Surveying PDF

INTRODUCTION TO SURVEYING ------------------------- **Surveying** -- the art and science of determining angular and linear measurements to establish the form, extent and relative position of points, lines and areas on or near the surface of the earth or on other extraterrestrial bodies through app...

INTRODUCTION TO SURVEYING ------------------------- **Surveying** -- the art and science of determining angular and linear measurements to establish the form, extent and relative position of points, lines and areas on or near the surface of the earth or on other extraterrestrial bodies through applied mathematics and the use of specialized equipment and techniques. TWO GENERAL CLASSIFICATIONS OF SURVEYING ======================================== **Plane surveying** -- that type of surveying in which the earth is considered to be a flat surface, and where distances and areas involved are of limited extent that the exact shape of the earth is disregarded. TYPES OF SURVEYS ================ **Cadastral surveys** -- usually closed surveys which are undertaken in urban and rural locations **City surveys** -- surveys of the areas in and near a city for the purpose of planning expansions or **Construction surveys** -- surveys which are undertaken at a construction site to provide data regarding grades, reference lines, dimensions, ground configuration and the location and elevation of structures which are of concern to engineers, architects and builders. **Forestry surveys** -- surveys executed in connection with forest management and mensuration, **Hydrographic surveys** -- refer to surveying streams, lakes, reservoirs, harbors, oceans and other bodies of water. These surveys are made to map shorelines, chart the shape of areas underlying water surfaces, and measure the flow of streams. They are of general importance in connection with navigation, development of water supply and resources, flood control, irrigation, production of hydroelectric power, subaqueous constructions and recreation. **Mine surveys** -- surveys which are performed to determine the position of all underground **Photogrammetric surveys** -- surveys which make use of photographs taken with specially **Route surveys** -- involve the determination of alignment, grades, earthwork quantities, location **Topographic surveys** -- surveys made for determining the shape of the ground, and the DEVELOPMENT OF SURVEYING INSTRUMENT ----------------------------------- **Astrolabe** -- The astrolabe of Hipparchus is considered to be one of the best known of the **Telescope** -- The invention of the telescope in 1607 is accredited to Lippershey. In 1609, **Transit** -- The invention of the transit is credited to Young and Draper who worked **Semicircumferentor** -- An early surveying instrument which was used to measure and lay off **Plane table** -- It consists of a board attached to a tripod in such a way that it can be leveled or **Dioptra** -- The dioptra, which was perfected by Heron of Alexandria, was used in leveling and **Roman Groma** -- It is an instrument for aligning or sighting points. It consisted basically of **Libella** -- The instrument had an A -- frame with a plumb line suspended from its apex and was **Vernier** -- The vernier is a short auxiliary scale placed alongside the graduated scale of an **Diopter** -- An instrument developed by the Greeks sometime in 130B.C. It was used for **Compass** -- The magnetic compass came into wide use during the 13^th^ century for determining **Gunter's Chain** -- The Gunter's Chain, which was invented by Sir Edmund Gunter in 1620, **Chorobates** -- This instrument was designed for leveling work. It consisted of a horizontal **Merchet** -- The merchet was a device for measuring time and meridian. It was first used by the **Measurement** -- the process of determining the extent, size or dimensions of a particular quantity in comparison to a given standard. It is a fact that the best surveyor is not the one who makes the most accurate and precise SURVEYING MEASUREMENTS ---------------------- **Direct measurement** -- a comparison of the measured quantity with a standard measuring unit **Indirect measurement** -- In this type of measurement, the observed value is determined by its **Meter** -- the international unit of linear measure. It is now defined as a length equal to 1,650,763.73 wavelengths of the orange-red light produced by burning the element krypton. UNITS OF MEASUREMENTS --------------------- The following more commonly used prefixes are added to basic names. **mega** -- = 1,000,000 **kilo** -- = 1,000 **hecto** -- = 100 **deca** -- = **10 deci** -- = 0.1 **centi** -- = 0.01 **milli** -- = 0.001 **micro** -- = 0.000001 **nano** -- = 0.000000001 The SI units for plane angles is the **radian**. The **radian** is defined as an angle subtended by an arc of a circle having a length equal to the radius of the circle. 1 rad = 57^o^ 17'44.8" or 57.2958^o^ 1^o^ = 0.1745 rad SIGNIFICANT FIGURES ------------------- Some general rules regarding significant figures: 1. Zeroes between other significant figures are significant. Example in the following values each contains 4 significant figures: 13.05, 49.01, 67.02, and 2008. 2. For values less than 1, zeroes immediately to the right of the decimal are not significant. They merely show the position of the decimal. 3 significant figures: 0.0150, 0.000768 3. Zeroes placed at the end of decimal numbers are significant. Ex.: 185.20, 255.00, 29.000 These three values all have five significant figures. **Rounding off numbers** -- the process of dropping one or more of the final digits so that the value contains only the significant figures required for further computation or for portraying the final results. **Digit is less than 5** -- When the digit to be dropped \< 5, the number is written without the digit. **Digit is equal to 5** -- When the digit to be dropped is exactly 5, the nearest even number is used **Digit is greater than 5** -- When the digit to be dropped is greater than 5, the number is written **Error** -- the difference between the true value and the measured value of a quantity. - a deviation of an observation or a calculation from the true value and is often beyond the **Mistakes** -- inaccuracies in measurements which occur because some aspect of a surveying operation is **Blunder** -- a large mistake. TYPES OF ERRORS --------------- **Systematic error** -- one which will always have the same sign and magnitude as long as field SOURCES OF ERRORS ----------------- **Instrumental errors** -- errors due to imperfections in the instruments used, either from faults in **Natural errors** -- errors caused by variations in the phenomena of nature such as changes in **Personal errors** -- errors arising principally from limitations of the senses of sight, touch and **Accuracy** -- indicates how close a given measurement is to the absolute or true value of the quantity measured. - implies the closeness between related measurements and their expectations. **Precision** -- refers to the degree of refinement and consistency with which any physical measurement is made. -- portrayed by the closeness to one another of a set of repeated measurements of a quantity. **Probability** -- the number of times something will probably occur over the range of possible occurrences. **Most probable value** (**mpv** or **x**) -- refers to a quantity which, based on available data, has more chances of being correct than has any other. **mpv = x = Σx / n** **Residual** -- sometimes referred to as deviation -- defined as the difference between any measured value of a quantity and its most probable value. **v = x - x** where: v -- residual in any measurement x -- measurement made of a particular quantity x -- most probable value of the quantity measured **Probable error** -- a quantity which, when added to and subtracted from the most probable value, **Σv^2^ Σv^2^** **PE~s~ = + 0.6745 PE~m~ = + 0.6745** **n - 1 n(n -- 1)** **Relative error**, sometimes called **relative precision** -- expressed by a fraction having the magnitude of the error in the numerator and the magnitude of the measured quantity in the denominator. **RP**~s~ = **PE~s~ / x** or **mpv RP**~m~ = **PE~m~ / x** or **mpv** Where: RP~s~ - relative precision of a single measurement RP~m~ - relative precision of the mean ### MEASUREMENT OF HORIZONTAL DISTANCES **Pacing** -- consists of counting the number of steps or paces in a required distance. **Pace** -- the length of a step in walking. **Stride** -- equivalent to two paces or a double step. **Pace factor** -- the length of one's pace. **Pedometer** -- a mechanical counter hand carried to register the number of paces. **Passometer** -- a mechanical counter strapped to the leg of the pacer. This device will register a pace by impact each time either foot touches the ground. **Tachymetry** or **tacheometry** -- based on the optical geometry of the instruments employed and is an indirect method of measurement. **Odometer** -- a simple device that can be attached to a wheel for purposes of roughly measuring surface **Measuring wheel** -- basically consists of a small wheel which is attached to a rod and handle, and can **Optical rangefinder** -- usually hand-held or mounted on a small tripod, can be used to determine distances approximately simply by focusing. Composition of Taping Party =========================== **Head tape man** -- the person responsible for the accuracy and speed of all linear measurements **Recorder** -- keeps a record of all measurements, sketches, and observations taken during the **Flagman** -- the person whose duty is to hold the range pole at selected points. **Rear tape man** -- the person whose duty is to assist the head tape man during a taping operation. He is the one who holds the 30-m end or any intermediate meter mark of the **The Procedure of Taping** - - - - - - **Breaking tape** -- holding the tape horizontally above ground and to plumb at one or both ends when taping on sloping or uneven terrain surfaces. **CORRECTIONS IN TAPING** **1^st^ Rule** -- When a line is measured with a tape that is '**too long'**, the corrections are applied to **2^nd^ Rule** -- When a required length is to be laid out with a tape that is '**too long'**, the corrections **3^rd^ Rule** -- When measuring or laying out lengths with a tape that is '**too short'**, the corrections **Correction due to incorrect tape length** **Corr = TL -- NL C~T~ = Corr (ML / NL) CL = ML + C~T~** Where: **TL** -- length of tape **NL** -- nominal length of tape **ML** -- measured length or length to be laid out **C~T~** -- total correction to be applied to the measured length or length to be laid out **Corr** -- correction per tape length **Correction due to slope** B s h A C d C~h~ **Slope = h / d (100%)** For gentle slopes (less than 20%): **C~h~ = h / 2s** For steep slopes (between 20% and 30%): **C~h~ = h / 2s + h / 8s** For very steep slopes (greater than 30%): **C~h~ = s (1 - cosθ)** Horizontal distance: **d = s -- C~h~** **Correction due to temperature** **C~t~ = kL(t~o~ -- t~s~)** where: **C~t~** -- correction due to temperature **k** -- coefficient of thermal expansion = 11.6 x 10^-6^ / ^o^C (steel) **L** -- length of tape or length of line measured **t~o~** -- observed or prevailing temperature **t~s~** -- standard temperature **Correction due to pull or tension** **C~p~ = (P~a~ -- P~s~) / AE** **E = unit stress / elongation per unit length** **A = W / L(unit weight)** where: **C~p~** -- correction due to pull or tension Correction due to sag **C~s~ = ω^2^ L^3^ / 24P^2^ C~s~ = W^2^ L / 24P^2^** Where: **C~s~** -- correction due to sag **ω** -- weight of tape per unit length **L** -- unsupported length of tape **W** -- total weight of tape between supports **P** -- tension or pull applied **Combined corrections** The corrections for the effects of incorrect length of tape, temperature, tension, slope, and sag may be **SURVEYS WITH TAPE** 1\. Erecting Perpendicular to Line a\. Chord-bisection method b\. 3:4:5 method 2\. Measuring Angles with Tape **Leveling Methods** points some distance apart by a series of set ups of a leveling instrument along a selected route. between two intervisible points located at a considerable distance apart and between which points leveling could not be performed in the usual manner. measured intervals along an established line to provide data from which a vertical section of the ground surface can be plotted. difference in elevation between two points from measurements of its horizontal or slope distance and the vertical angle between the points. can provide reasonable accuracy for preliminary surveys, mapping, and rough leveling where quick measurements are needed. **Barometric leveling** -- involves the determination of the differences in elevation between points by measuring the variation in atmospheric pressure at each point by means of a barometer. **Cross-section leveling** -- Short profiles at right angles to the line of work are usually plotted at **Borrow-pit leveling** -- method of determining the relative elevations of points in borrow-pit **Types of Levels** **Dumpy level** -- It is the most widely used direct leveling instrument. It has a long telescope **Wye level** -- It has a detachable telescope which rests in supports called wyes. It can be removed from the Y-shaped supports and turned end for end during adjustment by releasing the two clamping collars which fit across the tops of the Y's. **Builder's level** --used primarily in the different phases of building construction where a high **Automatic level** -- It has become popular for conventional leveling work because of the ease and speed of their operation. It does not use a level vial and its ability to level itself depends upon the action of a complex pendulum-and-prism device. **Tilting level** -- commonly employed for very precise leveling operations and in other general **Geodetic level** -- employed in first-order leveling work where extreme precision is an important requirement. It is equipped with stadia hairs in addition to the standard vertical and horizontal cross hairs to make it suitable for three-wire leveling. **Transit** -- universal surveying instrument. It can provide results which are fairly precise **Laser level** -- A laser system is a separate unit equipped with a portable power supply and may **Hand level** -- a hand-held instrument used on surveys involving short sights and where a low **Leveling rod** -- a graduated rod which is used for measuring the vertical distance between the line of sight through a leveling instrument and the point whose elevation is either required or known. **Rod level** -- a device used for fast and correct plumbing of a leveling rod. It is L-shaped in design and **Target** -- a small device attached to the rod when extremely long sights make direct reading of the rod difficult or impossible. **Telescope** -- a metal tube containing a system of lenses which are used to fix the direction of the line sight and in magnifying the apparent size of objects in its field of view. **Jan Lippershey**, a **Objective lens** -- a compound lens composed of crown and flint glass mounted in the objective **Eyepiece** -- a form of microscope containing either two or four lenses and is used to enlarge **Cross hairs** -- consist of a pair of lines which are perpendicular to each other and are used to **Magnification** -- the ratio of the apparent size of an object viewed through a telescope to its size as seen by the unaided eye from the same distance. **Level vial** -- a sealed graduated glass tube containing some amount of liquid and a small air bubble. **Coincidence bubble** -- used on most modern and precise instruments such as the tilting and automatic **Tripods** -- serve as abase to prevent movement of the instrument after it is set up. **Taking a rod reading** 1. Position the rod 2. Focus on the rod 3. Read the rod **Arm and hand signal** -- any gesture or motion that conveys information or gives a command, direction or warning. **ARM AND HAND SIGNALS** 1. **Move right or left** -- The instrumentman uses this signal to direct the rodman to move either to the left or to the right. 2. **Give a sight** -- The right or left hand is raised up and is held for a moment in a vertical position. 3. **All right** -- The levelman extends both arms horizontally and moves them up or down. When both arms are brought still and horizontal it is meant to transmit a command to 'hold steady'. 4. **This is a point** -- The rodman raises the rod and holds it in a horizontal position over his head. 5. **Move back** -- The instrumentman uses this signal to direct the rodman to move back farther. He transmits the command by raising his right hand with the palm facing toward the rodman and then moving it into a horizontal position with his palm faced down. 6. **Pick up instruments** -- When a new setup of the level is desired, the chief of party signals the instrumentman by first extending both arms downward then raising them up quickly as though an object is being lifted. 7. **Raise (or lower) target** -- The instrumentman motions to the rodman by either raising his arm above his shoulder to raise the rod, or by dropping his arm below his waist to lower the target. 8. **Come in** -- The chief of party or the instrumentman uses this signal to direct any member of the survey party to come in or assemble. It is executed by moving the arm into a circular motion starting from below the waist to the front of his face. 9. **Plumb the rod** -- The hand is extended vertically above the head and moved slowly in the direction it is desired to plumb the rod. 10. **Establish a turning point --** To establish a turning point, the arm is swung slowly in a circle above the end. 11. **This is a turning point --** To identify a turning point, the leveling rod (or range pole) is raised overhead in a horizontal position. It is then lowered into a vertical position and held on the point. 12. **Wave the rod --** The instrumentman holds his arm above his head and continuously waves it back and forth. 13. **Face the rod --** This is a signal given out by the instrumentman to direct the rodman to face the rod towards the line of sight. It is executed by raising both arms above the head and twisting both hands back and forth. 14. **Reverse the rod --** The command to reverse the rod is transmitted to the rodman by extending the arms above the head and slowly rotating both arms in a circular motion towards one side of the body. 15. **Move forward --** From a position where both arms are extended horizontally, the arms are slowly bent on the elbows and the hands raised into a vertical position. 16. **Use the long rod --** To give the signal to use the long rod, the instrumentman extends both arms downward then slowly raises it over his head. **SOURCES OF ERROR IN LEVELING** 1\. **Instrumental errors** a. Instrument out of adjustment b. Rod not of standard length c. Defective rod a\. Bubble not centered b. Parallax c. Faulty rod readings d. Rod not held plumb e. Incorrect setting of target f. Unequal backsight and foresight distances b. Atmospheric refraction c. Temperature variations d. Wind e. Settlement of the instrument **COMMON MISTAKES IN LEVELING** 1\. Misreading the rod 2\. Incorrect recording 3\. Erroneous computations 4\. Rod not fully extended 5\. Moving turning points **Adjustment of the line of sight** **Two-Peg Test** **DE~a~ = a -- b DE~b~ = d -- c;** if **DE~a~ ≠ DE~b~,** then **TDE = DE~a~ + DE~b~ / 2** **TDE = (a -- b) + (d -- c) / 2** **CURVATURE AND REFRACTION** **h = 0.0675K^2^** where: h -- the departure of a telescope line of sight from a level line (m) K -- length of the line of sight (km) **DIFFERENTIAL LEVELING** **Bench mark (BM)** -- a fixed point of reference whose elevation is either known or assumed. **Backsight (BS)** -- a reading taken on a rod held on a point of known or assumed elevation. **Foresight (FS)** -- a reading taken on a rod held on a point whose elevation is to be determined. **Backsight distance** -- measured from the center of the instrument to the rod on which a **Foresight distance** -- the horizontal distance from the center of the instrument to the rod on **Turning point (TP)** -- an intervening point between two bench marks upon which point foresight and backsight rod readings are taken to enable a leveling operation to continue from a new instrument position. **Height of instrument** or **height of collimation (HI)** -- the elevation of the line of sight of an **PROFILE LEVELING** **Profile --** curved line which graphically portrays the intersection of a vertical plane with the **Stationing** -- numerical designation given in terms of horizontal distance any point along a **Intermediate foresights** or **ground readings** -- tken along the centerline of the proposed **Full stations** -- points which are established along the profile level route at uniformly measured **Plus stations** -- any other intermediate point established along a profike level route which is not **Vertical exaggeration** -- a process of drawing the vertical scale for a profile much larger than **Profile paper** -- a special heavy grade graphing paper used for plotting profiles. **RECIPROCAL LEVELING** **DE~1~ = a -- b DE~2~ = d -- c;** if **DE~1~ ≠ DE~2~,** then **TDE = DE~1~ + DE~2~ / 2** **TDE = (a -- b) + (d -- c) / 2** **TRIGONOMETRIC LEVELING** leveling rod - DE~AB~ hi A D **VD = Dtanα** or **VD = Ssinα** **MEASUREMENT OF ANGLES AND DIRECTIONS** The **direction of a line** is usually defined by the horizontal angle it makes with a fixed reference line r direction. **Four Types of Meridians** **True meridian** -- sometimes known as the astronomic or geographic meridian. **Grid meridian** -- a fixed line of reference parallel to the central meridian of a system of plane **Assumed meridian** -- an arbitrarily chosen fixed line of reference which is taken for -- usually the direction from a survey station to an adjoining station or some **Units of Angular Measurement** **The Degree** -- The sexagesimal system is used in which the circumference of a circle is divided into 360 parts or degrees. obtain one complete revolution. **The Grad** -- the unit of measure in the centesimal system. **The Mil** -- The circumference is divided into 6400 parts called mils, or 1600 mils is equal to **The radian** -- One (1) radian is defined as the angle subtended at the center of the circle by an arc length exactly equal to the radius of the circle. -- One (1) radian equals 180^o^ / π or approximately 57.2958^o^, and, 1^o^ equals π / 180^o^ or approximately 0.0174533 radian. -- It is used in computations such as determining the length of circular arcs and where high speed electroniic digital computers are used.