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Practical Approach 
to Understanding 
and Using Grid 
Coordinates 
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New$Jersey$Society$of$!
Professional+Land+Surveyors!
SurvCon(2014
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Presented by 
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Joseph Paiva – CEO  
February 2014 
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New Jersey Society of Professional Land Surveyors 
SurvCon 2014 
Atlantic City 
Practical Approach to 
Understanding and 
Using Grid Coordinates 
Joseph V.R. Paiva – CEO  
Introduction 
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Overview of concepts 
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Projection, scale differences 
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How the mathematics operates 
rather than the mathematics itself 
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Practical applications in the field, in 
the office, in communications 
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Stress understanding of theory and 
mathematics used in the system 
© 2013 GeoLearn, LLC 
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The grid headache 
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Why do we have it anyway? 
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Is it those darn software 
manufacturers? 
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Why can’t we have the good old 
“ground” days? 
Topics 
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Surveys: limited scope vs. large 
extent; plane vs. geodetic surveys 
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Projections—the concept and the math 
for surveyors 
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SPCS Calculations 
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Strategies for dealing with the grid/
ground “thing” 
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Introduction 
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Most small-area surveys assume the 
earth is flat (plane surveys) 
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For large areas, Earth’s curvature 
has to be considered 
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This usually involves determining 
geodetic positions (latitude and 
longitude) of survey stations 
State Plane Coordinate System 
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SPCS was designed in the early 
1930s by the Coast and Geodetic 
survey to solve the problem of 
surveys of large extents for the 
“local” surveyor 
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In addition to allowing plane survey 
concepts to be used, it delivers 
several additional benefits 
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SPCS benefits 
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Simplifies calculations for surveys 
over large distances 
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Provides common datum of reference 
for all surveys (if tied in) 
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Well suited for engineering projects 
of large extent, i.e. highways, but 
also photogrammetry, large scale 
cadastral surveys, etc. 
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Supplies vital grid for GIS (other 
options exist) 
SPCs 
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When surveys are tied into the SPCS, 
their locations become (potentially) 
indestructible 
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With GPS, the problem of what 
coordinates to use once geocentric 
coordinates of GPS have been 
transformed in geodetic coordinates 
makes SPCs a natural choice 
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Projections 
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The basic problem with plane 
surveying is that it assumes the 
earth is flat 
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Some problems… 
Problems 
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meridians converge 
Parallel is curved 
except at equator 
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Problems 
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On the Earth, “straight lines” are not 
straight except for meridians (or the 
equator) and the difference gets 
larger as you extend them 
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Problems 
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Changes in elevation cannot be 
ignored, that is why all geodetic 
distances are at “sea level” 
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Projections 
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To have a plane coordinate system, 
it is necessary to distort the curved 
surface of the earth to a fit on a 
plane 
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Orange peel analogy 
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This process of flattening must be 
systematic in order to have accuracy 
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In surveying this process is called a 
projection 
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Projections / 2 
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Distortions inevitable (but 
systematic) 
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Different projections are used 
because each minimizes distortion in 
some properties at the expense of 
others 
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Different mathematical treatments 
are given to projections depending 
on the result desired 
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Developable surface 
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A shape that can be made into a 
plane 
• Cone  
• Cylinder 
• Plane (of course) 
General Classes 
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Cylindrical 
© 2013 GeoLearn, LLC 
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Tangent 
Secant 
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© 2013 GeoLearn, LLC 
Developing the surface 
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