## Coordinate Systems Self Study

### Question (3)

A survey in northern Wisconsin includes NSRS point QN0534 *Brent*. For direction orientation, NSRS point QN0533 *Swayne Tower L* is sighted from *Brent*. An angle of 212°55'14" is turned to the right to traverse point *Dog*. The measured horizontal distance from *Brent *to *Dog* is 1725.63 ft. Dog's scaled elevation is 1385 ft. The survey will be adjusted in Wisconsin's North SPC Zone in survey feet. Constants for the zone include N_{o} = 365,048.99 ft = 111,267.15 m, r_{o} = 20,927,206.92 ft = 6,378,625.43 m.

(a) What is the geodetic azimuth from *Brent* to *Swayne Tower L*?

(b) What is the SPC grid azimuth from *Brent* to *Swayne Tower L*?

(c) Is there a significant arc-to-chord correction for the measured angle?

(d) What is the grid distance from *Brent* to *Dog*?

#### Solution

Get the datasheets for *Brent* and *Swayne Tower L*.

(a) Geodetic azimuth from *Brent* to *Swayne Tower L*?

From* Brent*'s datasheet:

Geodetic Az = 309°02'49.4"

(b) SPC grid azimuth from *Brent* to *Swayne Tower L*?

Two ways to get

*(1) Use convergence and geodetic azimuth at Brent*

Brentis point 1;Swayne Tower Lis point 2.

Compute arc-to-chord correction to see if it's significant

Compute grid az

*(2) Inverse between SPC coords of the two points*

Brentis point 1;Swayne Tower Lis point 2.

Both ways get the same answer.

(c) Is there a significant arc-to-chord correction for the measured angle?

The BS correction was computed in the previous part: +0.33"

To compute the FS correction, need approx coords of *Dog:*

Compute FS correction

Determine total correction to angle

The angle correction is __-0.35"__ which may not be significant for measurements, but can come into play for comps.

(d) Grid distance from *Brent* to *Dog*?

UsingBrent's geoid ht and elevations ofBrentandDog, determine geodetic distance.

Different grid scale possibilities

Grid dist from Brent's scale, Brent and Dog average scale, weighted average; also, apply Combined Factor. Compare results.

__Grid Distance - 1725.497 ft__