land surveying chapter 2 leveling p2

Land Surveying / Engineering Surveying I

Chapter 4 : Levelling (Part 2)

3.7 Rise and Fall Method3.71 Sample Loop 13.72 Booking Observations3.73 Reducing Level (Rise & Fall)3.74 Loop Misclosure3.75 Adjusting Misclosure

3.8 Height of Collimation Method3.81 Reducing Level (HPC)3.82 Loop Misclosure

Contents

Sample Loop 1 shows all the readings for the leveling sequence recorded in a rise & fall field book.

The calculation proceeds in the following manner, in which the height of a point is related to that of a previous point.

3.7 Rise and Fall Method

BM A

CP 1

CP 2

CP 3

Kerb

Post

Kerb

Setup 1

Setup 2

Setup 3

Setup 4

3.71 Sample Loop 1

BM A

CP 1CP 2

CP 3

Kerb

Post

KerbSetup 1

BS IS FS Point

BM A

CP 1

1.321

3.986

3.72 Booking Observation

BM A

CP 1CP 2

CP 3

Kerb

Post

KerbSetup 1

Setup 2

BS IS FS Point

1.321 BM A

3.986 CP 1

Kerb

Post

CP 2

2.567

1.255

3.658

0.670

3.72 Booking Observation

BM A

CP 1CP 2

CP 3

Kerb

Post

KerbSetup 1

Setup 2

Setup 3

BS IS FS Point

1.321 BM A

2.567 3.986 CP 1

1.255 Kerb

3.658 Post

0.670 CP 2

Kerb

CP 3

3.492

2.586

1.542

3.72 Booking Observation

BM A

CP 1CP 2

CP 3

Kerb

Post

KerbSetup 1

Setup 4

Setup 2

Setup 3

BS IS FS Point

1.321 BM A

2.567 3.986 CP 1

1.255 Kerb

3.658 Post

3.492 0.670 CP 2

2.586 Kerb

1.542 CP 3

BM A2.643

3.817

3.72 Booking Observation

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 CP 1

1.255 Kerb3.658 Post

3.492 0.670 CP 22.586 Kerb

2.643 1.542 CP 33.817 BM A

3.73 Reducing Level (Rise & Fall)

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 2.665 47.335 CP 1

1.255 Kerb3.658 Post

3.492 0.670 CP 22.586 Kerb

2.643 1.542 CP 33.817 BM A

3.73 Reducing Level (Rise & Fall)

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 2.665 47.335 CP 1

1.255 1.312 48.647 Kerb3.658 Post

3.492 0.670 CP 22.586 Kerb

2.643 1.542 CP 33.817 BM A

3.73 Reducing Level (Rise & Fall)

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 2.665 47.335 CP 1

1.255 1.312 48.647 Kerb3.658 2.403 46.244 Post

3.492 0.670 CP 22.586 Kerb

2.643 1.542 CP 33.817 BM A

3.73 Reducing Level (Rise & Fall)

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 2.665 47.335 CP 1

1.255 1.312 48.647 Kerb3.658 2.403 46.244 Post

3.492 0.670 2.988 49.232 CP 22.586 Kerb

2.643 1.542 CP 33.817 BM A

3.73 Reducing Level (Rise & Fall)

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 2.665 47.335 CP 1

1.255 1.312 48.647 Kerb3.658 2.403 46.244 Post

3.492 0.670 2.988 49.232 CP 22.586 0.906 50.138 Kerb

2.643 1.542 CP 33.817 BM A

3.73 Reducing Level (Rise & Fall)

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 2.665 47.335 CP 1

1.255 1.312 48.647 Kerb3.658 2.403 46.244 Post

3.492 0.670 2.988 49.232 CP 22.586 0.906 50.138 Kerb

2.643 1.542 1.044 51.182 CP 3

3.817 BM A

3.73 Reducing Level (Rise & Fall)

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 2.665 47.335 CP 1

1.255 1.312 48.647 Kerb3.658 2.403 46.244 Post

3.492 0.670 2.988 49.232 CP 22.586 0.906 50.138 Kerb

2.643 1.542 1.044 51.182 CP 33.817 1.174 50.008 BM A

3.73 Reducing Level (Rise & Fall)

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 2.665 47.335 CP 1

1.255 1.312 48.647 Kerb3.658 2.403 46.244 Post

3.492 0.670 2.988 49.232 CP 22.586 0.906 50.138 Kerb

2.643 1.542 1.044 51.182 CP 33.817 1.174 50.008 BM A

10.023 10.015

3.73 Reducing Level (Rise & Fall)

When the Initial RL column of the table has been completed, a check on the arithmetic involved is possible and must always be applied.

This check is BS - FS = RISES - FALLS

= Last RL – First RL

3.73 Reducing Level (Rise & Fall)

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 2.665 47.335 CP 1

1.255 1.312 48.647 Kerb3.658 2.403 46.244 Post

3.492 0.670 2.988 49.232 CP 22.586 0.906 50.138 Kerb

2.643 1.542 1.044 51.182 CP 33.817 1.174 50.008 BM A

10.023 10.015

0.008

3.73 Reducing Level (Rise & Fall)

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 2.665 47.335 CP 1

1.255 1.312 48.647 Kerb3.658 2.403 46.244 Post

3.492 0.670 2.988 49.232 CP 22.586 0.906 50.138 Kerb

2.643 1.542 1.044 51.182 CP 33.817 1.174 50.008 BM A

10.023 10.015 6.250 6.242

0.008

3.73 Reducing Level (Rise & Fall)

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 2.665 47.335 CP 1

1.255 1.312 48.647 Kerb3.658 2.403 46.244 Post

3.492 0.670 2.988 49.232 CP 22.586 0.906 50.138 Kerb

2.643 1.542 1.044 51.182 CP 33.817 1.174 50.008 BM A

10.023 10.015 6.250 6.242

0.008 0.008

3.73 Reducing Level (Rise & Fall)

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 2.665 47.335 CP 1

1.255 1.312 48.647 Kerb3.658 2.403 46.244 Post

3.492 0.670 2.988 49.232 CP 22.586 0.906 50.138 Kerb

2.643 1.542 1.044 51.182 CP 33.817 1.174 50.008 BM A

10.023 10.015 6.250 6.242

0.008 0.008 0.008

3.73 Reducing Level (Rise & Fall)

BS IS FS Rise Fall RL Remarks1.321 50.000 BM A2.567 3.986 2.665 47.335 CP 1

1.255 1.312 48.647 Kerb3.658 2.403 46.244 Post

3.492 0.670 2.988 49.232 CP 22.586 0.906 50.138 Kerb

2.643 1.542 1.044 51.182 CP 33.817 1.174 50.008 BM A

10.023 10.015 6.250 6.242

0.008 0.008 0.008

3.73 Reducing Level (Rise & Fall)

Misclosure• The amount by which the measured height difference (DHmeas) differs

from the known height difference derived from the RLs of the starting

and finishing benchmarks (DHknown)

Misclosure = DHmeas – Dhknown

Misclosure = Last R.L. – Original R.L.

3.74 Loop Misclosure

3.74 Loop Misclosure

Acceptable misclosures as follows :

• Small misclosures in closed level loops are expected because of the

accumulation of errors.

• If the misclosure is small, it can be adjusted.

• If the misclosure is greater than the allowable misclosure then the

levelling must be repeated.

• The usual method of correction is to apply an equal, but cumulative,

amount of the misclosure to each instrument position.

• The sign of the adjustment being opposite to that of the misclosure.

The amount of misclosure we are prepared to accept depends on the accuracy we are hoping to achieve.

For routine levelling, the allowable misclosure is given by :

Allowable misclosure = ± mn mm

where m is a constant, and;n is the number of instrument

positions.

3.74 Loop Misclosure

From the loop, the misclosure is +8 mm.

Therefore, the allowable misclosure is ± 54 = ± 10 mm.

The misclosure of +8 mm is smaller than allowable misclosure.

3.75 Adjusting Misclosure

Adjustment is carried out to ensure that the measured and

known RLs of the closing benchmark agree.

The misclosure is linearly distributed according to the

number of set-ups.

The adjustment per set-up for the previous example is

( - 0.008 / 4 ) = - 0.002

3.75 Adjusting Misclosure

BS IS FS RL Adj. Adj. RL Remarks1.321 50.000 0.000 50.000 BM A

2.567 3.986 47.335 -0.002 47.333 CP 1

1.255 48.647 Kerb

3.658 46.244 Post

3.492 0.670 49.232 CP 2

2.586 50.138 Kerb

2.643 1.542 51.182 CP 3

3.817 50.008 BM A

-1x(0.008/4)

3.75 Adjusting Misclosure

BS IS FS RL Adj. Adj. RL Remarks1.321 50.000 0.000 50.000 BM A

2.567 3.986 47.335 -0.002 47.333 CP 1

1.255 48.647 -0.004 48.643 Kerb

3.658 46.244 -0.004 46.240 Post

3.492 0.670 49.232 -0.004 49.228 CP 2

2.586 50.138 Kerb

2.643 1.542 51.182 CP 3

3.817 50.008 BM A

-2x(0.008/4)

3.75 Adjusting Misclosure

BS IS FS RL Adj. Adj. RL Remarks1.321 50.000 0.000 50.000 BM A

2.567 3.986 47.335 -0.002 47.333 CP 1

1.255 48.647 -0.004 48.643 Kerb

3.658 46.244 -0.004 46.240 Post

3.492 0.670 49.232 -0.004 49.228 CP 2

2.586 50.138 -0.006 50.132 Kerb

2.643 1.542 51.182 -0.006 51.176 CP 3

3.817 50.008 BM A

-3x(0.008/4)

3.75 Adjusting Misclosure

BS IS FS RL Adj. Adj. RL Remarks1.321 50.000 0.000 50.000 BM A

2.567 3.986 47.335 -0.002 47.333 CP 1

1.255 48.647 -0.004 48.643 Kerb

3.658 46.244 -0.004 46.240 Post

3.492 0.670 49.232 -0.004 49.228 CP 2

2.586 50.138 -0.006 50.132 Kerb

2.643 1.542 51.182 -0.006 51.176 CP 3

3.817 50.008 -0.008 50.000 BM A

-4x(0.008/4)

3.75 Adjusting Misclosure

BS IS FS RL Adj. Adj. RL Remarks1.321 50.000 0.000 50.000 BM A

2.567 3.986 47.335 -0.002 47.333 CP 1

1.255 48.647 -0.004 48.643 Kerb

3.658 46.244 -0.004 46.240 Post

3.492 0.670 49.232 -0.004 49.228 CP 2

2.586 50.138 -0.006 50.132 Kerb

2.643 1.542 51.182 -0.006 51.176 CP 3

3.817 50.008 -0.008 50.000 BM A

3.75 Adjusting Misclosure

3.8 Height of Collimation Method

The level book for the reduction of the leveling is shown in the height of collimation form.

This method of reducing levels is based on the HPC being calculated for each instrument position.

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 CP 1

1.255 Kerb3.658 Post

3.492 0.670 CP 22.586 Kerb

2.643 1.542 CP 33.817 BM A

3.81 Reducing Level (HPC)

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 47.335 CP 1

1.255 Kerb3.658 Post

3.492 0.670 CP 22.586 Kerb

2.643 1.542 CP 33.817 BM A

3.81 Reducing Level (HPC)

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 Kerb3.658 Post

3.492 0.670 CP 22.586 Kerb

2.643 1.542 CP 33.817 BM A

3.81 Reducing Level (HPC)

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 Post

3.492 0.670 CP 22.586 Kerb

2.643 1.542 CP 33.817 BM A

3.81 Reducing Level (HPC)

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 CP 22.586 Kerb

2.643 1.542 CP 33.817 BM A

3.81 Reducing Level (HPC)

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 49.232 CP 22.586 Kerb

2.643 1.542 CP 33.817 BM A

3.81 Reducing Level (HPC)

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 52.724 49.232 CP 22.586 Kerb

2.643 1.542 CP 33.817 BM A

3.81 Reducing Level (HPC)

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 52.724 49.232 CP 22.586 50.138 Kerb

2.643 1.542 CP 33.817 BM A

3.81 Reducing Level (HPC)

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 52.724 49.232 CP 22.586 50.138 Kerb

2.643 1.542 51.182 CP 33.817 BM A

3.81 Reducing Level (HPC)

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 52.724 49.232 CP 22.586 50.138 Kerb

2.643 1.542 53.825 51.182 CP 33.817 BM A

3.81 Reducing Level (HPC)

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 52.724 49.232 CP 22.586 50.138 Kerb

2.643 1.542 53.825 51.182 CP 33.817 50.008 BM A

3.81 Reducing Level (HPC)

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 52.724 49.232 CP 22.586 50.138 Kerb

2.643 1.542 53.825 51.182 CP 33.817 50.008 BM A

3.81 Reducing Level (HPC)

Arithmetic Check:

With the initial RL column in the table completed, the following check can be applied

BS - FS = Last RL – First RL

The second check is given by

IS + FS + RLs except first = [each HPC x no. of applications]

3.82 Loop Misclosure

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 52.724 49.232 CP 22.586 50.138 Kerb

2.643 1.542 53.825 51.182 CP 33.817 50.008 BM A

10.023 10.015

3.81 Reducing Level (HPC)

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 52.724 49.232 CP 22.586 50.138 Kerb

2.643 1.542 53.825 51.182 CP 33.817 50.008 BM A

10.023 10.015

0.008

3.81 Reducing Level (HPC)

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 52.724 49.232 CP 22.586 50.138 Kerb

2.643 1.542 53.825 51.182 CP 33.817 50.008 BM A

10.023 10.015

0.008

3.82 Loop Misclosure

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 52.724 49.232 CP 22.586 50.138 Kerb

2.643 1.542 53.825 51.182 CP 33.817 50.008 BM A

10.023 10.015

0.008 0.008

3.82 Loop Misclosure

BS - FS = 10.023 – 10.015= 0.008 m

Last RL – First RL = 50.008 – 50.000= 0.008 m

BS - FS = Last RL – First RL

3.82 Loop Misclosure

IS + FS + RLs except first

3.82 Loop Misclosure

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 52.724 49.232 CP 22.586 50.138 Kerb

2.643 1.542 53.825 51.182 CP 33.817 50.008 BM A

10.023 7.499 10.015

0.008 0.008

3.82 Loop Misclosure

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 52.724 49.232 CP 22.586 50.138 Kerb

2.643 1.542 53.825 51.182 CP 33.817 50.008 BM A

10.023 7.499 10.015 342.786

0.008 0.008

3.82 Loop Misclosure

IS + FS + RLs except first

= 7.499 + 10.015 + 342.786= 360.300

3.82 Loop Misclosure

[each HPC x no. of applications]

3.82 Loop Misclosure

BS IS FS HPC RL Remarks1.321 51.321 50.000 BM A2.567 3.986 49.902 47.335 CP 1

1.255 48.647 Kerb3.658 46.244 Post

3.492 0.670 52.724 49.232 CP 22.586 50.138 Kerb

2.643 1.542 53.825 51.182 CP 33.817 50.008 BM A

10.023 7.499 10.015

0.008 0.008

3.82 Loop Misclosure

S [each HPC x no. of applications]

The first HPC of 51.321 m has been used once to calculate the reduced levels of CP1.

The second of 49.902 m has been used 3 times to calculate the reduced levels of Kerb, Post and CP2.

The third of 52.724 m has been used twice to calculate the reduced levels of Kerb and CP3.

The last HPC of 53.825 m has been used once to close the levels onto BM A.

= [51.321x1]+[49.902x3]+[52.724x2]+[53.825x1] = 360.300

3.82 Loop Misclosure

After applying the check, any acceptable misclosure is distributed as for the rise and fall method.

3.82 Loop Misclosure