FW_3 - Laying Out and Measuring Lines and Angles by Tape

FIELDWORK # 3 LAYING NG OUT AND MEASURING LINES AND ANGLES BY TAPE Objective:

To familiarize students with the use of a tape in measuring and laying out angles. To familiarize students with the use of a tape in laying out perpendicular and parallel lines. This is a group activity.

Instruments: 1 Steel Tape Marking Pins 2 Range Poles UST Field / Benavides Park

Site: Procedure:

Establishing Perpendicular Lines: A. 1. 2.

3.

4. 5.

3-4-5 Method Given Line: XY Establish line XY. Distance XY should be more than 5 meters. Lay out a distance of 3 meters along line XY from point A. Mark it with a marking pin an and call it as point B. From point A, lay out a distance of 4 meters; make a loop at the end to have the exact full meter mark and connect the other end of the tape to point with a distance equal to 5 meters. Then mark the loop point with marking pin and designate it as point C. ∠ BAC should be equal to 90°. Check the accuracy by measuring the angle laid. Compute the relative precision.

Given Point:

A (along line XY) loop

C

L2 = 4 meters

X

L3 = 5 meters

A

L1 = 3 meters

B

Y

FIGURE: Establishing Perpendicular Lines (3-4-5 (3 Method)

B. 1. 2. 3.

4.

5. 6. 7.

Chord Bisection Method: Given Line: JK Establish line JK. Hold firmly the zero end of the tape at point M. Unwind the tape up to the length which is more than sufficient to intersect the given line at two separate points. From point M, swing the tape and mark the points of intersection with the given line. Designate them as points N and O. Take note of the lengths hs of MN and MO. Measure distance NO and mark the midpoint as point P. ∠ MPN and ∠ MPO should be equal to 90°. Check the accuracy by measuring the angle laid. Compute the relative precision.

Given Point:

M (outside line JK) M

L1 L3 N

L2

O

J

K

FIGURE: Establishing Perpendicular Lines (Chord Bisection Method) FW#3: LAYING OUT AND MEASURING LINES AND ANGLES BY TAPE

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FORMULA: Discrepancy = θ – Φ Mean Angle

=

Relative Precision

where:

θ = angle laid, 90°

θ+Φ 2 =

Φ = angle measured

lDiscrepancyl Mean Angle

Establishing Parallel Lines: Given Line: DE Given Point: F (outside line DE) 1. Establish line DE and point F. 2. At point F, hold the zero end of the tape. 3. Unwind the tape such that it is sufficient to intersect the given line. 4. Swing the tape until a whole meter tape m mark ark intersects the given line. Mark the point of intersection with marking pin and designate it as point F’ 5. Mark also with marking pin the midpoint of the tape and designate it as point O. 6. Let one member hold the tape at point O. Transfer the two ends of the tape in opposite directions with midpoint still at its original position. Designate the new point on the given line as point G’ and the new position of the zero end as point G. 7. Measure lines FG’ and GF’.

F

G

O

L2

L3

L1

D

G’

F’

E

FIGURE: Establishing Parallel Lines FORMULA: Discrepancy = Length FG’ – Length GF’ or Discrepancy = Length 2 – Length 3

FW#3: LAYING OUT AND MEASURING LINES AND ANGLES BY TAPE

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Laying out a given horizontal acute angle by tape. 1. 2. 3.

4. 5.

Put a marking pin at any point on the ground. Call this as point A. This will be the vertex of the angle. From point A, lay out a 20-meter meter distance and mark the end with a marking pin and designate it as a point B. From point A, lay out a distance of 20cosθ; make a loop at the end to hav havee the exact full meter mark and connect the other end of the tape to point with a distance equal to 20sinθ. Then mark the loop point with marking pin and designate it as point C. sample. The angle laid is ∠ BAC which is equal to the given samp Let θ = 30° for the first trial and 45° and 90° for the second and third trials respectively. 20cosθ

C

A

FORMULA:

loop

θ

Laying out angle: AB = 20meters BC = 20sinθ AC = 20cosθ

20sinθ

D=20m

B

Figure: Laying out horizontal angle. Measuring a horizontal angle by chord bisection method: 1. Use the same angles laid from part 1. 2. Place the two range poles at points B and C. 3. With a certain distance from point A, say 8 meters, set points along lines AB and AC an and mark them with marking pins as points B’ and C’ respectively. 4. Measure the distance points B’ and C’. 5. Compute for ∠ BAC. 6. Repeat the same procedure for the 45° and 60° angles. 7. Compute the discrepancy and relative precision for each trial.

L A

A’

Measuring angle:

C

x 1 sin ∠BAC = 2 2 L

φ X

L Figure: Measuring horizontal angle.

B’ Where:

x L A B’ and C’ Φ

Discrepancy = θ − φ •

Mean _ Angle =

θ +φ 2

B

= =

chord distance (B’C’) length of the tape swung

= vertex of ∠ BAC = crossing points where the arc intersects lines AB and AC angle to be measured ( ∠ BAC) = Re lative Pr ecision =

Discrepancy MeanAngle

Instead of using mean angle in solving the relative precision, you may use the value of the given angle.

FW#3: LAYING OUT AND MEASURING LINES AND ANGLES BY TAPE

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FIELDWORK REPORT # 3 Title: _______________________________ Yr. & Sec.: Date Performed: Date Submitted: Weather Condition:

Group No. Time Started: Time Finished: Actual Site:

DUTY/IES

GROUP MEMBERS

DATA & RESULTS: Laying out horizontal angles: TRIAL 1

TRIAL 2

D (meters) θ (°) AB (meters) BC (meters) AC (meters)

Measuring horizontal angles: TRIAL 1

TRIAL 2

L (meters) θ(°) X or B’C’ (meters) Φ(°) Discrepancy ( ° ) Mean Angle ( ° ) Relative Precision

FW#3: LAYING OUT AND MEASURING LINES AND ANGLES BY TAPE

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Establishing Perpendicular Lines 3-4--5 Method Chord Bisection Method L1 (meters) L2(meters) L3 (meters) θ (°) Φ (°) Discrepancy (°) Mean Angle (°) Relative Precision

Establishing Parallel Lines

-

DRAWING/S: SOURCES OF ERRORS: REMARK/S:

FW#3: LAYING OUT AND MEASURING LINES AND ANGLES BY TAPE

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