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# Center coordinates of a horizontal curve.

How do we calculate the center coordinate of a circle,if we have the PI(point of intersection coordinates), radius of the circle, coordinates of the BC, MC, and EC(beginning, Middle and End of curve respectively). Also calculate the coordinates of chainages in the curve.

Thank you for all the replies in advance.

This Content Originally Published by a land surveyor to Land Surveyors United Network

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### Replies to This Discussion

Hi Nitesh,

It depend on what you are calculating with. Do you use a calculator.

First your heading for the discussion ( Center coordinates for a horizontal curve)

How do we calculate the center coordinate of a circle ??,if we have the PI(point of intersection coordinates), radius of the circle ??, coordinates of the BC, MC, and EC(beginning, Middle and End of curve respectively). Also calculate the coordinates of chainages in the curve.

A horizontal curve is not a circle, it is part of a circle. if you have the radius,you already have the center.

Are you asking for the center or mid point in a horizontal curve which you say you already have,MC or you asking to calculate the coordinates of the Radius, If you have the PI coors.,the BC coors., the MC coors and the EC coors, but all you have is a radius length. and you want to know the Radius coordinates. I will send you file that has the parts of a curve and all the equations to them. It also has a lot more on the math you need to calculate the coordinates. Calculating stations on a curve is another story. But this will get you started and you can go from there.

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Thank you very much for your fast reply.  I wanted the coordinates of center of the circle of which my horizontal curve is a sector of the circle. And because it is a part of alignment and my road program can provide me BC, MC EC coordinates or any chainage interval. I wanted it so i create my own excel spreadsheet which can do such calculation, so that other field member can calculate necessary coordinates of different chainage interval of a alignment and also the WCB(Whole circle bearing) at any point of the alignment.

Thank you, Nitesh,

The equations in the file I sent you are Algebraic Notation Logic, this is the math most everyone uses.

I use Reverse Polish Notation Logic, manly use in Hp calculators, there are a few more that use this notation and some computers and some surveying devices. There are many Horiz. Curve programs for these calculators, you can also write and store equations in them in a equation library, that can be used just like programs. If you like to read  more about calculating curves Old school and modern calculations,  and more about HP calculators then read these two discussion. They contain more material than just curves so you will have to search to find the curve references, But you may enjoy reading all of it. There is a lot of good information on a lot of different material and programs for the HP calculators.

There are several ways to calculate coordinates to a Radius using programs or not. Both these discussion go over each solving angles ,dist. or coors. plus what you have already.

http://landsurveyorsunited.com/forum/topics/once-upon-a-time

http://landsurveyorsunited.com/forum/topics/the-little-big-calculat...

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