Levelling and Contouring Questions and Answers

Answer: D

The RL of the underside of the beam is 53.903 m.

The height of instrument is the bench mark's RL plus the back sight. A staff held upside down against an overhead point is read as a negative staff reading, so the inverted fore sight is added to the height of instrument instead of subtracted:

\[ \begin{aligned} HI &= 48 + 1.258 = 49.258 \\ RL &= 49.258 + 4.645 = 53.903 \end{aligned} \]

The point must be above the line of sight, since the staff hangs down from the beam to it. 44.613 subtracts the fore sight as for an ordinary staff held on the ground, which would put the beam below the instrument. 46.936 and 51.581 match no consistent combination of the two readings.

Answer: B

The error of closure is 0.04 m.

The reduced level of a point is the starting level plus all back sights minus all fore sights, with the reading on the point itself counted as its final sight:

\[ \begin{aligned} RL &= 53.85 + 50.28 - 16.30 - 2.42 \\ &= 85.41\ \text{m} \end{aligned} \]

The bench mark's known elevation is 85.45 m, so the survey closes with an error of \(85.41 - 85.45 = -0.04\) m, a closing error of 0.04 m (the levels run 0.04 m low).

Leaving out the 2.42 m sight would give a nonsensical error of over 2 m, and 0.02, 0.06 and 0.08 m do not follow from the given sums.

Answer: C

The method is the rise and fall method.

In the rise and fall method, the difference between each staff reading and the one before it is worked out. If the new reading is smaller, the ground has risen by the difference; if larger, it has fallen. Each rise or fall is added to or subtracted from the previous reduced level (RL). The arithmetic check, sum of back sights minus sum of fore sights equals sum of rises minus sum of falls equals last RL minus first RL, checks every intermediate reading.

The height of instrument method finds each RL by subtracting the staff reading from the height of the line of collimation, not from differences between readings. 'Contour method' is not a method of reducing levels.

Answer: A

Straight, parallel and equally spaced contours represent a plane surface.

Contour spacing shows slope: equal spacing means a uniform slope, and straight parallel lines mean the surface does not bend. Together they describe an inclined plane, a surface of uniform gradient. (Contours on a level plane would not appear at all within it, since every point has the same elevation.)

A hill top shows as closed contours with higher values inside, and a depression as closed contours with lower values inside. Neither gives straight, parallel lines, so those options do not fit.

Answer: B

It represents a hill top.

A closed contour with one or more closed contours of higher elevation inside it shows ground rising towards the centre: a hill or a summit. The highest closed contour marks the top.

The reverse, closed contours with lower values inside, shows a depression such as a pond or a pit. A plane surface is shown by straight, parallel, equally spaced contours, not closed loops. So the hilly top is the only option that fits rising values towards the centre.

Answer: A

A fixed reference point of known elevation is a bench mark.

A bench mark (BM) is a permanent point whose reduced level is known, used as the starting or closing point in levelling. The Survey of India's great trigonometrical survey bench marks (GTS BMs) are the national ones; temporary bench marks are set up on a project for convenience.

A change point (also called a turning point) is a temporary point where both a fore sight and a back sight are taken while moving the instrument; its level is worked out, not known in advance. A reduced level is the elevation of a point, a value rather than a reference point.

Answer: A

The vertical distance of a point above or below the datum is its reduced level.

The reduced level (RL) of a point is its height relative to a chosen datum, usually mean sea level. Points above the datum have positive RLs and points below it negative ones. In levelling, the staff readings are 'reduced' to these levels, which is where the name comes from.

A bench mark is a reference point whose RL is known, not the distance itself. The height of instrument is the RL of the line of collimation of the level, a property of the instrument setting rather than of a point on the ground.

Answer: B

A staff reading taken on a point of known elevation is a back sight.

A back sight (BS) is the first reading taken after setting up the level, on a bench mark or a point whose reduced level is already known. Adding it to that RL gives the height of instrument: HI = RL + BS.

A fore sight is the last reading before moving the instrument, taken on a point whose level is to be found. 'Plane of sight' (line of collimation) is the horizontal line through the instrument, not a reading.

Answer: C

A staff reading on a point whose elevation is to be determined is a fore sight.

The fore sight (FS) is the last staff reading taken from a setting of the level, on a point whose reduced level is unknown, often a change point or the end of the line. Its RL is the height of instrument minus the fore sight: RL = HI − FS.

A back sight is taken on a point of known level. A back bearing belongs to compass traversing and is a direction, not a staff reading. A bench mark is a point of known level, not a reading.

Answer: A

The point is a change point (turning point).

When the distance or the ground makes it impossible to level from one setting, the level has to be shifted. A point is chosen on which a fore sight is taken from the old setting and a back sight from the new one. This point, which carries the levels forward and marks the shifting of the instrument, is the change point.

An intermediate point (intermediate sight) is any other staff station between the back sight and fore sight of one setting, at which only one reading is taken; the instrument is not shifted there. 'Middle point' and 'Closing point' are not standard terms for this.