The Geoid and Different Height Systems - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 154

ð ð

gdh ¼ gdh : ð 4 : 36 Þ

OA OB

because

g m 6¼ g m ,

A
m

B
m

ʳ 6¼ ʳ :

Thus it can be seen from ( 4.33 ) and ( 4.34 ) that:

H O 6¼ H O ,

H N 6¼ H N :

This would cause inconvenience to the design and construction of large-scale
water conservancy projects. A new height system is therefore needed to make “the
height of each point on the same level surface equal.” Hence, a dynamic height
system is usually adopted in a water conservancy project. The dynamic height (H D )
of point B is:

ð gdh

1

H D ¼

: ð 4 : 37 Þ

B
45

ʳ

The above equation shows that the dynamic height is obtained by replacing ʳ m in

( 4.34 ) with ʳ 45 , the normal gravity at latitude 45 . Points on the same level surface

have the same dynamic height. So the dynamic height system is a system where the
dynamic height of each point is represented by the normal height (H N ) of the point
at 45 latitude.
“Local dynamic height system” is adopted by some authorities to bring the
dynamic height over an area closer to the normal height in the same area, that is:

ð gdh,

1
ʳ ˆm

H LD ¼ ð 4 : 38 Þ

where ˆ m of the survey area.

The dynamic height and the normal height of a surface point can be easily
interconverted. From ( 4.34 ) and ( 4.36 ), we have:

ʳ ˆm is the normal gravity value at mean latitude

m H N ¼ ʳ

B

45 H D ,

B

ʳ

m 45

H D ʳ

ʳ

H N ¼ H D : ð 4 : 39 Þ

ʳ

m