MAPUA INSTITUTE OF TECHNOLOGY

INTRAMUROS, MANILA

ELEMENTARY SURVEYING

RESEARCH 1

SUBMITTED BY:

NAME: CORDANO, HAZEL F.

COURSE AND SECTION: CE120-0F/A4

STUDENT NO.: 2013108712

SUBMITTED TO:

PROFESSOR: ENGR. IRA BALMORIS

GRADE

SOURCES OF ERROR IN TOPOGRAPHIC SURVEY

FIRST WHAT IS TOPOGRAPHIC SURVEYING???

TOPOGRAPHIC SURVEYING OR LAND SURVEYING

are used to identify and map of contour of the ground and existing features on the surface of

the earth or slightly above or below the earth’s surface like the trees, buildings, streets,

walkways, manholes, utility poles and retaining walls.

Error

Distances and angles can never be determined exactly; measurements are subject to error.

Error can be controlled through procedure and instrumentation. Surveys are conducted

according to standard levels of accuracy (first order, second order, etc.).

The desired level of accuracy depends on the intended us of the survey data (e.g. locating

permanent stations or surveying bridges and dams versus surveying for terrain analysis or

orienteering).For topographic mapping, the desired level accuracy is the plot table error, the

shortest distance that can be depicted on a map at a given scale. The drafting of lines generally

is accurate to within 0.25 mm. At 1:1000, 0.25 = 250 mm or 0.25 m on the ground. Optical

measuring devices will provide this level of accuracy. At 1:25,000, 0.25 mm = 6.25 m on the

ground. Pacing of distance will provide this level of accuracy, although in practise accuracy is

greater than the plot table error by as much as one-third (e.g. 80 mm rather than 250 mm at a

scale of 1:250,000) so that plotting and surveying errors are not compounded.

Adjusting For Closure Error

Horizontal angles

In a closed polygon, the sum of the interior angles = 180o (n-2), where n is the number of

sides in the polygon, thus the sum of the horizontal angles in a triangle (n = 3) is 180o;

an equal angle is subtracted or added to each measurement to satisfy the equation for

interior angles; if the closure error is not equally divisible by n, make the largest

adjustments to the largest angles.

The sum of deflection angles for any closed polygon is always 360o; this provides for

another means of determining and adjusting for closure error.

Difference in elevation

Closure error can be determined for closed and closed-loop traverses. The closure error can be

divided by the number of stations on the traverse or the correction at each station can be

calculated according to the distance from the origin of the survey:

Ci = di/L * Ec, where

Ci = the correction applied to station I

di = the distance to station I from the origin of the traverse

L = the total length of the traverse

Ec = the closure error

This method accounts for the propagation of error with distance.

Horizontal distances

As with leveling, closure error can be determined for closed and closed-loop traverses, where

the coordinates of the end points are identical or known. Location in the horizontal plane are

given by x and y coordinates (e.g. northing and easting). Using the measured horizontal

distances and adjusted angles, calculate the coordinates of each station. The difference

between the calculated and known coordinates of the end control point is dx and dy, the closure

error in x and y. As with leveling, the adjustment is a function of the distance traversed (Li)

relative to the total length of the traverse (L):

Cdxi = dx * Li/L Cdyi = dy * Lii/L,   where Cdxi and Cdyi are the adjustments in x and y

coordinates at station I

The relative accuracy of distance measurements can be expressed as ((dx2 + dy2)1/2)/L. An

angular error of one minute is equivalent to a distance measurement error of 3 cm over a

distance of 100 m, since the sine of 1/60o is .00029.

ERRORS IN TOPOGRAPHIC SURVEY FROM LINEAR MEASUREMENT

There are lots of things which we call errors. We also use a lot of other terms for this. The

fundamental issue is that we can never know the true value of any measured quantity, so we

always have some uncertainty associated with the value we adopt

We can use a lot of methods to try to minimize our errors, but we can never eliminate them. For

the purposes of working with errors, we can divide them into three groups: gross, systematic

and random errors. This division is based on what causes the errors and how we deal with

them, rather than any other aspect of their nature. You will see other classification 

schemes, but this one is both comprehensive and useful.

GROSS ERROR

Are those which we can also call `blunders'. They can be of any size or nature, and tend to

occur through carelessness. Writing down the wrong value, reading the instrument incorrectly,

measuring to the wrong mark; these are gross errors. They can be caused by people,

machinery, weather conditions and various other things. We deal with gross errors by 

careful procedures and relentless checking of our work.

SYSTEMATIC ERROR

Are those which we can model mathematically and corrected. They are caused by the

mathematical model of the procedure that we are using being different to what is going on in the

real world. We reduce and compute with measurements on the basis of models and if the

models are not complete, we will have discrepancies. For example, if we measure a distance

without allowing for the slope of the tape, we will have a systematic error, which can be

eliminated if we use the correct model of the measurement process. We can eliminate, or at

least minimize, systematic errors by careful work, using the appropriate model for the process in

use, and by using checks that will reveal systematic errors in measurements. Note that checks

that use the same measurement processes may not detect some systematic errors, so you

have to be fairly creative in developing methods for detecting systematic errors.

RANDOM ERRORS 

Are those which have no apparent cause, but are a consequence of the measurement process itself. All measurements have to be done to some limit of precision and we cannot predict the exact measurement we will obtain. However, random errors have very definite statistical behaviour and so can be dealt with by statistical methods.

Random errors are the small differences between repeated measurements of the same quantity, often of the order of the finest division in the measuring scale. We can eliminate or minimize the effects of random errors by statistical procedures: for example we can adopt the mean of a set of measurements as the value to be used in later calculations. With the idea of the ubiquity of errors in all our measurements and everything we do, we can now look at one measurement process and see how error affect it. It will begin by looking at linear measurement such as those we make with tapes and such equipment as EDM.

References:

http://www.state.nj.us/transportation/eng/documents/survey/Chapter3.shtm#3.3

http://www.adobeinc.com/faq/what-topographic-survey-and-when-it-needed

http://uregina.ca/~sauchyn/geog411/topographic_surveying.html

https://www.e-education.psu.edu/geog160/node/1926