiven the PC station as n: 4787.06 e: 3617.56 and the pt station as n:5177.86 e: 5924.97 on a circular curve, with a radius of 3569.96 feet. What are the coords of the PI station?

Any help with this would be greatly appreciated?:-)duane-frymire replied 11 years, 8 months ago 6 Members · 7 Replies- 7 Replies

> Given the PC station as n: 4787.06 e: 3617.56 and the pt station as n:5177.86 e: 5924.97 on a circular curve, with a radius of 3569.96 feet. What are the coords of the PI station?

> Any help with this would be greatly appreciated?:-)Inverse between the 2 and Long chord = 2r sine delta/2

You should be able to solve it from there.

Ralph

He could also do a dist-dist intersection using the R value and solve from that..I think he is looking for PI coordinates though, not a PI station.

My bad…Coordinates are his goal.

Yeah, I see it as solving for delta and t and turning the angle PT-PC-T and the distance T.

Ralph

Looks to me like there are two possiblities for the radius point, depending on which way the curve runs. That means there would be 2 possiblities for PI’s.

N. 5382.72

E. 4703.47or

N. 4582.20

E. 4839.06>

*N. 5382.72*

> E. 4703.47That is the answer I am looking for. Just need to know how to do it long hand.

Thanks for all your help.There are eight right triangles in a simple curve sketch (hint: simple curves are symmetrical and radial lines always meet tangent at right angle at PC and PT). Draw the curve between the tangents and draw the radial lines (sketch). Sketch in the triangles. Any right triangle can be solved if you know two parts of it, here you will see you have the length of two sides of a triangle (after you inverse coordinates for a bearing and distance). Solve for the angle and distance needed to calculate latitude and departure from known coordinate to unknown coordinate. Bingo, you’re there. BTW, you should memorize one magic formula (and you need to know the definition of D) to solve for all parts of the curve. D=5729.578/R. For extra credit; where does the magic number derive from? Of course, all this assumes that you have a curve that is tangent rather than non-tangent.

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