Microsoft Word - Hwk 8 Elliptical Coordinates (3).rtf

SUR 440 Geodesy and GPS

Surveying

Transformation of Elliptical

Coordinates

Use the Geodetic Reference System of 1980 (GRS 80).

1. Given the geodetic coordinates of Station Avenel:

φ = 400 47' XXXXXXXXXX" N

λ = XXXXXXXXXX' XXXXXXXXXX" W

he = XXXXXXXXXXmeters

Compute the geocentric coordinates ( X, Y, Z).

2. Given the geocentric coordinates of Station AP STA

82:

X = -2,104,345.449

meters

Y = -4,352,866.903

meters

Z = 4,148, XXXXXXXXXXmeters

Compute the geodetic coordinates ( φ, λ, he).

3. Compute the mark-to-mark (chord) distance between the two

stations.

4. Compute the geodetic distance ( on the ellipsoid surface)

etween the two points. Use of the geodetic tool kit on the NGS

Website is acceptable.

Alterative CoordT (4).pdf

EllipT Matlab Program

EllipT Matlab Program

%Convert Geocentric Coordinates of a Control Station near Banks,

Alabama to Geodetic Coordinates.

format long

X= XXXXXXXXXX;

Y= XXXXXXXXXX;

Z= XXXXXXXXXX;

a=6378137;

e2= XXXXXXXXXX;

pi= XXXXXXXXXX;

%Find initial Approximation for Latitude

Lat0=atan(Z/sqrt(X^2+Y^2)*(1/(1-e2)))

%Iterate solution for Latitude

N0=a/sqrt(1-e2*sin(Lat0)^2)

Lat1=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N0*sin(Lat0)/Z)))

N1=a/sqrt(1-e2*sin(Lat1)^2)

Lat2=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N1*sin(Lat1)/Z)))

N2=a/sqrt(1-e2*sin(Lat2)^2)

Lat3=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N2*sin(Lat2)/Z)))

N3=a/sqrt(1-e2*sin(Lat3)^2)

Lat4=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N3*sin(Lat3)/Z)))

N4=a/sqrt(1-e2*sin(Lat4)^2)

Lat5=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N4*sin(Lat4)/Z)))

%Update N

N5=a/sqrt(1-e2*sin(Lat5)^2)

%Compute h

h=sqrt(X^2+Y^2)/cos(Lat5)-N5

%Report Lat in Decimal Degrees

Lat5DD=Lat5*180/pi

EllipT

Output_EllipT

Find Initial Approximation for Latitude

Lat0 =

XXXXXXXXXX

Iterate Latitude

N0 =

6.383925708075581e+006

Lat1 =

XXXXXXXXXX

N1 =

6.383925707263495e+006

Lat2 =

XXXXXXXXXX

N2 =

6.383925707259524e+006

Lat3 =

XXXXXXXXXX

N3 =

6.383925707259504e+006

Lat4 =

XXXXXXXXXX

N4 =

6.383925707259504e+006

Lat5 =

XXXXXXXXXX

Use Latitude to Update N

N =

6.383925707259504e+006

Use Iterated Latitude and Updated N to find h

h =

XXXXXXXXXX

Report Latitude in Decimal Degrees

Lat5DD =

XXXXXXXXXX

Geocentric to Geodetic (Closed Form Solution given by Vincenty 1980)

Geocentric to Geodetic (Closed Form Solution given by

Vincenty 1980)

SUR 440 Geodesy and GPS

Surveying

Transformation of Elliptical

Coordinates

Use the Geodetic Reference System of 1980 (GRS 80).

1. Given the geodetic coordinates of Station Avenel:

φ = 400 47' XXXXXXXXXX" N

λ = XXXXXXXXXX' XXXXXXXXXX" W

he = XXXXXXXXXXmeters

Compute the geocentric coordinates ( X, Y, Z).

2. Given the geocentric coordinates of Station AP STA

82:

X = -2,104,345.449

meters

Y = -4,352,866.903

meters

Z = 4,148, XXXXXXXXXXmeters

Compute the geodetic coordinates ( φ, λ, he).

3. Compute the mark-to-mark (chord) distance between the two

stations.

4. Compute the geodetic distance ( on the ellipsoid surface)

etween the two points. Use of the geodetic tool kit on the NGS

Website is acceptable.

Alterative CoordT (4).pdf

EllipT Matlab Program

EllipT Matlab Program

%Convert Geocentric Coordinates of a Control Station near Banks,

Alabama to Geodetic Coordinates.

format long

X= XXXXXXXXXX;

Y= XXXXXXXXXX;

Z= XXXXXXXXXX;

a=6378137;

e2= XXXXXXXXXX;

pi= XXXXXXXXXX;

%Find initial Approximation for Latitude

Lat0=atan(Z/sqrt(X^2+Y^2)*(1/(1-e2)))

%Iterate solution for Latitude

N0=a/sqrt(1-e2*sin(Lat0)^2)

Lat1=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N0*sin(Lat0)/Z)))

N1=a/sqrt(1-e2*sin(Lat1)^2)

Lat2=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N1*sin(Lat1)/Z)))

N2=a/sqrt(1-e2*sin(Lat2)^2)

Lat3=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N2*sin(Lat2)/Z)))

N3=a/sqrt(1-e2*sin(Lat3)^2)

Lat4=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N3*sin(Lat3)/Z)))

N4=a/sqrt(1-e2*sin(Lat4)^2)

Lat5=atan((Z/sqrt(X^2+Y^2))*(1+(e2*N4*sin(Lat4)/Z)))

%Update N

N5=a/sqrt(1-e2*sin(Lat5)^2)

%Compute h

h=sqrt(X^2+Y^2)/cos(Lat5)-N5

%Report Lat in Decimal Degrees

Lat5DD=Lat5*180/pi

EllipT

Output_EllipT

Find Initial Approximation for Latitude

Lat0 =

XXXXXXXXXX

Iterate Latitude

N0 =

6.383925708075581e+006

Lat1 =

XXXXXXXXXX

N1 =

6.383925707263495e+006

Lat2 =

XXXXXXXXXX

N2 =

6.383925707259524e+006

Lat3 =

XXXXXXXXXX

N3 =

6.383925707259504e+006

Lat4 =

XXXXXXXXXX

N4 =

6.383925707259504e+006

Lat5 =

XXXXXXXXXX

Use Latitude to Update N

N =

6.383925707259504e+006

Use Iterated Latitude and Updated N to find h

h =

XXXXXXXXXX

Report Latitude in Decimal Degrees

Lat5DD =

XXXXXXXXXX

Geocentric to Geodetic (Closed Form Solution given by Vincenty 1980)

Geocentric to Geodetic (Closed Form Solution given by

Vincenty 1980)

Answered Same DayNov 25, 2021

Question 1: Geocentric coordinates (X, Y, Z)

As per the given data in the question for geodetic coordinates of Station Avenel are as follows:

φ = 40ᶿ 47' 45.52443" N

λ = 115ᶿ 50' 54.61950" W

he = 1537.54 meters

Now for the calculation Geocentric coordinates (X, Y, Z):

Where N is equal to

And the values of e can be calculated by the following element:

Now putting the above given values of φ, λ and he in the above formula will get:

X, m = -2108719.51250085

Y, m = -4352688.04765656

Z, m = 4146301.95361686

Question 2: Geodetic coordinates (φ, λ, he).

As per the given data in the question for geocentric coordinates of Station AP STA 82 are as follows:

X = -2,104,345.449

Y = -4,352,866.903

he = 4,148,293.126 meters

Now for the calculation...

As per the given data in the question for geodetic coordinates of Station Avenel are as follows:

φ = 40ᶿ 47' 45.52443" N

λ = 115ᶿ 50' 54.61950" W

he = 1537.54 meters

Now for the calculation Geocentric coordinates (X, Y, Z):

Where N is equal to

And the values of e can be calculated by the following element:

Now putting the above given values of φ, λ and he in the above formula will get:

X, m = -2108719.51250085

Y, m = -4352688.04765656

Z, m = 4146301.95361686

Question 2: Geodetic coordinates (φ, λ, he).

As per the given data in the question for geocentric coordinates of Station AP STA 82 are as follows:

X = -2,104,345.449

Y = -4,352,866.903

he = 4,148,293.126 meters

Now for the calculation...

SOLUTION.PDF## Answer To This Question Is Available To Download

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