Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 194

Fig. 5.15 Length of a
parallel arc

with increasing latitude, short in the south and long in the north. The parallel arc
length of the unit longitude difference decreases sharply with increasing latitude,
long in the south and short in the north, as depicted in Fig. 5.16 .
Table 5.4 lists the arc lengths at different latitudes for a quantitative grasp of the
meridian and parallel arc lengths.
Table 5.4 outlines the variations in lengths of a meridian arc and a parallel arc
with latitude. The length of 1 of latitude averages 110 km; 1 0 (one minute) of
latitude covers approximately 1.8 km and 1 00 (one second) is about 30 m. The length
of a parallel arc is almost equivalent to the length of the meridian arc near the
equator, but they increasingly diverge from each other with increasing latitude.
M and R are more or less the same. In some approximate calculations, the Earth
can be considered as a sphere. The relationships between the arc length on the
sphere and its subtended angle at the center are as follows:
1 arc length 110 km

1 0 arc length 1.8 km

1 00 arc length 30 m

and

30 00 arc length 1km

0.03 00 arc length 1m

0.0003 00 arc length

1cm

1.852 km, which corresponds approximately to
the value of a minute of arc along a meridian. In fact, the nautical mile was defined
as the average length along the meridian arc represented by one minute of latitude.

We know that 1 nautical mile ﾼ