COGO: inverse, traverse and curves

Inverse between points with grid and ground distances, compute points from bearings, close and adjust a deed traverse, and solve curves.

On this page

Tools → COGO is the calculator for work between measurements. It has four operations, chosen with the control at the top:

  • Inverse between two points.
  • Traverse out to a new point.
  • Close a deed's run of courses.
  • Curve, solved from two known elements.

COGO never shows "the distance" on its own. Grid and ground distances appear together, and so do grid and geodetic azimuths, because they differ by amounts that matter on a plat.

Before you start

  • Set a coordinate system. COGO works on the project's grid and in its unit, for example ftUS on a Kentucky ftUS zone. Without a zone, it uses a local Transverse Mercator on your data: correct locally, but not a published system.
  • Collect or import points. Inverse, Traverse and Close pick from the project's point assets. Lines and areas aren't offered.
  • Get heights where you can. Points with an elevation give a proper elevation factor.

The Working frame section at the bottom of Inverse, Traverse and Close states the zone, the unit and the horizontal datum in use.

Inverse

  1. Tap Inverse.
  2. Under Between, choose From and To.
  3. Read the results:
Row Meaning
Grid Distance on the grid, in the zone's unit.
Ground The same line on the ground: what a tape reads.
ΔZ (to − from) Rise from the first point to the second. Needs a height on both points.
Slope Straight-line distance between the marks.
Combined factor Grid ÷ ground: the point scale factor times the elevation factor.
Grid azimuth / Grid bearing Direction from grid north, as an azimuth and a quadrant bearing.
Geodetic azimuth Direction from true north.
Convergence The angle between grid north and true north here.
Back azimuth The grid azimuth from the other end.

If neither point has a height, the elevation factor is taken as 1, and an orange note warns that the ground distance is short by about 1 part in 6,400 per 1,000 m of unrecorded elevation. If only one point has a height, ΔZ and slope show —: the rise is unknown, not zero.

Traverse to a point

  1. Tap Traverse.
  2. Under From, pick the start Point.
  3. Type a Bearing: a quadrant bearing such as N 45-30-00 E, or a bare azimuth.
  4. Type a Ground distance in the project's unit. It's reduced to the grid before it's applied.
  5. Read the Computed point: latitude, longitude, easting and northing.
  6. Tap Store as design point to save it.

A bare number is read as an azimuth. If you typed one, an orange note reminds you to write N 45-30-00 E if you meant a quadrant bearing: the two can differ by up to 270°.

The stored point is a design point: a computed coordinate, not a measured one. You can stake it out or check against it, and it's kept out of field-collected exports.

Close a deed traverse

  1. Tap Close.
  2. Under Start, choose the Point the deed starts from and the Adjustment:
    • Compass (Bowditch): spreads the misclosure in proportion to each course's length. The usual choice.
    • Transit: spreads it in proportion to each course's latitude and departure. Suited to good angles and rougher distances.
    • Unadjusted: leaves the misclosure where it fell.
  3. Under Courses, type each bearing and distance in the order the deed reads them, in the project's unit, and tap +. Swipe a course to delete it. The figure is assumed to close back on the start.
  4. Read Closure:
    • Perimeter
    • Misclosure (the gap)
    • Direction (of the gap)
    • Precision, for example 1 in 12400
    • Largest shift: the most any corner moved in the adjustment.
  5. Read Area, on the Ground and on the Grid.
  6. Tap Store corners as design points to save the adjusted corners. Each one carries the rule and the precision in its description.

If the transit rule has nothing to apportion against, for example when every course runs due east, it falls back to the compass rule for that part and says so.

Saved deeds

Under Keep this deed, type a Deed reference and tap Save. The app stores the courses, the rule and the start point, not the corners. When you reopen it from Saved deeds, the figure is recomputed from the start point's current position, so re-observing the start moves the traverse with it.

  • Tap a saved deed to load it. Change it and tap Update, or tap Save as a new deed to keep both.
  • The list shows the number of courses and the total ground length in the project's unit. Swipe to delete.
  • If the start point has been deleted, the app says so and keeps the courses exactly as typed. Pick a new start to compute again.

Curve

  1. Tap Curve.
  2. Under Known, choose two elements and type their values. The elements are Radius, Delta (central angle), Arc length, Tangent and Long chord. Type the delta as an angle, such as 45-30-00.
  3. Read Solved:
    • Radius
    • Delta
    • Arc length
    • Tangent
    • Long chord
    • Middle ordinate
    • External
    • Degree of curve (arc)

The curve solver is pure geometry, so lengths come out in whatever unit you typed. Degree of curve uses the arc definition and is only meaningful when the radius is in feet. If the two values can't describe a curve, for example a chord longer than the diameter, the app says so.