Characteristics of Contours - Brief Theory

Hi,

Do you know what is a contour?
First, here are certain terms which are useful in understanding the contours.

• Contour -  Contour is an imaginary line on ground joining points of equal or constant elevations. contours are important to draw the topographical maps in which vertical distances are also shown using the contour lines.
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• Contour interval: Vertical distance between any two consecutive contours is known as the contour interval. It depends upon the scale of the map, nature of the ground and availability of the fund  and time.
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• Horizontal equivalent/ horizontal interval:  It is the shortest horizontal distance between the two consecutive contours. 
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• Contour Gradient: Imaginary line on the surface of the earth, maintains a constant angle to the horizontal. 

Characteristics of the contours:

1. Two contours of different elevation do not cross each other with only exception in the contours of a overhanging cliff.
2. Contours of different elevations do not combine or overlap to each other with exception in the contours of a vertical cliff.
3. When contours are drawn closer to each other, it shows a steep slope on the ground and when they are far apart it shows the gentle slope on the ground.
4. When contours are equally spaced they represent a uniform slope, and when they are parallel straight and equivalent they represent a plane surface. 
5. A contour is perpendicular to a line of the steepest slope.
6. A contour must close itself in the map or must go out of the boundaries of the map.
7. A set of ring contours with higher values of contour inside and lower values outside represents a hill and if the higher values are outside and lower values inside then it represents a depression like a pond.
8. When contours cross a ridge they form a V- shape across them. While if they cross a valley they form a u-shape or may a V shape also difference being, the concavity of the contour lines lies towards the lower contours in case of valley while it is convexity lying towards the another lower value in case of contours of a ridge.

Uses of Contours:

1.  To study the general character of the tract of the country without visiting the ground. With the knowledge of characteristics of contours, it is easy to visualize whether country is flat, undulating or mountainous.
2. To decide the sites for engineering works such as reservoirs, canals, roads and railways etc. on the basis of the economy.
3. To determine the catchment area of the drainage basin and hence capacity of the proposed reservoir.
4. To compute the earth work required for filling or cutting along the linear alignment of the projects such as canals, roads, etc.
5. To find out the inter-visibility of the points.
6. To trace out a contour gradient for road alignments.
7. To draw longitudinal and cross- sections to ascertain nature of  the ground.

Thank you!!

References and Books:

Surveying Vol-I  by Dr. B. C. Punmia

   

A Brief Theory of Plane Table Surveying

Hi,

A short introduction to Plane Table Survey- A graphical method of Surveying.

Plane Table Survey:

Plane Table Survey is a method of plotting the plans on the sheet, in which field work and the office work are done simultaneously. It is also known as the graphical method of Surveying. Therefore the main characteristic of the map is that, there is no need of carrying a field book to note various readings.

List of Instruments used in Surveying:

1.  Plane Table
2. Alidade
3.  Plumbing fork and Plumb bob
4. Spirit Level
5. Chain or Tape
6. Rain roof cover for the plane table
7.  Compass
8. Ranging Rods
9. Drawing Sheets
10.  Drawing equipment.

Procedure: 
To perform the plane table survey one has to follow the following procedure at every plane table set-up at various stations.

(a) Fixing the plane table to the tripod stand
(b)Setting up and temporary adjustments:

1.   Leveling the plane table with the help of spirit level
2.  Centering with the help of plumbing fork
3.  Orientation by trough compass or by back sighting

• (c) Sighting the points with the help of Alidade

Methods of plane tabling:

1. For locating details: 

(a) Radiation Method: 
With the help of Alidade, a ray is drawn towards the point. Then using the Chain or Tape the horizontal distance is measured from the Plane Table to the point. Then using the scale of plotting, this point is located on the sheet.

(b) Intersection Method: 
In this method no chain or tape is needed, just two instrument stations are needed. Intersecting rays are drawn from these two stations whose location is already plotted on sheet(by measuring the distance between them). The point of intersection of the two rays is the location of the point of interest.

2. For locating Plane Table Stations: 

(a) Traversing: In this method the location of the Plane Table station is located in the following manner:

(1) At previous station a ray is drawn in the forward direction(toward next station) and point is plotted by measuring the horizontal distance and plotting it to scale.

(2) Instrument is shifted to next station(which is just located in first step) and the previous station is back-sighted to orient the plane table.

(b) Resection: 
Resection is the process/method of finding the position of a station where plane table is placed. Sights are taken towards the known and visible points and rays are plotted.

Procedure :

First of all the plane table is oriented correctly by one of the four given methods:

(1) Orientation by trough compass

(2) Orientation by back sighting

(3) Orientation by two point problem

(4) Orientation by three point problem

Then afterwards point is located.

Thank You!

Note: If reader want details of any of the topic please, leave a comment below.

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Thanks!

Tacheometry (Surveying) - Theory and Formulae

Hi,

Tacheometry is the branch of Surveying in which we determine the horizontal and vertical distances between points by taking some angular measurements with the help of an instrument caled Tacheometer. 

       

This is not so accurate method of finding the horizontal distances as the Chaining is, but it is most suitable for carrying out the surveys to find the distances in the hilly area where other methods are quite difficult being carried out. It is generally used to locate contours, hydrographic surveys and laying out routes of highways, railways etc.

The instruments required for carrying out the Tacheometric survey are:

(1) A Tacheometer 
(2) A Stadia Rod.

• Tacheometer: Tacheometer is more or less a Theodolite installed with  a stadia diaphragm. Stadia diaphragm is equipped with three horizontal hairs and one vertical hair. So we can take three vertical staff reading at the same instruments setting, lowermost hair reading, central hair reading and the top hair reading. The difference between the lower hair reading and the upper hair reading gives the staff intercept(s).

The Tacheometer with the analactic lens are famous because their additive constant is zero. There is one concave lens introduced between the eyepiece and the object piece to eliminate the additive constant of the instrument. It simplifies the calculations.

Methods of Tacheometric Survey:

(A) Stadia Hair Method

1. Fixed Hair Method
2. Movable Hair Method

(B) Tangential Method

(A)Stadia Hair Method: 

• As the name suggests in this method theodolite with the stadia diaphragm is used to find out the staff intercept between the lower and upper hairs and also the central hair reading is noted.

Principle of Stadia hair method is that the ratio of the length of perpendicular to the base is constant in case of similar triangles.

1. Fixed Hair Method: In the fixed hair method the cross hairs of the diaphragm are kept at a constant distance apart and the staff intercept varies with the horizontal and vertical position of the staff with respect to the Theodolite.
2. Movable Hair Method: In this method the staff intercept between the lower hair and the upper hair is kept constant by moving the horizontal cross hairs in the vertical plane.

Formula to carry out calculation works:

Case:  

(a) Staff held vertical:

Tacheometry -Staff held vertical

             D = (f/i).s+ (f+d)

   where, f/i = multiplying constant

               s = staff intercept between the bottom and top hair

               f+d = Additive constant

              D = Horizontal distance between the staff station and the observer's position

(b) Inclined sights staff held vertical:

            D = (f/i).s. cos^2A + (f+d) cosA

            V = {(f/i).s.} .[{sin(2A)}/2] + (f+d) sinA

                Where A is the angle of elevation or angle of depression.

(c) Inclined sights upwards, staff held normal:

    D = [(f/i).s+ (f+d)]cosA - h.sinA  ;    V= [(f/i).s+ (f+d)].sinA

     h= central hair reading.

R.L. of staff = H.I. + [(f/i).s+ (f+d)].sinA - hcosA

(d) Inclined sights downwards, staff held normal:

  D = [(f/i).s+ (f+d)].cosA - h.sinA  ; 

 V= [(f/i).s+ (f+d)].sinA ;

 R.L. of staff = H.I. + [(f/i).s+ (f+d)].sinA - h.cosA

(B)Tangential Method:

In Tangential method only central hair reading is noted down and generally two angular observations are taken to calculate the horizontal and vertical distances.

Thanks!

List of the Surveying Minor Instruments

Hi,
There are some instruments used for the rough surveys, which are not used for the precise surveys. These instruments are also known as minor instruments. 

 These are the following.

•  Hand Level:

It is a compact instrument used for locating contours, taking cross sections in reconnaissance surveys.

• Clinometer:

It is a light, compact instrument used for measuring vertical angles, finding out the slope of the ground, and for locating points on a given grade. There are three commonly used forms of clinometers:

 (i) Abney's level

(ii) Tangent Clinometer

 (iii) Ceylon Ghat Tracer

• Box Sextant: 

It is a reflecting instrument capable of measuring up to 120 degrees with an accuracy of one minute. It is one of the most precise hand instruments.

• Pantograph: It is used to reduce or enlarge the given figure.

• Planimeter: It is used to measure the area of the given figure.

Thanks for your kind visit!

Error and Correction for the Curvature of the Earth, and Refraction (Surveying)

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 as well. Reason is that larger areas are surveyed in Geodetic Surveying, more than about 256 km2 and therefore one can not ignore the curvature of earth. 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!

    

Various Terms and Definitions used in Field Astronomy (Surveying)

Hello!

Field astronomy deals with the determination of the relative positions of the celestial bodies by taking the astronomical observations.
       

Related terms:

1. Celestial sphere: If we assume the space to be a sphere having the earth as its center and all the star lying on its surface, or studded in it. The celestial sphere can be of few kilometers to many thousand kilometer.

2. Zenith and Nadir : These are two points on the celestial sphere opposite to each other and lying above and below the observer. Zenith is the point on the celestial sphere, above the head of the observer and Zenith is the point on the celestial sphere below the observer. Alternatively, these are the points of intersection of the plumb line(drawn through the point of observation) with the celestial sphere.

3.Terrestrial poles and equator: Terrestrial poles are the points of intersection of the axis of rotation of the earth with the earth sphere, and the terrestrial equator is the great circle of the earth which is perpendicular to the the axis of rotation of the earth.

4. Celestial poles and Celestial equator: If the earth's axis of rotation is extending on both direction, it will intersect with the celestial sphere at the two points, celestial poles. Similarly Celestial equator is the great circle of the celestial sphere, in which the plane of intersection of the terrestrial equator with the celestial sphere lies.

5. Sensible Horizon: In the celestial sphere the point of observation is taken as the center. Sensible horizon is a great circle of the celestial sphere which passes through the point of observation and is tangential to the earth surface, or which is perpendicular to the zenith-nadir line.

6.Vertical Circle: The vertical circle of a celestial sphere is a circle passing through the zenith and nadir and therefore all the vertical circles are perpendicular to the horizon.

7. Observer's meridian: It is a circle which passes through the zenith and nadir of the observation point as well as through the poles of the celestial sphere. So it is a vertical circle.

8.Prime meridian: It is a vertical circle which is at right angles to the observer's meridian.

9. Azimuth: It is the angular distance between the observer's meridian and the vertical circle passing through the observer(Zenith and Nadir) and the heavenly body.

10. Hour Angle: It is the angular distance between the declination circle and the observer's meridian.

11. Latitude: It is the angular distance of the zenith from the equator.

12. Co-latitude: It is complementary angle of the latitude, i.e. 90 - latitude. It is also known as the zenith distance from the poles.

13. Right Ascension: Right ascension is the angular distance along the equator of the heavenly body from the point of Aries. It is simply written as R.A. and is always measured in the right direction from 0 to 360.

14. Ecliptic: It is the the path of the Sun around the earth assuming the earth to be stationary, traveled in one complete year. Ecliptic intersects the equator at the point of Aries and the Libra just opposite to Aries. It is the spring season when summer enters into Aries to the northern hemisphere, and it is the start of winter in the northern hemisphere when it passes the Libra and enters into the southern hemisphere.

There are some important things to discuss to understand the position of the star, or a heavenly body.

Napier's Rule: Napier's rule can be be used to solve the spherical trigonometry dealing with the right angled spherical triangles. If we arrange the 5 remaining angles in a circle in the manner as shown in fig. below, then we can get the other three angles if two of the angles are known.

The formula used is written in the photo itself. It says the sine of the middle angle is equal to the product of the tangents of the adjacent angles and product of the cosines of the opposite angles.

Star at elongation: The star is said to be at elongation when it is at its farthest point towards east or towards the west from the observer's meridian. This is point where the path of the star is tangent to the vertical circle passing through the star and the zenith nadir line. So in this position the star angle M is 90 degrees.

Star at prime vertical: When the star is on the prime vertical which is the vertical circle at right angle to the observer's meridian, the star is said to be at the prime vertical. So in this position the Azimuth is 90 degrees.

Star at horizon: When the star is at the horizon then the altitude of the star is zero, so the co-altitude or the zenith distance is 90 degrees.

Star at culmination: When the star is on the observer's meridian, either culminating from the east to west or from west to east, the star is said to be at culmination.

Aphelion: This is the point on the elliptic path of the Sun when it is at its farthest distance from the earth (Earth is assumed to be stationary, at one of the foci of the ellipse.)

Perihelion: Perihelion is another point on the ecliptic when the Sun is at the nearest distance from the earth. When the Sun is at its nearest distance to the earth, the apparent motion of the Sun is faster, as compared to other positions. 

Note:The Sun is always stationary, but it astronomy we assume the earth to be the center of the universe, so we assume the Sun to be moving. It is called its apparent motion.

Sidereal Time: It is a time which is obtained using the sidereal time system. In the Sidereal time system, the time at any place can be measured by measuring the longitude eastwards from the first point of Aries to the meridian of the place along the equator.

If at any moment, Sun's Right Ascension is known and the hour angle is known, then we can find the Local sidereal time = Right Ascension of the sun + Hour angle of the Sun

Apparent/ True Solar Time: It is the time obtained based on the Sun's motion above a given place. In this system the time is measured as 0 hours 0 min 0 Sec, when the Sun is at its lower transit, means when it is midnight at the place. It is 12 Hours 0min 0sec, when the Sun is over the head of the place. So a day is the time interval between two consecutive transits of the Sun from the place.

The day is divided into 24 hours, so each hour Sun moves 15 degrees westwards. unfortunately the length of the day is not the same throughout the year, so this system can not be adopted in the digital watches of the modern day.

The days are of variable length due to the obliquity of the path of the Sun and the non-uniform motion of the Sun around the earth.

Mean Solar Time: So a new system is originated to measure the time, it is known as the mean solar time. There is a mean Sun, which revolves around the earth in a uniform speed, on the equatorial path. So the days are of the uniform length throughout the year. A mean solar day is the average of the lengths of the 365 days of a year. The watches give us the mean solar time.

Equation of Time: So as we know that there is a difference between the true solar time and the mean solar time, this difference is known as the equation of time.

So the equation of time = Apparent Solar time - Mean solar time

The apparent solar time and mean solar time, are one behind the other at various time periods of a year. Sometimes, the Apparent solar time is forward of Mean Solar time and sometime vice verse. So the equation of time is either positive or it is negative. There are four times in a year when the equation of time becomes zero, one such day is April 16 of the year.

It can all be understood by considering the obliquity of the path of the Sun and the non-uniform motion of the Sun around the earth.

Standard Time: To have the same time at all the places on the earth, the meridian passing through the Greenwich is taken as the standard. So when the mean Sun passes through the standard meridian, the standard time is 12h 0m 0sec in the noon. The standard time is same at all the places in the earth, but the local times can be found out by knowing the longitude of the place, from the Greenwich meridian, and adding or subtracting it, whether it is on the east or west of the standard meridian, respectively.

Converting angular distance  into hourly time:

If I want to change the angular distance (longitude) into the time, I use the following relationships:

•  360 degrees(Angular) = 24 hours. (time)             1 hour(time) = 15 degrees.(angular)
• 1 degrees (angular) = 4 min.  (time)                     1 min (time)= 15 minutes(angular)
• 1 min(angular) = 4 seconds(time)         1 seconds(time) = 15 seconds(angular)    

So a longitude of 82 degrees 30 minutes   = 5 hours 30 minutes

Thanks