The HP 35s Calculator—A Field Surveyor’s Companion: Part 8—Area

A 166Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE

Example Data and Running The Program
According to Brown, Robillard, and Wilson’s Boundary Control and Legal Principles third edition, area is the second least controlling factor in the order of conflicting title elements and followed only by coordinates. However in the public’s eye area is a most important factor in identifying land. I believe that the simple description "Jason’s 10 acres in Mohave County, Arizona," could serve to effectively and legally convey land. I’d be willing to bet that the PLSS guys are already thinking "660′ x 660′ ", the Colonial Boys are on their way to the courthouse to get my neighbor’s deeds, and the Texans don’t count anything under 40. Land ownership seems to be commonly associated with quantity. I suppose that’s because quantity is an easy metric to scale with currency. The irony of that concept is that folks will fight over pennies, and real estate escrow accounts must balance at exactly $0.00, but the surveyor has been graced with the expectation of expressing quantities "more or less". Count your blessings and recognize the imprecision of your measurements when expressing significant digits.

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This Month’s Program
Program K: The Area program simply resolves the "area by coordinates" of a flat sided polygon then adds or subtracts the area of a segment of a circle for curve areas. Segments are added or subtracted accordingly dependent on if the curve is an "outie" or an "inny" to the polygon. Curve segment area formulae can be easily wrangled up on the fruited prairie of information we call "the internet". "Area by coordinates" can be referenced in many land surveying texts including Elementary Surveying Eleventh edition by Wolf and Ghilani. I find my oldest reference in Surveying by Davis, Foote, and Rayner copyright 1928. A boundary retracement surveyor is well served by pole-catting through the used book stores. Historic Engineering and Surveying textbooks demonstrate the techniques used by our predecessors. It stands to reason that knowing how your predecessor measured is requisite to successful retracement surveying.

*A 1.4 square foot difference (308,263.21) should show between last month’s computed coordinates and the two place decimal values presented herein.

*Follow consistent rules when computing to a level of precision. "Four decimal places" is well beyond my reasonable ability to measure as well as beyond the quality of any computed value in this example. Using the radius value carried out to 152.2316 yields a square footage of 308,261.82 whereas the value of 152.23 yields the value of 308,261.73 which equates to .09 of a square foot or the area of a classroom ruler. I honestly don’t measure land that well, nor do you! However, you may want to expend some attention when large highway curves are encountered. Understanding the effects of computations is important in a mechanical sense but ultimately the varying computations should collectively net consistent and tolerable results. Society is not interested in the claim that your answer is "more righter" than mine. They simply expect us to agree…and another thing, please kindly round up those decimally inordinate "nines" for the Planning and Zoning folks. You have professional the discretion to round and interpret, whereas they most likely don’t.

Use the data from the previous "Compass Rule Adjustment" routine. In addition to the five existing points I have introduced a curve with P.I. #6 and the P.T. #7 to show the complete function of the routine. I will demonstrate how to construct the curve and solve for the p.i. and p.t. in at a later date.

See the PDF for the program listing and a bonus equation

Jason Foose is the County Surveyor of Mohave County Arizona. He has been licensed for  441,504,000 seconds…no wait, 441,504,001 seconds…no wait, 441,504,002 seconds…

A 166Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE

About the Author

Jason Foose, PS

Jason Foose originally hails from the Connecticut Western Reserve Township 3, range XIV West of Ellicott’s Line Surveyed in 1785 but now resides in Township 21 North, Range 17 West of the Gila & Salt River Base Line and Meridian. He is also the Managing Editor of the magazine.