Linear Measurement NG1H703 & BE1S204 David Harper

Introduction to today’s lecture Linear measurement – equipment Calculations – triangles Slope Correction Overcoming obstacles to linear measurement Worked examples

Linear measurement - equipment Steel tape measure -30 metres -complete with tension handle. Note – the tension handle applies a constant tension to the tape and thus virtually eliminates any error due to the tape being allowed to sag.

Linear measurement – equipment (cont.) Ranging Rods – brightly coloured rods approx. 2.0 m long used for the establishment of straight lines, especially when the distance to be measured exceed the length of the tape.

Linear measurement – equipment (cont.) Station or Reference Pegs – usually softwood 50mm square and at least 500mm long.

Linear measurement – equipment (cont.) 0/60

Linear measurement – equipment (cont.) Sundries: Claw hammer Nails Pocket spirit level Chalk String line Bag- large enough to hold all items except ranging rods and station pegs Stands for supporting ranging rods on firm ground

Calculations - triangles

Calculations – triangles (cont.)

Calculations – triangles (cont.)

Calculations – triangles (cont.)

Calculations – triangles (cont.)

Calculations – triangles (cont.)

Calculations – triangles (cont.) – Pythagoras’ Theorem

Calculations – triangles (cont.) – Pythagoras’ Theorem

Calculations – triangles (cont.) – Pythagoras’ Theorem

Calculations – triangles (cont.) – Pythagoras’ Theorem

Calculations – triangles (cont.) – Pythagoras’ Theorem

Calculations – triangles (cont.) – Pythagoras & Isosceles triangle If the base AC is bisected at B, then lines AB = BC and the line extended through D then the angle DBC = DBA = 900

Calculations – triangles (cont.) – Equilateral triangles

Calculations – triangles (cont.) X N.B. The acronym S.O.H.C.A.H.T.O.A.

Calculations – triangles (cont.) – Similar triangles

Calculations – triangles (cont.) – Slope Correction or d² = s² - h²

Calculations – Slope Correction (Cont.) d C h

Calculations – Slope Correction (cont.) – Step Chaining

Calculations – Slope Correction (cont.) – Step Chaining (cont.)

Overcoming obstacles to linear measurement

Overcoming obstacles to linear measurement

Overcoming an obstacle which obstructs measurement

Overcoming an obstacle which obstructs measurement (cont.)

Overcoming an obstacle which obstructs measurement (cont.)

Overcoming an obstacle which obstructs measurement (cont.) X

Overcoming an obstacle which cannot be measured around

Overcoming an obstacle which cannot be measured around (cont.) =XD1

Measurement: Mistakes and Checks

Measurement: Mistakes and Checks (cont.) if

Worked examples – Measurement of a straight line

Worked examples – Measurement of a straight line (cont.)

Worked examples – Measurement around an obstacle

Worked examples – Measurement around an obstacle (cont.)

Worked examples – Measurement around an obstacle (cont.)

Worked examples – Measurement around an obstacle (cont.)

Summary of today’s lecture Linear measurement – equipment Calculations – triangles Slope Correction Overcoming obstacles to linear measurement Worked examples