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Measuring Distances, Angles and Areas. AGME 1613 Fundamentals of Agricultural Systems Technology. Objectives. Describe the advantages and disadvantages of four methods of measuring distance. Use each of the four methods in a simulated survey. Determine the area of standard geometric shapes.

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Measuring Distances, Angles and Areas

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Measuring Distances, Angles and Areas

AGME 1613

Fundamentals of Agricultural Systems Technology


Objectives

  • Describe the advantages and disadvantages of four methods of measuring distance.

  • Use each of the four methods in a simulated survey.

  • Determine the area of standard geometric shapes.

  • Determine the area of irregularly shaped fields.


Common Units of Distance

  • Feet

  • Yards

  • Rods (16.5-ft.)

  • Chain (88-ft.)

  • Mile (5280-ft.)

  • Meters (.3084-ft.)

  • Kilometers (.6214 miles)


Four Methods of Measuring Distance

  • Pacing

  • Odometer wheel

  • Taping

  • Stadia Method


Pacing

  • Simplest and easiest method of determining distances.

  • Requires only one person.

  • D = Pace factor x # of paces

  • With practice, accuracy of

    + 2% is possible.

  • Measures “surface distance.”


Odometer Wheel

  • Mechanical device for measuring distance.

    • Direct reading or

    • Revolution counting

  • D = # Rev x Circumference

  • Only one person required.

  • Accuracy of + 1%.

  • Measures “surface distance.”

Determine the distance if the wheel makes 200.5 revolutions.


Stadia Method

  • Very quick method of determining distance.

  • D = (TSR – BSR) x 100

  • More accurate than chaining.

  • Requires “leveling equipment.”

  • Requires two people.

  • What is the distance from the level to the rod in this example?


Taping

  • Most accurate method of determining distance.

  • Accuracy + .03 %.

  • Requires:

    • Specialized equipment

    • Minimum of two surveyors

    • Skill

  • Equipment:

    • 100-ft. steel tape,

    • chaining pins,

    • range poles,

    • plumb bobs,

    • hand level


Additional methods

  • Optical range finders

  • Electronic distance measurement

  • Global Positioning System (GPS) receivers


Determining Land Areas

  • Why would you need to be able to determine land areas?

  • How is land area typically expressed?


Standard Geometric Shapes

  • Square

  • Rectangle

  • Parallelogram

  • Trapezoid

  • Triangle

  • Circle

  • Sector


Square and Rectangle

  • Formula

    • A (ft2) = B’ x H’

    • A (ac) = B’ x H’

43,560

250-ft.

750-ft


Parallelogram

  • Formula

    • A (ft2) = B’ x H’

    • A (ac) = B’ x H’

43,560

H

B

What is the area (ft2), if the Base = 1200-ft and the Height = 300-ft?


What is the area of the trapezoid below?

700-ft.

375-ft.

300-ft.

Trapezoid

  • Formula

    • A (ft2) = H x [(a+b)/2]

A

H

B


400-ft.

325-ft.

Triangle

  • A (ft2) = ½ x B x H

  • What is the acreage of the field at left?

H

B


600-ft.

Circle

  • A (ft2) = pi x r2

  • A chemical needs to be applied to this field at a rate of 3.0-lbs/ac. How much chemical should be applied?

r


600-ft.

Sector

  • A (ft2) = pi x r2 x O

360


Irregularly Shaped Fields


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