The hook
Applied geodesy is what happens when geodesy meets a deadline. Pick a datum, pick a projection, transform your coordinates between them. The State Plane Coordinate System (SPCS) is the workhorse — grid coordinates over a state-sized area without hand-rolling a projection every time.
Memorize these
Concepts that show up on the exam
Datum
A reference frame that defines where coordinates "are." Horizontal: NAD27, NAD83 (and realizations like 2011), NAD83(2022). Vertical: NAVD88, NGVD29.
Projection
A mapping from the curved earth to a flat plane. Trades accuracy in one direction for usability. SPCS uses Lambert (E–W states) or TM (N–S states) to keep distortion low.
SPCS zone
A piece of a state mapped via one projection. Each state has 1–7 zones. Texas has 5; Delaware has 1. Project work picks the zone the site falls in.
NAD27 → NAD83
The big U.S. datum shift in the 1980s. Coordinate values move 10–100 m. Old deeds in NAD27 must be transformed before plotting.
Local vs. grid distance
A line on the ground has a "ground" distance and a "grid" distance. Differ by the combined scale factor. Mixing the two is a classic blunder.
Combined scale factor
Grid scale factor (from projection) × elevation factor (R / (R+h)). Multiplies ground distance to give grid distance. Often 0.9999 to 1.0001.
Convergence (γ)
The angle between grid north and true north at a point. Different at every location in the zone. Required to convert geodetic azimuth to grid azimuth.
Keep these in muscle memory
Formulas to know cold
Grid distance from ground
D_grid = D_ground × CSFCSF = combined scale factor
Combined scale factor
CSF = k × (R / (R + h))k = projection scale factorR = mean earth radius (~20,906,000 ft)h = station elevation
Grid azimuth from geodetic
az_grid = az_geo − γγ = convergence at the station (sign convention varies — check zone)
Try it before you peek
Worked example
The problem
A traverse leg measures 1,200.00 ft on the ground at an average elevation of 800 ft. The grid scale factor at the project location is 0.99987. Compute the grid distance.
Don't fall for these
What trips people up
Mixing ground and grid in the same computation
You can\'t check a closed traverse using ground distances if the published control coordinates are on the grid. Reduce ALL distances to grid (or scale all coordinates back to ground) before adjusting.
Forgetting the elevation factor
The grid scale factor is just for the projection. Elevation matters whenever the work is significantly above/below the ellipsoid. At 5,000 ft, elevation factor alone is 0.99976 — nearly 1 in 4,000.
NAD83 has multiple realizations
NAD83(1986), NAD83(2011), NAD83(2022) — each is officially "NAD83" but coordinates differ at the cm level. State plane software needs the right realization.
Test yourself
How well did it stick?
A quick 5-question check on Applied Geodesy. See where you stand and what to review.