Gauss and UTM Conformal Projections and the Plane Rectangular Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 289

y 4 9

=

t f t f

24M f N f

2M f N f y 2 -

3t f þʷ

2
f

2

f t f

B f B ﾼ 5 þ 9 ʷ

y 3 y 5 :

1
N f cosB f y

1
6N f cosB f

1
120N f cosB f

;

2t f þʷ

2
f

28t f þ 24t f l ﾼ 1 þ þ 5 þ

ð 6 : 46 Þ

3.5 ∘ , the accuracy of the computation according to ( 6.46 ) is 0.01 00 .If
the desired accuracy is 0.0001 00 , the series in ( 6.46 ) can be further expanded:

When l <

y 4

9
=

ﾼ

t f
2M f N f y 2

t f
24M f N f

3t f þ ʷ

2 2

f t f

B f B 5 þ

f

9 ʷ

y 6

t f
720M f N f

90t f þ 45t f þ 61 þ

: ð 6 : 47 Þ

y 3

1
N f cos B f y

1
6N f cos B f

;

2t f þ ʷ

2
f

l ﾼ 1 þ

y 5

1
120N f cos B f

28t f þ 24 f þ

2
f

2

f t f

þ 5 þ 6 ʷ þ 8 ʷ

L and B can finally be obtained according to:

L ﾼ L 0 þ l

: ð 6 : 48 Þ

B ﾼ B f B f B

Practical Formulae

Formulae for the Inverse Solution of the Gauss Projection (Accurate
to 0.0001 00 ; The Results Are Measured in Degrees)

From ( 6.47 ), we have:

9
=

2
4

0
@

1
A

0
@

1
A

2 4

1
2 V f t f

y
N f

1
12

y
N f

3t f þ ʷ

f f t f

B ∘ ﾼ B f

5 þ 9 ʷ

0 1 3

6

1
360

y
N f

180
ˀ

@ A 5

90t f þ 45t f þ 61 þ

2 0 1 0 1 , ð 6 : 49 Þ

3

;

1
cos B f

y
N f

1
6

y
N f

4 @ A @ A

l ∘ ﾼ 2t f þ ʷ

2
f

1 þ

0
@

1
A

3
5

5

1
120

y
N f

180
ˀ

28t f þ 24t f þ

2
f

2

f t f

þ 5 þ 6 ʷ þ 8 ʷ