I. Errors, Mistakes, Accuracy and Precision of Data Surveyed. A. Errors
October 7, 2022 | Author: Anonymous | Category: N/A
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I.
Er Erro rors rs,, Mis Mista take kes, s, Accu Accura racy cy a and nd P Pre reci cisi sion on o off dat data a sur survey veyed ed.. A. ERRORS It is deined as the difference between the true value and measure of a quantity. E = X - X Errors are inherent in all measurements measurements and result from sources which cannot be avoided. These effects such as caused of type of the equipment used or by the way in which equipment is employed. Moreover, the imperfections of the senses of the person undertaking the measurement or by natural causes. However, it can be minimized by careful work and by applying corrections. In any surveying operation of the surveyor is continuously dealing with the errors. As surveyor understand thoroughly the different kinds of error, their sources and behavior, magnitude, and effects upon ield measurements; his work must be performed to exacting standards. Thus, he can intelligently select the instruments and survey methods to be used which will reduce errors to acceptable limits.
TYPES OF ERRORS 1. SY SYST STEM EMAT ATIC IC ER ERRO RORS RS It will repeat itself in other measurements, still maintaining the same sign, and thus will accumulate. It is for the reason that this type of error is also called cumulative error.
2. AC ACCI CIDEN DENTA TAL L ER ERRO RORS RS Also known as random errors. The occurrence of such errors are matters of chance as they are likely to be positive or negative, and may tend in part to compensate or average out according to laws to probability.
3. GR GRO OSS E ERR RRO ORS
These are, in fact, not errors at all, but the results of mistakes are due to carelessness of the observer. It must be detected and eliminated from the survey measurements before such measurements can be used.
SOURCES OF ERRORS 1. IN INST STRU RUMEN MENTA TAL L ERRO ERRORS RS These are due to imperfections imperfections of the instruments used, either from faults in their construction or from improper adjustments between the different parts prior to their use.
2. NA NATU TURA RAL L ERR ERROR ORS S It is caused by variations in the phenomena of nature such as changes in magnetic declination, temperature, humidity, wind, refraction, gravity, and curvature of the earth.
3. PE PERS RSON ONAL AL ER ERRO RORS RS These errors arise from the limitation of the senses of sight, touch and hearing of the human observer which are likely to be erroneous or inaccurate.
B. MI MIST STAK AKES ES Mistakes are inaccurate in measurements which occur because some aspect of surveying operation is performed by the surveyor with carelessness, carelessness, inattention, poor judgement, and improper execution. It is also caused by a misunderstanding misunderstan ding of the problem, inexperience, or indifference of the surveyor. A large mistake is referred to as a blunder. Mistakes and blunders are not classiied as errors because they usually are so large in magnitude when compared to errors.
C. AC ACCU CURA RACY CY AND AND PRE PRECI CISI SION ON A discrepancy is the difference between the two observed values of the same quantity. A small discrepancy indicates there are probably no mistakes and random errors are small. However, small discrepancies do not preclude the presence of systematic errors. Accuracy and precision are two terms which are constantly used in ssurveying urveying yet their correct meanings are often misunderstood. misunderstood. These two should not be used interchangeably. interchangeably. The surveyor should always attempt to obtain measurements measuremen ts which are not only accurate but also precise. Precision refers to the degree of the reinement or consistency of a group of observations and is evaluated on the basis of discrepancy size. If multiple observations are made of the same quantity and small discrepancies result, this indicates high precision. The degree of precision attainable is dependent on equipment sensitivity and observer skill. Accuracy denotes the absolute nearness of observed quantities to their true values. It implies the closeness between related measurements and their expectations. The difference between the measured value of a quantity and its
actual value represents the total error in the measurement. As the measured value approaches the actual value, the magnitude of the error becomes smaller and smaller; and as the magnitude of the total error is decreased, the accuracy of the measurement increases. Thus, a measurement is termed less accurate if it deviates by a signiicant amount from its expected value, and it is more accurate if the deviation is relatively small.
MULT PLE CHO CE 1. An error error is dein deined ed as as the diffe differenc rence e between between the a) True value value and the the appropri appropriate ate value value of a quantity quantity b) Most proba probable ble value value and and the true value value c) True value value and and the the measured measured value of a quantity quantity d) Two measur measured ed values values of the the same same quantity quantity 2. The adjuste adjusted d value value of an observ observed ed quanti quantity ty may contai contain n a) Smal Smalll gros grosss erro errors rs b) Small Small syste systemat matic ic error errorss c) Small Small ra rand ndom om er erro rors rs d) All All of th the e abo above ve 3. One of of the characte characteristi ristics cs of rand random om error error is is that that a) Small errors errors occur occur as frequ frequently ently as as the large large errors errors b) Positive errors occur more frequently frequently than the negative errors c) Small errors errors occur more more frequentl frequently y than the the large error errorss d) Large Large errors errors may occur occur more more frequen frequently tly 4. Theory Theory of of proba probabil bility ity iiss appli applied ed to a) Gros Grosss err error orss b) System Systemati aticc er error rorss c) Rand Random om er erro rors rs d) All All of th the e abo above ve 5. Accuracy is a term which indicates indicates the degree of conformity of a measurement measurement to its a) Most Most prob probabl able e valu value e b) Me Mean an va valu lue e c) Stan Stand dard ard erro errorr d) Tru True val valu ue 6. Variance Variance of a quantity quantity is an an indica indicator tor of a) Pr Prec eciision sion b) Ra Rand ndom omne ness ss c) Accuracy d) Re Regu gula larr natu nature re 7. A line, known to be 150.000 150.000 m long, is measured measured ive times times with a steel tape in the following order: 150.004, 149.998, 149.997, and 150.005 meters, respectively. The more accurate of the ive measurements is the a) 1st measurement
b) 2nd measurement c) 3rd measurement d) 4th measurement 8. Five separate separate measurements measurements were made made of a line and their degrees degrees of precision computed as follows: 1st trial, 1/5000; 2nd trial, 1/1000; 3rd trial, 1/2500; 4th trial, 1/10000. The measurement which is of a higher degree of precision was the one
done in the a) 4th trial b) 3rd trial c) 2nd trial d) 1st trial 9. The most probable probable value of several measurements measurements of a line line is 546.75 546.75 m. If ±0.15 represents the probable probable error of the mean value, the chances are even that the true value a) Is equ equal al to to 546. 546.60 60 m b) Is equ equal al to to 546 546.90 .90 m c) Lies between between 546.60 546.60 m and 546.90 546.90 m, as it is also also probable probable that the the true value lies outside of this limiting values d) Lies betwe between en 546.60 546.60 m and and 546.7 546.75 5m 10. The systematic systematic errors a) May be be posit positiv ive e or negat negativ ive e b) Are alway alwayss posit positiv ive e c) Are Are alwa always ys neg negat ativ ive e d) Have same sign as the the gross gross errors errors
II.
Weights o off o ob bservation It is not only always possible to obtain measurements of equal reliability under similar conditions. It is evident that some observations are more precise than others because of better equipment, equipment, improved techniques, and superior ield conditions. In making adjustments, it is consequently desirable to assign relative weights to individuall observations. It can logically be concluded that if an observation is very individua precise, it will have a small standard deviation or variance, and thus should be weighted more heavily (held closer to its observed value) in an adjustment adjustment than observation of the lower precision. From this seasoning, it is deduced that weights of observation should bear an inverse relationship to precision. W a ∝
1 2
σ a W
Where
a
2
is the weight of an observation o bservation a, which has a variance of σ a
Thus, the higher the precision (the smaller the variance), the larger should be the relative weight of the observed value being adjusted. If a quantity is observed repeatedly repeated ly and the individual observations have varying weights, the weighted mean can be computed from the expression M W =
∑ WM ∑ W
∑
WM the WM the sum of the individual weight times their Where M W is the weighted mean, corresponding observations, and ∑W the sum of the weights.
PROBLEM SOLV NG 1. Suppose four four observations observations of the distance are recorded recorded as 483.16 ft, 483.17 483.17 ft, 483.20 ft, and 483.18 ft and given weights of 2, 3, 3, 5, respectively, by the surveyor. Determine the weighted mean. SOLUT ON M W = 483.16 ( 2 ) + 483.17 ( 3 ) + 483.20 ( 3 ) + 483.18 ( 5 ) = 483.18 ft . 2
+ 3 + 3 +5
2. Assume Assume the observed observed angles angles of a certain certain plane plane triangle, triangle, and their their relative relative weights, are A=49 51’15”, W a =1; B=60 32’08”, W b =2; C=69 36’33”, W c = 3. Compute the weighted mean of the angles. ⸰
⸰
⸰
SOLUT ON Observed Angle A B C
SUM
⸰
49 51’15” 60 32’08” 69 36’33” 179 59’56” ⸰ ⸰
⸰
Wt
Correction
Numerical Corr.
Rounded Corr.
Adjusted Angle
1 2 3
6x 3x 2x
+2.18” +1.09” +0.73”
+2” +1” +1”
6
11x
+4.00”
+4”
49 51’17” 60 32’09” 69 36’34” 180 00’00”
⸰ ⸰ ⸰
⸰
11x = 4” and x = +0.36” 3. Four measurements measurements of a distance distance were recorded as 284.18, 284.18, 284.19, 284.19, 284.22, 284.22, and and 284.20 meters and given weights of 1, 3, 2, and 4, respectively. Determine the weighted mean. SOLUT ON MEAS2 U8R4E.1 D8Lm ENGTH
ASS GNED 1 WE GHT
W4M 28 .18
284.19 m 284.22 m 284.20 m
M W =
3 2 4 ∑W = 10
852.57 568.44 1136.80 ∑WM= 2841.99
∑ WM = 2841.99 =284.20 m4. It is desired to determine the most probable ∑
10 W value of an angle which has been measured at different times by different observers with equal care. The values observed were as follows: 74 39’50” (in two measurements), 74 39’32” (in four measurements) and 74 39’40” (in six measurements). ⸰
⸰
⸰
SOLUT ON
Measured Values
No. of Observations
74 39’50” 74 39’32”
2 4
⸰ ⸰ ⸰
M W =
74 39’40” SUM WM 895
∑ = ∑ W
⸰
⸰
6 12 55 ’ 48 ”
⸰
12
=74
39 ’ 39 ”5.
⸰
Product of the two quantities 149 9’40” 298 38’8” ⸰
447 58’0” 895 55’48”
⸰
Five measurements were made to
determine the length of a line and recorded as follows: 350.33, 350.22, 350.30, 350.27, and 350.30 meters. If these measurements were given weights of 4, 5, 1, 4, and 6, respectively, what is the most probable value of the length measured? SOLUT ON M W =
∑ WM = 350.33 ( 4 )+350.22 ( 5 ) +350.30 +350.27 ( 4) +350.30 ( 6 ) =350.28 m 20 ∑ W
6. Lines of levels to establish the elevation of a point are run over four different routes. The observed elevations of the point with the probable errors are given below. Determine the most probable value of the elevation point. L NE
1 2 3 4
OBSERVED ELEV 219.832 m 219.930 219.701 220.021
PROBABLE ERROR (E) ±0.006 m ±0.012 m ±0.018 m ±0.024 m
E
2
0.000036 0.000144 0.000324 0.000576
1
W = 2 E 27778 6944 3086 1736
RELAT VE SOLUT ON
L NE
1 2 3 4
WE GHT (RW) 16.00 4.00 1.78 1.00
P = ELEV (RW)
3517.312 879.720 391.068 220.021
SUM
22.78
5008.121
RW 1=
W 1 W 4
=
27778 1736
RW 2= RW 3=
W 2 W 4 W 3
=16.00
=
6944 1736
= 4.00
= 3086 =1.78
W 4 1736 W 4 1736 = =1.00 RW 4= W 4 1736 M W =
5008.121 22.78
=219.847 m
7. The length of a line was measured repeatedly on the three different occasions and the probable error of each mean value was computed with the following results: 1st set of measurements = 1201.50±0.02 m 2nd set of measurements = 1201.45±0.04 m rd
3 set of measurements = 1201.62±0.05 m Determine the weighted mean of the three sets of measurements. SOLUT ON
M W =
MEASUREMENT
OBSERVED ELEV
1 2 3
1201.50 1201.45 1201.62
10585.26 8.81
PROBAB LE ERROR (E) ±0.02 m ±0.04 m ±0.05 m
E
2
0.0004 0.0016 0.0025
W = 2 E
RELAT VE WE GHT (RW)
P = ELEV (RW)
2500 625 400 SUM
6.25 1.56 1.00 8.81
7509.38 1874.26 1201.62 10585.26
1
=1201.51 m
8. If an angle angle A is measured three times, determine the values obtained below. 1. 40*10’ weight= 1 2. 40*15’ weight= 1 3. 40*40’ weight= 1 SOLUTION: 40*10+40*15’ +40*40’ / 3= 40*21.66’ Answer is =3 9. If the weight of an angle angle A is 3 and weight of angle B is 4, what will be the weight of (3A-B+90 degrees)? a.)1/7
b.) 1 c.) 4/13 d.) 91 SOLUTION Given, A=3 ,B= 4 Weight of 3A= 3/3^2= 1/3 1/3 Weight of 3A-B= 1/(3+1/4)=4/13 Weight of 3A-B+90= 4/13 Answer is (c) 10. If the weight of an angle A= 40*24’24 is 2 then the weight of the angle A/3= 13*28’08 will be a.) 4 b.) 67 c.) 9 d.) 18 SOLUTION: A/3= (3)^2 x 2 = 18 Answer is (d)
III. III.
Me Meas asur urem emen entt of Ho Hori rizo zont ntal al D Dis ista tanc nces es MEASUREMENTS OF DISTANCE: 1. BY PACING Pacing consists of counting the number of steps or paces in a required distance. A pace is deined as the length of a step-in s tep-in walking. walking. It may be measured from heel to heel or from toe to toe. In surveying, pacing means moving with measured steps; and if the steps are counted, distances can be determined if the length of a step is known. The surveyors preferred preferre d counting strides instead of paces. A stride is equivalent two paces or a double step. It is one of the most valuable things learned in surveying because of its many practical applications. Under average average conditions, a good pacer will have little dificulty in pacing distances with a relative precision of 1/200. To pace a distance, it is necessary to irst determine the length of one’s pace. This is referred to as the pace factor. There are two methods that can be used to calibrate one’s pace; one method is to determine the average length of an individual’s individual’s normal
step. The other method is to adjust one’s pace to some predetermin predetermined ed length, such as 1 meter.
FACTORS AFFECTING LENGTH OF PACE:
Speed of pacing Roughness of the ground
Weight of clothing and shoes used Fatigue on part of the pacer Slope of the terrain Age and sex of the individual
MECHANICAL PACE COUNTERS:
PEDOMETER It records the number of steps made on the body’s movement PASSOMETER It registers a pace by impact each time a foot touches the ground. It is strapped to the leg of the pacer.
2. BY TAPING The most common method of measuring or laying out horizontal distance distancess is the use of a graduated tape. It is a form of direct measurement which is widely used in the construction of buildings, dams, bridges, canals, and many other engineering as well as non-engineering activities. Taping consists of stretching a calibrated tape between two points and reading the distance indicated on the tape. Chain was used for measurement measurement before the advent of the steel tape. Measurement Measurement of distances using chains is called chaining and persons who are undertaking undertaking measurement using chains preferably called chainmen.
3. It BY TACH CHYM YMET ETRY is TA also known asRY tacheometry; tacheometry; another procedure of obtaining horizontal distances. It is based on the optical geometry of the instruments employed (indirect method of measurement). Tachymetric measurements are performed either by the stadia method or the subtense bar method.
a. ST STAD ADIA IA ME METH THO OD It was introduced by James Watt of Scotland in 1771 and was at the time referred to as a micrometer for measuring distances. This method provides a rapid means of determining horizontal distances and will yield a relative precision of only between 1/300 and 1/1000. FACTORS AFFECTING PRECISION:
Reinement with which the instrument was manufactured Reinement Skill of the observer Length of measurement Effects of refraction and parallax
The equation is employed in computing horizontal distances from stadia intervals when sight is horizontal. D = Ks + C Where: K – stadia interval factor of instrument s – difference between the upper stadia hair C – distance from the center of the instrument to the principal focus (instrument constant)
b. SU SUBTE BTENS NSE EB BAR AR METHO METHOD D It is a convenient and practical device used for quick and accurate measurementt of horizontal distances. The bar, which is precisely 2 meters measuremen long, consist of a rounded steel tube through which runs a thin invar rod. Using a theodolite, horizontal distance is measured by setting up the subtense bar at the distant station and measuring the horizontal angle subtended by the distance between the two targets. t argets. Horizontal distance is obtained directly and no slope correction is required. s α D= cot 2
2
Where: s – length of the subtense bar α – – angle subtended by the targets It yields a relative precision of 1/3000 for sights of 150m or less and using a 1 sec theodolite. This method is often used in obtaining distanc distances es over very rough or inaccessible terrain such as across canyons, wide rivers, ravines, and even across busy city streets.
4. BY G GRAP RAPHIC HICAL AL AND AND MATH MATHEMA EMATICA TICAL L These methods are widely employed in plane table surveys, and in triangulation work. Determining distances by scaling from maps or aerial photographs could also provide suficiently accurate result. Unknown distances may be determined through their relationship with known distances geometrically. geometrically.
5. BY M MECH ECHAN ANIC ICAL AL D DEVI EVICE CES S
These devices are only applicable for low precision surveys or where quick measurements are desired.
a. ODOMETER A device attached to a wheel for measuring surface distances. It will yield a precision of 1/200 (on fairly level terrain)
b. ME MEAS ASUR URIN ING G WH WHEE EEL L A more portable and self-contained measuring device than the odometer. It consists of a small wheel attached to a rod and handle
c. OP OPTI TICAL CAL RA RANG NGEF EFIN INDER DER It determines distance by focusing and usually handheld or mounted on a small tripod. Its precision of 1/50 (for distances less than 500)
6. BY PH PHOT OTOG OGRA RAMM MMETR ETRY Y The term photogrammetry refers to the measurement measurement of images on a photograph. Distances can be measured on photographs with a precision of about 1/3000 to 1/5000
MULT PLE CHO CE 1. The subtense subtense bar bar is convenient and practical device used for for quick and accurate accurate measurementt of horizontal distances. measuremen distances. It consists or rounded steel tube through which runs a thin invar rod and at each end of the frame the target marks are house exactly a) 2.00 m b) 1.50 m c) 3.00 m d) 1.00 m 2. The method method measuring measuring or laying out horizontal horizontal distances distances by stretching a calibrated calibrated tape between two points and reading the distance indicated on the tape is referred to as a) Pacing b) Taping c) Stad Stadia ia meas measur urem emen ent t d) Ta Tach cheo eome metr try y 3. A pace is dein deined ed as the length length of a step-in step-in walki walking. ng. It may be be measured measured from from a) Toe Toe tto o he heel b) He Heel el to toe toe c) Heel Heel to hee heell d) Mid-to Mid-toe e to mid-h mid-heel eel 4. Who introduced introduced the Stadia Stadia Method Method in 1771 1771 and and was at the time time referred referred to as a micrometer for measuring distances? a) Pi Pier erre re Vern Vernie ierr
b) Sir Edmun Edmund d Gunt Gunter er c) Jam James Wa Watt d) Erik Erik Berg Bergst stra rand nd 5. A mechanical mechanical pace pace counter counter which records the number number of steps made made on the body’s body’s movement a) Pass Passom omet eter er b) Pedo Pedom meter eter c) Geo eod dimet imete er d) Baro Barome mete terr 6. A stadia rod held at a distance distance point point B is is slighted by an instrument set set up at at A. The upper and lower stadia hair readings were observed as 1.300 m and 0.900 m, respectively,, if the stadia interval (K) is 100, and the instrumental constant is zero, respectively determine the length of line AB a) 39.998 m b) 39.9 .98 88 m c) 39.999 m d) 40.000 m 7. A surveyor counted 50, 50, 52, 53, 51, 51, 53, and and 51 paces in walking along along a 45-m 45-m course laid out on a concrete pavement. He then took 768, 771, 772, 769, and 770 paces in walking an unknown distance XY. His pace factor should be equal to a) 0. 0.08 0871 71 m/pa m/pace ce b) 0. 0.06 067 7 m/pa m/pace ce c) 1.14 1.148 8 m/p m/pac ace e d) 14 14.9 .904 04 m/pa m/pace ce 8. Related to the question question 7, the length of XY based based on the paces paces factor of the surveyor surveyor equal to a) 651.5 .59 9m b) 676.08 .08 m c) 670 m d) 670.6 .67 7m 9. Related to the question question 7, determine the percentage percentage of error in the measurement measurement if the taped length in XY is 682.89 m a) 1.79% b) 1.78% c) 1.77% d) 1.80% 10. Two points, A and B, are established established along the same direction from the theod theodolite olite station. If the subtended angle read on a subtense bar held at A and B are 0 55’20’’ and 0 23’44 23’44’’, ’’, respectively, the horizontal distance between the two point is a) 87.87 m b) 165.4 .45 5m ⸰
⸰
c) 124.2 .25 5m
d) 206.98 .98 m
IV.. IV
Me Meas asur urem emen entt o off h hor oriz izon onta tall dist distan ance cess ELECTRONICS DISTANCE MEASUREMENT (EDM) It has provided a signiicant advance in surveying instrumentation and techniques. BASIC PRINCIPLE: The time required for a radio or light wave to travel from one end of a line to the other is a function of the length measured. CLASSIFICATION: a. ELECTR ELECTRO-O O-OPTI PTICAL CAL INSTR INSTRUM UMENT ENTS S The type of instruments which transmit wavelength within or slightly beyond the visible region of the spectrum. b. MICRO MICROWAV WAVE E IN INSTR STRUME UMENT NTS S The type of instruments which transmit microwaves with wavelength of 1.0 mm to 8.6 mm. It consists of two identical units which includes a transmitter and a receiver.
ADVANTAGES AND DISADVANTAGES: These devices were quite bulky and heavy, aside from being very expensive when it was irst introduced. None of these instruments were designed to be used for simultaneously measuring the length and direction of a line. The development of small light emitting diodes sometime in 1965 greatly improved the design of earlier EDM instruments. Light- wave instruments were also further improved when coherent laser light was incorporated to it. Some of the signiicant advantages of the newer models of EDM instruments are the following: advantages a. Speed Speed and and accu accurac racy y in measu measure remen ment t b. Lightw Lightwei eight ght an and d porta portable ble c. Low Low pow power er re requ quir irem emen ent t d. Easy Easy to op oper erat ate e e. Ease in meas measurem urement ent over accessibl accessible e terra terrain in f. App Applicab licable le to the measure measurement ment of short short and long lengths lengths g. Automatica Automatically lly measures measures displays displays and record records, s, slope range, range, azimuth, azimuth, vertical vertical angle, horizontal distance, departure and latitude. h. Slope measure measurement mentss are internall internally y reduced reduced to horizonta horizontall and vertical vertical components by built-in computers thereby eliminating the need to calculate these values.
i.
Automatica Automatically lly accumula accumulates, tes, and and average averagess reading reading for for slope rang range, e, horizont horizontal al and vertical angles.
USES: They are extremely useful in measuring distances over rough and rugged terrain which are dificult to access, or where conventional conventional taping methods would be impractical. OPERATING RANGES: a. Short Short rang range e – dista distance nce less less than than 25 km km b. Medium Medium range range – distance distance from 25 km km to 75 75 km c. Long Long range range – dista distance ncess of 75 75 km or or longe longerr
GEODIMETER It is an acronym for geodetic distance meter. It is an electro-optical device developed in 1948 by Erik Bergstrand, a Swedish physicist. Its use is based upon the known velocity of light. The maximum range varies from 5 to 10 km during daytime and up to about 25 to 30 km at night time and usually depends on atmospheric conditions. The precision of measurement attainable is about 1/200,000 of the distance but the stations are intervisible and that a clear line of light exists.
TELLUROMETER It utilized high frequency microwave transmission and was capable of measuring distances up to 80 km day or night. Dr. T.L. Wadley of South Africa announced his invention in 1957 which was to be the world’s second EDM instruments. A distinct advantage of this instrument is that observations can be made on rainy days, during a fog, or other unfavorable weather conditions. The tellurometer system can be expected to attain a precision of 1/300,000 under favorable conditions.
MEASURING TAPES 1. STEEL TAPE - Also Also know known n as as surve surveyor yor’s ’s or en engin ginee eer’s r’s tape tape - It is made made of of ribbon ribbon of steel steel 0.5 0.5 to 1.0 1.0 cm in in width width and weights weights 0.8 0.8 to 1.5 1.5 kg per per 30 meters - Most convention conventional al measur measuremen ements ts in surveyin surveying g and and engine engineerin ering g work work 2. METAL ETALL LIC TA TAPE - Some Someti time mess cal calle led d wov woven en ta tape pe - It’s made made of water-p water-proof roof linen linen fabric fabric with with woven woven small small brass, brass, copper, copper, or or bronze bronze wires to increase its strength and reduce stretching - For For meas measur urin ing g shor shortt di dist stan ance cess 3. NONNON-ME META TALL LLIC IC TA TAPE PE - A type type of tape tape woven woven from from synthe synthetic tic materi materials als with with strong strong dimens dimensiona ionall stability stability.. -
Coated Coated with with plasti plasticc materi material al to reduce reduce effects effects of moistur moisture, e, humidi humidity, ty, and and abrasion
4. INVAR TA TAPE - A special special type type made made of an an alloy alloy of nickel nickel (35% (35%)) and steel steel (65% (65%)) with very low coeficient of thermal expansion (1/30 to 1/60 that of steel tape). - Derived Derived from from the the word word invari invariable able since it is less affected affected by tempe temperatur rature e changes compare to a steel tape. - It is is used used onl only y for for prec precis ise e meas measur urem emen ents ts - Ten times times as as expe expensi nsive ve as ordi ordina nary ry stee steell tape tape 5. LOVAR TAPE - It has properti properties es and costs betwe between en convent conventiona ionall steel steel tapes tapes and and invar invar tapes tapes 6. FIBE FIBERG RGLA LASS SS TAP TAPE E - Woven Woven with with iberglas iberglasss iin n a longitudi longitudinal nal and transver transverse se patte pattern rn - It is is best best used used in vici vicini nity ty of electr electrica icall equip equipme ment nt - It does does not shrin shrink k or stretch stretch with with chang changes es in in tempe temperatur rature e and and humidi humidity ty 7. WIRES - It was was utilized utilized in in measurin measuring g lengths lengths before before thin thin lat lat steel steel tapes tapes were were produ produced. ced. - It stil stilll u use sed d iin n hyd hydro rogr grap aphi hicc surv survey ey 8. BUIL BUILDE DER’ R’S S TAPE TAPE - It has has small smaller er cros crosss sectio sections ns and and lighte lighterr than than stee steell tape tape - It is us used ed in buil buildi ding ng cons constr truc ucti tion on 9. PHOS PHOSPH PHOR OR-B -BRO RONZ NZE E TAP TAPE E - A rust-p rust-proof roof tape designe designed d for for use in the the vicin vicinity ity of of salt salt water. water. 10. NYLON COATED COATED STEEL TAPE - It is is design designed ed to to be resistant resistant to corrosi corrosion on and and is is immune immune to rust. rust. - Coated Coated with with per perman manent ently ly bond bonded ed nonnon-con conduc ductin ting g nylon. nylon.
TAPING ACCESSORIES 1. RANGE PO POLE
-
Also Also know known n as as la lags gs or lini lining ng ro rods ds Usua Usuall leng length th:: 2.0 2.0 to 3.0 3.0 mete meters rs Marked Marked with alternat alternate e red red and and white white sections sections 30 cm to 50 cm cm long long It is used used as as temporar temporary y signals signals to indic indicate ate the the location location of of points points or direc direction tion of of lines, and to mark alignment. 2. TAPE TAPE CLA CLAMP MPIN ING G HAND HANDLE LES S
-
It applie appliess tension tension with with a quick quick grip grip on any part part of a steel steel tape without without causing causing damage to the tape or hands of the tape man 3. CHAI CHAINI NING NG PI PINS NS
-
Also Also calle called d as as surve surveyor yor’s ’s arro arrows ws or or tapi taping ng pins pins Made Made of heavy heavy wire wire 30 30 cm long long and and painted painted with alter alternate nate red and and white white bands bands Sets Sets of 11 pin pinss carr carried ied on a steel steel ring ring ar are e stan standa dard rd It stuck stuck in the the ground ground to mark mark the the ends ends of measur measured ed tape tape lengths lengths or or partial partial tape tape lengths 4. TENS TENSIO ION N HAND HANDLE LE
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Al Also so know known n as spri spring ng sc scal ale e Used Used in prec precis isio ion n ta tapi ping ng At one one end of a tape tape ensurin ensuring g the appli applicati cation on of the the correct correct amount amount of pull on on the
tape during measurement 5. TAPE TAPE THE THERM RMOM OMET ETER ER
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About About 10 to 15 15 cm cm long long an and d iiss gradu graduate ated d from from -3 -30 0 C to 50 50 C in 2 to to 5 degree degreess divisions Determine the temperature of the air and the approximate temperature of the tape during measurement ⸰
⸰
6. PLUMB BO BOB
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Projecti Projecting ng the tape ends ends to the ground ground when when the tape tape must must be suspend suspended ed above above the measure line Weighs Weighs 0.25 0.25 kg kg and and attache attached d to 1.5 m long string string or cord which which is free free of knots knots
7. WOOD WOODEN EN STAK STAKE E OR OR HUB HUB
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Wood made of 5 cm x 5 cm x 30 30 cm to to mark mark points, points, corne corners, rs, or stations stations in in the ground 8. LEAT LEATHE HER R THON THONGS GS
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Attached Attached to a ring ring located located near near the zerozero-mete meterr mark of the tape tape to provid provide ea comfortable grip on the tape t ape when measuring 9. HAND HAND LEVE LEVEL L AND AND CLINOM CLINOMETE ETER R
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A 15 cm long long devic device e which which consists consists of a metal metal sighting sighting tube tube with with a level level bubble bubble Used to keep keep the the tape tape ends ends to equal equal elevati elevations ons when when measu measuring ring over rugged rugged terrain, in approximately determining difference in elevation of points, and in other ield operation where it is required to produce a level sight 10. TAPE REPAIR REPAIR KIT KIT
- Allows Allows emerge emergency ncy repa repairs irs to to be made made on damaged damaged or broke broken n tapes tapes 11. CRAYONS CRAYONS
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About About 10 cm lon long g and and hexa hexagon gonal al in in cross cross sectio section n Marki Marking ng crayon crayonss used used in survey surveying ing are are usuall usually y lumber lumber cray crayons ons Used for markin marking g points, points, corner corners, s, or statio stations ns by indic indicatin ating g cross marks marks on paved paved roads, sidewalks, or walls
PROCEDURE OF TAPING 1. Al Alig igni ning ng the the ta tape pe 2. Stre Stretc tchi hing ng th the e ta tape pe
3. 4. 5. 6.
Plumbing Marki Marking ng full full tap tape e len length gthss Tallyi Tallying ng tap taped ed meas measure ureme ments nts Measu Measurin ring g fract fraction ional al leng lengths ths BREAKING TAPE – measurement of shorter distances which are accumulated to total a full tape length SLOPE TAPING – tape measurements made directly along the slopes when the ground is of uniform inclination and fairly smooth d = s cos α d = √ s + s Where: d – horizontal distance s – slope distance h – difference in elevation α – angle of inclination of the slope 2
h
CORRECTIONS IN TAPING Too Long
Too Short
Measuring
+
-
Laying out
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+
a. Corre Correcti ction on due due to incorr incorrect ect ta tape pe lengt length h Due to manufacturing manufacturing defects the absolute length of the tape may be different from its designated or nominal length. Also, with use the tape t ape may stretch causing change in the length and it is imperative imperative that the tape is regularly checked under standard conditions to determine its absolute length. Corr =TL− NL ML C 1=Corr NL CL= ML ± C 1
( )
Where: TL – true or actual length of the tape NL – nominal length of the tape t ape ML – measured length CL – corrected length C1 – total correction to be applied
If the absolute length is more than the nominal length the sign of the correction is positive and vice versa b. Corr Correc ecti tion on due due to to slop slope e If the sides s is is measured on the slope, it must be reduced to its horizontal cos θ . equivalent s cos d = s −C s
Gentle Slopes (Less than 20%) C h=h / 2 s Steep Slopes (20% to 30%) 2 4 h h C h= + 3 2s 8s Very Steep Slopes (Greater than 30%) C h= s ( 1 −cos θ ) 2
The sign of this correction is always negative c. Corr Correc ecti tion on due due to to alig alignm nmen ent t If the intermediate points are not in correct alignment with ends od the line, a correction for alignment given below is applied to the measured length. 2
d C m= 2 L
Where: d = the distance by which the other end of the tape is out of alignment The correction for alignment is always negative. -
The linea linearr error error due to inaccura inaccuracy cy in align alignment ment of of a tape tape is simil similar ar to the the effect effect of slope and can be computed in the same manner d. Corre Correcti ction on due due to to temp tempera eratur ture e If the tape is used at a ield temperature different from the standardization temperature,, then the temperature correction to measured length is temperature
C TT = αL ( T − T O ) Where: α – coeficient of linear expansion per degree change in temperature L – length of the tape measured T – observed temperature To – temperature of standardized tape
For steel tapes: α = 0.0000116/℃C e. Corr Correc ecti tion on due due to to Tens Tensio ion n If the pull applied to the tape in the ield is different from the standardization pull, the pull correction is to be applied to the measured length. C p= A =
( P− P o) L AE
W Lγ
Where: P – measured pull Po – standard pull L – length of tape measured A – cross sectional area of the tape E – modulus of elasticity of the tape W – total weight of the tape γ – unit weight weight of the tape For the steel tapes: A = 0.02 to 0.06 cm2 E = 2.00 x 106 to 2.10 x 106 kg/cm2 γ = 7.866 x 10-3 kg/cm3
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f. Corr Correc ecti tion on due due to Sag Sag Sag shorte shortens ns the the horizont horizontal al distan distance ce betwee between n end end gradua graduations tions of the the tape tape 2 3 w L C s= 2 24 P 2 W L C s= 2 24 P 2 2 2 W =w L Where: w- weight of tape per unit length W – total weight of the tape between supports L – interval between supports (unsupported length of tape)
P – pull or tension applied on the tape
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g. Corr Correc ecti tion on due due to to Win Wind d Its effe effect ct is si simi milar lar tto o the effe effect ct of sag sag but but usuall usually y much much less less h. Norm Norma al Tens Tensio ion n
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The appli applied ed pull pull length lengthens ens the the tape tape to equal equal the shortenin shortening g caused caused by by sag AE 0.204 W √ √ AE P N = P N − PS √ P Where: P N – normal tension or pull to eliminate the effect of sag PS – standard pull for the tape W – total weight of the tape between supports A – cross sectional area of tape E – modulus of elasticity of tape
MULT PLE CHO CE 1. Electric Electric dista distance nce measu measureme rement nt instrum instruments ents are a) X-rays b) Ligh Lightt wav waves es c) So Soun und d wa waves ves d) Magn Magnet etic ic l lux ux 2. Modern Modern EDM instru instrument mentss work on on the princi principle ple of measuri measuring ng a) The relected relected energy generated generated by electromagnetic electromagnetic waves waves b) Total time taken by electromagnetic electromagnetic wave in travelling travelling the distance distance c) The change change in frequen frequency cy of the electrom electromagne agnetic tic waves waves d) The phase dif differenc ference e between the the transmitted transmitted and the relected relected electromagnetic waves 3. The range range of infrared EDM instruments instruments is is generally generally limited limited to measuring the distances a) 2 to 30 30 km b) 30 tto o 33 33 km km c) 2 to 3 km d) 10 to to 13 13 km km 4. Electromag Electromagneti neticc waves waves are unaffect unaffected ed by a) Win ind d sp speed eed b) Vapo Vapour ur pre press ssur ure e c) At Atmos mosph pheri ericc pr press essure ure d) Air Air tem tempe pera ratu ture re 5. The tempe temperatur rature e correcti correction on and and pull pull correctio correction n a) May May hav have e sam same e sig sign n b) Alw Always ays have have oppos opposite ite sign signss
c) Alwa Always ys hav have e same same sig sign n d) Always Always hav have e positi positive ve sign sign 6. The sag correc correctio tion n on hills hills a) May be eithe eitherr positiv positive e or negat negative ive b) Is posi positi tive ve c) Is zero d) s neg negati ative 7. The steel steel tape tape with with a crosscross-secti sectional onal area area of 0.03 cm2 is 30.00 cm long under a pull of 5 kg when supported through-out. It is used in measuring a line 875.63 m long under a steady pull of 10 kg. Assuming E=2.0 x 10 6 kg/cm2, the elongation of the tape due to increase in tension is a) 0.0025 m b) 0.0 .04 43 m c) 0.0730 m d) 0.7 .73 30 m 8. In question question 7, 7, the correcti correction on length length of the the measure measured d line is is a) 875.56 m b) 875.6 .60 0m c) 875.68 m d) 875.70 m 9. A line measured with 30-m 30-m steel tape was was recorded recorded as 325.70 325.70 m. m. If the tape is is found to be 30.05 m long during standardization, the correct length of the line is a) 325.16 m b) 325.4 .44 4m c) 326.24 m d) 327.4 .45 5m 10. A 30-m steel tape weighs weighs 1.05 kg and is supported at its end poin points ts and at the 10-m and 25-m marks. If a pull of 6.0 kg is applied at the ends of the tape,
the correction due to sag for a full tape length is a) 0.050 m b) 0.006 m c) 0.038 m d) 0.06 m
V.
Me Meas asur urem emen entt o off a ang ngle less and and di dire rect ctio ions ns A. ME MERI RIDI DIAN AN This is done with reference to a meridian which lies in a vertical plane passing through a ixed point of reference and through the observer’s position. There are four types of meridians: meridians: true, magnetic, grid and assumed.
1. TRUE TRUE MERI MERIDI DIAN AN It is sometimes known as the astronomic or geographic geographic meridian. It is the generally adapted reference line in surveying practice. This line passes through the geographic north and south poles of the earth and the observer’s position. It is also used for marking these bounda boundaries ries of land. 2. MAGN MAGNET ETIC IC ME MERI RIDI DIAN AN It is a ixed line of the reference which lies parallel with the magnetic lines of force of the earth. Magnetic meridians are not parallel to the true meridians since they converge at a magnetic pole which is located some distance away from the true geographic poles. 3. GRI RID D MERI MERIDI DIAN AN It is ixed line of reference parallel parallel to the central meridian of a system of plane rectangular coordinates. coordinates. The use of this is applicable only to plane surveys of limited extent. 4. ASSU ASSUME MED D MERI MERIDI DIAN AN It is an arbitrarily chosen ixed line of reference which is taken for convenience. convenienc e. It is used only on plane surveys of limited extent since they are dificult or may be impossible to re-establish if the original reference points are lost or obliterated.
B. EXPEDITION METHODS OF ESTABLISHING MERIDIANS
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1. Establishi Establishing ng Magne Magnetic tic Merid Meridian ian by Compa Compass ss 2. Determin Determining ing True True North North by Aid of of Sun and and Plumb Plumb Line Line 3. Determin Determining ing the True North North by the the Rising Rising and Setti Setting ng of the Sun Sun 4. Determ Determini ining ng Tr True ue North North by by Polari Polariss Big Dipp Dipper er – a useful useful referen reference ce constel constellatio lation n of the the northe northern rn hemisph hemisphere ere The two two stars, stars, Merak Merak and and Dubhe Dubhe,, forming forming the side of of the dipp dipper er which which is farthe farthest st from the handle are known as the pointer stars 5. Determin Determining ing True South by the the Southe Southern rn Cross Cross Southern Southern Cross – a conste constellati llation on of the southe southern rn hemisp hemisphere here which serves serves as a reference group of stars for determining the location of the earth’s south pole 6. Determin Determining ing Directi Direction on of True True North North (or South) South) by a Wrist Wrist Watch Watch
C. UNITS IN ANGULAR MEASUREMENT 1. The Degree The sexagesimal system is used in which the circumference of a circle divided into 360 parts or degrees. 2. The Grad The unit measure in the centesimal system. In this system the circumference of a circle is divided into 400 parts called grads. It is a standard unit use used in Europe.
3. The Mil It is commonly used in military operations operations as in ire direction of artillery units. The circumference is divided into 6400 parts called mils, or 1600 mils is equal to 90 degrees. 4. The Radian Another measure of angles used frequently for a host of calculations. Radian is sometimes referred to as the natural unit of angle because there is no arbitrary number in its deinition. One radian is deined as the angle subtended at the center of a circle by an arc length exactly equal to the radius of the circle.
D. DESIGNATION OF NOTRTH POINT -
1. True North The The nor north th poin pointt of th the e tru true e mer merid idia ian n Sy Symb mbol ol:: a ast ste erisk risk or TN 2. Magn Magnet etic ic Nort North h A north north point point that that is establi established shed by means means of a magneti magnetized zed compa compass ss needle needle when when there are no local attractions affecting it Symb Symbol ol:: h hal alff a arr rrow owhe head ad or MN 3. Grid North A north north point point which which is estab establishe lished d by the the lines lines on a map which which are are paralle parallell to a selected central meridian Symb Symbol ol:: fful ulll a arr rrow owhe head ad or GN or Y 4. Assu Assume med d Nor North Used to portra portray y the the location location of any any arbit arbitrari rarily ly chosen chosen north point point Symb Symbol ol:: ssma mall ll bl blac ack k cir circl cle e or or AN AN
E. DIR DIRECT ECTIO ION NO OF FL LIN INES ES Deine as the horizontal angle the t he line makes with an established line of reference. There are various kinds of angles which can be used to describe the direction of lines. In surveying practice, directions may be deined by means of: interior angles, delection, angles, angles to the right, bearings, and azimuths. 1. INTERIOR ANGLE The angles between adjacent adjacent lines in a closed polygon. When the value of an interior angle is greater than 180 degrees it is referred to as re-entrant angle . It should be remembered that for any closed polygon the sum of the interior angles is equal to (n-2)18 (n-2)180 0∘, where n is the number of sides. 2. DEFLECTION ANGLE The angle between a line and the prolongation of the preceding line. It may be turned clockwise or counterclockwise and it is always necessary to
append the letters R or L to the numerical value to deine the direction in which the angle has been turned. 3. ANGLE TO THE RIGHT Angles that are measured clockwise from the preceding line to the succeeding line. 4. BEARING The acute horizontal angle between the reference meridian and the line. - Forward bearing – when the bearing of a line is observed in the direction in which the survey progresses. - Back bearing – when the bearing of the line is observed in an opposite direction. 5. AZIMUTH Angle between the meridian and the line measured in a clockwise direction from either the north or south branch of the meridian. The azimuth of a line is its direction as given by the angle between the meridian and the line measured in a clockwise direction from either the north or south branch of the meridian. To avoid confusion in the interpretation clearly specify in the ield notes the type of reference meridian used.
F. TH THE EC CO OMP MPAS ASS S A hand-held instrument for determining the horizontal direction of a line with reference to the magnetic meridian.
1. CO COMP MPAS ASS SB BO OX It has a horizontal circle which is graduated from 0 to 90 degrees in each quadrant.
2. LIN INE E OF OF S SIG IGHT HT It is ixed along the index mark on the north graduation of the circle.
3. MA MAGN GNET ETIC IC N NEE EEDL DLE E The compass needle is of magnetized tempered steel balanced at its center on a jeweled pivot so that it swings freely in a horizontal position.
G. TY TYPE PE O OF F CO COMP MPAS ASSE SES S 1. BR BRUN UNTO TON N COMP COMPAS ASS S It combines the main feature of a prismatic compass, sighting compass, hand level, and clinometer. Brunton compass compass is one of the most versatile and widely used. It consists of a brass case hinged on two sides.
2. LE LENS NSAT ATIC IC CO COMP MPAS ASS S This was designed for military use. It consists of an aluminum case containing a magnetic dial balanced on a pivot, a hinged cover with a sighting wire, a hinged eyepiece containing a magnifying lens for reading the dial graduations, and a sighting slot for viewing the distant object.
3. SU SURV RVEY EYOR OR’S ’S C COM OMPA PASS SS Its main parts include a compass box containing a graduated circle, two sight vanes, a magnetic needle, and two clamping crews.
4. PL PLAI AIN N PO POCK CKET ET C COM OMPA PASS SS Similar to surveyor’s compass except that it has no sight s ight vanes.
5. PR PRIS ISMA MATI TIC C CO COMP MPAS ASS S The graduations are found on a rotating card instead of being in the compass box.
6. FO FORES RESTER TER’S ’S CO COMP MPAS ASS S A type of pocket compass which is usually made of aluminum or some type of metal which does not affect the free movement and positioning of the magnetic needle.
7. TR TRAN ANSI SIT T CO COMP MPAS ASS S It has a compass box similar to surveyor’s compass which is mounted on the upper plate of the transit and often used to check horizontal angles and directions measured or laid off during transit surveys
H. MAGN MAGNETIC ETIC DECL DECLINA INATIO TION N The horizontal angle and direction by which the needle of a compass delects from the true meridian at any particular locality.
I. VA VARIA RIATIO TIONS NS IN MAG MAGNE NETI TIC C DECLIN DECLINAT ATIO ION N 1. DA DAIL ILY Y VA VARI RIAT ATIO ION N - also called diurnal variation - an oscillation of the compass needle through a cycle from its mean position over a 24-hour period - extreme eastern position of the needle → occurs early in the t he morning - extreme western position of the needle → occurs just about after noon time - daily variation is greater in higher latitudes than near the equator
2. AN ANNU NUAL AL VA VARI RIAT ATIO ION N - Another form of periodic swing taken by the magnetic meridian with respect to the true meridian - It usually amounts to only less than 1 minute of arc
3. SEC SECUL ULAR AR VARI VARIAT ATIO ION N - Covers a period of so many years that its exact cause and character is not thoroughly understood
4. IR IRREG REGUL ULAR AR V VAR ARIA IATIO TION N - A type of variation uncertain in character and cannot be predicted as to amount or occurrence
J. IS ISO OGONIC CHART A chart or map which shows lines connecting points where the magnetic declin declination ation of the compass needle is the same at a given time. agonic lines – lines connecting parts the chart with zero magnetic declination * In areas west of the agonic line, theof needle has an easterly declination * In areas east of the t he agonic line, the needle has a westerly declination
K. US USE E OF TH THE E CO COMP MPAS ASS S The north end of the needle indicates the angular part of the bearing and, the quadrant in which the bearing lines is determined by observing the markings on the t he compass box. Bearings are usually read to the nearest 10 to 15 minutes although it is possible to estimate much smaller values. The south end, which is easily identiied by a ine wire coiled around the needle, is only read if it is desired to determine the back bearing of a line or to check the reading on the other end of the needle. Bearings read from both ends of the needle should be exactly opposite each other in direction.
L. LO LOCA CAL L AT ATTR TRAC ACTI TION ON Any deviation of the magnetic needle of a compass from its normal pointing towards magnetic north.
M. MAG MAGNE NETIC TIC DI DIP P A characteristic phenomenon of the compass needle to be attracted downward from the horizontal plane due to the earth’s magnetic lines of force.
N. CO COMP MPAS ASS S SUR SURVEY VEYS S 1. TRAVER ERS SE– a series of lines connecting successive points whose lengths and directions have been determined from ield measurements. 2. TRAVERSING– process of measuring the lengths and directions of the lines of the traverse for the purpose of locating the position of certain points.
3. TR TRAV AVER ERSE SE ST STAT ATIO ION N – sometimes called angle points because an angle is usually measured at such stations. Any temporary or permanent point of reference over which the instrument is set up.
4. TR TRAV AVER ERSE SE LI LINE NES S – lines connecting traverse stations and whose lengths and directions are determined.
O. TYP TYPES ES O OF F CO COMPA MPASS SS SURVEY SURVEYS S 1. OP OPEN EN C COM OMPA PASS SS T TRAV RAVER ERSE SE It consists of a series of lines of known lengths and magnetic bearings which are continuous but do not return to the starting point or close upon a point of known position.
2. CL CLOS OSED ED COMP COMPAS ASS S TRAVER TRAVERSE SE It consists of a series of lines of known lengths and magnetic bearings which form a closed loop or begin and end at points whose positions have been ixed by other surveys of higher position.
P. ADJU ADJUSTM STMENT ENT OF AN OPEN OPEN CO COMPA MPASS SS TRA TRAVERS VERSE E When adjusting an open compass traverse there are two important steps to perform: the irst is to determine determine which among the traverse lines is free from the local attraction, and the second step is to perform the adjustment adjustment of successive lines by starting from either end of the selected line. The unaffected line is referred to as the “best line” and it is assumed that there is no local attraction anywhere on this line. Also, forward and back bearings taken at either end of the line are accepted as correct.
Q. ADJUST ADJUSTMENT MENT O OF F CLO CLOSED SED CO COMPASS MPASS TRAVERS TRAVERSE E The adjustment of closed compass traverse is similar to the adjustment of an open compass traverse except that in a closed traverse the effects of the observational errors are considered. The following are the three important steps performed during the adjustments: (a) computing and adjusting the interior angles, (b) selecting the best line or the line in the traverse which is unaffected by local attraction, and (c) adjusting the observed bearings bearings of successive lines. It will be noted that the last two steps are similarly done in the adjustment of an open compass traverse.
R. PRE PRECIS CISION ION OF C COMP OMPASS ASS RE READIN ADINGS GS It must irst of all be clearly understood that the compass is not an instrument of precision. When using a magnetic compass, precise work should not be attempted nor expected. The compass is not recommended for laying out directions with the type of precision required in most modern engineering constructions. A magnetic compass is designed to be used only for ordinary surveys requiring low accuracy and precision. It is also ideal for exploratory surveys required in geologic and forestry work.
S. SOU SOURCES RCES OF ERR ERROR OR IIN N CO COMPA MPASS SS W WORK ORK 1. BENT ENT NEED EEDLE 2. BENT PI PIVOT 3. SLUG SLUGGI GISH SH NEE NEEDL DLE E
4. 5. 6. 7. 8.
PLANE PLANE OF OF SIGH SIGHT T NOT NOT VERT VERTICA ICAL L ELECTR ELECTRICA ICALL LLY Y CHANGED CHANGED COMPA COMPASS SS BOX LOCA LOCAL L ATTR ATTRAC ACTI TION ON MAGN MAGNET ETIC IC VAR VARIA IATI TION ONS S ERRORS ERRORS IN READ READING ING THE THE NEEDL NEEDLE E
T. MISTAKES IN COMPASS WORK a) Reading Reading the the wrong wrong end end of the magnet magnetic ic needle needle b) Falling to observe observe the reverse reverse bearings bearings or azimuths azimuths of lines in the traverse traverse c) Not releasing releasing the needle completely and not allowing it it to swing freely about about the pivot. d) Misreading Misreading the quadrant quadrant letters when when taking a bearing near the cardinal cardinal points points ∘ ∘ of the compass. For example, a bearing of N15 25’W, is misread as N15 25’E, or a bearing of S76∘15’E is misread as N76∘15’E. e) Bearing letters are not changed changed when using the reversed reversed bearing of a line. line. f) Setting Setting off the the magnetic magnetic decli declinatio nation n on the wrong wrong side side of north. north. g) Falling to adjust the observed traverse angles angles prior prior to calculating calculating bearings bearings or azimuths of traverse lines. h) Mixing or interchanging interchanging the recording recording of azimuths from from north and and south, magnetic and true bearings, clockwise and counterclockwise angles, or forward and back bearings. i) Selectin Selecting g a line for referenci referencing ng arbitrar arbitrary y directions directions which which may be dificul dificultt to locate later.
MULT PLE CHO CE 1. The true meridian is the generally generally adapted adapted reference reference line in surveying practice. This line passes through the geographic north and south poles of the earth and the observer’s position. Since all true meridians meridians converge at poles, they are a) Parall Parallel el to ea each ch other other b) Perpend Perpendicula icularr to magnetic magnetic lines lines of force of the the earth earth c) Coincide Coincident nt with with the the grid grid meridi meridian an lines lines d) Not para paralle llell to each each other other e) Deviated Deviated at the the highe higherr latitud latitudes es 2. The magnitude magnitude of an angle can be expressed in different different unit systems which are basically derived from the division of the circumference of a circle. One such system used is the centesimal system in which the unit of measure is the a) Degree b) Mil c) Grad d) Ster Sterad adia ian n e) Radian
3. A common common method method employed employed in in designati designating ng the directio direction n of a line is by the the use of azimuths. The azimuth of a line is its direction as given by the angle between the meridian and the line measured a) Countercl Counterclockw ockwise ise from the north north or south branch branch of the meridia meridian n b) n a clockwise clockwise direction direction from from either either the north north or south south branch of the the meridian c) From the east east or west west branch branch of the referen reference ce parallel parallel in a clockwis clockwise e direction d) In a counterclockwise counterclockwise direction from the north branch branch of the meridian e) Only clockwi clockwise se from the the type south south branch branch of the meridi meridian an 4. The compass compass is a hand-held hand-held instrument instrument for determining determining the horizontal horizontal direction direction of a line with reference to the a) Magne Magneti ticc meri meridi dian an b) Gr Grid id meri meridi dian an c) True True meri meridi dian an d) Astron Astronomi omicc merid meridian ian e) Ass ssum ume ed me me 5. The horizont horizontal al angle and and direction direction by which which the needle needle of a compass compass delects delects from the true meridian at any particular locality is called the a) Loca Locall at attr trac acti tion on b) Magn Magnet etic ic di dip p c) Secu Secula larr var varia iati tion on d) Cyclic Cyclic luctu luctuati ation on e) Magne Magneti ticc declin declinat atio ion n 6. A chart chart of a map which which shows lines lines connectin connecting g points points where the the magnetic magnetic declination of the compass needle is the same at a given time is called a) A luctu luctuati ation on charts charts b) An iso isogo goni nicc cha chart rt c) An agon agonic ic map map d) A decli declinat nation ion dia diagra gram m e) Magn Magnet etic ic char chart t 7. A series series of lines lines of known length lengthss and directio directions ns which which begin begin or end at points points whose positions have been ixed by other surveys of higher precision is referred to as a) A clo close sed d tra trave vers rse e b) An ope open n trav traver erse se c) A dele delecti ction on angl angle e trave traverse rse d) An a angle ngle to the the right right trave traverse rse e) A direc directio tiona nall trav travers erse e 8. An angular angular measure measurement ment of 151.0 151.0000 000 grads grads is equiva equivalent lent to a) 2413 mild mild b) 2.70 .703 ra rad
c) 135.85 .85 deg d) 135∘54’ e) 2316 mils mils 9. The The equ equiv ival alen entt of 270 270∘00’ in the centesimal system is a) 300 gr grads b) 4800 mi mils c) 4. 4.71 7123 2389 89 rad radia ians ns d) 270. 270.00 00 degr degree eess e) 15.55 15.5500 00 stera steradia dians ns 10. The forward bearing bearing of a line is N45∘00’E. Its back azimuth measured from north is equal to a) S45∘00’ W b) 224∘30’ c) 250 grads d) 3750 mi mils e) 50 gr grads
VI.. VI
Circ Circle le g gra radu duat atio ion, n, V Ver erni nier er ssca cale le,, an and d Le Leas astt co coun unt t CIRCLE GRADUATION OF TRANSITS The engineer’s transit transit has two graduated circles or limbs. One, which is called the horizontal circle, is used when measuring horizontal angles. When angles are measured along the vertical plane, the other one, called the vertical circle, is used. Graduated circles are usually made of glass, aluminum, or solid silver mounted in bronze. 1. HORI HORIZO ZONT NTAL AL CIRC CIRCLE LES S In this type of graduation there are two sets of markings which are numbered continuously around the circle at 10 degrees intervals. Numbering is continuous from 0 to 360 degrees in both directions. The inside row of igures increases in a clockwise direction, and the outside row in a counterclockwise direction. 2. VERT VERTIC ICAL AL CIR CIRCL CLES ES The vertical circle is fastened securely to the horizontal axis of the telescope. It moves as the telescope is elevated or depressed and may be set in a ixed position by the telescope clamp. After it is clamped, it still could be turned through a small range of movement by means of the telescope slow-motion or tangent screw.
VERNIERS A vernier is a small graduated mechanical device attached and made to slide along linear or circular scales in order to increase to a higher degree of accuracy the readings obtained such scales. When employed, the device can help determine the fractional part of the smallest division of a main scale more accurately than
estimating by eye. It was invented in 1620 by a French mathematician named Pierre Vernier. There are two main types of verniers – direct and retrograde. Most verniers on surveying instruments are of the direct type 1. DI DIRE RECT CT VERN VERNIE IER R In this type the vernier the main scale and the vernier scale are read in the same direction. Direct verniers are widely used in surveying instruments such as transit. 2. RETR RETROG OGRA RADE DE VERN VERNIE IER R In this type of vernier the length n+1 divisions on the main scale are divided into n divisions on the vernier scale. Consequently, the smallest division on the vernier is slightly longer than the smallest division on the main scale. In the retrograde vernier, the main scale and the vernier scale are read in opposite directions. In order to determine determine what fractional part of the smallest main scale division may be read with the vernier, the least count or ineness of reading of the vernier and main scale unit must irst be known. This value is determined by dividing the length of the smallest division on the main scale by the total number of vernier divisions. It is given by the following expression s n Where: LC = is the least count or the smallest division that can be read on the main scale s = value of the smallest space or division on the main scale n = number of divisions on the vernier
LC =
MULT PLE CHO CE
1. What is the the least count count of a direct direct vernier vernier on a scale scale which which is graduate graduated d to 1/6 degrees if 60 divisions on the vernier ate equal to 59 on the main scale? a) 20 sec. b) 15 sec. c) 10 sec. d) 17 sec. 2. The value value of the smalle smallest st division division on the the main scale scale of a horizonta horizontall circle is is graduated to 1/3 degrees. If 40 divisions on the vernier are equal to 39 on the main scale, the least count or ineness of reading is a) 30 sec. b) 29 sec. c) 33 sec.
d) 27 sec. 3. In the equati equation, on, LC = s/n, s/n, s represents represents the the value of of the smallest smallest space space or division division on the main scale and n represents the number of a) Divisi Divisions ons on on the the main main scal scale e b) Spaces Spaces on on the the exten extension sion scale scale c) Divi Divisi sion onss on the the verni vernier er 4.
5.
6.
7.
d) Spaces Spaces on on the main main scale scale The value value of the smalle smallest st division division on the the main scale scale of a horizonta horizontall circle is is graduated from 1/6 of a degree. If there are 60 divisions on the vernier, the least count or ineness of reading is a) 10 mins b) 0. 0.16 1667 67 sec. sec. c) 5 sec. d) 10 se sec. In this type type the vernier vernier the main scale scale and the vernier vernier scale are read read in the same direction. a) Direct b) Retr Retrog ogra rade de c) Hori Horizo zont ntal al cir circl cles es d) Vert Vertic ical al circ circle less When angle angless are measure measured d along the the vertical vertical plane, plane, the other other one is is used a) Hori Horizo zont ntal al circl circles es b) Verti Vertical cal circ circle less c) Gr Grad adua uate ted d circ circle less d) Retr Retrog ogra rade de Invented Inventedthe the vernier vernierss in 1671 who who is a French French mathema mathematicia tician n a) Pier Pierre re Ver Verni nier er b) Pi Pier er Vern Vernie iers rs c) Perr Perrii Vern Vernie iers rs
d) Pe Perr rre e Ver Verni nier er 8. What is a small small graduated graduated mechanical mechanical device device attached attached and made made to slide along along linear or circular scales in order to increase to a higher degree of accuracy the readings obtained such scales? a) Gr Grad adua uate ted d circ circle le b) Tran ranst stiit c) Vernier d) Geod Geodim imet eter er 9. It is usually usually made made of glass, glass, aluminum, aluminum, or solid solid silver silver mounted mounted in bronze bronze a) Gradua Graduated ted cylind cylinder er b) Gr Grad adua uate ted d circ circle less c) Vernier d) Tran ransi sitt
10. Engineer’s Engineer’s transit has two limbs, these these are: a) Direct Direct an and d retr retrogr ograd ade e b) Hor Horizo izonta ntall and vertic vertical al circle circless c) Single Single an and d doubl double e verni vernier er d) Fold Folded ed ver verni nier er
VII. VI I.
Me Measu asuri ring ng ho hori rizo zont ntal al an and d ve vert rtic ical al an angl gles es MEASURING HORIZONTAL ANGLES The most common operation performe performed d with the engineer’s engineer’s transit is the measurementt of a horizontal angle. It consists of setting up and leveling the transit measuremen over a selected point, taking a backsight on a point, and turning the telescope through an angle to foresight, another point.
CLOSING THE HORIZON The process of measuring horizontal angles about a point is termed closing the horizon. This provides an easy way of testing instrument readings and pointing since a check is obtained if the sum of the angles equals to 360 degrees. In order to fully understand the operation of the transit or theodolite the student should irst learn how to use the instrument in measuring angles about a point.
LAYING OFF ANGLES If an angle such as APB is to be laid off from line PA, the transit is set up at P and any convenient reference mark is established along PA. the A vernier is set at zero and the line of sight is directed towards towards the reference mark. When the upper clamp is loosened, the telescope is turned to the desired direction until the index mark of the vernier is approximately at the required angle. The next step is to tighten the upper clamp and set the vernier exactly to read the required angle by means of the upper tangent crew. The cross hairs on the telescope should now point to the opposite side of the angle which has been laid off.
MEASURING VERTICAL ANGLES When a vertical angle is to be measured the transit is set up over a point and the horizontal plates are carefully leveled. leveled. The intersection of the cross hairs is set approximately approximate ly on the point to which a vertical angle is to be measured, and the telescope is clamped into position. Exact pointing is achieved by using the telescope tangent screw. Then the vertical circle and vernier are read to determine the angle above or below the horizontal plane. When using the transit with a full circle it is advantageous to measure a vertical angle once with the telescope in normal position and once in reversed position. The mean of the two readings will be the correct value of the vertical angle since both measurements are made independently of each other, thus
∝
1
=(
∝ N
+
∝ R
)/ 2
Where: ∝
1
= correct value of the measured vertical angle
∝
= vertical angle measured with telescope in direct or normal position
∝
= same vertical angle measured with telescope in reversed or plunged position
N
R
This process eliminates the index error and all other errors of adjustment. It also minimizes the possibility of mistakes since the reading is taken twice.
INDEX CORRECTION One way of determining the index error is to measure a vertical angle once with the telescope in direct position and also once in reversed position. The difference between the two measured quantities divided by 2 gives the value of the index error due to vertical circle which is out of the adjustment. IE =(∝ N −∝ R )/ 2
Where: IE = index error ∝
= vertical angle measured with telescope in direct or normal position
∝
= same vertical angle measured with telescope in reversed or plunged position
N
R
MULT PLE CHO CE 1. A vertical vertical angle angle is measured measured to a signa signall mounted mounted on top of a tower. tower. With the the ∘ transit telescope in direct position the reading reading on the circle is +22 32’. If the ∘ reading on the circle is +22 38’ with the telescope in reversed position, the index error and the index correction, respectively are a) -0 -06’ 6’ and and +0 +06’ b) -03’ -03’ an and d +03 +03’’ c) +06’ +06’ and and -06 -06’’ d) +03’ +03’ and and -03 -03’’ 2. A vertical vertical angle measured by a single observation observation with a transit is recorded recorded as ∘ ∘ -13 56’. If the index error is +0 04’, the correct value of the angle is a) -14∘00’ b) -13∘56’ c) -14∘05’ ∘
d) -13 58’
3. A horizontal horizontal angle angle was was measured measured by repetition six times times with an engineer’s engineer’s ∘ transit. Prior to measurement, the horizontal scale was set at 0 00’ and the reading on the scale was 84∘38’ after the angle was measured once, if the inal reading was 147∘42’, the average value of the angle measured is a) 84∘36’ b) 84∘39’
c) 84∘40’ d) 84∘37’ 4. The horizont horizontal al angles angles about point point P were measured measured and and recorded recorded as follows: follows: ℃ ' ' ' ℃ ℃ ℃ ℃ ℃ θ1=17 30 10 , θ2= 22 18 ' 02 ' ' , θ3=87 43 ' 33 ' ' , θ4 =103 10 ' 24 ' ' , θ5= 48 50 ' 44 44 ' ' , θ 6 =80 27 ' 01 ' ' . a) +0∘00’06” b) +0∘06’06” c) -0∘04’06” d) -0∘06’06” 5. Related Related to questio question n 4, assuming assuming that that the error error is the name name for each angle angle,, the sum of the adjusted values of the irst three listed angles is a) 127∘31’46” ∘
b) 127∘31’48” c) 127 31’47” d) 127∘31’49” 6. One way of determining determining the index error error is to measure a vertical vertical angle once once with the telescope in direct position and also once in reversed position. What is the equation for it? a) IE = s/n b) IE =(∝ N −∝ R )/ 6 c) IE =(∝ N −∝ R )/ 4 d) IE =(∝ N −∝ R )/ 2 7. . It consists consists of setting up and leveling the transit over a selected point, taking taking a backsight on a point, and turning the telescope through an angle to foresight, another point. a) Measu Measurem remen entt of angles angles b) Measu Measurem remen entt of horiz horizont ontal al c) Measu Measurem remen entt of vertic vertical al d) Measur Measuring ing horiz horizont ontal al angles angles 8. When a ______ __________ ____ is to be measure measured d the transi transitt is set up over over a point point and and the horizontal plates are carefully leveled a) hori horizo zont ntal al angl angles es b) vert vertic ical al angle angless c) in inte teri rior or an angl gles es d) exte exteri rior or angl angles es
9. The process process of measu measuring ring horiz horizontal ontal angle angless about a point point is is a) Open Openin ing g of hor horiz izon on
b) Open Openin ing g of angl angles es c) Clos Closin ing g of of hor horiz izon on d) Clos Closin ing g of poi point ntss 10. Closing the horizon provides provides an easy way of testing instrument rea readings dings and pointing since a check is obtained if the sum of the angles equals to a) 90 deg degrree eess b) 180 180 degr degree eess c) 270 270 degre egrees es d) 36 360 0 deg degre rees es
VIII VI II..
La Lati titu tude de an and d dep depar artu ture re,, Are Area a by DP DPD, D, DM DMD D an and d coo coord rdin inat ates es LATITUDE AND DEPARTURE The latitude of a line is its projection onto the reference meridia meridian n or a north-south line. Latitudes are sometimes referred to as northings and southings. Latitudes of lines with northerly bearings are designated as being north (N) or positive (+); those in a southerly direction are designated as south (S) or negative (-). On the t he other hand, the departure of a line is its projection onto the reference para parallel llel or an east-west line. Departures are east (E) or positive (+) for lines having easterly bearings and west (W) or negative (-) for lines having westerly bearings. The horizontal length of a line is designated by d and its bearing angle by following equations may be obtained for lines AB, CD, GH, and EF:
, the
∝
Lat ab=d ab cos ∝ab Lat cd= d cd cos ∝cd Lat gh= d gh cos ∝gf Lat ef = d ef cos ∝ef Depab= d ab cos ∝ab Dep =d cos ∝ cd cd cd Depgh= d gh cos ∝gf Depef =d ef cos ∝ef
AREA BY DMD METHOD To determine the area of a closed traverse. The double meridian distance is an adaptation of the method of determining areas by coordinates. Thus, if the latitudes and departures of a traverse are known and have been adjusted the area of the traverse may be computed conveniently by the DMD method. To obtain the double area of such igures, the DMD of the course is multiplied by the corresponding correspondi ng adjusted latitude of the course, or
Double Area= DMD ( Adjusted Latitude )
Since the sign of the latitude must be used in the multiplications, some double areas will yield positive values and some will have negative values. The double areas are in turn recorded in plus (+) or minus (-) columns which correspond to north double area (NDA) or south double areas (SDA). The traverse area is then equal to one-half the algebraic sum of the north double areas and the south double areas, or AREA =(1 / 2 )(
∑ NDA +∑ SDA )
Where ∑NDA and ∑SDA are the sum of the north double areas and south double areas, respectively.
AREA BY DPD METHOD The double parallel distance method of area computation is similar to the DMD method. Double areas can be determined by multiplying the DPD of each course by the corresponding adjusted departure departure of the course, or Double Area= DPD ( Adjusted Latitude )
Double areas are recorded in plus (+) or minus (-) columns which correspond to east double areas (EDA) and west double areas (WDA), respectively. Also, the traverse area is equal to one-half the algebraic sum of both double areas, or AREA =(1 / 2 )( EDA + WDA ) Where ∑EDA and ∑WDA are the sum of the east double areas and west double areas, respectively.
∑
∑
COORDINATE METHOD The coordinate method adjustment may be employed when the preliminary coordina coordinates tesof oftraverse the stations along the traverse have been determined. determine d. This method of adjustment is simply an application of the compass rule since the corrections applied are proportionate proportionate to the lengths being adjusted. The following formulas are used in this method of adjustment: d = √ ( X ¿ ¿ 2− X 1) +( Y ¿ ¿ 2−Y 1 ) ¿ ¿ 2
C X = X K − X C C Y =Y K −Y C
2
C X + C Y √ C RP = 2
2
D
x =d
( )
y = d
C x D
( ) C y D
1
X = X ± x 1
Y =Y ± y Where: d = distance between any two stations whose x and y coordinates are known X 2 = coordinate along the x-axis of a succeeding station Y 2= coor coordinate dinate alongthe along they-axis of a succeeding s ucceeding station X 1 = coordinate along the x-axis of a preceding station Y 1= coordinate along the y-axis of a preceding station C x = error of closure along the x-axis C Y =error of closure along the y-axis X K = known, coordinate along the x-axis of the distant terminal station X C = computed coordinate along the x-axis of the distant terminal station Y K = known, coordinate along the y-axis of the distant terminal station Y C =computed coordinate coordinate along the y-axis of the distant terminal station RP = relative precision of closure D = total length l ength or perimeter of the traverse from the initial station to the distant terminal station x = coordinate correction along the x-axis y = coordinate correction along the y-axis 1 coordinate X of a station X = adjusted coordinate 1 Y = adjusted coordinate Y of a station
MULT PLE CHO CE 1. What What does does DMD DMD stan stands ds for? for? a) Double Double meridi meridian an distanc distance e b) Double Double mean mean diff differe erence nce c) Doub Double le mod mode e dist distan ance ce d) Double Double medi median an dista distance nce 2. It is someti sometimes mes refer referred red to to as northi northings ngs and and southing southings. s. a) Depa epartu turre b) La Lati titu tude de
c) Double Double pa paral rallel lel di dista stance nce d) Double Double merid meridian ian dista distance nce 3. Its projecti projection on onto the the referenc reference e parallel parallel or an east-we east-west st line. line. a) Lat atiitu tud de b) Depar epartu turre c) Bearings 4.
5.
6.
7.
d) Do Doub uble le area area What What does does DPD DPD sstan tands ds for? for? a) Double Double plane plane di dista stance nce b) Double Double poin pointt differ differenc ence e c) Double Double paralle parallell distanc distance e d) Double Double phase phase dist distan ance ce This method method of adjustm adjustment ent is simply simply an applic application ation of of the compass compass rule rule since the the corrections applied are proportionate to the lengths being adjusted. a) Distan Distance ce betw between een ttwo wo point pointss b) Pytha Pythagor gorea ean n theor theorem em c) Distance d) Coor Coordi dinat nate e method method The latitude latitude of a line is its project projection ion onto the refer reference ence meridi meridian an while while the departure departur e of a line is its projection onto the a) Pola olar ax axis b) Equa Equato tori rial al axi axiss c) Refer Referenc ence e pa para rall llel el d) Nort Northh-So Sout uth h line line In closed traverse the the measured measured length of line AB AB is 245.08. 245.08. If If the bearing bearing of the ∘ line is S40 35’E, the latitude of the line should be a) – 18 186.13 m b) + 15 159.44 .44 m c) -175.6 .64 4m
d) -1 -159 59.4 .44 4m 8. The length length of a traverse traverse line line CD is 316.4 316.48 8 m and the magneti magneticc azimuth azimuth from ∘ south of the line is 153 54’. The departure of CD is a) + 248.21 .21 m b) +144.0 .05 5m c) -139.23 .23 m d) -2 -284 84.2 .21 1m 9. The merid meridian ian distan distance ce of a line line is is deined deined as the a) Longest distance distance from the center center of the line to the reference reference meridian meridian b) Shortest Shortest distance distance from the midpoint midpoint of the the line to the reference reference meri meridian dian c) Mean distance distance from the center of the line to the reference reference meridian d) Offset distance measured from from either the the reference reference meridian or reference reference parallel
10. The double meridian meridian distance of the last course of a closed traverse is numerically equal to the a) Latitude Latitude of the the course course itself itself with with its sign sign reversed reversed b) Departur Departure e of the course course itself itself c) Either Either the latitude latitude or departure departure of the course, course, but with with the opposite opposite sign d) Depar Departure ture of the the course itself, itself, but but with the the opposite opposite sign.
IX.
Omitted measurements 1. CASES OF TH THE E OM OMITTED ITTED M MEASUREME EASUREMENTS NTS IN INVOLVIN VOLVING G ADJO ADJOINING INING SIDES. 1ST CASE: Length of One Side and Bearing of Another Side Unknown
It shows closed traverse for which the length of the side CD and the bearing of side DE are unknown. The lengths and bearings of the other sides AB, BC, and EA are known. Since the latitudes and departures departures of the known sides may be calculated, the length and bearing of the closing line EC may in turn be determined.
By Sine Law DE CE sin C CE = and sin D = sin C DE sin D For this particular case, however, if the angle between the side of unknown bearing and the side unknown length is close to 90This degrees, the solution may be very weak and willofyield unsatisfactory answers. is because the value of the sine near 90 degrees changes very slowly and a small variation in the calculated values can cause a relatively, large error in the angle calculated by the sine law. 2ND CASE: Lengths of Two Sides Unknown
By Sine Law BC CD BD BD sin D BD sin B = = CD = and BD = sin D sin B sin C sin C sin C 3RD CASE: Bearings of Two Sides Unknown By Cosine Law 2 2 2 c = a + b −2 ab cos C LET a = DE, b = AD, c = EA, and C = A cos A
=¿ ¿
2. CASES OF TH THE E OM OMITTED ITTED M MEASUREME EASUREMENTS NTS IN INVOLVIN VOLVING G ADJO ADJOINING INING SIDES. 1st CASE: LENGTH OF ONE SIDE AND BEARING OF ANOTHER SIDE UNKNOWN 2ND CASE: LENGTHS OF TWO SIDES UNKNOWN 3RD CASE: BEARINGS OF TWO SIDES UNKNOWN For the different cases of omitted measurements involving non-adjoining non-adjoining sides the following principles are adapted: 1st PRINCIPLE: A line may be moved from one location to a second location parallel with the irst, and its latitude and departure will remain unchanged. 2nd PRINCIPLE: The algebraic sum of the latitudes and the algebraic sum of the departures departur es of any system of lines forming a closed igure must be zero, regardless regardle ss of the t he order in which the lines are placed.
MULT PLE CHO CE
1. When the length or direction of a line line within a closed traverse cannot be determined determined by iled observation, these missing quantities may be determined analytically to obtain a complete set of notes for the traverse provided a) There are are only only three three or more more unknown unknown quantiti quantities es b) They do do not exceed exceed two two unknown unknown quanti quantities ties c) The sides sides with unknown unknown quantities quantities are parts of an adjusted adjusted open traverse d) The sides sides with unknown unknown quantities quantities are non-adj non-adjoini oining ng 2. When the two sides sides of a closed closed traverse traverse are non-adjoining, non-adjoining, the determination determination of the unknown quantities is undertaken with an added graphical solution. For example, a line (or lines) may be moved from one location to a second location parallel with the irst. This principle is adapted since the a) Area of the the travers traverse e remain remainss constant constant b) Latitude Latitude and departure departure of any of of the lines lines moved remain remainss unchanged unchanged c) Coordinat Coordinates es of all points points or corners corners deining deining the traverse traverse will will correspondingly correspondin gly be adjusted d) Linear Linear error error of closure closure will remain remain invari invariable able 3. Whether Whether the sides sides of a closed travers traverse e with unknown unknown quantiti quantities es are adjoini adjoining ng or non-adjoining, non-adjoin ing, it must be deinite that the algebraic sum of the latitudes and the algebraic sum of the departures must be zero, a) And correspo correspondin ndingly gly the sum of the residual residualss must also be a minimum minimum b) And the length of each course is proportional proportional to the the total length length of traverse traverse c) Provided Provided the sides sides are arrang arranged ed in proper proper order order or sequence sequence d) Regar Regardless dless of the order order in which which the the sides are are placed placed
4. Given Given the following following tabulate tabulated d data for a closed closed traverse traverse in which which the length and and bearing of course CD are unknown LENGTH (m) 255.75
COURSE AB
BEARING N04∘30’E
LATITUDE +N -S 254.96
DEPARTURE +E -W 20.07
∘
BD C 410.06 N42 15’E 303U .5N 3KNOWN 275.71 C DE 852.65 S30∘19’W 736.05 430.40 ∘ EA 230.28 N46 45’W 157.78 167.73 The length of course CD is a) 303.00 m b) 322.13 .13 m c) 17.95 m d) 301.70 .70 m 5. Related to question 4, the bearing of course CD, rounded rounded to to the nearest nearest minute, minute, is a) N86∘15’W b) N03∘45’E ∘
c) S03 45’E d) N86∘15’E 6. Given the following tabulated tabulated data data for a closed traverse traverse in which the lengths of sides CD and DE are unknown COURSE
LENGTH (m) 541.55 795.62
BEARING
LATITUDE +N -S 38.09 794.47
DEPARTURE +E -W 540.21 42.80
AB S85∘58’E BC S03∘05’W CD S52∘50’W UNKNOWN UNKNOWN DE N12∘42’W EA 650.25 N40∘15’E 496.29 420.14 If CE is chosen as the closing line, its length is a) 35.41 m b) 24.11 m c) 581.2 .28 8m d) 977.2 .23 3m 7. In Question Question 6, the the bearing bearing of the closing closing line line CE, rounded rounded to to the nearest nearest minute minute,, is ∘ a) S69 52’E b) N64∘32’W c) N69∘52’W d) S70∘09’E 8. In Ques Questio tion n 6, the the len length gth sid side e CD is is a) 1058.5 .58 8m b) / c) 1057.00 m
d) 903.48 .48 m 9. In Ques Questio tion n 6, the the len length gth sid side e DE is is a) 903.48 m b) 902.13 .13 m c) 1058.58 m d) 105 1057. 7.00 00 m 10. If the angle between the side of unknown unknown bearing and the side of unkn unknown own length is close to 90 degrees, a) Regardle Regardless ss of the order order in which which the sides sides are placed placed b) Area of the traverse traverse remains remains constant constant c) The solution solution may be very very weak weak and will yield yield unsatisfa unsatisfactory ctory answer answerss d) Provided the sides sides are arranged arranged in proper proper order or sequence sequence
X.
Subdivision The process of subdivision may require the application of the principles of geometry and trigonometry or the use of special techniques in computations. Other cases are performed by trial-and-error methods. This usually involves an initial assumption such as the starting point or the direction to be taken by a selected cut off line which will separate a certain area from the main parcel. Most of the problems encountered are so common and frequently involved in the working out of more complicated cases. Four of the most common cases encountered in subdivision subdivision of land will be explained. These cases are: 1. Dividin Dividing g an area area into two two parts parts by a line line between between two two points. points. 2. Dividin Dividing g an area area by a line line running running through through a point point and and in a given given direction 3. To cut off off a requi required red area area by by a line line through through a given given point point 4. To cut off off a required required area area by by a line runni running ng in a given given directi direction. on. For any of these, a survey is run, the latitude and departures are determined, the surveyed traverse is balanced, and the area of the entire tract is computed. When computing the desire subdivision s ubdivision scheme only the adjusted latitudes and departures are used.
DIVIDING AN AREA INTO TWO PARTS BY A LINE BETWEEN TWO POINTS It is assumed that the length and direction of each course has been earlier determined, the latitudes and departures computed and adjusted, and the area of the whole tract computed.
DIVIDING AN AREA BY A LINE RUNNING THROUGH A POINT AND IN A GIVEN DIRECTION It is assumed that the length and direction of each course known, the latitudes and departures computed and adjusted, and the area of the whole tract computed. The solution will require the calculation of the lengths BP and FP and the area of each of the two tracts.
TO CUT OFF A REQUIRED AREA BY A LINE THROUGH A GIVEN POINT A dividing line is to pass through a certain point cutting a required area from the tract. The traverse may be subdivided subdivided into tracts of equal areas or into any desired proportional parts. Sometimes, the tract will be of such shape that a line drawn from a given point in the boundary to any corner will cut off an area nowhere near that required. Under these circumstances or when the traverse has a large number of sides, it is advisable to irst plot the traverse to scale and to establish a trial line of subdivision. As rough check the planimeter may be used to advantage for determining the area cut off by a trial line. The line may be shifted until the area cut off agrees closely with that required.
TO CUT OFF A REQUIRED AREA BY A LINE RUNNING IN A GIVEN DIRECTION An irregular parcel of land with courses of known lengths and bearings, the latitudes and departures computed and adjusted, adjusted, and the total area of the tract calculated. The parcel of land is to be divided into two parts, each of a required area, by a line running in a given direction. The subdivision scheme may require the subdivision of the whole parcel into equal areas or into any other desired proportional parts. Out of the desired division, tract is formed on one side of the dividing line and another tract on the other side. EXAMPLES: 1. DIVIDI DIVIDING NG A TRACT TRACT OF LAN LAND D INTO INTO TWO PARTS BY A LINE BETWEEN TWO POINTS. Given the following data of a tract of land, determin determine e the area east of a line running F to C and calculate the length and bearing of FC.
Solution: a) Determining Area of tract ABCDEF. (Area of whole traverse):
2. DIVIDING DIVIDING A TRACT TRACT OF LAND LAND BY A LINE LINE RUNNING RUNNING IN A GIVEN GIVEN DIRECT DIRECTION. ION. Given Given the following data of a tract of land, ind the area of each of the two parts into which the tract is divided bu a line through A with a bearing of N 75°30’ E.
Solution: a) Determining Area of tract ABCDEF. (Area of whole traverse):
3. MULT MULT PLE PLE CHO CHO CE CE
1. LINEAR MEASUREMENTS. The measured length of airport runways in ive major cities in the Philippines are: 125.00, 1375.50, 1410.75, 1550.25, abd 1750.00 neters. Determine the equivalent length of each runway in kilimeters, decimeters, and centimeters. Tabulate values accordingly. 2. AREA MEASUREMENTS. Given the dimenstions of the following tracts of land: a) 108.75 m by 76.82 m b) 940.05 m by 1296.73 m c) 13.36 m by 50.05m d) 1258.30 m by 624.03 m e) 8476.55 m by 121.79 m
3. AREA MEASUREMENTS. Given the area and width of the following rectangular shaped pieces of property: a) 2.575 ha and 195.42 m b) 125.42 sq m and 545.0 cm c) 0.85 sq kmn and 925.09, d) 50.0 ares and 100.0 m e) 42545.19 sq m and 346.72 m Determine the length of each property in meters 4. VOLUME MEASUREMENTS. Following area dimension, length, width and depth of ive excavated borrow of a highway project: a) 133.26 m, 35.48 m, abd 18.60 , b) 50.05m, 39.25 m, and 7.14 m c) 243.55 m, 76.18m, and 26.66 m d) 42.055 m, 8.605 m, and 12.332 m e) 9.5 m, 6.3m, and 4.9m 5. VOLUME MEASUREMENTS. Given the approximate lat area and depth of excavation of the following borrow pits: a)3750.0 sq m and 758.0 cm b) 0.035 sq km and 180.0 m c) 15.6 ares and 495.0 m d) 9.250 ha and 250.0 m e) 6750 sq n and 195.0 m Determine the volume of earth removed from each pit in cubic meter. MULLTIPLE MULLTIPL E CHOICE: 6. The process of ________ may require the application of the principles of geometry and trigonometry or the use of special techniques in computations. a.) subdivision b.) area
c.) survey d.) none of the above answer is a 7. This usually involves an initial assumption such as the starting point or the direction to be taken by a selected cut off line which will separate a certain area from the main parcel. a.) trial and error method b.) theory based method c.)both a and b d.) none of the above answer is a 8. Which does not belong to the group: a.)Dividing an area into two parts by a line between two points. b.)Dividing an area by a line running through a point and in a given direction c.)To make area for a parking lot through a given point d.)To cut off a required area by a line running in a given direction. answer is c 9. A _____is to pass through a certain point cutting a required area from the tract. a.) subdvison line b.) dividing line c.) imaginary line d.) none of the above answer is b 10.________ may be used to advantage advantage for determining determining the area cut off by a trial line. a.) planimeter b.) panonimeter c.) perliometer d.) none of the above answer is A
Honor Pledge for Completion Requirement: "I afirm that I shall not give or receive any unauthorized help on this requirement and that all work shall be my own."
TRULY YOURS’
ABAYON, JETT C.
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