6 Differential Level

7/30/2019 6 Differential Level

1/27

Differential Leveling


2/27

Introduction

Differential surveying is used to

determine the difference in

elevation between two or morepoints.

It is commonly used to establish

the elevation of a benchmark

referenced to an existing

benchmark.

It is also useful for comparing the

elevation of several points or

objects.


3/27

Differential Leveling Example

An example of

comparing theelevation of multiple

points is setting the

top of the forms

before placing

concrete.

In common practice, abacksight would be

recorded from the

bench mark and the

target would be set for

the desired elevation

of the forms.

The rod holder would then place the rod at

several point along the forms to determine if

they were at the correct height.


4/27

Establishing A Benchmark

Another use of differential leveling

is establishing the elevation of abenchmark.

When the existing benchmark and

the location of the new benchmark

can be seen from one instrument

position, the procedure is very

simple. The instrument is set up halfway

between the points and leveled.

A rod reading is taken on the

existing benchmark, this iscalled a backsight.

The backsight reading is added

to the elevation of the

benchmark to establish the

instrument height (reference

line).

HI = Elevation + Backsight


5/27

Benchmark Example-cont.

In this example the benchmark

elevation is 850.47 feet and the

backsight is 3.56 ft.

The height of the instrument is:

HI = 850.47 ft + 3.56 ft = 854.03 ft


6/27

Benchmark Example-cont.

The instrument isrotated until it is alignedwith the second

benchmark. A rod reading

(foresight) is recordedfor the secondbenchmark.

In this example the

foresight is 5.21 ft.

The rod reading is subtracted from the height of

the instrument to find the elevation of the second

benchmark.

The elevation is:

Elev = HI - FS

= 854.03 ft - 5.21 ft

= 848.82 ft

BM1 is 1.65 feet higher

than BM2.


7/27

Benchmark Example TP

When both

benchmarks cannotbe reached from one

instrument position,

turning points are

used.

Because a turning

point is a temporarybenchmark, it must

be a stable structure.

A backsight is taken on BM1. The 4.31 is added to the elevation of the bench

mark to find the height of the instrument (104.31).


8/27

Benchmark Example TP-cont.

A turning point is establishedand a foresight is recorded

(4.92).

The foresight is subtracted from

the height of instrument to

determine the elevation of the

turning point (99.39) .

Then the instrument is moved toa point between the turning

point and the next station.

In this example the next station

is BM2.


9/27


A backsight is taken on theturning point (4.22).

The backsight is added to theelevation of the turning point tofind the new instrument height(103.61).

The instrument is rotated and aforesight is recorded on BM2.


10/27


The foresight on BM2 (2.35) is

subtracted from the instrument

height to determine the

elevation of BM2 (101.08)

Tables are an excellent way oforganizing numbers.

Surveyors have developed a

standard table for differential

leveling.


11/27

Differential Leveling Table

STA BS HI FS ELEV

BM1 4.31 104.31 100.0TP 4.22 103.61 4.92 99.39

BM2 2.53 101.08

Five columns are used.

STA = Station IdentificationBS = Backsight

HI = Instrument Height

FS = Foresight

ELEV = Elevation

The table for this example:101.08 - 100.0 = 1.08BM2 is 1.08 feet higher than BM1


12/27


Assuming no errors occurred during the survey, BM2 is 1.08 feet

higher than BM1.

This is not a good assumption.

Differential leveling uses three checks for errors.


13/27

Three Checks For Error

1. Closing the loop

2. Note check

3. Allowable error check


14/27

1. Closing the Loop

To close the loop the survey is continued back to the beginning.

In the previous example, surveying from BM1 to BM2 resulted in adifference in elevation between the two benchmarks of 1.08 feet.

Surveying from BM2 to BM1 should result in the same difference in

elevation.

Any difference in elevation for BM1 between the initial elevation of

BM1 and the closing elevation of BM1 is error.


15/27

Closing the Loop Example

The steps are the same.

The instrument is moved and a backsight is recorded for BM2 (3.27).


16/27

Closing the Loop Example-cont.

The instrument is rotated.

A foresight is recorded on TP2 (2.21) .


17/27


The instrument is moved between TP2 and BM1

A BS is recorded on TP2 (3.29).


18/27


The instrument is rotated.

The loop is closed by recording a foresight on BM1 (5.42).


19/27

Differential Table

STA BS HI FS Elev

BM1 4.31 104.31 100

TP1 4.22 103.61 4.92 99.39

BM2 3.27 104.35 2.53 101.08

TP2 3.29 105.43 2.21 102.14

BM1 5.42 100.01

When the closing data is entered into the table thefirst error check is completed.

The second check for error is called the note check.

The note check uses an equation:

| BS - FS |=| BM1i - BM1c |

If the equation is true, there is no math error in the

notes.

If the equation is not true, the notes have a math error.

What should you do if the note check is not true?


20/27

2. Note Check

The note check statement is true.

The 0.01 difference in the elevation of BM1i and BM1c is not

caused by a math error in the notes

BM1i

BM1c

STA BS HI FS Elev

BM1 4.31 104.31 100.00

TP1 4.22 103.61 4.92 99.39

BM2 3.27 104.35 2.53 101.08

TP2 3.29 105.43 2.21 102.14

BM1 5.42 100.01

15.09 - 15.08

0.01 = 0.01

OK


21/27

3. Allowable Error of Closure

The third check for error is called the allowable error.

Early surveyors realized that the sources of error were so large that itwould be impossible to control for all of them.

It is common practice for the agency/individual contracting the work to

specify the acceptable level of error.

Professional standards may also specify allowable error.

A simple one is called the allowable error and it is based on an

equation:

AE = k M

k = 1.0 to 0.01

M = Distance surveyed (miles)


22/27

Allowable Error of Closure-cont.

For the differential example, the distance between BM1 and BM2 waspaced and a distance of 1.100 feet was recorded.

A k value of 0.1 is acceptable for general work.

AE = k M = 0.1 1,100 x 25280

= 0.1 x 0.417 = 0.04

Is pacing an appropriate method for measuring distance?


23/27

Allowable Error of Closure-cont.

The actual error was 0.01 and the allowable error is 0.04, thereforethe survey is acceptable.

0.01 < 0.0


24/27

The Complete Data Table

STA BS HI FS Elev

BM1 4.31 104.31 100.00

TP1 4.22 103.61 4.92 99.39

BM2 3.27 104.35 2.53 101.08

TP2 3.29 105.43 2.21 102.14

BM1 5.42 100.01

15.09 - 15.08

0.01 = 0.01

OK

AE = k M = 0.1 1100 x 2

5280= 0.06

0.01 < 0.06


25/27

Allowable Error-cont.

In this example the actual error was less than the allowable error.

What should happen if the actual error is greater than the allowable error?


26/27

Allowable Error-cont.

What would be the conclusion about the error in the data if a higher

standard was used, k = 0.01.

AE = 0.01 x 0.417 = 0.004

0.01 > 0.004

The data would be unacceptable.


27/27

Documents

6 Differential Level