NSPS CST Level IV flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Geoid undulation

The separation N between the reference ellipsoid and the geoid at a location. Ellipsoid height h equals orthometric height H plus N, linking GNSS heights to leveling-derived elevations.

Combined factor

The product of the elevation factor and the grid (projection) scale factor. Multiplying a ground distance by the combined factor converts it to a State Plane or other grid distance.

Elevation factor

Approximately R divided by R plus H, where R is mean Earth radius and H is orthometric height. It reduces ground distances to the ellipsoid and is always less than one above the ellipsoid.

State Plane zone design

Zones elongated east-west use Lambert Conformal Conic; zones elongated north-south use Transverse Mercator. Scale is exact along the standard parallels or central meridian and departs from one elsewhere.

UTM central meridian

For zone number n, the central meridian longitude is 6n minus 183 degrees. False easting of 500,000 meters is assigned at that meridian to keep eastings positive.

Traverse linear misclosure

The square root of the sum of squared easting and northing misclosures. Relative precision expresses it as 1:N, where N is total traverse length divided by misclosure.

Danger circle

In three-point resection, the circle passing through the three known stations. If the instrument occupies a point on that circle, the position is indeterminate or poorly conditioned.

RTK accuracy statement

Typical specification of 8 mm plus 1 ppm horizontally and 15 mm plus 1 ppm vertically at 68 percent confidence. The ppm term scales with baseline length in kilometers.

Level loop misclosure limit

A tolerance of the form C times the square root of loop length in kilometers or miles. Exceeding it requires reobservation before the run is adjusted or accepted.

Reciprocal vertical angle method

Observing a target from both ends of a line and averaging the vertical angles. This cancels curvature and refraction effects when direct leveling is impractical.

Earth curvature and refraction

Combined correction approximates 0.0675 times distance in kilometers squared, in meters. It is subtracted from rod readings and grows rapidly with sight distance.

Turning point in leveling

A temporary point occupied by the rod between instrument setups. Both a foresight and the next backsight are taken on it, advancing the elevation datum.

Closing a boundary description

Summing bearings and distances from the point of beginning back to itself. The computed closure must fall within stated precision and area must reconcile with the record.

Monumentation hierarchy

Evidence of original corners generally outranks position by measurement, which outranks record measurement. Courts and standards treat undisturbed original monuments as controlling over later dimensions.

Total station collimation check

Comparing direct and reversed readings to the same target. Half the difference gives the collimation error, which should be adjusted out or applied as an instrument correction.

Trigonometric leveling formula

Elevation difference equals horizontal distance times the tangent of the vertical angle, plus instrument height, minus target height, with curvature and refraction applied separately.

Coordinate rotation equations

For clockwise rotation by theta: E prime equals E cosine theta plus N sine theta; N prime equals negative E sine theta plus N cosine theta. Translation follows rotation.

Least-squares normal equations

The solution satisfies A-transpose-W-A times x equals A-transpose-W-L. Weights reflect observation quality, and residuals feed the variance factor computation.

A posteriori variance factor

Computed as V-transpose-W-V divided by n minus u, with n observations and u unknowns. Values near one suggest weights consistent with actual observation scatter.

Shoelace area formula

Twice the area equals the sum around the closed figure of E-sub-i times N-sub-i-plus-one minus E-sub-i-plus-one times N-sub-i. The sign reveals traversal direction.

Horizontal curve tangent

T equals R times the tangent of half the deflection angle. Together with curve length, external, and middle ordinate, it defines the curve geometry for staking.

Horizontal curve length

L equals R times the deflection angle in radians, or R times delta in degrees times pi divided by 180. It is the arc distance from PC to PT.

Error propagation for sums

For a sum or difference of independent observations, variances add. The standard error of the result is the square root of the summed variances, not the sum of standard errors.

Error propagation for products

For a product or quotient of independent quantities, relative variances add. Compute each standard error divided by its value, square, sum, then take the square root.

Grid-to-ground conversion

Divide a grid distance by the combined factor to obtain ground distance. Multiply ground distance by the combined factor to obtain grid distance for mapping or coordinates.

Datum epoch significance

Modern reference frames specify a coordinate epoch because plate motion changes coordinates over time. Mixing epochs without transformation introduces decimeter-level error at active sites.

Spatial metadata core elements

Coordinate reference system, datum and epoch, units, accuracy statement, source and date, and lineage description. These allow another party to use the data correctly.

Bearing to azimuth conversion

In the northeast quadrant azimuth equals bearing; southeast, 180 minus bearing; southwest, 180 plus bearing; northwest, 360 minus bearing. Azimuths are measured clockwise from north.

Latitude and departure

Latitude is distance times the cosine of bearing; departure is distance times the sine of bearing. Summed latitudes and departures give the traverse misclosure components.

Compass rule adjustment

Misclosure in latitude and departure is distributed in proportion to the length of each course relative to total traverse length. It is used when angles and distances are of comparable quality.

Transit rule adjustment

Misclosure components are distributed in proportion to the absolute latitude or departure of each course. Preferred when distances are less precise than angles, as in stadia work.

Vertical curve offset

The offset from the tangent equals A times x squared divided by 2L, where A is algebraic grade change in percent, x is distance from the curve start, and L is curve length.