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.”

19"

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.

9

5

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

Taping• Equipment:

– 100-ft. steel tape, – chaining pins,– range poles,– plumb bobs,– hand level

• Most accurate method of determining distance.

• Accuracy + .03 %.

• Requires:

• Specialized equipment

• Minimum of two surveyors

• Skill

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

750-ft

250-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?

Trapezoid

• Formula– A (ft2) = H x [(a+b)/2] A

B

H What is the area of the trapezoid below?

700-ft.

300-ft.

375-ft.

Triangle

• A (ft2) = ½ x B x H• What is the acreage of

the field at left?

B

H400-ft.

325-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

600-ft.

Irregularly Shaped Fields