What is height of instrument and Rise & fall method of levelling?

To obtain the reduced level of a point in the field from staff readings, we have 2 methods:

Height of Instrument or Collimation method Rise and fall method.

Height of instrument method deals with obtaining the RL of the line of collimation by adding BS reading of a point whose RL is known. The RL of line of collimation is called Height of Instrument. From this, the staff readings of all intermediate stations is subtracted to get the RL at those points.

Now, what is the rise and fall method?

Here, instead of calculating the height of instrument, we calculate the difference of staff readings at the two stations. The two stations where staff readings are taken are such that we know the RL of ground of one station and we want to find the RL of other.

A level is set at such a position from where max. no of stations can be visible. Now, the staff is placed at the station whose RL is known and the reading is observed say R1. The staff is then transferred to a station whose RL is to be determined and the reading is observed say R2.

Now, if R1 > R2, it means ground at former station is lower than ground at latter station. So, there is rise in ground surface

Similarly, if R2 > R1, the ground at latter station is deeper / lower than ground at former station. So there is a fall in ground surface

Now that you know what rise and fall is, the question arises how to use this concept to obtain RL of various successive stations?

After taking readings at two stations, the difference of readings i.e. (R1 - R2) is added to the RL of first station to get the RL of second station

=> RL of Station 1 +(R1-R2) = RL of Station 2

Now to find the RL of third station, the staff reading is observed say R3 and (R2-R3) is obtained.

Then,

RL of station 2 + (R2-R3) = RL of station 3

This can be used indefinitely till the last point whose RL is required is reached.

The difference of staff readings is nothing but the rise or fall of ground.

if fore sight reading is greater than back sight reading, there is fall in ground surface. This fall is then subtracted from RL of previous station to obtain RL of next station

This method is a bit laborious as staff reading at each station after the first, is compared with that of the preceding station

There are 3 checks for arithmetical accuracy. These are the “sum of back sight readings minus sum of fore sight readings should be equal to the difference between the sum of rises and sum of falls which in turn should be equal to the difference between first RL and last RL?

Height of Instrument :

It is the method which deals with the obtaining of RL of the line of collimation by adding BS reading of a known RL point. Thus, RL of the line of collimation is called the Height of Instrument. It is always measured from the benchmark. Hence the benchmark is the point on the sea derived from mean sea level.

- method to calculate RL;

height of collimation (H of C) = reduced level(R.L.) + backsight (B.S.)

reduced level (R.L.) = height of collimation (H of C) - foresight (F.S.)

reduced level (R.L.) = height of collimation (H of C) - intermediate sight (I.S.)

Rise & fall method :

It is the method which gives the difference of elevation between consecutive points by comparing each point after the first that immediately preceding it. Rise and fall are indicated by the difference in staff reading. After that RL is found by adding the rise to or subtracting the fall from the reduced level of the preceding point.

- method to calculate RL;

fall (F) = foresight (F.S.) - backsight (B.S.)

fall (F) = intermediate sight (I.S.) - backsight (B.S.)

rise (R) = backsight (B.S.) - foresight (F.S.)

reduced level (R.L.) = precede reduced level + rise (R)

reduced level (R.L.) = precede reduce level - fall (F)

In simple English,

The height of instrument always measures form benchmark.

The benchmark is a Point on the sea derived from mean sea level.

Rise and Fall method:

The rise and fall of ground between two adjacent ranging rod are measures with levelling staff.

High reading= fall of ground level. Low reading= rise of ground level.

RL = HI - FS

RL= Reduced level

HI = Height of instrument

FS= Foresight distance.

Height of Instrument (HI) method: consider the readings taken in the operation shown below:

Reduce level can be computed using the following expression:

RL of a point = HI - FS = ( RLBM +BS) - FS

Arithmetic check: ΣBS – ΣFS= Last RL – first R

Where:

RL: Reduce Level

HI: height of instrument

FS: foresight

BS: Back sight

BM: Bench Marks

Rise and fall (RF) method: the rise or fall of the ground between successive rod stations is considered. For the same instrument set up,

If 2nd rod reading > first rod reading ⇒ fall

If 2nd rod reading < first rod reading ⇒ rise

Then RL of 2nd station = RL of first station - fall or

RL of first station + rise