What are Mistakes,Systematic error and Accidental Errors, in Surveying

Hi,
This post contains mostly the theory of the Errors, as we define them in Surveying. 

Error:- The difference between the observed value and the true value is known as error.

There are three types of errors which occurs while we do the surveying:

1. Mistakes: These are the errors which occur due to the inexperience, inattention, carelessness or due to lack of judgement or poor judgement. If mistakes are not found then they may affect the result to a great extent.
2. Systematic errors: These are the errors which follow a system when they occur, and they have the same nature whenever they occur. They can be eliminated by testing the instruments before they are used or by applied the necessary correction, by using the mathematical formulae after the error is known.
3. Accidental errors: These are the kind of errors which occur accidentally and can of any nature positive or negative. These are the errors which are byond the human control and can not be calculated to their true value, but only we can apply the theory of the probability to calculate them.

Weight of an observation: Weight of an observation is its relative importance to the other observations taken under the identical conditions.

Mean value: Mean value of a set of observation is the arithmetic or the weighted arithmetic mean of the observations.

Probable Error of a single observation:

Probable error of a single observation in a set of observation is derived using the formula,

Es = +-0.6745√(∑v²/ n-1)

where, v= difference between the observation and the mean value of the set of observation.

And n= numbers of observations in the given set.

Probable error of the mean:

The probable value of the error in a mean of the set of observation can be determined using the following formula = Es/√n

Principle of least squares:

Most probable value of a given quantity from the given available set of observation is the one for which the sum of the squares of the residual errors is a minimum.

Alternatively, the most probable values of the errors in the given set of observations of equal weight are those for which the sum of their squares is a minimum.

It can be proved that the mean value is the true value in case the numbers of observations are very large in numbers.

The sum of the squares of the residuals found by the arithmetic mean value is a minimum. This is thus the fundamental law of least squares. 
Hi,

Adjustments of the errors in the triangulation:
The triangulation errors are adjusted in three different ways or steps:
(a) Adjustments of the single angle error (b) Adjustments of the station observation
(c) Adjustments of the figures


(a) Adjustments of the single angle error: When an angle is measured a numbers of times, then the most probable value of the angle is the mean value of the observed values. If all the values observed are of the same weight then the most probable value is the simple arithmetic mean, but if the observations taken are of different weight then the most probable value is the weighted arithmetic mean.

(b)Station adjustments:
When there are numbers of observations taken at the same station, then the condition that the sum of all the angles should be equal to 360 degrees must be satisfied, if not then the difference from 360 is the error of that station. Now there arise two more cases:
(i) When all the angles measured have the same weight: In this case the error is distributed equally among all the angles. 
(ii) When the angles are of different weight: In this case the error is distributed in the proportion of inverse of the weight of the different angles.  
(iii) When the angles and some other combined observations are taken: In such cases when combined observations are also taken along with the observation of the single angles, we have to make use of the normal equation, to find out the errors. 
There is another method known as the method of difference, which can be used in more simple way to get the errors, because the method of normal equations is more laborious. 

(c) Adjustments of the figures: 
There are different conditions which can be opted to calculate the errors of the different angles. In a triangular figure, the sum of three angles is always equal to 360 degrees. 
Similarly there can be other conditions which can opted to find out the condition equations for other figures like quadrilateral, or central figures. 
For a closed traverse, sum of internal angles is (2n-4)*90 degrees, where n is the no. of sides, or total no. of angles. 

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Relevant Books that you might buy:

       

Trigonometric Leveling - Theory and Formulas for Calculations.

Hi,

Trigonometric Leveling is the branch of Surveying in which we find out the vertical distance between two points with the help of some measurements of the vertical angles and the known distances. The known distances are either assumed to be horizontal or the geodetic lengths at the mean sea level(MSL). The distances are measured directly(as in the plane surveying) or they are computed as in the geodetic surveying.

The trigonometric Leveling can be done in two ways:

1. Observations taken for the height and distances
2. Geodetic Observations.

In the first, we can measure the horizontal distance between the given points if it is accessible.

We take the observation of the vertical angles and then compute the distances using them. If the distances are large enough then we have to provide the correction for the curvature and refraction and that we provide to the linearly to the distances that we have computed. 

In the second, i.e geodetic observations, the distances between the two points are geodetic distances and the principles of the plane surveying are not applicable here. The corrections for the curvature and refraction are applied directly to the angles directly.

Now we will discuss the various cases to find out the difference in elevation between the two Points.

(1) The two points are at known distance, i.e. The base of the object is accessible.

When the two points are at a known horizontal distance then we can find out the distance between them by taking the vertical angle observations.

If the vertical angle of elevation from the point to be observed to the instrument axis is known we can calculate the vertical distance using trigonometry.

Horizontal distance*tangent(vertical angle) = Vertical difference between the two.

If the points are at small distance apart then there is no need to apply the correction for the curvature and refraction else you can apply the correction as given below:

C= 0.06728D*D

Where D is the horizontal distance between the given two points in Kilometers.

but the Correction is in meters (m).

(2) The base of the object is not accessible :

(a) When the instrument is shifted to the nearby place and the observations are taken from the same level of the line of sight: 

In such case we have to take the two angular observations of the vertical angles. The instrument is shifted to a nearby place of known distance, and then with the known distance between these two and the angular observations from these two stations, we can find the vertical difference in distance between the line of sight of the instrument and the top point of the object.

(b) When the line of sights of the two instrument setting is different :

Here again there are two cases:

1.  When the line of sights are at a small vertical distance which can be measured through the vertical staff readings. 
2. When the difference is larger than the staff height.

(i) In first case, It is advised to apply the formula for the difference in the height of the top of the object from these two lines of sights. The difference in lines of sights is same as the staff readings difference, when the staff is kept at a little distance from these two points. So we can get the solution for the vertical distance easily.

(ii) In the second case, there is a need to put a vane staff at the first instrument station and the angle of elevation is measured from the second point of observation. This gives us the difference in the line of the sights between the two points of instrument station. Then again we do the same.

(c) When the instrument station and the top of object are not in same vertical plane:

In this case there is a need to measure at-least two horizontal angles of the horizontal triangle formed by the two instrument stations and the base of the object.

Again we will take the vertical angular observations from the two instrument stations also and then we can apply the sine rule to solve the horizontal distances of the triangle. With the help of these angles and the distances we can get the vertical distance between any two point(Instrument station and the top of object).

Reference:

       

Thanks!

What is Local Attraction, and How Does it Affect the Readings of Compass.

Hi,

Local Attraction: 

A compass shows the direction of the magnetic meridian on the principle of magnetism. 
Now whenever you bring any magnet attracting material(Ferrous metals), needle will show deflection. Please note that in its undisturbed condition, needle is always pointed towards magnetic north. 

So when that ferrous material is near to it, needle will not longer be in north south alignment, so that is how the error is introduced into your readings. This error is known as the local attraction.

Materials which are most likely to be present there, while you are doing the compass surveying, are such as an iron chain, metallic wrist band or ear rings(metallic) that one might be wearing.

Other things such as an electric pole or electric wires may also produce local attraction. The needle is attracted to these objects, so this will deviate from the true direction of the magnetic meridian.

If local attraction is available at a station then all the readings taken from that station will have the same amount of the error, and we have to correct the readings to get the true results.

There are methods to get the corrections to be applied on the erroneous readings in the traversing. The two methods which are used in general will be discussed here briefly.

(1) In first method we have to find out the stations where no local attraction exists. To find out this we have to look for a line where the difference between the fore bearing and the back bearing is exactly equal to 180 degrees. If we find such line then that means the two end stations of that line are free from any local attraction. After finding that line we apply the correction to the bearings of the other lines.

(2) In the second method we find the line where there is no local attraction. We know that even if the local attraction is present at every station the measured included angles will not be incorrect and we can calculate them correctly. With the help of the  readings from the stations which are free from local attraction and the correct included angles we can find out the bearings of all the lines.

If we do not find any line where the both stations are free from the local attraction, we have to take the line where the error is minimum and then apply the mean correction to both the stations and then take them as the correct readings. After that start as usual.

If you want further assistance with the topic, please leave a comment.

Thanks for your kind visit!

       

Solved- Traffic Flow Distribution among Routes at Equilibrium

Hi,

Prob: There are two routes, such that the time consumed is given by the following. 
t1 = 15 + 0.005q1 , t2 = 12 + 0.003q2, 
in peak hour the traffic flow is 6600 veh/hr, estimate the traffic flow distribution among the two routes at the equilibrium.

Solution:

Question Paper 2014- Highway Engineering (CE - 6004) - HPU

[Total No. of Questions -9]                                                         [Total No. of Printed Pages - 3]

  14706

 B.Tech. 6th Semester Examination

Highway Engineering

CE- 6004

Time: 3 Hours                                                                                      Max Marks:  100
The Candidate shall limit their answer precisely within the answer-sheet(40 pages) issued to them and no supplementary/continuation sheet will be issued.

Note: Attempt five questions in all, selecting one question from each of the sections A, B, C and D and all the sub-parts of question in section E.

SECTION - A

1. (a) Write down the construction steps of Macadam's construction along with a typical cross-section.              (10)                                                                                                        (b) What are the various surveys to be carried out before planning a highway system for a given area? Explain briefly.             (10)
2.  (a) Compare Nagpur Road Plan and the second twenty year road plan, discuss the merits of each.                      (10)                                                                                                    (b) Explain how the road lengths of different categories for a state are determined for the year 2001, using the third road development plan concept.          (10)                                                                                     SECTION - B
3. (a) Write down the various factors affection friction offered by pavement surface.  (5)           (b)  Draw a typical cross-section of a divided highway in urban area including the width of pavement, roadway and land.                                                                           (7)              14706/1900                                                                                                  [P.T.O.]                                                                   2                                                                      (c) Derive and expression for finding the stopping sight distance of a vehicle at level.  (8)
4. (a) Enumerate the various steps for practical design of super-elevation.               (10)             (b) A vertical summit curve is formed when an ascending gradient of 1 in 25 meet another ascending gradient of 1 in 100. Find the length of the summit curve to provide the required stopping sight distance for a design speed of 80 kmph.                                       (10)                                                           SECTION - C
5. (a) Indicate how the spot speed data are presented and the results used in Traffic engineering?          (10)                                                                                                      (b) Explain various patterns of kerb parking with diagram.                 (10)
6. (a) Explain briefly the various design factors that are to be considered in rotary intersection design.                                                                                         (12)                              (b) What are the advantages and disadvantages of Traffic signals?       (8)                                                                            SECTION - D
7. (a) What are the various tests for judging the suitability of road aggregates? Discuss the objectives, their advantages and limitations?                                      (12)                            (b) Define the term 'Group Index' of soils. How it is obtained?           (8)
8. (a) Discuss the desirable properties of bitumen. Compare tar and bitumen.    (10)                    (b) Write down the desirable properties of bituminous mixer in brief.            (10)                                                                         3                                                          14706                                                                                                                                                                                              SECTION - E
9. Write short notes on the following:

• (a) CRRI
• (b) Obligatory points
• (c) Cross slope
• (d) Ovetaking zones
• (e) Three E's
• (f) Level of service
• (g) Grade Separated Intersections
• (h) Uses of rubber modified bitumen in bituminous mixer.
• (i) Emulsions uses in road construction.
• (j) Grade compensation on curves.                                                         (10*2)

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