Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 196

Fig. 5.17 Trapezoidal map
sheet

ð ð

lb 2 ð

L 2 B 2 B 2

cos B

P ﾼ MN cos BdBdL ﾼ

2 dB,

ð 5 : 46 Þ

ð 1 e 2 sin 2 B Þ

L 1 B 1 B 1

where l L 1 . Expanding the above function according to binomial theorem

and integrating gives:

ﾼ L 2

b 2 A 0 sin 1

2 B 2

B 1 cos3B m

l
90 ˀ

B 0 sin 3

P ﾼ

2 B 2

ð B 1 Þ cosB m

2 B 2

B 1 cos7B m þ

2 B 2

B 1 cos9B m : C 0 sin 5 D 0 sin 7 E 0 sin 9 þ

2 B 2

ð B 1 Þ cos5B m

ð 5 : 47 Þ

1

In the equation, B m ﾼ

2 B 1 þ

ð B 2 Þ . The coefficients are:

9
=

1
2 e 2

3
8 e 4

5
16 e 6

35
128 e 8

A 0 ﾼ 1 þ þ þ þ

1
6 e 2

3
16 e 4

3
16 e 6

35
192 e 8

B 0 ﾼ þ þ þ

3
80 e 4

1
16 e 6

5
64 e 8

C 0

ﾼ þ þ

:

;

1
112 e 6

5
156 e 8

D 0 ﾼ þ

5
2304 e 8

E 0 ﾼ