Plat Plotter has a Calculate Curve Table feature that generates a sequence of points for use in drawing plot lines. To put another way, it converts a curve into several short, straight segments approximating the curve.

thence South 13°0'00" West 201.05 feet to the beginning of a tangent 180.00 foot radius curve, concave Northwesterly; thence Southerly and Westerly along the arc of said curve through an angle of 98° a distance of 307.87 feet; thence tangent to said curve North 69°00'00" West 255.0 feet to the West line of the Northeast Quarter of the Southeast Quarter of said Section 5;

For this example, the straight lines before and after the arc are entered as:

S 13 W 201.05 and N 69 W 255.00

The Calculate Curve Table feature will create a sequence of values that can be placed between the above two entries given a Chord & Radius.

How does one get from the:

to the beginning of a tangent 180.00 foot radius curve, concave Northwesterly; thence Southerly and Westerly along the arc of said curve through an angle of 98° a distance of 307.87 feet; thence tangent to said curve

to the Chord and Radius values needed by Plat Plotter?

The Chord for Plat Plotter is an angle which will be "S" ddmmss "W" in this case and length fff.ff feet. I assume that the Radius can be taken directly from this legal description, 180.

Chord:  S ddmmss W fff.ff
Radius: 180

So, more specifically, how to calculate ddmmss and fff.ff?

  • New user, user3513153 commented: Hmm. I have not seen many examples of curve tables so I designed the Plat Plotter input around what I have seen: the call, radius and curving to the left or right. Is the radius, curve length and degree of curve a common construct? May 29 '15 at 21:29
  • In the dozen or so legal descriptions that I have seen with curves in San Diego County the example is typical. Assuming you are Jason Rushton, thanks for Plat Plotter. May 29 '15 at 21:36
  • @jrinwv It depends on the region/jurisdiction/software as to how curves are specified, and sometimes whether they're tangent or not. Around here we usually get at least one piece of redundant information, and typically a total of six attributes - direction, radius, arc angle, arc length, chord bearing, chord length. Direction can be given as left/right or concave to a direction (ie SW). C.W., I'm guessing the approximation of the curve doesn't matter for your purposes or true curves aren't supported by the software/format you're using?
    – Chris W
    May 30 '15 at 9:42
  • @ChrisW - Surveyors i used to work with liked to mock ArcInfo because, despite the name, it couldn't represent real arcs properly ;-)
    – Martin F
    May 30 '15 at 16:46
  • @MartinF Sad but true. I can't imagine having worked with LineView, LineINFO, LineGIS, etc. all these years though. :D
    – Chris W
    May 30 '15 at 20:29

The legal description is giving you a delta angle of the curve, the radius, and the distance traveled along the curve.

Simple Curve Formula:

R = Radius L = Length of Curve D = Degree of Curve T = Tangent Long Chord = LC

From your data you have a 180 ft radius curve that has a 98 degree delta angle since the bearing entering the curve is 98 degrees less than the bearing exiting the curve.

Long Chord = 2R sin 1/2 Delta so:

(2*180) (sin 49)

360 * 0.754710 = 271.695449 feet.

I hope this helps.

  • There are many software solutions available for curves, I just put the formula in since it is easily solved with any type of calculator with scientific functions. Deed Plotter, the Map Check software mentioned by Martin F below, and several other solutions are readily available. You can also put a formula into Excel, or other spreadsheet software to have it calculate curve data. I have always preferred using radius distance, and delta angle for curves, plus direction right or left of the tangent to the radius point. It always seemed the simplest solution for me, and that is how I wrote code.
    – jbgramm
    May 31 '15 at 15:04

The math in the answer by @user30641 is correct. The given arc length was redundant but useful as a check.

In case it helps, there's another free online tool for deed plotting at underhill.ca/map_check.php. It allows you to enter curve data via the "in" and "out" radial lines, derivable from the metes in your description via simple addition/subtraction. (There are quite a few alternatives used in different jurisdictions for specifying curve data.)

Here's a screenshot with your data:

enter image description here

The first radial is S 13 W + 90 = N 77 W because it's a tangent curve.
The second radial is S 13 W - 90 + 98 = S 21 W (the reverse of the first radial, plus the arc angle).

It's a little tricky until you get use to it.

The coordinates of the start point are arbitrary. Replace with actual ones if known.

It says "misclosure" because it assumes you're closing back onto the start point, but you only gave us a sample of the boundary.

  1. Yes, I wrote & maintain Plat Plotter, so I thought my explanation of which parameters were required and why was relevant to C.W.Holeman's question.
  2. No, I don't have enough points to add a comment

As for why Plat Plotter creates line segments instead of a 'true curve' and all of the discussions of various narrative formats for curve descriptions, maybe I need to start another thread?

  • 1
    We're more Q&A than discussion board here, so it's less about threads (you might want to review the tour). If you can bundle the information into an answer that would work. Unfortunately until 50 rep you can't comment. We have a chat, but that also requires rep. It would be nice if we could offer a bonus to software authors/company employees so they could comment right off the bat - I'll see about suggesting that.
    – Chris W
    Jun 8 '15 at 22:23

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