TYPES OF MEASURING SCALES - SURVEYING (StudyCivilEngg.com)
TYPES OF MEASURING SCALES - SURVEYING
SUBJECT : SURVEYING
TYPES OF MEASURING SCALE
A measuring scale or a plotting scale is required for preparation of plans and for measuring distances from the plans. The measuring scales are classified as under.
- Plain scale
- Diagonal scale
- Chord scale
A good scale should satisfy the following requirements
- It should read to the required accuracy.
- It should be of suitable length, generally not longer than 300 mm.
- The scale should be accurately divided and numbered.
- The scale ratio or R.F. should be clearly written on the scale.
- The main divisions should preferably represent units, one-tenth of a unit and one-hundredth of a unit.
- The scale should be convenient to use. The distances are measured easily if the zero of the scale is placed between the units and its subdivisions.
Please note the difference between a measuring (plotting) scale and the scale of a map as mentioned in our post - DIFFERENCES BETWEEN A PLAN AND A MAP
Plain Scales
A plain scale measures some unit and its submultiples. For example, meter and decimeter, IS: 1491–1959 gives the specifications of plain scales made of varnished cardboard or of plastic. The code recommends 6 different types of plain scales for the use of engineers, architects and surveyors. As each scale has two measuring edges, 6 scales have 12 different reductions.
Below figure shows a plain scale, with a R.F. of 1: 500, to measure a distance upto 70 m. A distance of 44 m is marked on the scale.
Diagonal Scales
A diagonal scale reads some unit, its submultiple and further submultiple. For example, metres, decimetres and centimetres. Thus a unit, its one-tenth part and its one-hundred part can. be measured with a diagonal scale having metres, decimetres and centimetres.
Below figure shows a diagonal scale, with a R.F. of 1: 250, to measure distances upto 40 m. The space between the two edges is divided into 10 equal parts and horizontal parallel lines are drawn. The vertical lines indicate the divisions at 10 m. The length on the left of zero is divided into 10 subdivisions to indicate 1 m each. Likewise, the top edge is also divided into 10 subdivisions.
The subdivisions of the bottom edge and those of the top edge are joined diagonally. The intersections of the diagonal lines and the parallel lines give further parts of subdivisions. For example, the intersection of the fourth parallel line from the bottom with the diagonal represents 0.4 m. A distance of 34.4 m is marked on the scale. The scale shown measures in the units of 10 m, 1 m and 0.1 m.
It may be noted that diagonal lines and parallel lines divide each subdivision into 10 parts in this case, increasing 0.1 m to 1.0 m from bottom to top edge. According to IS: 1562–1962, the diagonal scales are designated as A, B, C and D
- The A-scale is 150 mm long, and it has only one scale, with R.F. equal tol: 1
- The scale B has a graduated length of 100 mm. The scales B have three different R.F. of 1: 25,000; 1: 50,000 and 1: 100,000
- The scale C has a graduated length of 150 mm. These scales also have the R.F. equal to those in B scales.
- The scale D has a graduated length of 150 mm. These scales have the R.F. of 1: 4,000; 1: 8,000; and 1: 10,000
Chord Scales
The chord scales are used to measure and to set out angles, without using a protractor. It is rectangular in shape just like a plain scale, but it is marked with letters C or C H O, and has graduations from 0 to 90°
The chord scale utilises the chord distances of a circular arc (Above Figure). The chord distance AB = 2R sin θ/ 2. If the distance AB is equal to the radius R, the angle θ is equal to 60°. Likewise, for other chord distances, the corresponding angles can be found. Figure below (a) shows the principle of the construction of the chord scale.
- A quadrant ADB of the circle of a suitable radius is drawn
- The arc length AB is divided into 9 equal parts, each part representing an angle of 10°
- The line AD is produced to the point C so that the distance AC is equal to the arc length AB
- With A as the centre and the arc length A -1 as a radius, an arc is drawn to cut the line AC at E
The distance AE is equal to the chord distance corresponding to an angle of 10°. The point E is marked 10°. Likewise, other arcs are drawn to locate points corresponding to 20°, 30°...90°. The 90° mark coincides with the point C. It may be noted that the chord of 60° is equal to the radius AD of the quadrant. Figure (b) shows a chord scale (For clarity, the subdivisions of degrees are not shown).
Use of Chord Scale for Measurement of Angles
The included angle θ between two lines PQ and PS (Below Figure (a) can be determined as explained below:
- With the centre at P and a radius equal to the distance AD from the zero to 60° mark of the chord scale shown in Figure (b), an arc is drawn to cut the lines PQ and PS at T and U, respectively.
- The distance TU is measured with a divider.
- If one leg is kept at the zero mark of the chord scale, the other leg gives the required angle.
Use of the Chord Scale for Setting out Angles
The chord scale shown in Figure (b) can be used to set out a line PS making an angle of, say 30° with PQ (Figure (b))
- With the centre at P and a radius equal to the distance AD from the zero to 60° mark on the chord scale, an arc is described cutting the line PQ at F.
- With the centre at F, and a radius equal to the distance from the zero to 30° mark of the chord scale, another arc is drawn to cut the first arc at G.
- If the points P and G are joined and the line PG is extended to the point S, the line PS makes an angle of 30° with PQ.
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