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 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 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 (ft 2 ) = B’ x H’ –A (ac) = B’ x H’ 43, ft 250-ft.

Parallelogram Formula –A (ft 2 ) = B’ x H’ –A (ac) = B’ x H’ 43,560 H B What is the area (ft 2 ), if the Base = 1200-ft and the Height = 300-ft?

Trapezoid Formula –A (ft 2 ) = H x [(a+b)/2] A B H What is the area of the trapezoid below? 700-ft. 300-ft. 375-ft.

Triangle A (ft 2 ) = ½ x B x H What is the acreage of the field at left? B H 400-ft. 325-ft.

Circle A (ft 2 ) = pi x r 2 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 (ft 2 ) = pi x r2 x O ft.

Irregularly Shaped Fields