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  • GIS Library Measurement Units: International Foot vs. US Survey Foot

    Data in our library is in NAD83 HPGN/HARN, stateplane projection FIPS Zone 0202 (AZ central), international feet. This page explains why we use international feet. It was researched by Ron Platt in the City of Tucson.

    Arizona Revised Statue 33-132

    Arizona Revised Statue 33-132 specifically defines the value of the foot to be used in our NAD83, Arizona Central State Plane Coordinate system. In part, the first paragraph of the statute reads:

      33-132. Coordinates of system; zone definitions

      A. The plane coordinates of a point on the earth's surface, to be used in the position or location of such point in the appropriate zone of the system, shall consist of two distances, expressed in feet and decimals of a foot (foot value 0.3048 meter exact). One of these distances, to be known as the "X-coordinate", shall give the position in an east-and-west direction, and the other, to be known as the "Y-coordinate", shall give the position in a north-and-south direction. These coordinates shall depend on and conform to the coordinates on the Arizona coordinate system, 1983, of the horizontal control stations of the national geodetic survey in this state, as these coordinates have been determined by the survey.

    It is from the 0.3048 meter per foot value we get the 3.280839895 feet per meter value used in our projection files. I.E., the ratio derived is 1 foot / 0.3048 meter = x feet / 1 meter.

    The question whether this value is "International Foot" or the "Survey Foot" (or "U.S. Survey Foot") is answered as follows:

      Researching foot conversions one can find that the "US foot" = 0.3048006096 meters (to ten decimal places) and that the "International foot" = 0.3048 meters.

      The NGS has a PDF format document from the National Bureau of Standards called Refinement of Values for the Yard and Pound that defines the "U.S. Survey foot" as 1200/3937 meter or 0.3048006096 meters.

      So, two different sources confirm the value of the "U.S.Survey Foot". It is also now obvious that the value specified by statute (0.3048 meter exact), and the value of 3.280839895 feet per meter (as derived from 0.3048 meter exact) used locally in our projections is NOT the "U.S. Survey Foot".

    The final question whether we are certain the value we use is the "International Foot" or not, is best answered through further study of the NGS document Refinementof Values for the Yard and Pound. A portion of said document refers to the "International Yard" as 0.9144 meter (or one foot = 0.3048 meter exact from dividing by 3 feet), we can be fairly certain the division of the "International Yard" may in definition be extrapolated to verbally mean "International Foot". I am sure there is a real statement to this effect out there somewhere. We may also conclude the answer is "yes we use the International Foot even though ARS 33-132 did not expressly say so".

    Lastly, one might ask why we use the "International Foot"? Especially since the NGS designed the State Plane Coordinate System as a "Geodetic" network, and since some suggest geodetic applications be based on the "U.S. Survey Foot".

    The NGS document discussing state planecoordinate system units of measure is the policy by which authority is vested with the states to decide which value is used. The Arizona State Legislature obviously chose the International Foot.

    National Geodetic Survey FAQ

    The National Geodetic SurveyFAQ has a section called What are the "official"conversions that are used by NGS to convert 1) meters to inches, and 2) meters to feet?that clearly explains and defines the U.S Survey Foot and the International Foot, including meter conversion constants.

    You may also find the ESRI ArcGIS topic About setting distance units helpful.

    ESRI's ArcInfo documentation provides this additional explanation:

    In 1959, the directors of the National Bureau of Standards and the United States Coast and Geodetic Survey agreed on a redefinition of the inch-centimeter relationship. This redefinition defined 1 inch as equal to 2.54 centimeters, exactly, or 1 foot as equal to 0.3048 meters, exactly. However, their agreement stipulated that the older value for 1 meter equaling 39.37 inches,. exactly, be retained for identifying the ‘U.S. survey foot’. One of the reasons for this retention was that the State Plane Coordinate Systems, which are derived from the national geodetic control network, are based on the relationship of 1 meter equaling 39.37 inches, exactly. The difference between these two values for the foot is very small, two parts per million, which is hardly measurable but not trivial when computational consistency is desired. Fundamental survey units, such as rods, chains, statute miles, acres, sections, and townships, all depend on the relationship of 1 meter equaling 39.37 inches, exactly.

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