Gauss and UTM Conformal Projections and the Plane Rectangular Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 322

Review and Study Questions

1. Why are geodetic elements on the ellipsoid projected onto a plane?
2. What is the conformality of conformal projection? Please demonstrate.
3. Write out the Cauchy-Riemann differential equation for conformal projection
from the ellipsoid onto the plane and from the plane onto the ellipsoid, and give
the relationship between isometric latitude and geodetic latitude.
4. What is zone division and how can an area of interest be divided into zones?
5. What are the three conditions for the Gauss projection and how does one
express these conditions with formulae?
6. Draw a geometric figure to explain the expansion point of the direct and inverse
solutions of Gauss projection, and explain the term “footprint latitude.”
7. Illustrate the basics of the transformation between adjacent zones and how to
transform coordinates between 3 zones and 6 zones.
8. What is involved in the reduction of a horizontal geodetic control network to
the Gauss plane?
9. Derive the approximate formula for arc-to-chord correction with an accuracy of
0.1 m.
10. Derive the formula for checking arc-to-chord correction.
11. Analyze the distortion property of the Gauss projection according to the
formula for distance distortion m

y 4
24R 4 .
12. Analyze the signs of the two corrected values when reducing the terrestrial
observed distance to the plane.
13. Analyze the desired accuracy for coordinates in computations of distance
correction and arc-to-chord correction of the first-order triangulateration con-
trol network (let R

y 2
2R 2

1 ﾼ þ

50 km).
14. Draw a geometric figure to derive the relational expression for computing the
grid convergence:

ﾼ 6,400 km, y and Δ x ﾼ 300 km, and S ﾼ

∂ x

∂ l

tan ʳ ﾼ :

∂ y

∂ l

15. Explain the concepts of the Universal Transverse Mercator (UTM) projection.