Chapter 20, Problem 20.34P

To determine

The scale factor used with Lambert conformal conic map projection and Mercator map projection when creating an LDP that is secant to the earth at height of $h_{avg}$ .

The expression for scale factor used in Lambert conformal conic map projection is given below.

$k_{LDP}=1+\frac{h_{avg}}{R_E}$

Here, $h_{avg}$ is average geodetic height of the project site, $R_e$ is average radius of earth, and $k_{LDP}$ is scale factor used for creating LDP.

In case of transverse Mercator map projection one extra factor $k_0$ , the value of which is $0.9999$ , is multiplied to the expression for scale factor used in Lambert conformal conic map projection to increase the precision.

Thus, the expression for scale factor used in transverse Mercator map projection is given below.

$k_{LDP}=0.9999\left(1+\frac{h_{avg}}{R_E}\right)$