Lambert

SPCS 1927 Lat-Long -> X, Y

SPCS 1927 Conversion Formulae Constants###

Convert from Lat/Long to X,Y ###

###

Using the Clark 1866 Ellipsoidconformallatitude

D.MMSSssssPoint (HP Calc. format) mLatitude 35°. 00' 00'' ·000 NLongitude 75°. 00' 00'' ·000 W

mStandard N 45°. 00' 00'' ·000 NParallels S 33°. 00' 00'' ·000 N

n = Origin tLatitude 23°. 00' 00'' ·000 NLongitude 96°. 00' 00'' ·000 W

Origin meters US Survey feet F = X offset 0 0Y offset 0 0

r =

Using the conformal latitude method (as per formulae)meters US Survey feet

X = 1,894,410.899 6,215,246.424 ###Y = 1,564,649.472 5,133,354.142 ###k = 0.997 0171 0.997 0171 ###

Using the geocentric latitude method (as per the tables)meters US Survey feet

X = 1,894,410.689 6,215,245.737Y = 1,564,645.245 5,133,340.274k = 0.997 0171 0.997 0171

User Instructions

Enter the required data in the boxes with the red border. You can use eithermeters or US Survey feet for the offsets. Enter latitudes and longitudes inD.MMSSssss (HP calculator) format, and the entry will be formatted in a more readable form.

Data returned are the co-ordinates of the entered point, in meters of feet,

f = l =

f2 = f1 =

f0 = l0 =

r0 =

q =

SPCS 1927 Lat-Long -> X, Y

together with the point scale factor at the latitude of the point in the.boxes with the green borders.

Note that two methods of obtaining co-ordinates are used. The 'geocentriclatitude' method is what was used in the old SPCS 1927 tables, and so willgive a result that is closer to old values. The 'conformal latitude' methodis based on more exact formulae and should be used if you are sure that thefull computation was done for the SPCS 1927 co-ordinates.

You will see that there isn't a great deal of difference between the co-ordinatesobtained. Consult Snyder's 'Map Projections - A Working Manual' for moredetails on this issue.

© 1998 Bill Hazelton and OSU. This spreadsheet may be distributed freely,provided that no charge is made, or any attempt is made to profit by it.All rights are reserved by the copyright holders.

Formulae are hidden on this spreadsheet for convenience and neatness,but can be easily recovered by the user.

SPCS 1927 X, Y -> Lat-Long

SPCS 1927 Conversion Formulae

Convert from X,Y to Lat/Long

Using the Clark 1866 Ellipsoid

Enter the X and Y co-ordinates

Geocentric US Survey Feet MetersX = 1894410.9Y = 1564649.5

Conformal US Survey Feet MetersX = 1894410.9Y = 1564649.5

Origin Data US Survey Feet MetersX offset = Y offset =

D.MMSSssssLatitude = 23°. 00' 00'' ·000 N

Longitude = 96°. 00' 00'' ·000 W

Standard N 45°. 00' 00'' ·000 NParallels S 33°. 00' 00'' ·000 N

Results

Using the conformal latitude method (as per formulae)35°. 00' 00'' ·000 N74°. 59' 60'' ·000 W

k = 0.997 0171

Using the geocentric latitude method (as per the tables)35°. 00' 00'' ·244 N74°. 59' 60'' ·000 W

k = 0.997 0180

User Instructions

Decide whether you have co-ordinates that were computed using the conformal

f = l =

f = l =

SPCS 1927 X, Y -> Lat-Long

latitude formulae (as per the given formulae) or using the geocentric latitudeformulae (as per the SPCS 1927 tables). Enter the values in either US Surveyfeet or meters (which will have been converted from meters previously.)

Enter the offset values for X and Y (false origin).Enter the latitude and longitude of the grid system's co-ordinate origin.Enter the standard parallels for the particular zone under consideration.

All data entry occurs in the boxes with the red outline.

The latitude and longitude of the point is returned in the green outlined areas.The two results will differ slightly in latitude, if the same value was enteredfor both geocentric and conformal computations.

NAD27 to NAD83 Conversion

NAD 1927 Values

Latitude Longitude Ellipsoidal Heightf l h

(D.MMSSssss N) (D.MMSSssss W) (meters)

34°. 47' 08'' ·833 86°. 34' 52'' ·175 100

NAD 1983 Values

Latitude Longitude Ellipsoidal Heightf l h

(D.MMSSssss N) (D.MMSSssss W) (meters)

34°. 47' 09'' ·189 86°. 34' 52'' ·095 61.94

Precision Precision Precision±1.3 m or ±1.3 m or ±1.2 m

0.042'' 0.035''

Differences

Latitude Longitude Ellipsoidal HeightDf Dl

(seconds) (seconds) (meters)

0.356'' 0.080'' -38.06

User Directions

Key in the NAD27 values to be converted in the red outlined area.Values should be entered as DDD.MMSSsss (HP calculator format)and will be re-formatted after <Enter> is pressed.Key in geodetic latitude of point, North positive.Key in geodetic longitude of point, West positive.Key in ellipsoidal height in meters (zero will give you thevalue to be used for correction).

The NAD83 values will be returned in the blue outlined area.The values are in HP calculator format, but with DMS notationadded, for ease of interpretation.With the values are the estimated precision of the values, assuming that the NAD27 values are perfect, i.e., the error in theformulae is given. You will have to add the precision of the NAD27values to this estimate.

The corrections themselves are returned in the green outline area.

Dh

NAD27 to NAD83 Conversion

The latitude and longitude values are in seconds. The height is inmeters.

©1998 N.W.J. Hazelton and The Ohio State University.

This spreadsheet may be freely copied and distributed,provided that this notice remains with the spreadsheet and thatthe distribution is not made for any monetary or other exchange.Formulae used are freely available and may be used by anyone.They are hidden in this spreadsheet for convenience only andmay be viewed quite easily.

Disclaimer: The Author and The Ohio State University are notliable for any incidental, special or consequential damages arising from the use of this product. The user accepts all riskswhen using this product, and should check their work by independent means.

SPCS 1983 Lat-Long -> E, N


Convert from Lat/Long to E,N

Using the GRS80 (WGS-84) Ellipsoid

D.MMSSssssPoint (HP Calc. format)Latitude 35°. 00' 00'' ·000 NLongitude 75°. 00' 00'' ·000 W


OriginLatitude 23°. 00' 00'' ·000 NLongitude 96°. 00' 00'' ·000 W

Origin metersX offset 0Y offset 0

Results

metersE = 1,894,366.824N = 1,564,695.562k = 0.997 0170

User Instructions

Enter the latitude and longitude of the point in question, together withthe latitudes of the standard parallels, and the latitude and longitude ofthe origin of the projection. Also enter the offset (false origin) valuesfor the origin point.

All data entry occurs in the boxes with the red border.

The results are returned in the boxes with the green border.The results are the E and N co-ordinates of the point, together withthe point scale factor at the point (k).

SPCS 1983 Lat-Long -> E, N

Entered values for angular measure should be made in HP calculatorformat, D.MMSSssss, which will be formatted into something moreeasily readable.

All values are worked in meters on SPCS 1983. You will have toconvert the co-ordinates to the feet of your chosing, if you wish todo so.

SPCS 1983 E, N -> Lat-Long


Convert from E,N to Lat/Long

Using the GRS80 (WGS-84) Ellipsoid

Enter the E and N co-ordinates

Meters US Survey Feet International FeetE = 1894366.824N = 1564695.562

Origin Data Meters US Survey Feet International FeetE offset = N offset =

D.MMSSssssLatitude = 23°. 00' 00'' ·000 N

Longitude = 96°. 00' 00'' ·000 W


Results

35°. 00' 00'' ·000 N75°. 00' 00'' ·000 W

k = 0.997 0170

User Instructions

Enter all input values into the boxes with the red borders.Enter the E, N co-ordinates of the point. If you enter them in a value other thanmeters, they will be corrected, provided you get the right kind of feet.

Enter angular measure in HP calculator format, D.MMSSssss, which will be convertedinto something more readable by the spreadsheet.

The results are displayed in the boxes with the green border. The latitude andlongitude are returned, along with the scale factor for the point.

f = l =

Lambert

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