The Professional Edition of TPC includes geodetic tools for computations on the ellipsoid. These involve classic direct and inverse computations on the ellipsoid, along with geodetic areas and intersections.

Learning Geodetics

Relating Coordinates and Geodetic Positions

A survey can have one Coordinate Reference System (CRS) that relates it's geodetic and rectangular (Cartesian) coordinates. The CRS defines the ellipsoid used in the geodetic direct and inverse computations. TPC computes geodetic distances by inversing between two geodetic positions on the ellipsoid surface and applying the appropriate elevation factor (converting between the ellipsoid surface and the ground elevation). Since the CRS relates the coordinates of a point to its geodetic position, TPC can compute both the coordinate distance and a geodetic distance between any two survey points.

The transformation between Cartesian coordinates and geodetic positions compute a scale factor and convergence angle for each survey point. These can be reported along with the other point data like coordinates, latitude and longitude. They are also be used to compute mean bearings of geodetic lines.

Geodetic Distances

Geodetic distances are derived from geodetic positions (latitude / longitude) as opposed to coordinate distances which are derived from grid (plane) coordinates (northings / eastings). Geodetic distances (geodesics) are always an arc distance at some height relative to the ellipsoid surface. As such, there are only three options for the elevation at which they are computed: 1) the mean course elevation or 2) the project elevation or 3) on the ellipsoid surface itself.

When you select any of the geodetic distance options, TPC uses the equations from Thaddeus Vincenty in his 'Direct and Inverse Solutions of Geodesics on the Ellipsoid with application of nested equations'. Published in 1975, these are the classic, iterative solutions to computing a geodesic foresight (Direct) and inversing the geodesic distance and end point directions (Inverse) between two geodetic positions.

Any geodetic point can be related back Cartesian coordinates through the CRS.

Geodetic Directions

All geodetic computations assume true bearings/azimuths. When you choose a Geodetic Distance option, TPC check to make sure you have selected a corresponding Geodetic Direction..

TPC also includes the option to compute on latitudinal arcs per the Public Lands Survey System. These are Rhumb lines, not geodesics. See Geodesic vs. Rhumb Lines.

Default Distance and Direction Types

Each survey has a default distance and direction type. Until you choose an alternate type, TPC will use these default types for Traverses, Drawings and COGO.

From the TPC desktop, choose Tools | Survey Information, Project Factors. TPC displays the plays the Project Factors dialog.

Enter a project elevation

From the Distance pulldown, choose 'Geodetic Distance (project elevation x,xxx,xx)'

From the Direction pulldown, choose 'True Bearing/Azimuth (mean course convergence)'

That's it. TPC now thinks like you do, in geodetic ground distance at the specified project elevation and true bearings or azimuths. Pretty simple.

Geodetic Area

TPC computes geodetic area by factoring the corresponding planar coordinate area.

Geodetic COGO

COGO routines in TPC can work with geodetic positions just as easily as grid coordinates. You just select the distance and direction types for each COGO routine. We call it Geodetic COGO.

Offsets to a Geodetic Line

COGO routines like Offset to Line and Offset Interval can compute offsets to a geodetic line vs a straight line (line of sight).  These computations are currently limited to using the radius of the mean latitude of the line being offset to. TPC uses the equations from the BLM Manual of Survey Instruction 2009, page 31 to compute this radius. These offsets are not exact for lines that do not run cardinal East/West but they do provide a good approximate offset.

Future versions of TPC Desktop may introduce more rigorous computation of offsets to geodetic lines.

Geodetic Drawings

TPC Desktop 2011 makes drawing geodetic lines as simple as selecting a Distance Type and Direction Type. You used these same selections to enter your data, compute your COGO and now to create your map. Just tell TPC what you want to draw and it does the rest.Geoids

Beginning in TPC Desktop 2019 R1, you can select a geoid model to relate elevations with ellipse heights.

Related Topics

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