SOME TERMS USED IN LEVELLING OPERATIONS
1. Bench mark (BM): it is a fixed point on the earth’s surface whose level above ordance
datum is known.
2. Ordnance Datum (OD): it is the mean sea level to which all other levels are related.
3. Back sight (BS): is the first sight taken after the level has been set up. A sight taken to a
point whose height is known or can be calculated.
4. Foresight (FS): The last sight taken. A sight taken to a point whose height is required to
carry on the line of level.
5. Intermediate Sight (IS): it is any other sight taken.
6. Reduced Level (RL): calculated level of a point above or below the datum.
7. Height of Instrument (HI): The height of the line of collimation above the datum.
8. Line of Collimation (LM): It is an imaginary horizontal line drawn between two points.
9. Rise and fall: The difference is height or is level between two is referred to as a rise or fall.
10. Change Point (CP): the point at which both a foresight and then a back sight are taken.
LEVELING INSTRUMENTS
These include:
. A Level e.g. theodolite, transit dumpy level(automatic level),e.t.c.
. A staff
. Devices for angle measurements e.g. graphometer, magnetic compass, prismatic compass,
orientation compass
. Chain or tape
. Pegs, arrows and ranging poles
Land Survey, Setting-Out Engineering, GIS Processing, Structural/Civil Works and General Contracts Call +2347064649087 www.heroizutechng.blogspot.com.ng
Tuesday 9 August 2016
Sunday 7 August 2016
LESSON NOTE ON INTRODUCTION TO SPHERICAL TRIANGLE
Solution of triangles Solution of triangles, is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known. The triangle can be located on a plane or on a sphere. Applications requiring triangle solutions include geodesy, astronomy, construction, and navigation.
Solving plane triangles Edit Standard notation for a triangle A general form triangle has six main characteristics (see picture): three linear (side lengths a, b, c) and three angular (α, β, γ). The classical plane trigonometry problem is to specify three of the six characteristics and determine the other three. A triangle can be uniquely determined in this sense when given any of the following:[1][2] Three sides (SSS) Two sides and the included angle (SAS) Two sides and an angle not included between them (SSA), if the side length adjacent to the angle is shorter than the other side length. A side and the two angles adjacent to it (ASA) A side, the angle opposite to it and an angle adjacent to it (AAS).
Three angles (AAA) on the sphere (but not in the plane). For all cases in the plane, at least one of the side lengths must be specified. If only the angles are given, the side lengths cannot be determined, because any similar triangle is a solution. Main theorems Edit  Overview of particular steps and tools used when solving plane triangles The standard method of solving the problem is to use fundamental relations. Law of cosines {\displaystyle a^{2}=b^{2}+c^{2}-2bc\cos \alpha } {\displaystyle b^{2}=a^{2}+c^{2}-2ac\cos \beta } {\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos \gamma } Law of sines {\displaystyle {\frac {a}{\sin \alpha }}={\frac {b}{\sin \beta }}={\frac {c}{\sin \gamma }}} Sum of angles {\displaystyle \alpha +\beta +\gamma =180^{\circ }} Law of tangents {\displaystyle {\frac {a-b}{a+b}}={\frac {\mathrm {tan} [{\frac {1}{2}}(\alpha -\beta )]}{\mathrm {tan} [{\frac {1}{2}}(\alpha +\beta )]}}.} There are other (sometimes practically useful) universal relations: the law of cotangents and Mollweide's formula. Notes Edit To find an unknown angle, the law of cosines is safer than the law of sines. The reason is that the value of sine for the angle of the triangle does not uniquely determine this angle. For example, if sin β = 0.5, the angle β can equal either 30° or 150°. Using the law of cosines avoids this problem: within the interval from 0° to 180° the cosine value unambiguously determines its angle. On the other hand, if the angle is small (or close to 180°), then it is more robust numerically to determine it from its sine than its cosine because the arc-cosine function has a divergent derivative at 1 (or −1). We assume that the relative position of specified characteristics is known. If not, the mirror reflection of the triangle will also be a solution. For example, three side lengths uniquely define either a triangle or its reflection.  Three sides given Three sides given (SSS) Edit Let three side lengths a, b, c be specified. To find the angles α, β, the law of cosines can be used:[3] {\displaystyle \alpha =\arccos {\frac {b^{2}+c^{2}-a^{2}}{2bc}}} {\displaystyle \beta =\arccos {\frac {a^{2}+c^{2}-b^{2}}{2ac}}.} Then angle γ = 180° − α − β. Some sources recommend to find angle β from the law of sines but (as Note 1 above states) there is a risk of confusing an acute angle value with an obtuse one. Another method of calculating the angles from known sides is to apply the law of cotangents.  Two sides and the included angle given Two sides and the included angle given (SAS) Edit Here the lengths of sides a, b and the angle γ between these sides are known. The third side can be determined from the law of cosines:[4] {\displaystyle c={\sqrt {a^{2}+b^{2}-2ab\cos \gamma }}.} Now we use law of cosines to find the second angle: {\displaystyle \alpha =\arccos {\frac {b^{2}+c^{2}-a^{2}}{2bc}}.} Finally, β = 180° − α − γ.  Two sides and a non-included angle given Two sides and non-included angle given (SSA) Edit This case is not solvable in all cases; a solution is guaranteed to be unique only if the side length adjacent to the angle is shorter than the other side length. Assume that two sides b, c and the angle β are known. The equation for the angle γ can be implied from the law of sines:[5] {\displaystyle \sin \gamma ={\frac {c}{b}}\sin \beta .} We denote further D = c / b sin β (the equation's right side). There are four possible cases: If D > 1, no such triangle exists because the side b does not reach line BC. For the same reason a solution does not exist if the angle β ≥ 90° and b ≤ c. If D = 1, a unique solution exists: γ = 90°, i.e., the triangle is right-angled.  Two solutions for the triangle If D < 1 two alternatives are possible. If b < c, the angle γ may be acute: γ = arcsin D or obtuse: γ′ = 180° - γ. The picture on right shows the point C, the side b and the angle γ as the first solution, and the point C′, side b′ and the angle γ′ as the second solution. If b ≥ c then β ≥ γ (the larger side corresponds to a larger angle). Since no triangle can have two obtuse angles, γ is an acute angle and the solution γ = arcsin D is unique. Once γ is obtained, the third angle α = 180° − β − γ. The third side can then be found from the law of sines: {\displaystyle a=b\ {\frac {\sin \alpha }{\sin \beta }}}  One side and two adjacent angles given A side and two adjacent angles given (ASA) Edit The known characteristics are the side c and the angles α, β. The third angle γ = 180° − α − β. Two unknown side can be calculated from the law of sines:[6] {\displaystyle a=c\ {\frac {\sin \alpha }{\sin \gamma }};\quad b=c\ {\frac {\sin \beta }{\sin \gamma }}.} A side, one adjacent angle and the opposite angle given (AAS) Edit The procedure for solving an AAS triangle is same as that for an ASA triangle: First, find the third angle by using the angle sum property of a triangle, then find the other two sides using the law of sines. 
LESSON NOTE ON INTRODUCTION TO SPHERICAL TRIANGLE
Solution of triangles Solution of triangles, is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known. The triangle can be located on a plane or on a sphere. Applications requiring triangle solutions include geodesy, astronomy, construction, and navigation.
Solving plane triangles Edit Standard notation for a triangle A general form triangle has six main characteristics (see picture): three linear (side lengths a, b, c) and three angular (α, β, γ). The classical plane trigonometry problem is to specify three of the six characteristics and determine the other three. A triangle can be uniquely determined in this sense when given any of the following:[1][2] Three sides (SSS) Two sides and the included angle (SAS) Two sides and an angle not included between them (SSA), if the side length adjacent to the angle is shorter than the other side length. A side and the two angles adjacent to it (ASA) A side, the angle opposite to it and an angle adjacent to it (AAS).
Three angles (AAA) on the sphere (but not in the plane). For all cases in the plane, at least one of the side lengths must be specified. If only the angles are given, the side lengths cannot be determined, because any similar triangle is a solution. Main theorems Edit  Overview of particular steps and tools used when solving plane triangles The standard method of solving the problem is to use fundamental relations. Law of cosines {\displaystyle a^{2}=b^{2}+c^{2}-2bc\cos \alpha } {\displaystyle b^{2}=a^{2}+c^{2}-2ac\cos \beta } {\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos \gamma } Law of sines {\displaystyle {\frac {a}{\sin \alpha }}={\frac {b}{\sin \beta }}={\frac {c}{\sin \gamma }}} Sum of angles {\displaystyle \alpha +\beta +\gamma =180^{\circ }} Law of tangents {\displaystyle {\frac {a-b}{a+b}}={\frac {\mathrm {tan} [{\frac {1}{2}}(\alpha -\beta )]}{\mathrm {tan} [{\frac {1}{2}}(\alpha +\beta )]}}.} There are other (sometimes practically useful) universal relations: the law of cotangents and Mollweide's formula. Notes Edit To find an unknown angle, the law of cosines is safer than the law of sines. The reason is that the value of sine for the angle of the triangle does not uniquely determine this angle. For example, if sin β = 0.5, the angle β can equal either 30° or 150°. Using the law of cosines avoids this problem: within the interval from 0° to 180° the cosine value unambiguously determines its angle. On the other hand, if the angle is small (or close to 180°), then it is more robust numerically to determine it from its sine than its cosine because the arc-cosine function has a divergent derivative at 1 (or −1). We assume that the relative position of specified characteristics is known. If not, the mirror reflection of the triangle will also be a solution. For example, three side lengths uniquely define either a triangle or its reflection.  Three sides given Three sides given (SSS) Edit Let three side lengths a, b, c be specified. To find the angles α, β, the law of cosines can be used:[3] {\displaystyle \alpha =\arccos {\frac {b^{2}+c^{2}-a^{2}}{2bc}}} {\displaystyle \beta =\arccos {\frac {a^{2}+c^{2}-b^{2}}{2ac}}.} Then angle γ = 180° − α − β. Some sources recommend to find angle β from the law of sines but (as Note 1 above states) there is a risk of confusing an acute angle value with an obtuse one. Another method of calculating the angles from known sides is to apply the law of cotangents.  Two sides and the included angle given Two sides and the included angle given (SAS) Edit Here the lengths of sides a, b and the angle γ between these sides are known. The third side can be determined from the law of cosines:[4] {\displaystyle c={\sqrt {a^{2}+b^{2}-2ab\cos \gamma }}.} Now we use law of cosines to find the second angle: {\displaystyle \alpha =\arccos {\frac {b^{2}+c^{2}-a^{2}}{2bc}}.} Finally, β = 180° − α − γ.  Two sides and a non-included angle given Two sides and non-included angle given (SSA) Edit This case is not solvable in all cases; a solution is guaranteed to be unique only if the side length adjacent to the angle is shorter than the other side length. Assume that two sides b, c and the angle β are known. The equation for the angle γ can be implied from the law of sines:[5] {\displaystyle \sin \gamma ={\frac {c}{b}}\sin \beta .} We denote further D = c / b sin β (the equation's right side). There are four possible cases: If D > 1, no such triangle exists because the side b does not reach line BC. For the same reason a solution does not exist if the angle β ≥ 90° and b ≤ c. If D = 1, a unique solution exists: γ = 90°, i.e., the triangle is right-angled.  Two solutions for the triangle If D < 1 two alternatives are possible. If b < c, the angle γ may be acute: γ = arcsin D or obtuse: γ′ = 180° - γ. The picture on right shows the point C, the side b and the angle γ as the first solution, and the point C′, side b′ and the angle γ′ as the second solution. If b ≥ c then β ≥ γ (the larger side corresponds to a larger angle). Since no triangle can have two obtuse angles, γ is an acute angle and the solution γ = arcsin D is unique. Once γ is obtained, the third angle α = 180° − β − γ. The third side can then be found from the law of sines: {\displaystyle a=b\ {\frac {\sin \alpha }{\sin \beta }}}  One side and two adjacent angles given A side and two adjacent angles given (ASA) Edit The known characteristics are the side c and the angles α, β. The third angle γ = 180° − α − β. Two unknown side can be calculated from the law of sines:[6] {\displaystyle a=c\ {\frac {\sin \alpha }{\sin \gamma }};\quad b=c\ {\frac {\sin \beta }{\sin \gamma }}.} A side, one adjacent angle and the opposite angle given (AAS) Edit The procedure for solving an AAS triangle is same as that for an ASA triangle: First, find the third angle by using the angle sum property of a triangle, then find the other two sides using the law of sines. 
Wednesday 3 August 2016
LessonNote On Procedure of Chaining
Procedure of Chaining
It must be remembered in surveying, that under most circumstances, all distances are presumed to be horizontal distances and not surface distances.
• This dictates that every field measurement taken be either measured horizontally or, if not, reduced to a horizontal distance mathematically.
• In many instances, it is easiest to simply measure the horizontal distance by keeping both ends of the chain at the same elevation. This is not difficult if there is less than five feet or so of elevation change between points. A hand level or “pea gun” is very helpful for maintaining the horizontal position of the chain when “level chaining.” A pointed weight on the end of a string called a “plumb bob” is used to carry the location of the point on the ground up to the elevated chain by simply suspending the plumb bob from the chain such that the point of the plumb bob hangs directly above the point on the ground.
• When the difference in elevation along the measurement becomes too great for level chaining, other methods are called for. One option, “break chaining”, involves simply breaking the measurement into two or more measurements that can be chained level.
Distance Measuring (Electronic Distance Meters)
In the early 1950’s the first Electronic Distance Measuring (EDM) equipment were developed. These primarily consisted of electro-optical (light waves) and electromagnetic (microwave) instruments. They were bulky, heavy and expensive. The typical EDM today uses the electro-optical principle. They are small, reasonably light weight, highly accurate, but still expensive.
Principle of Chaining
• To measure any distance, you simply compare it to a known or calibrated distance; for example by using a scale or tape to measure the length of an object. In EDM’s the same comparison principle is used. The calibrated distance, in this case, is the wavelength of the modulation on a carrier wave.
• Modern EDM’s use the precision of a Quartz Crystal Oscillator and the measurement of phase-shift to determine the distance.
• The EDM is set up at one end of the distance to be measured and a reflector at the other end.
• The EDM generates an infrared continuous-wave carrier beam, which is modulated by an electronic shutter (Quartz crystal oscillator).
• This beam is then transmitted through the aiming optics to the reflector.
• The reflector returns the beam to the receiving optics, where the incoming light is converted to an electrical signal, allowing a phase comparison between transmitted and received signals.
• The amount by which the transmitted and received wavelengths are out of phase, can be measured electronically and registered on a meter to within a millimeter or two.
Angle Measuring
Measuring distances alone in surveying does not establish the location of an object. We need to locate the object in 3 dimensions. To accomplish that we need:
1. Horizontal length (distance)
2. Difference in height (elevation)
3. Angular direction.
An angle is defined as the difference in direction between two convergent lines. A horizontal angle is formed by the directions to two objects in a horizontal plane. A vertical angle is formed by two intersecting lines in a vertical plane, one of these lines horizontal. A zenith angle is the complementary angle to the vertical angle and is formed by two intersecting lines in a vertical plane, one of these lines directed toward the zenith.
Types of Measured Angles
• Interior angles are measured clockwise or counter-clockwise between two adjacent lines on the inside of a closed polygon figure.
• Exterior angles are measured clockwise or counter-clockwise between two adjacent lines on the outside of a closed polygon figure.
• Deflection angles, right or left, are measured from an extension of the preceding course and the ahead line. It must be noted when the deflection is right (R) or left (L).
A Theodolite is a precision surveying instrument; consisting of an alidade with a telescope and an accurately graduated circle; and equipped with the necessary levels and optical-reading circles. The glass horizontal and vertical circles, optical-reading system, and all mechanical parts are enclosed in an alidade section along with 3 leveling screws contained in a detachable base or tribrach.
A Transit is a surveying instrument having a horizontal circle divided into degrees, minutes, and seconds. It has a vertical circle or arc. Transits are used to measure horizontal and vertical angles. The graduated circles (plates) are on the outside of the instrument and angles have to be read by using a vernier.
Bearings and Azimuths
The Relative directions of lines connecting survey points may be obtained in a variety of ways. The figure below on the left shows lines intersecting at a point. The direction of any line with respect to an adjacent line is given by the horizontal angle between the 2 lines and the direction of rotation. The figure on the right shows the same system of lines but with all the angles measured from a line of reference (O-M). The direction of any line with respect to the line of reference is given by the angle between the lines and its direction of rotation.
It must be remembered in surveying, that under most circumstances, all distances are presumed to be horizontal distances and not surface distances.
• This dictates that every field measurement taken be either measured horizontally or, if not, reduced to a horizontal distance mathematically.
• In many instances, it is easiest to simply measure the horizontal distance by keeping both ends of the chain at the same elevation. This is not difficult if there is less than five feet or so of elevation change between points. A hand level or “pea gun” is very helpful for maintaining the horizontal position of the chain when “level chaining.” A pointed weight on the end of a string called a “plumb bob” is used to carry the location of the point on the ground up to the elevated chain by simply suspending the plumb bob from the chain such that the point of the plumb bob hangs directly above the point on the ground.
• When the difference in elevation along the measurement becomes too great for level chaining, other methods are called for. One option, “break chaining”, involves simply breaking the measurement into two or more measurements that can be chained level.
Distance Measuring (Electronic Distance Meters)
In the early 1950’s the first Electronic Distance Measuring (EDM) equipment were developed. These primarily consisted of electro-optical (light waves) and electromagnetic (microwave) instruments. They were bulky, heavy and expensive. The typical EDM today uses the electro-optical principle. They are small, reasonably light weight, highly accurate, but still expensive.
Principle of Chaining
• To measure any distance, you simply compare it to a known or calibrated distance; for example by using a scale or tape to measure the length of an object. In EDM’s the same comparison principle is used. The calibrated distance, in this case, is the wavelength of the modulation on a carrier wave.
• Modern EDM’s use the precision of a Quartz Crystal Oscillator and the measurement of phase-shift to determine the distance.
• The EDM is set up at one end of the distance to be measured and a reflector at the other end.
• The EDM generates an infrared continuous-wave carrier beam, which is modulated by an electronic shutter (Quartz crystal oscillator).
• This beam is then transmitted through the aiming optics to the reflector.
• The reflector returns the beam to the receiving optics, where the incoming light is converted to an electrical signal, allowing a phase comparison between transmitted and received signals.
• The amount by which the transmitted and received wavelengths are out of phase, can be measured electronically and registered on a meter to within a millimeter or two.
Angle Measuring
Measuring distances alone in surveying does not establish the location of an object. We need to locate the object in 3 dimensions. To accomplish that we need:
1. Horizontal length (distance)
2. Difference in height (elevation)
3. Angular direction.
An angle is defined as the difference in direction between two convergent lines. A horizontal angle is formed by the directions to two objects in a horizontal plane. A vertical angle is formed by two intersecting lines in a vertical plane, one of these lines horizontal. A zenith angle is the complementary angle to the vertical angle and is formed by two intersecting lines in a vertical plane, one of these lines directed toward the zenith.
Types of Measured Angles
• Interior angles are measured clockwise or counter-clockwise between two adjacent lines on the inside of a closed polygon figure.
• Exterior angles are measured clockwise or counter-clockwise between two adjacent lines on the outside of a closed polygon figure.
• Deflection angles, right or left, are measured from an extension of the preceding course and the ahead line. It must be noted when the deflection is right (R) or left (L).
A Theodolite is a precision surveying instrument; consisting of an alidade with a telescope and an accurately graduated circle; and equipped with the necessary levels and optical-reading circles. The glass horizontal and vertical circles, optical-reading system, and all mechanical parts are enclosed in an alidade section along with 3 leveling screws contained in a detachable base or tribrach.
A Transit is a surveying instrument having a horizontal circle divided into degrees, minutes, and seconds. It has a vertical circle or arc. Transits are used to measure horizontal and vertical angles. The graduated circles (plates) are on the outside of the instrument and angles have to be read by using a vernier.
Bearings and Azimuths
The Relative directions of lines connecting survey points may be obtained in a variety of ways. The figure below on the left shows lines intersecting at a point. The direction of any line with respect to an adjacent line is given by the horizontal angle between the 2 lines and the direction of rotation. The figure on the right shows the same system of lines but with all the angles measured from a line of reference (O-M). The direction of any line with respect to the line of reference is given by the angle between the lines and its direction of rotation.
METHODS EMPLOYED IN LOCATING SOUNDINGS
METHODS EMPLOYED IN LOCATING SOUNDINGS
The soundings are located with reference to the shore traverse by observations made
(i) entirely from the boat,
(ii) entirely from the shore or
(iii) from both. The following are the methods of location
1. By cross rope.
2. By range and time intervals.
3. By range and one angle from the shore.
4. By range and one angle from the boat.
5. By two angles from the shore.
6. By two angles from the boat.
7. By one angle from shore and one from boat.
8. By intersecting ranges.
9. By tacheometry.
Range: A range or range line is the line on which soundings are taken. They are, in general, laid perpendicular to the shore line and parallel to each other if the shore is straight or are arranged radiating from a prominent object when the shore line is very irregular.
Shore signals.
Each range line is marked by means of signals erected at two points on it at a considerable distance apart. Signals can be constructed in a variety of ways. They should be readily seen and easily distinguished from each other. The most satisfactory and economic type of signal is a wooden tripod structure dressed with white and coloured signal of cloth. The position of the signals should be located very accurately since all the soundings are to be located with reference to these signals.
Location by Cross-Rope
This is the most accurate method of locating the soundings and may be used for rivers, narrow lakes and for harbours. It is also used to determine the quantity of materials removed by dredging the soundings being taken before and after the dredging work is done. A single wire or rope is stretched across the channel etc. as shown in Fig.4.6 and is marked by metal tags at appropriate known distance along the wire from a reference point or zero station on shore. The soundings are then taken by a weighted pole. The position of the pole during a sounding is given by the graduated rope or line. In another method, specially used for harbours etc., a reel boat is used to stretch the rope. The zero end of the rope is attached to a spike or any other attachment on one shore. The rope is would on a drum on the reel boat. The reel boat is then rowed across the line of sounding, thus unwinding the rope as it proceeds. When the reel boat reaches the other shore, its anchor is taken ashore and the rope is wound as tightly as possible. If anchoring is not possible, the reel is taken ashore and spiked down. Another boat, known as the sounding boat, then starts from the previous shore and soundings are taken against each tag of the rope. At the end of the soundings along that line, the reel boat is rowed back along the line thus winding in the rope. The work thus proceeds.
Location by Range and Time Intervals
In this method, the boat is kept in range with the two signals on the shore and is rowed along it at constant speed. Soundings are taken at different time intervals. Knowing the constant speed and the total time elapsed at the instant of sounding, the distance of the total point can be known along the range. The method is used when the width of channel is small and when great degree of accuracy is not required. However, the method is used in conjunction with other methods, in which case the first and the last soundings along a range are located by angles from the shore and the intermediate soundings are located by interpolation according to time intervals.
Location by Range and One Angle from the Shore
In this method, the boat is ranged in line with the two shore signals and rowed along the ranges. The point where sounding is taken is fixed on the range by observation of the angle from the shore. As the boat proceeds along the shore, other soundings are also fixed by the observations of angles from the shore. Thus B is the instrument station, A1 A2 is the range along which the boat is rowed and α1, α2, α3 etc., are the angles measured at B from points 1, 2, 3 etc. The method is very accurate and very convenient for plotting. However, if the angle at the sounding point (say angle β) is less than 30°, the fix becomes poor. The nearer the intersection angle (β) is to a right angle, the better. If the angle diminishes to about 30° a new instrument station must be chosen. The only defect of the method is that the surveyor does not have an immediate control in all the observation. If all the points are to be fixed by angular observations from the shore, a note-keeper will also be required along with the instrument man at shore since the observations and the recordings are to be done rapidly. Generally, the first and last soundings and every tenth sounding are fixed by angular observations and the intermediate points are fixed by time intervals. Thus the points with round mark are fixed by angular observations from the shore and the points with cross marks are fixed by time intervals. The arrows show the course of the boat, seaward and shoreward on alternate sections.
To fix a point by observations from the shore, the instrument man at B orients his line of sight towards a shore signal or any other prominent point (known on the plan) when the reading is zero. He then directs the telescope towards the leadsman or the bow of the boat, and is kept continually pointing towards the boat as it moves. The surveyor on the boat holds a flag for a few seconds and on the fall of the flag, the sounding and the angle are observed simultaneously.
The angles are generally observed to the nearest 5 minutes. The time at which the flag falls is also recorded both by the instrument man as well as on the boat. In order to avoid acute intersections, the lines of soundings are previously drawn on the plan and suitable instrument stations are selected.
Location by Range and One Angle from the Boat
The method is exactly similar to the previous one except that the angular fix is made by angular observation from the boat. The boat is kept in range with the two shore signals and is rowed along it. At the instant the sounding is taken, the angle, subtended at the point between the range and some prominent point B on the sore is measured with the help of sextant. The telescope is directed on the range signals, and the side object is brought into coincidence at the instant the sounding is taken. The accuracy and ease of plotting is the same as obtained in the previous method. Generally, the first and the last soundings, and some of the intermediate soundings are located by angular observations and the rest of the soundings are located by time intervals.
As compared to the previous methods, this method has the following advantages :
1. Since all the observations are taken from the boat, the surveyor has better control over the operations.
2. The mistakes in booking are reduced since the recorder books the readings directly as they are measured.
3. On important fixes, check may be obtained by measuring a second angle towards some other signal on the shore.
4. The obtain good intersections throughout, different shore objects may be used for reference to measure the angles.
Location by Two Angles from the Shore
In this method, a point is fixed independent of the range by angular observations from two points on the shore. The method is generally used to locate some isolated points. If this method is used on an extensive survey, the boat should be run on a series of approximate ranges. Two instruments and two instrument men are required. The position of instrument is selected in such a way that a strong fix is obtained. New instrument stations should be chosen when the intersection angle (θ) falls below 30°. Thus A and B are the two instrument stations. The distance d between them is very accuarately measured. The instrument stations A and B are precisely connected to the ground traverse or triangulation, and their positions on plan are known. With both the plates clamped to zero, the instrument man at A
bisects B ; similarly with both the plates clamped to zero, the instrument man at B bisects A. Both the instrument men then direct the line of sight of the telescope towards the leadsman and continuously follow it as the boat moves. The surveyor on the boat holds a flag for a few seconds, and on the fall of the flag the sounding and the angles are observed simultaneously. The co-ordinates of the position P of the sounding may be computed from the relations :
The method has got the following advantages:
1. The preliminary work of setting out and erecting range signals is eliminated.
2. It is useful when there are strong currents due to which it is difficult to row the boat along the range line.
The method is, however, laborious and requires two instruments and two instrument men.
Location by Two Angles from the Boat
In this method, the position of the boat can be located by the solution of the three point problem by observing the two angles subtended at the boat by three suitable shore objects of known position. The three-shore points should be well-defined and clearly visible. Prominent natural objects such as church spire, lighthouse, flagstaff, buoys etc., are selected for this purpose. If such points are not available, range poles or shore signals may be taken. Thus A, B and C are the shore objects and P is the position of the boat from which the angles α and β are measured. Both the angles should be observed simultaneously with the help of two sextants, at the instant the sounding is taken. If both the angles are observed by surveyor alone, very little time should be lost in taking the observation. The angles on the circle are read afterwards. The method is used to take the soundings at isolated points. The surveyor has better control on the operations since the survey party is concentrated in one boat. If sufficient number of prominent points are available on the shore, preliminary work o setting out and erecting range signals is eliminated. The position of the boat is located by the solution of the three point problem either analytically or graphically.
Location by One Angle from the Shore and the other from the Boat
This method is the combination of methods 5 and 6 described above and is used to locate the isolated points where soundings are taken. Two points A and B are chosen on the shore, one of the points (say A) is the instrument station where a theodolite is set up, and the other (say B) is a shore signal or any other prominent object. At the instant the sounding is taken at P, the angle α at A is measured with the help of a sextant. Knowing the distance d between the two points A and B by ground survey, the position of P can be located by calculating the two co-ordinates x and y.
Location by Intersecting Ranges
This method is used when it is required to determine by periodical sounding at the same points, the rate at which silting or scouring is taking place. This is very essential on the harbors and reservoirs. The position of sounding is located by the intersection of two ranges, thus completely avoiding the angular observations. Suitable signals are erected at the shore. The boat is rowed along a range perpendicular to the shore and soundings are taken at the points in which inclined ranges intersect the range, as illustrated in Fig. 4.12. However, in order to avoid the confusion, a definite system of flagging the range poles is necessary. The position of the range poles is determined very accurately by ground survey.
Location by Tacheometric Observations
The method is very much useful in smooth waters. The position of the boat is located by tacheometric observations from the shore on a staff kept vertically on the boat. Observing the staff intercept s at the instant the sounding is taken, the horizontal distance between the instrument stations and the boat is calculated by
The direction of the boat (P) is established by observing the angle (α) at the instrument station B with reference to any prominent object A The transit station should be near the water level so that there will be no need to read vertical angles. The method is unsuitable when soundings are taken far from shore.
The soundings are located with reference to the shore traverse by observations made
(i) entirely from the boat,
(ii) entirely from the shore or
(iii) from both. The following are the methods of location
1. By cross rope.
2. By range and time intervals.
3. By range and one angle from the shore.
4. By range and one angle from the boat.
5. By two angles from the shore.
6. By two angles from the boat.
7. By one angle from shore and one from boat.
8. By intersecting ranges.
9. By tacheometry.
Range: A range or range line is the line on which soundings are taken. They are, in general, laid perpendicular to the shore line and parallel to each other if the shore is straight or are arranged radiating from a prominent object when the shore line is very irregular.
Shore signals.
Each range line is marked by means of signals erected at two points on it at a considerable distance apart. Signals can be constructed in a variety of ways. They should be readily seen and easily distinguished from each other. The most satisfactory and economic type of signal is a wooden tripod structure dressed with white and coloured signal of cloth. The position of the signals should be located very accurately since all the soundings are to be located with reference to these signals.
Location by Cross-Rope
This is the most accurate method of locating the soundings and may be used for rivers, narrow lakes and for harbours. It is also used to determine the quantity of materials removed by dredging the soundings being taken before and after the dredging work is done. A single wire or rope is stretched across the channel etc. as shown in Fig.4.6 and is marked by metal tags at appropriate known distance along the wire from a reference point or zero station on shore. The soundings are then taken by a weighted pole. The position of the pole during a sounding is given by the graduated rope or line. In another method, specially used for harbours etc., a reel boat is used to stretch the rope. The zero end of the rope is attached to a spike or any other attachment on one shore. The rope is would on a drum on the reel boat. The reel boat is then rowed across the line of sounding, thus unwinding the rope as it proceeds. When the reel boat reaches the other shore, its anchor is taken ashore and the rope is wound as tightly as possible. If anchoring is not possible, the reel is taken ashore and spiked down. Another boat, known as the sounding boat, then starts from the previous shore and soundings are taken against each tag of the rope. At the end of the soundings along that line, the reel boat is rowed back along the line thus winding in the rope. The work thus proceeds.
Location by Range and Time Intervals
In this method, the boat is kept in range with the two signals on the shore and is rowed along it at constant speed. Soundings are taken at different time intervals. Knowing the constant speed and the total time elapsed at the instant of sounding, the distance of the total point can be known along the range. The method is used when the width of channel is small and when great degree of accuracy is not required. However, the method is used in conjunction with other methods, in which case the first and the last soundings along a range are located by angles from the shore and the intermediate soundings are located by interpolation according to time intervals.
Location by Range and One Angle from the Shore
In this method, the boat is ranged in line with the two shore signals and rowed along the ranges. The point where sounding is taken is fixed on the range by observation of the angle from the shore. As the boat proceeds along the shore, other soundings are also fixed by the observations of angles from the shore. Thus B is the instrument station, A1 A2 is the range along which the boat is rowed and α1, α2, α3 etc., are the angles measured at B from points 1, 2, 3 etc. The method is very accurate and very convenient for plotting. However, if the angle at the sounding point (say angle β) is less than 30°, the fix becomes poor. The nearer the intersection angle (β) is to a right angle, the better. If the angle diminishes to about 30° a new instrument station must be chosen. The only defect of the method is that the surveyor does not have an immediate control in all the observation. If all the points are to be fixed by angular observations from the shore, a note-keeper will also be required along with the instrument man at shore since the observations and the recordings are to be done rapidly. Generally, the first and last soundings and every tenth sounding are fixed by angular observations and the intermediate points are fixed by time intervals. Thus the points with round mark are fixed by angular observations from the shore and the points with cross marks are fixed by time intervals. The arrows show the course of the boat, seaward and shoreward on alternate sections.
To fix a point by observations from the shore, the instrument man at B orients his line of sight towards a shore signal or any other prominent point (known on the plan) when the reading is zero. He then directs the telescope towards the leadsman or the bow of the boat, and is kept continually pointing towards the boat as it moves. The surveyor on the boat holds a flag for a few seconds and on the fall of the flag, the sounding and the angle are observed simultaneously.
The angles are generally observed to the nearest 5 minutes. The time at which the flag falls is also recorded both by the instrument man as well as on the boat. In order to avoid acute intersections, the lines of soundings are previously drawn on the plan and suitable instrument stations are selected.
Location by Range and One Angle from the Boat
The method is exactly similar to the previous one except that the angular fix is made by angular observation from the boat. The boat is kept in range with the two shore signals and is rowed along it. At the instant the sounding is taken, the angle, subtended at the point between the range and some prominent point B on the sore is measured with the help of sextant. The telescope is directed on the range signals, and the side object is brought into coincidence at the instant the sounding is taken. The accuracy and ease of plotting is the same as obtained in the previous method. Generally, the first and the last soundings, and some of the intermediate soundings are located by angular observations and the rest of the soundings are located by time intervals.
As compared to the previous methods, this method has the following advantages :
1. Since all the observations are taken from the boat, the surveyor has better control over the operations.
2. The mistakes in booking are reduced since the recorder books the readings directly as they are measured.
3. On important fixes, check may be obtained by measuring a second angle towards some other signal on the shore.
4. The obtain good intersections throughout, different shore objects may be used for reference to measure the angles.
Location by Two Angles from the Shore
In this method, a point is fixed independent of the range by angular observations from two points on the shore. The method is generally used to locate some isolated points. If this method is used on an extensive survey, the boat should be run on a series of approximate ranges. Two instruments and two instrument men are required. The position of instrument is selected in such a way that a strong fix is obtained. New instrument stations should be chosen when the intersection angle (θ) falls below 30°. Thus A and B are the two instrument stations. The distance d between them is very accuarately measured. The instrument stations A and B are precisely connected to the ground traverse or triangulation, and their positions on plan are known. With both the plates clamped to zero, the instrument man at A
bisects B ; similarly with both the plates clamped to zero, the instrument man at B bisects A. Both the instrument men then direct the line of sight of the telescope towards the leadsman and continuously follow it as the boat moves. The surveyor on the boat holds a flag for a few seconds, and on the fall of the flag the sounding and the angles are observed simultaneously. The co-ordinates of the position P of the sounding may be computed from the relations :
The method has got the following advantages:
1. The preliminary work of setting out and erecting range signals is eliminated.
2. It is useful when there are strong currents due to which it is difficult to row the boat along the range line.
The method is, however, laborious and requires two instruments and two instrument men.
Location by Two Angles from the Boat
In this method, the position of the boat can be located by the solution of the three point problem by observing the two angles subtended at the boat by three suitable shore objects of known position. The three-shore points should be well-defined and clearly visible. Prominent natural objects such as church spire, lighthouse, flagstaff, buoys etc., are selected for this purpose. If such points are not available, range poles or shore signals may be taken. Thus A, B and C are the shore objects and P is the position of the boat from which the angles α and β are measured. Both the angles should be observed simultaneously with the help of two sextants, at the instant the sounding is taken. If both the angles are observed by surveyor alone, very little time should be lost in taking the observation. The angles on the circle are read afterwards. The method is used to take the soundings at isolated points. The surveyor has better control on the operations since the survey party is concentrated in one boat. If sufficient number of prominent points are available on the shore, preliminary work o setting out and erecting range signals is eliminated. The position of the boat is located by the solution of the three point problem either analytically or graphically.
Location by One Angle from the Shore and the other from the Boat
This method is the combination of methods 5 and 6 described above and is used to locate the isolated points where soundings are taken. Two points A and B are chosen on the shore, one of the points (say A) is the instrument station where a theodolite is set up, and the other (say B) is a shore signal or any other prominent object. At the instant the sounding is taken at P, the angle α at A is measured with the help of a sextant. Knowing the distance d between the two points A and B by ground survey, the position of P can be located by calculating the two co-ordinates x and y.
Location by Intersecting Ranges
This method is used when it is required to determine by periodical sounding at the same points, the rate at which silting or scouring is taking place. This is very essential on the harbors and reservoirs. The position of sounding is located by the intersection of two ranges, thus completely avoiding the angular observations. Suitable signals are erected at the shore. The boat is rowed along a range perpendicular to the shore and soundings are taken at the points in which inclined ranges intersect the range, as illustrated in Fig. 4.12. However, in order to avoid the confusion, a definite system of flagging the range poles is necessary. The position of the range poles is determined very accurately by ground survey.
Location by Tacheometric Observations
The method is very much useful in smooth waters. The position of the boat is located by tacheometric observations from the shore on a staff kept vertically on the boat. Observing the staff intercept s at the instant the sounding is taken, the horizontal distance between the instrument stations and the boat is calculated by
The direction of the boat (P) is established by observing the angle (α) at the instrument station B with reference to any prominent object A The transit station should be near the water level so that there will be no need to read vertical angles. The method is unsuitable when soundings are taken far from shore.
Wednesday 27 July 2016
How To Create a TIN Surface in Civil 3D
To Create a
TIN Surface
1.
Click Home tab
Create Ground Data panel
Surfaces drop-down
Create Surface
.
2.
Click
to select a
layer.
Note: If you do not select a layer, the surface is placed on the
current layer.
3.
In the properties grid, click the Value column for the Name property and enter a name for the
surface.
Note: To name the surface, click its default name and enter a new
name, or use the Name
Template.
4.
To change the style for the surface, click the Style property in the properties grid and
click
in the Value column.
The Select Surface Style dialog
box is displayed.
5.
To change the render material for the surface, click the Render Material property in the properties grid and
click
in the Valuecolumn.
The Select Render Material dialog
box is displayed.
6.
Click OK to create the
surface.
The surface name is displayed under the Surfaces collection in the Prospector tree.
LESSON NOTE ON MAP
WHAT
IS A MAP?
Introduction
1. Even from the earliest days
the urge for man to explore has been great. The early travellers used natural
features to help them find their way from place to place.
By noting the position of the
stars, the moon and the sun, man devised a method of finding out where he was.
This meant exploration past known boundaries was now possible. As the explorer
ventured further and further from home and recognizable features disappeared,
he would often sketch his surroundings so that the way home could be found more
easily. These early ‘maps’ where often drawn on animal hide, stone or reed paper.
2. If we think of the earth as a
sphere, we can imagine how it could be covered with imaginary lines to help
pinpoint a position on the surface. First of all the earth has an axis, running
from the True North pole to the True South pole - the only 2 points on earth
that do not rotate. Next, imagine a line that runs around the middle of the
earth half way between the North and South poles- this circular line is called the
equator.
3. If we add more lines running
parallel to the equator, they will also be circular, though smaller than the
equator; they are called lines of latitude. Lines on the Earth’s surface drawn
from pole to pole are called lines of longitude.
Longitude
4. Longitude lines, also called
meridians, are circular. They are numbered and have a starting point at
Greenwich in England. This line is numbered zero and called the prime meridian-
all other lines are either east or west of it. Every meridian from one pole to
the other - is a semi-circle, and has an anti-meridian on the opposite side of
the earth. A meridian and its anti-meridian together make a full circle round
the earth.
5. By numbering the lines, it
means that the whole of the earth can be covered.
The position of each line is
expressed in degrees away from the prime meridian.
For example in the diagram point ‘A’
is about 20° (degrees) west of the prime meridian. Point ‘B’ is about 40° east
of the prime meridian. Although this system can give reasonably accurate
positioning it is not accurate enough for everyday use, so each degree is
further broken down into 60 minutes. This now gives us a system of describing a
point’s location in terms of degrees and minutes either east or west of the
prime meridian (Greenwich).
Latitude
Lines of
Latitude
6. Lines of latitude are circles
drawn around the earth, parallel to the equator.
The equator, at zero degrees,
splits the earth into two halves, the northern hemisphere and southern
hemisphere. Using the lines of latitude you can describe any point’s location
in degrees and minutes either north or south of the equator.
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