Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Solution to Geodetic Coordinate Transformation using Bowring Method, Study notes of Engineering

Ferris State University (FSU)Engineering

The solution to the geodetic coordinate transformation problem using the bowring method. The given quantities, constants for grs 80, some useful angle functions, and the steps to calculate the geodetic coordinates from the cartesian coordinates. The solution is presented in iterative form, with the initial estimate of the parameter βo and its refinement in the second iteration.

Typology: Study notes

Pre 2010

Uploaded on 08/07/2009

koofers-user-vyg-1
koofers-user-vyg-1 🇺🇸

10 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
βo0.7837191028=βoatan a
b
Z
W
⋅
:=
The initial estimate of the parameter βo is
W 4517803.010902=WX
2Y2
+:=
dms λr2d⋅
()
84.00000000−=λ atan2 X Y,():=
ep2 0.0067394968=ep2 a2b2
−
b2
:=
Solution:
_______________________________________________________________________________
Z 4487560.5408:=Y 4493054.0133−:=X 472239.0061:=
Given Quantities:
_______________________________________________________________________________
e20.00669438002290:=b 6356752.3141:=a 6378137:=
Constants for GRS 80:
_______________________________________________________________________________
r2d 180
π
:=
dms ang( ) degree floor ang()←
rem ang degree−()60⋅←
mins floor rem()←
rem1 rem mins−()←
secs rem1 60.0⋅←
degree mins
100
+secs
10000
+
:=
radians ang( ) d dd ang()←
dπ
180.0
⋅
:=dd ang( ) degree floor ang()←
mins ang degree−( ) 100.0⋅←
minutes floor mins()←
seconds mins minutes−( ) 100.0⋅←
degree minutes
60.0
+seconds
3600.0
+
:=
Some useful angle functions
_______________________________________________________________________________
Transformation Between Cartesian to Geodetic Coordinates
Bowring Method
pf2

Partial preview of the text

Download Solution to Geodetic Coordinate Transformation using Bowring Method and more Study notes Engineering in PDF only on Docsity!

βo atan a βo =0. b

Z

W

The initial estimate of the parameter βo is

W := X^2 +Y^2 W =4517803.

λ :=atan2 X Y( , ) dms (^ λ ⋅r2d)^ =−84.

e (^) p2 a^ e (^) p2 =0.

(^2) −b 2

b 2

Solution:

_______________________________________________________________________________

X :=472239.0061 Y :=−4493054.0133 Z :=4487560.

Given Quantities:

_______________________________________________________________________________

a := 6378137 b :=6356752.3141 e 2 :=0.

Constants for GRS 80:

_______________________________________________________________________________

r2d 180 π

dms ang( ) degree ←floor ang( ) rem ←( ang −degree) 60⋅ mins ←floor rem( ) rem1 ←( rem −mins) secs ←rem1 60.0⋅

degree mins 100

  • secs 10000

radians ang( ) d ←dd ang( )

d π

dd ang( ) degree ←floor ang( ) := mins ←( ang −degree) 100.0⋅ minutes ←floor mins( ) seconds ←( mins −minutes) 100.0⋅

degree minutes

  • seconds

Some useful angle functions

_______________________________________________________________________________

Transformation Between Cartesian to Geodetic Coordinates Bowring Method

Cartesian to Geodetic Coordinate Transformation

Bowring Method Page 2 of 2

H W H =300.

cos( φ)^

a  1 −e 2 ⋅(^ sin (^ φ))^2 

− 1 2 := − ⋅

The end of the iterations

dms ( β − βo⋅r2d) = 0

β atan b β =0. a

 ⋅tan ( φ)

φ atan dms (^ φ ⋅r2d)^ =45.

Z +e p2 ⋅ b ⋅( sin ( βo))^3

W −a e⋅ 2 ⋅( cos ( βo))^3

βo :=β βo =0.

The second iteration

dms ( β − βo⋅r2d) =0.

β atan b β =0. a

 ⋅tan ( φ)

φ atan dms (^ φ ⋅r2d)^ =45.

Z +e p2 ⋅ b ⋅( sin ( βo))^3

W −a e⋅ 2 ⋅( cos ( βo))^3