PHILADELPHIA UNIVERSITY

Faculty of Engineering Department of Civil Engineering.

SURVEYING

Chapter 2 Measurements

Chapter 2

Measurements

ERE 371

Measurement Science Introduction • Observations

• measurements

-The difference between observations and measurements :

• Observation work: work that is done to get one single value directly and without correction of the device or surveying tool . • Measurement works: are the actions which take place (before, during and after) the observation process for the

final surveyed value (closest to the true value).

- Works before observation : Calibration - set the device to the point. - During the observation: allocating, tightening tape - reading device. -Work after observation: taking averages of readings - make tables accounts. • Any person can carry out the observation, but surveying engineer which is only able to carry out the observation and correct the

measurements.

Types of measurements:

1- Linear: Distance , 3-d coordinates Point location , Area and Volume

2- Non-linear (Angular): Horizontal angle Vertical angle

What is measured? •Distances - to calculate areas, volumes, etc. -to draw plans, maps, etc.

•Angles -both horizontal and vertical

•Heights - levels or elevations (the third dimension)

Which instrument should be used? • Distances - taping (steel tape), tacheometry (theodolite), electronic (EDM, GPS) • Angles -tacheometry (theodolite)

• Heights - leveling (level, theodolite)

Facts about measurements

- All measurements contain errors.( No measurement is exact) . - You can not determine the absolute value of the error -But you can determine the values closest to the true values through standards and statistical standards.

Sources of Errors : - Natural Errors: Errors that occur as a result of natural phenomena such as heat - wind and Moisture . -Instrumental Errors: result from lack of precision -in the manufacture of devices and in grading and measurement units or as a result of the different in materials used in manufacturing . -Personal Errors : As a result of defect in the observer vision or lack of familiarity with the

technical work in the field.

Type of errors: 1- Blunder error (Gross Errors ):- error is due to carelessness of human. These are serious mistakes made by surveyor, such as reading 15.45 instead of 5.45 or writing 9.64 instead of 6.94.

2- Systematic error( Constant error) :- ( mathematic model) cause by environment, i.e. elongation or Shrinkage , and have cumulative effect. As an example, you have a meter to measure distance with a production error. It shows 1 meter but in reality the distance is 99.5 cm. Then you measure always longer than the real distance

3- Random error :- An error always there due to instrument and human, It is not easy to detect (small value) i.e. Reading , Recording, positioning 4- Accidental Errors These are unavoidable errors arising from weather condition, change in temperature, humidity, mood of observer, etc.

MEASUREMENTS Errors : 1-True error: ei = xi - x X : true value Xi : measured value

2- estimated error: vi = xi - Xi : measured value : average value

3- Standerd error:

4-RMS / root error of the mean :

4- Maximmum error Probability is 50% standerd error =1

Probability is 99.7% standerd error = 3

ACCURACY: Accuracy is how far the measurement are from the true value. PRECISION: Precision is the amount by which a measurement deviates from its mean. Suppose that you measure the same line five times. .

Examples: The true length of the line is 736.72 m The first team reports the following measurements: 736.80, 736.70, 736.75, 736.85, and 736.65 m. (more accurate) The second team reports the following measurements: 736.42, 736.40, 736.40, 736.42, and 736.41 m. (more precise)

PRECISION & ACCURACY Measurements that has high precision has small standard . Measurements has high accuracy if it is close to the true value. High precision does not necessary

mean also high accuracy.

Measurement that has highly precise is also highly accurate if it is contain little or no systematic error . To obtain high precision and high accuracy : 1- eliminate all blunders 2- eliminate or correct all systematic errors 3- minimize random errors

Relative precision :

Precision increase with the increase of number of time of the measurement repeated

Example

Example :

Examples :

Distance measurement:

1.Pace. 2.Chain. 3.Tape. 4.Odiometer. 5.Tacheometer. 6.EDM. 7.Disto-instrument. 8.Total station ( x, y , z ).

There are three methods of Distance measurements: 1-DDM(direct distance measurements) 2-ODM(optical distance measurements) 3–EDM(electronic distance measurements) DDM methods: Direct distance measurements involves : ( pacing , measuring by use tapes and chains ranging and odometer and pedometer devices)

1.Pacing

2- TAPING

4- Odiometer

Steel tape

3- pedometer

Ranning rod Plumb--bob

INSTRUMENTES OF DISTANCE MEASUREMENT

chain

Chaining pins

FIELDWORK 1- Set up a rod at a point in vertical position (to make the road plumb) 2- Ranging a line (to locate a rod at an intermediate point on a line) 3- Hand signals in ranging 4- Measuring the horizontal distance between two points 5 - Write a report what you have done and difficulties you encountered while you are working. - Each member of subgroup should measure individually and check the measurements.

The position of any point can be determined by taking two measurements : 1- Two line: a-right angle B-non right angle 2- Line and angle( polar way) 3- Two angles

Offsets

2- Arc method 1- Minimum distance

Offsets

3- phythagorion theorem (3 - 4 – 5) oC2 = a2 + b2

4- Arcing perpindecular from a point on the line

Triangulation

d :

Horizantal distance d= s cos α

There are five distance (Tape ) corrections 2- slope correction :

1-Standardisation correction =

: Tape length : measured length

S = slope distansce

4-Tension correction :

3- Temperature correction : Ct = .0000116 *L( TI-Tه) for steel Tape

TI : actual temperature

Tه : standard temperature

5- sag correction :

The distance (Tape ) corrections are compined to one general equation : A +

+B

D -

α

.0000116 *L( TI-Tه) - D= L - L cos α

Example : L = 76.462 m ,α = 1 25` Tape has nominal length = 20 m Standardized length = 20.11 m T20 = ه C , P50 = ه N Tape laid on the surface of ground TI = 10 c , Pi = 70 N A = 1.9 mm2 , E = 200000 N/ mm2 Solution : First step is to decide which correction is necessary. 1- No sag correction because tape laid on the sarface. 2-Standardisation correction =76.462 ( 20.011 – 20 ) 3- Slope correction = =-76.462( )= - 0.0251 m 4- Tension correction = 76.462( 70-50)

A +

+B D

α

20 = 0.0421m

1.9*200000 = 0.0040 m

5- Temperature correction = 0.0000116 *76.462 ( 10-20) = - 0.0086 m D = 76.462+0.421- 0.0234 + 0.0040 – 0.0086 D = 76.4761m , D=76.47m ( to nearest mm

Accuracy : • Synthetic tapes( Fiberglas tape and metal chains standardization and slope only apply 1/1000 accuracy • Steel tapes if standardization and slope correction only considered then 1/5000 accuracy (The difference in accuracy between the two tapes is reflected in the gradation on the tapes scale, steel tapes are graded to the nearest mm while fibreglass tapes are graded to the nearest cm). • if tension and slope condition are considered then the accuracy 1/10000 – 1/20000 -Sag correction apply only if in catenaries

ODM method optical distance measurements involves (stadia Tachometry )

Stadia hairs

Horizontal distance D = K* S cos α +C cos α K : constant =100 , C : constant =0.0 D = 100 S cos α , Given α = 02 17’ 27” S= 2.140 – 1.774 = 0.366 m D = 100* 0.366 * cos (02 17’ 27”) = 36.542 m =36.5 m

(to nearest 100 mm) hi : height of Thedeolite on A

RLA: reduce level to the point A

RLB : reduce level to the point B

RLB = RLA +hi v – m V : vertical component of the sloping distance

m : middle hair reading .

2.140 1.956

1.774

α

2

ه 2

ه

example :

2

V= ½ k sin 2 α + c sin α V= 50*0.366*sin (2* (02 17’ 27”)) =1.462 m Given RA = 111.43 m hi = 1.51 m

Then RB = 111.43+1.51+1.461-1.956

RB = 112.446 = 112.45 m ( to the nearest 50 mm)

ه

EDM : Electronic distance measurements

laser distance meter Accuracy = + 1.5 mm

-

EDM Devices

obstacle distance measurement

Set out

lay out