Error due to Refraction and Curvature

Hi,

Finally, today I thought to write about this particular topic, which is important to study when we are talking about Geodetic Surveying.

       

As we know, in Geodetic Surveying we have to consider the error due to the curvature of the earth and the refraction too. Reason is because a larger area is surveyed in Geodetic Surveying, more than about 256 km2. In such large areas, the error due to curvature of the earth has to be considered to calculate the linear distances and also in case of the angular measurements.

We have to consider the refraction error too, because here we are dealing with the large distances and in order to get the correct results we have to apply these correction.

• What is the Error due to Curvature? 

To understand this simple concept of error due to curvature of the earth, first you have to understand the shape of the earth and the methods and instruments which we employ for calculating these distances.

When we do leveling with Theodolite or Autolevel, the line of sight first is set horizontal. Then we measure the vertical angle to the target and by applying some trigonometrical formulae we can calculate the vertical distance of the target from that horizontal line.

Error due to curvature comes into play, because in the cases of long distances, the horizontal line and level line do not coincide. Level line is a curved line, parallel to the level surface, but the horizontal lines goes straight.

This means that the vertical distance of that target from the level line is going to be larger than the distance which we calculate from the horizontal line. Please refer the figure given above, the amount of correction depends upon the magnitude of the horizontal distance between the target and the instrument station.

• What is Error due to Refraction?

Error to refraction can be understood easily once you understand the phenomenon which takes place when light passes from one density system to another density system. Refraction is nothing but the phenomenon by which when light travels from a denser media to the lighter media, it deflects away from the normal to the plane of the media.

Phenomenon occurs vice-versa when light travels from lighter media to denser media. This phenomenon has to be considered in the calculation of the distances in case of Geodetic Surveying. Suppose a man is taking the observation of the top of a hill from a point, which is at a considerable down far vertical distance from it to change the density of the air.

We know that density of air decreases with the height, this will effect your line of sight. The line of sight of a person who is taking observation to a point at a quite higher distance, will be a curved path, because light will continuously change its direction due to the continuous change in the density of the air.

Imporant question to ask is, how does it effect our observations? Well, the observed angle will be to high in case of taking the observation of an elevated object and the observed angle will be small in case of taking observations to an object in depressions.

• Correction for the Error due to Curvature and Refraction:

There are a numbers of textbooks, which explains the procedure to calculate the correction for the refraction and curvature.

Formulae:

Curvature correction, Cc = - 0.07849.D^2 meter

Refraction Correction, Cr = 0.01121.D^2 meter

Combined Correction C = Cc+Cr= -0.06728. D^2  meter;   here D is in kilometer

Thanks for your kind visit!

       

Training Program on Total Station

Hi dear,
Yesterday, I read a notice from the HOD(Head of Department) which  informed about a training program on the working and using the "Total Station".

This program is going to be held at our own institute and this will be free for the students and teachers of the institute. I have written blogs about almost every topic on the basics of Surveying in this blog and Total station is a topic which I think is still un-touched here.

So, hopefully soon I will post about Total Station and if that comes out to be useful for you too, I will be most happy.

Total station is used where we need fast and very accurate results in terms of the observations which we have to take to check the leveling and distances of the points. Specifically in case of the tunneling and bridge constructions, we have to be very accurate with our measurements.

Any small error can result in the failure of the project and may result in the loss of a huge amount of money. In that manner, Total Station is a requirement of every Civil engineer working in such projects.
This instrument is a little costly but still people who can afford it, will surely use it instead of any other instrument.

Thanks for your visit!

Take care!

How to find out the area using Planimeter

Hi, 

Planimeter is a Surveying instrument which can be used to find out the area of a map or plan.  A Swiss mathematician Jacob Amsler Laffon built first modern planimeter in 1854. Many developments followed Amsler's famous Planimeter including the electronic planimeter.

A Polar Planimeter (source: wikipedia)

We have three mechanical types of Planimeters:

1. Polar 
2. Linear
3. Hatchet Planimeter

All Planimeter work on the same principle.

There is a linkage, at one end is a pointer and the other is fixed for a polar planimeter and is restricted for a linear.The pointer is traced along the perimeter of the area of the shape is indicated on a scale.

There is a wheel attached to planimeter which rolls when the movement of the pointer is perpendicular to the axis of the wheel so, this movement is recorded.

It will skid when the movement of the wheel is parallel to the axis so, this movement is ignored.

Linear Planimeter (Source : Wikipedia)

That means that planimeter measures the distance which is traveled by the rolling of the wheel. Area of the shape is proportional to the nos. of turns through which the measuring wheel turns.

The area calculations can be proved by using Green's Theorem.

Please visit wikipedia for detailed study.

In order to find out the area, all you have to do is to trace the perimeter of the area on the map, and note down the reading.

To get more accurate results one should be skilled in tracing the exact perimeter of the shape.
You can convert the area to the field area using the scale of the map.
These days digital planimeters are in the market which are more easy to use.

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Classifications of Theodolites

Hello there,

Theodolite is one of the basic instrument which has many uses including traversing. Theodolite is broadly classified into two categories:

• Transit Theodolite In this type of Theodolite, line of sight can be reversed by revolving the telescope 180 degrees along the vertical plane.

• Non-Transit Theodolite In this type of Theodolite, the line of sight can not be revolved in the vertical plane.

There are other classifications of the Theodolite:

• Vernier Theodolites.
• Micro-meter Theodolites.

Size of Theodolite: This is defined by the diameter of the graduated circle of the lower plate. Common sizes are 8 cm to 12 cm while 14 cm to 25 cm are used for triangulation work or you can say for more precise works.

EDM

Main parts of a transit vernier Theodolite are 

1. Leveling head
2. lower circular plate
3. Upper plate
4. Telescope
5. Vertical circle

There are some fundamental lines of Transit Theodolite:

1. Vertical axis
2. Horizontal axis or Trunion axis
3. Axis of the altitude bubble or Azimuthal axis
4. Line of collimation
5. Axis of the plate bubble
6. Axis of striding level if present.

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Surveying notes for GATE and PSUs exams. - Part 11

Hello there, 

The following facts are taken from many references, mainly from the book titled "Civil Engineering objectives" by S P Gupta and S P Gupta.

• Bowditch method has used the assumptions:  Errors in linear measurements are proportional to under root of L.; Correction to latitude or departure of any side = Total error in L(or D) * (Length of that side/ Perimeter of traverse).
• To determine the length of a bridge proposed to be built across a wide river, the triangulation method of surveying will be preferred over tacheometry, chain surveying.
• Heliograph is a type of sun signal used in triangulation work.
• A 100 m tape is held 1 m out of line. The true length will be 99.995 m
• When the line of collimation is not perpendicular to the horizontal axis taking face-left and face-right observations reduces the error.
• It is not necessary to do the exact centering of plane table to do the small scale surveys.
• Saddle line is also known as ridge line or valley line.
• Line of drainage basin is the line which passes through ridges and saddles setting up a domain.
• Longitude of a place is measured by wireless time signal and transportation of chronometers.
• In tilting level the vertical axis is not perpendicular to the line of collimation.
• Inverted staff readings are taken for the points above the line of collimation.
• Reciprocal levelling eliminates the error due to inclined line of collimation also.

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Surveying notes for GATE, PSUs - Part 10

Hello there,
How have you been? Here is 10th part of one liners for the preparation of the GATE and PSUs.

All information is learned through books and practical exercises.

• To find the R.L. of a roof slab of a building, staff readings were taken from a particular set-up of the levelling instrument. The readings were 1.050 m with staff on the benchmark and 2.300 m with staff below the roof slab and held inverted. Taking the R.L. of the B.M. as 135.150 m, the R.L. of the roof slab will be 138.500 m.
• Operations involved in a spire test are : 1) Sight a well-defined high point on a high building 2) Clamp horizontal plates  3) Depress the telescope and sight a point on the ground nearer to the instrument 4) Change face and repeat the procedure.
• Accurate centering in plane table surveying is necessary for large scale maps.
• Exact orientation is more important than accurate centering for small scale maps.
• The intersection method of plane table surveying is particularly employed for inaccessible points.
• Plane table survey is useful for open country with good inter-visibility.
• Simpson's method estimates best the area of an irregular and curved boundary.
• In a closed traverse, the sum of south latitudes exceeds the sum of north latitudes and the sum of east departures exceeds the sum of west departures. The closing line will lie in N-W quadrant.
• In reciprocal levelling, the difference in elevation of two points is calculated by taking the average of the differences obtained by taking measurements from two different instrument settings, one at near to first station and second at near to second station.
• A lemniscate curve between the tangents is transitional throughout,the polar deflection angle of its apex is equal to A/6.

Other parts :

 part 4 : http://surveying2012.blogspot.com/2013/12/gate-psus-surveying-one-liners.html
part 5: http://surveying2012.blogspot.com/2013/12/surveying-notes-for-gate-psus-part-5.html
part 6: http://surveying2012.blogspot.com/2014/01/surveying-notes-for-gate-psus-part-6.html
part 7 : http://surveying2012.blogspot.com/2014/01/surveying-notes-for-gate-psus-part-7.html
part 8 : http://surveying2012.blogspot.com/2014/01/surveying-notes-for-gate-psus-part-8.html
part 9 : http://surveying2012.blogspot.com/2014/01/surveying-notes-for-gate-psus-part-9.html

Thanks for visit!

Surveying notes for GATE, PSUs - Part 9

Hello there,
How have you been? Here is 9th part of one liners for the preparation of the GATE and PSUs.

All information is learned through books and practical exercises.

• If quantity A has a weight of 3, then the weight of A/3 will be 27.
• In a parabolic vertical curve, the rising grade g1= +0.80% and the falling grade g2= -0.70%. The rate of change of grade is 0.05 per chain, then the length of the vertical curve is 30 chains.
• While measuring horizontal angles by the method of repetition with a theodolite, readings are taken on both the vernier. Error due to imperfect graduations will be eliminated.
• An angle-measuring instrument reading up to one-sixth of a degree on the main scale is equipped with a vernier having 19 main scale divisions divided into 20 parts. The correct least count for the instrument is 30 seconds.
• If it is required to produce the plan of a small area under the magnetic influence, plane table survey will be the best choice.
• Clinometer- An angle measuring instrument.
• Tellurometer - microwave instrument
• Pantograph- Plan enlarging instrument
• Ghat tracer - Grading finding instrument.
• Offsets are lateral measurements made with respect to main survey line.

Other parts :

 part 4 : http://surveying2012.blogspot.com/2013/12/gate-psus-surveying-one-liners.html
part 5: http://surveying2012.blogspot.com/2013/12/surveying-notes-for-gate-psus-part-5.html
part 6: http://surveying2012.blogspot.com/2014/01/surveying-notes-for-gate-psus-part-6.html
part 7 : http://surveying2012.blogspot.com/2014/01/surveying-notes-for-gate-psus-part-7.html
part 8 : http://surveying2012.blogspot.com/2014/01/surveying-notes-for-gate-psus-part-8.html

Thanks for visit!