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DOCUMENT RESUME

ED 086 881 CE 000 918

AUTHOR Fimmano, Ralph; Kacharian, John C.TITLE Highway Surveying. Instructor's Guide for an Adult

Course. Highway Technicians Program Unit III.INSTITUTION New York State Education Dept., Albany. Bureau of

Continuing Education Curriculum Development.PUB DATE 71NOTE 172p.; Revised edition of 1962 document by Fimmano

and Frank E. Howard

EDRS PRICE MF-$0.65 HC-$6.58DESCRIPTORS Adult Education Programs; Career Education; *Civil

Engineering; *Highway Engineering Aides; *RoadConstruction; *Teaching Guides; *Technical Education;Vocational Education

IDENTIFIERS *Highway Surveying; New York State

ABSTRACTThe revised instructor's guide, which is part of the

New York State Highway Technician's Program to provide neededtechnicians and engineers by upgrading people in the lower-leveltechnician jobs, is geared toward the improvement of technical skillsand knowledge in highway surveying. In view of the shortage ofqualified technicians and engineers caused by the rapid expansion inthe building of State and Federal highways, local school districtsand other sponsors of adult education programs are being encouragedto offer the courses in this program as part of occupationaleducation. Each of the fourteen lessons includes enough subjectmatter for about 2 1/2 hours of classroom instruction. All lessonsare written with a content outline on the left half of the page andcorresponding teaching points and techniques on the right half of thepage. Lessons cover technical skills, such as: elements of surveying;measuring distances; leveling, measurement of angles and directions;the transit; traverse and stadia surveying; field astronomy;horizontal and vertical curvature; preliminary, construction, andfinal surveys. Also included is a flnal examination. (EA)

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The University of the State of New YorkTHE STATE EDUCATION DEPARTMENT

Bureau of Continuing EducationCurriculum Development

Alban; , New York 12224, 1971

HIGHWAY SURVEYINGInstructor's Guide for an Adult Course

Highway Technicians ProgramUNIT III

The University of the State of New YorkTHE STATE EDUCATION DEPARTMENT

Bureau of Continuing Education Curriculum Development.Albany, New York 12224

1971

THE UNIVERSITY OF THE STATE OF NEW YORK

Regents of the University (with years when terms expire)

1984 Joseph W. McGovern, A.B. , LL.B., L.H.D., LL.D., D.C.L.Chancellor New York

1085 Everett J. Penny, B.C.S., D.C.S., Vice Chancellor - - White Plains1978 Alexander J. Allan, Jr., LL.D., Litt.D. Troy1973 Charles W. Millard, jr., A.B., LL.D., L.H.D. Buffalo1972 Carl H. Pforzheimer, Jr., A.B., M.B.A., D.C.S., H.H.D.- - Purchase1975 Edward M. M. Warburg, B.S., L.H.D. New York1977 Joseph T. King, LL.B. Queens1974 Joseph C. Indelicato, M.D. Brooklyn1976 Mrs. Helen B. Power, A.B., Litt.D., L.}1.D., LL.D. - - Rochester1979 Francis W. McGinley, B.S., LL.B., LL.D. Glens Falls1980 Max J. Rubin, LL.D., L.H.D. New York1986 Kenneth B. Clark, A.B., M.S., Ph.D., Litt.D.- - - - Hastings

on Hudson1982 Stephen K. Bailey, A.B., B.A.; M.A., Ph.D., LL.D. - - - - Syracuse1983 Harold E. Newcomb, B.A. Owego1981 Theodore M. Black, A.B. Sands Point

President of the University and Commissioner of EducationEwald B. Nyquist

Executive Deputy Commissioner of EducationGordon M. Ambach

Deputy Commissioner for Elementary,Secondary, and Continuing EducationThomas D. Sheldon

Associate Commissioner for Instructional ServicesPhilip B. Langworthy

Assistant Commissioner for Instructional Services (General Education)Bernard F. Haake

Director, Division of School SupervisionH. George Murphy

Chief, Bureau of Continuing Education Curriculum DevelopmentHerbert Bothamley

Assistant Commissioner for Occupational EducationRobert S. Seckendnrf

Director, Division of Occupational Education InstructionRobert H. Bielefeld

Chief, Bureau of Trade and Technical Education

PORI SWORD

This instructor's guide, Highway Surveying, is a revision of Unit IIIin the Highway Technicians Program. It was produced by the New York StateEducation Department with the help of the New York State Department ofTransportation (formerly the Department of Public Works), which hadrequested the program originally.

John L. DeLee, now principal civil engineer in the Bureau of HighwayPlanning of the Department of Transportation, (with the help of other per-sonnel from the district offices of the Department) carried on the planningfor the original series of nine units (or courses) in the Highway TechniciansProgram. Edward Umiker, now associate civil engineer in the Buffalo Reg-ional Office of the Department of Transportation, and Ralph Fimmano, seniorcivil engineer in the Utica Regional Office, collaborated in developing thetopical outlines for the nine units.

The first edition of this Guide (published in 1962) was written byRalph Fimmano under the guidance of Berton P. Plummer, who was then anassociate in the Bureau of Occupational Extension and Industrial Servicesof the Education Department. Frank E. Howard, former associate in theBureau of Vocational Curriculum Development and Industrial Teaching Training,also cooperated in the production of the 1962 edition. Mr. Fimmano preparedthe major part of the revised edition, while John C. Kacharian, chiefengineer, Post Engineer's Office, Watervliet Arsenal, Watervliet, made someadditional revisions. E. Noah Gould, associate in the Bureau of ContinuingCurriculum Development, supervised the revisions and the final preparationof the manuscript for publication.

To all the agencies and individuals mentioned above this Bureau makesgrateful acknowledgment for the responsibilities which they so faithfullyfulfilled.

H. GEORGE MURPHY, DirectorDivision of School Supervision

iii

HERBERT BOTHAMLEY, ChiefBureau of Continuing Education

Curriculum Development

MESSAGE TO THE INSTRUCTOR

The rapid expansion in the building of state and Federal highways hascaused a serious shortage of qualified technicians and engineers. The NewYork State Department of Transportation and the State Education Departmenthave collaborated in the Highway Technicians Program to overcome thisshortage.

This program is expected to provide the needed technicians and engi-neers by upgr,ding people in the lower-level technician jobs. Thisinstructor's guide, Highway Surveying, and the others in the program areintended to improve the skills and technical knowledge of those technicians.

Local school districts and other sponsors of adult education programsare being encouraged to offer the courses in this program as part ofoccupational education. Besides attracting students from the Department ofTransportation, students will be drawn from the public works departments ofcounties, cities, and towns. Employees of construction contractors willalso be found in these classes.

Each lesson in this guide includes enough subject matter for about2 1/2 hours of classroom instruction. The total length of the course,however, may be adjusted to fit the needs of the enrollees.

ROBERT H. BIELEFELD, DirectorDivision of Occupational Education

iv

CONTENTS.Page

Foreword iii

Message to the Instructor iv

Lesson

1 Introduction to the Course 1

2 The Elements of Surveying 6

3 Measuring Distances 14

4 Leveling 23

5 Leveling (continued) 32

6 Leveling (continued) 42

7 Measurement of Angles and Directions 53

8 The Transit 62

9 The Transit (continued) 74

10 The Traverse and Stadia Surveying 86

11 Principles of Field Astronomy 103

12 Horizontal Curvature 116

13 Vertical Curvature 132

14 The Preliminary, Construction, and Final Surveys 144

Final Examination 159

ILLUSTRATIONS

Figure Page

1 Radius of a 1° Curve 118

2 Derivation of Elements of the Simple Curve 119

3 Relationship of A, D, and T 120

4 Elements of the Spiral Curve 129

5 The Parabola Used as a Vertical Curve 134

6 Crest Vertical 136

7 Alternate Analysis of the Crest Vertical 137

8 Sag Vertical 138

9 Sag Vertical (Low Point) 140

10 Unsymmetrical Vertical 142

11 Problem Using a Hold Control 143

vi

Lesson

INTRODUCTION TO THE COURSEREFERENCES CITED THROUGHOUT THIS COURSE

Davis, R.E., Foote, F.S., and Kelly, J.W. Surveying: Theory andPractice. 5th edition. New York, N.Y. McGraw-Hill. 1966.

(Referred to in this unit as "Ref. A")

Bouchard, H., and Moffitt, F.H. Surveying. 5th edition. Scranton.International Textbook Co. 1965. (Referred to in this unit as

B")

OBJECTIVES1. To get acquainted with class members2. To explain the purpose of the course and role of the surveyor in

the Department of Transportation3. To provide a general description of the course4. To orient the student in several areas of surveying

CONTENT OUTLINE TEACHING POINTS AND TECHNIQUES

I. Introduction Write the name of the course and yourname on the chalkboard. Give thesturlents a brief description of yourexperience.

A. Course purpose

B. Introduction of classmembers

Explain that the course is being givento technicians and to constructioninspectors to supplement their knowl-edge and to assist them in upgradingthemselves in their jobs.

Add that the course is also valuabletraining for taking Department ofTransportation examinations for engi-neering positions.

Have each student introduce himself tothe class and give such information asoccupation and where employed.

C. Required student equipment Write the title and author of-Ref. Aon the chalkboard.

1

HIGHWAY SURVEYING

CONTENT OUTLINE

1. Basic textbook

Introduction

TEACHING POINTS AND TECHNIQUES

State that it would be advisable foreach student to buy a copy of thebook since it is very useful for thecourse and can also be used in thefuture.

Ask the students to sign a sheet ofpaper, if they wish, so a group ordercan be made.

2. Looseleaf notebook Tell the class that a looseleaf note-book is also needed for course notes.

3. Field notebook

4. Engineer's scale, pro-tractor, and triangles

5. 'phemeris

II. Characteristics of aSuccessful Surveyor

2

Ask the students to sign a sheet ofpaper, if they wish,so a group ordermay be made for a small field note-book.

Point out that the engineer's scale,protractor, and triangles will beused; small traingles are preferred.

Add that an ephemeris will be pro-vided for each student by one of thesurveying equipment companies.

State that technical knowledge andskills are essential in a good sur-veyor. However, certain traits ofcharacter are often more important.A successful surveyor:

1. Believes in and applies thescientific method

2. Is stable, able to control histemper, and is considerate ofothers

3. Is able to see facts clearly andhas sound judgment

4. Has initiative, resourcefulness,and energy

5. Is watchful of the interests ofhis employer and is respected byhis associates

HIGHWAY SURVEYING

CONTENT OUTLINE

III. Course Description

Introduction

TACHING POINTS AND TECHNIQUES

State that only the basic elements ofsurveying will be covered in thiscourse.

A. Title and brief resume of Discuss briefly the content of thiseach lesson course 1,), giving an explanatory state-

ment of the scope and content of eachlesson.

1. Introduction

2. The elements of sur-veying

3. Measuring distances

4. Leveling

5. Leveling (continued)

6. Leveling (continued)

Lesson 1 briefly describes the purifseof the course, and the importance andcharacteristics of the surveyor. In

this lesson the teacher explainthe role of the surveyor in highwayplanning and construction, stressinghis relationship with the Departmentof Transpc/ation.

Lesc:,11 2 introduces the student to ther.oncept of surveying. Covered are thevarious types of surveying, the ter-minology used, measurements, precision,and errors. Also, the student isgiven an introduction to the instru-ments and accessories used.

Lesson 3 discusses the different waysof measuring distances between pointson the surface of the earth. Errorsand mistakes in measuring are included,along with an explanation of precisionand accuracy.

Lesson 4 describes the leveling pro-cess whereby eleva -. is of points aredetermined. Also Jvered are descrip-tions of types instruments and rods,:sed in levelg, and the importantfactors of care.

3

Lesson 5 introduces the student to thepurposes of leveling in highwayengineering. Further, the kind ofleveling that is used for each purposeis covered. Described is the procedurefor setting up the instruments, takingreadings, and use of recorded data.

Lesson 6 continues by describing typesof leveling and the note-taking process.

HiCkltiAY SURVEYING Introduction

CONTENT OUTLINE

7. Measurement of anglesand directions

IFACHINO POINTS AND TECHNIQUES

Also, the student is given the methodsused in signalling between the instru-ment man and the rod man. Anothersegment of this lesson considers theerrors that may be encountered inleveling and the adjustments that areto be made to correct the sources oferrors.

Lesson 7 delves into another portionof the surveying responsibility: themeasuring of angles and directions.Also, the exact location of any point,line, or survey is determined. Theeffect of magnetic forces is studiedin this lesson.

8. The transit Lesson 8 describes the construction ofthe transit in detail. Followingthis, the mechanics of setting up theinstrument are described along withthe methodology of measuring anglesand laying out lines. Errors result-ing from maladjustment are describedand a brief mention is made of pro-cedure for running a traverse.

9. The transit (continued) Lesson -9 continues to discuss thetransit and the errors that can occurin its use. Then the numerous pro-cedures for correcting errors aredescribed. Also, in this lesson arethe methods for using the transit infield operations: locating lines,running lines, setting lines, applica-tion of triangulation, and plotting.

10. The traverse and stadia Lesson 10 concerns the computation ofsurveying the traverse, the coordinate system,

and the New York State CoordinateSystem; relationship to geodeticsurveying is also included. The otherportion of this lesson covers stadiasurveying for obtaining horizontaldistance and differences in elevation.

11. Principles of fieldastronomy

4

Lesson 11 introduces the student toastronomy as used in surveying. Thisaspect-is used in determining latitude,time, longitude, and azimuth.

HIGHWAY SURVEYING

CONTENT OUTLINE

12. Horizontal curvature

13. Vertical curvature

Introduction


Lesson-12 familiarizes the studentwith horizontal curvature and its usein highway alignment. Many of theformulas used in computations aredescribed. Also included are procedural steps for use of the transit oncurves.

Lesson 13 discusses the vertical curvefor use in highway alignment. Thistype of curvature also requires use ofvarious geometrical formulas, describedin this lesson.

14. The preliminary, con- Lesson 14 describes the preliminary,struction, and final construction, and final surveys forsurveys highway systems. The major differences

in the procedures for conducting theseare covered. Also, discussed are thesequential operations of the threephases.

15. Final examination A final exam will be given for thiscourse. The examination will high-light student weaknesses. Correctingthe test in class and discussing testquestions will help strengthen anyweak areas. Students will also obtainan evaluation of their interest tocontinue and progress in surveying.

ASSIGNMENTIn Ref. A read all of Chapters 1 and 2 and pages 72-76 in Chapter 5.

5

Lesson 2

ELEMENTS OF SURVEYINGOBJECTIVES

1. To provide the student with the concept of surveying2. To identify and explain terminology used in surveying3. To acquaint the student with surveying instruments and accessories


I. Definition of Surveying Define surveying as a system oflocating the positions of points onor near the surface of the earth.(Ref. A, p. 1; Ref. B, p. 1)

A. Scope of this course

Explain that surveying entails:

1. Measuring horizontal and verticaldistances between terrestrialobjects

2. Measuring angles between terres-trial lines

3. Determihing the direction of lines

4. Establishing points by predeter-mined angular and linear measure-ments

State that this course embraces thatpart of surveying used to prepareplans and profiles for the design andconstruction of highways and bridges.

6

Point out that the survey process isdivided into field work (the takingof measurements) and office work (themathematical calculations).

HIGHWAY SURVEYING Elements of Surveying

CONTENT OUTLINE

II. Types of Surveying

A. Classification based onassumed shape of earth'ssurface

1. Plane surveying

2. Geodetic surveying

B. Classification based onpurpose of survey

1. Control survey


Explain that one way of classifyingkinds of surveying is based on whetherthe earth is assumed to be a planesurface or a curved surface. Thisway of classifying divides surveyinginto plane and geodetic surveying.(Ref. A, pp. 4-5; Ref. B, p.5)

State that plane surveying is thetype most often used on constructionsurveys. In plane surveying:

7

1. The mean surface of the earthis considered a plane.

2. All level lines are consideredto be mathematically straight.

3. All plumb lines are consideredto be parallel to each other.

4. Elevations are referred to aspheroidal surface called a datum.

State that in geodetic surveying thecurvature of the earth is taken intoaccount and that:

1. It covers very high-precisionsurveys which extend over verylarge areas.

2. If the area is as large as astate, the earth is assumed tobe a sphere. If the area is acontinent, the true shape of theearth is used.

Explain that types of surveying canalso be classified on the basis ofpurpose or method. Each of the seventypes of survey in this classificationcan be applied in both plane andgeodetic surveys.

A survey made to establish horizontaland vertical positions of arbitrary

points

HIGHWAY SURVEYING

CONTENT OUTLINE

2. Property survey

3. Topographic survey

4. Hydrographic survey

5. Route survey

6. Underground survey

7. Photogrammetric survey

III. Terminology

A. Surfaces, lines and Planes

1. Level surface

2. Vertical line

3. Horizontal line

4. Vertical plane

5. Horizontal plane

B. Angles, elevation, etc.

1. Horizontal angle

Elements of Surveying


A survey made to determine the lengthsand directions of boundary lines andthe areas bounded by the lines (Ref.

A, pp. 7-8)

A survey conducted to determine theconfiguration of the ground (Ref. A,p. 5)

A survey made to determine the con-figuration of a body of water, in-cluding the topography of the shore-line (Ref. A, p. 6)

A survey to locate a highway, a rail-road, a canal, a transmission line,or a pipeline

A survey which deals primarily withunderground work

Survey using photography to makemeasurements (Ref. A, p. 7)

Introduce the special words andexpressions which will be used in thiscourse. (Ref. A, p. 9; Ref. B, pp.4-5)

A surface parallel to the meanspheroidal surface of the earth

A line which follows the direction ofgravity at any point

A line tangent to a level surface andperpendicular to a vertical line

A plane which contains a vertical line

A plane tangent to a level surface

An angle formed by the intersection oftwo lines in a horizontal plane

2. Vertical angle An angle between two intersecting linesin a vertical plane

8



3. Elevation of a point The vertical position of a point aboveor below a given surface

4. Difference in elevation The vertical distance between twobetween two points level surfaces containing the points

5. Horizontal distance The distance between plumb linesmeasured in a horizontal plane

6. Contour line A line which joins all points of equalelevation on the ground

IV. Measurement and Precision Mention that surveying entails bothlinear and angular measurements.(Ref. A, pp. 9-10; Ref. B, pp. 5-7)

A. Kinds of Measurement

1. Linear

2. Area

Feet and decimal parts of a foot areused for linear measurement. Note:On a bridge stakeout, it is oftennecessary to use fractions of an inchinstead of decimals of a foot.

Area is measured in square feet andacres. An acre is equivalent to43,560 square feet.

3. Volume Volume is computed in cubic feet andcubic yards.

4. Angular Angles are measured by use of thedegree, the minute, and the second.

B. Precision of measurement Explain that all physical measurementsare correct only within certain limitsbecause of errors which cannot becompletely eliminated. (Ref. A, pp.10-11)

1. Degree of precision

9

State that the degree of precisiondepends on the instruments and methodsused. Note that high precision isdesirable, but getting it takes muchtime and labor.

Point out that the degree of precisionof a survey should be as high as itspurpose justifies.

HIGHWAY SURVEYING

CONTENT OUTLINE

2. Errors

a. Sources of errors

(1) Instruments

(2) Survey crew

(3) Naturalconditions

b. Classification oferrors

(1) Systematicerrors

Elements of Surveying


State *hat a surveyor must know thekinds of error, their sources, andtheir effect upon field measurements.(Ref. A, p. 10; Ref. B, pp. 7-8)

Point out that the surveyor must knowhow to keep the magnitude of errorswithin allowable limits.

Explain that the measured value of anangle or a distance may approach thetrue value. This occurs when thenumber of errors and their size becomesmaller and smaller as the measurementsare repeated.

Mention that errors arise from instru-mental imperfections, personal limi-tations, and natural conditions.(Ref. A, p. 72; Ref. B, pp. 7-8)

Point out that an instrumental errorcan be caused by: a tape of incorrectlength, an error in the graduations ofthe circles of the transit or somemaladjustment in the level of thetransit.

State that a personal error is causedby such things as: an observer havingdifficulty bisecting the target, orreading a vernier exactly, or placingthe bubble perfectly on center at thetime of a reading. Also, a tapemanmay not have the proper tension onthe tape. These errors are reallycaused by human limitations.

Explain that natural factors such astemperature change, wind, gravity,atmospheric condition, and local mag-netism may affect a measurement.

Indicate that an error can be eithersystematic or random. (Ref. A, pp.73-76; Ref. B, p. 7)

Point out that a systematic erroralways follows some definite mathe-matical or physical law. Also, that

IC



(2) Random errors

c. Mistakes

a correction can be determined andapplied to the measurement for bothmagnitude and direction.

Note that if the cause of an errorvaries (as with varying temperature)the error is called a variable systematicerror.

Add that if the cause of an error doesnot change, it is called a constantsystematic error. A short tape is anexample of this.

Explain that the magnitude and direct-ion of a random error (often calledaccidental error) cannot be determined.This is because such an error iscaused by a combination of factorsbeyond the ability of the observer tocontrol. The causative factors involvedare impossible to correct.

State that these errors tend to besmall. When many measurements aretaken, the errors are distributedequally above and below the true value.That is, there are as many measurementsgreater than true value as there areless than true value.

Point out that these errors follow thelaws of probability. They tend tocompensate for each other.

Tell the class that a mistake is apersonal blunder not an error. It isan 'inintentional fault arising frompoor judgment or carelessness. (Ref.

A, p. 73; Ref. B, p. 8)

(1) Examples of Give the following examples of mistakes:mistakes

1. Failure to record each full 100ft. in taping.

2. Misreading a tape.

3. Reversing digits in a number.

11


CONTENT OUTLINE

V. Instruments and Accessories

A. Tape, pole, pins, etc.

1. Tape

2. Range poles

3. Plumb bobs

4. Compass


Impress upon the students that allmistakes can be corrected by a goodsystem of checking.

List the principal instruments andaccessories used in surveying. (Ref.

A, pp. 13-15, 121-123)

Explain briefly the construction anduses of the accessories. Pass aroundeach instrument so the students maylearn its nomenclature and use.

Describe a tape as a graduated,flexible ribbon used for measuringdistances. Show samples of both clothand steel tapes of different lengths;include the reel type and the freetype.

Show steel, wood, and aluminum polesand explain their red and whitemarkings.

Show different weights of plumb bobsand demonstrate the insertion of thecord.

Describe the compass and explain thatit is used only for general orientation.

5. Taping pins or nail hubs Demonstrate how taping pins and nailhubs are used for marking off measureddistances.

B. Rod, level,and transit

1. Rod (direct readingleveling rod)

. Hand. level (Locke)

3. Engineer's level

Show the Philadelphia ZeveZ rod andexplain how a reading is obtained.

Explain the hand level.. Point outthat this provides no magnificationbut that it does tell an observerwhen he is holding it on a level line.

Describe the engineer's level as atelescope with an attached spirit leveltube, all revolving about a verticalaxis. This instrument is mounted ona tripod.

12



State that the level is used for de-termining differences in elevation.The process is called leveling.

4. Transit (the universal Explain the transit as a mounted tele-instrument) scope which may be revolved on either

a horizontal or a vertical axis.

Tell the class that the transit isused principally for measuring hori-zontal and vertical angles and forextending a straight line. It isusually equipped with a compass andthe entire unit is mounted on a tripod.

QUESTIONS FOR REVIEW1. Name seven kind& of surveys and briefly describe the purpose of each

one.

2. Why is the ordinary construction survey considered to be planesurveying?

3. Define vertical line and horizontal line.

4. What is a contour?

5. Without changing your irFtruments or equipment, how can you increasethe degree of precision?

6. Mention two kinds of personal error.

7. What is a conditional error?

8. Describe the difference between a systematic error and a randomerror.

9. Give three examples of mistakes as differentiated from errors.

10. What type of linear measurement is used in surveying?

ASSIGNMENTIn Ref. A read Chapter 3 and pages 115-141.

13

Lesson 3

MEASURING DISTANCESOBJECTIVES

1. To describe the diffe,:ent ways of determining the distance betweentwo points on the surface of the earth

2. To provide information on measuring a distance within certain limitsof precision

3. To describe the taping method of measuring


I. Methods of Measuring Distances Explain that the measurement of dis-tance between points on the surfaceof the earth is one of the main con-cerns of all surveying.

A. Pacing

B. Use of an odometer

State that there are a number ofmethods to measure distance, and eachhas different degrees of accuracy.(Ref. A, pp. 115-120; Ref. B, pp. 9-15)

Show how any person can measure hisnatural stride and use the pacingsystem to measure a distance.

Explain that the odometer is a deviceattached to a vehicle, registeringrevolutions of a wheel. It can beused to measure distances when a pre-cise measurement is not required.

C. Stadia measurement method Explain that the upper and lower cross-hairs of the transit, level, andalidade are stadia hairs. Distance isindicated by intercept between hairsas shown on a graduated rod.

Describe briefly the spacing of thecrosshairs with respect to a 1-ft.intercept at 100 ft. of distance.

14

HIGHWAY SURVEING

CONTENT OUTLINE

D. Use of subtense bar

E. The Geodimeter

Measuring Distances


Show on the chalkboard the fundamentalsof measuring with a subtense bar.Point out that the length of the baris known precise].y. A theodolite ortransit is used for the angular measure-ment and the distance is computed bytrigonometry.

Point out that the Geodimeter useslight waves to measure distance. In

this method the length of a lightwave is the unit of measurement fordetermining the slope distance betweentwo points. The Geodimeter is anexpensive instrument but accurate to1 part in 100,000.

State that the Geodimeter is susceptibleto error from stray light and fromchanges in atmospheric conditions.Measurements with this instrument aremost successful at night.

Explain that any slope distance measuredcan be changed to an equivalent hori-zontal distance by computation.

F. The Tellurometer Describe the Tellurometer as a refinedtype of radar.

C. Taping (or chaining)

List the following facts about thisinstrument:

1. Accurate to 1 part in 100,000

2. Uses radio microwaves; can beused in light or dark, fog orrain

3. Needs correction for other at-mospheric conditions and wavereflections

4. Easily portable

Explain that the surveyor's chain(66 ft.) was once used regularly forsurveying. The chain had 100 links,each 7.92 in. long.

15

HIGHWAY SURVEYING Measuring Distances


State that the chain is now rarelyused but the expression chaining issometimes used to describe the tapingprocedure.

Point out that in taping (or chaining)a distance, a steel tape is used whichis graduated in feet and decimals ofa foot.

II. Measuring Distance With a Tape Explain that the measuring of distancesby use of tapes is an extensively usedmethod.

A. Horizontal taping

Note that the horizontal distance be-tween two points can be obtained twoways with a tape. One, by holding thetape horizontally. Or, by measuringalong the sloping ground and applyinga correction to the measured distance.(Ref. B, pp. 17-23)

Tell the class that it is best to useone type of tape in a given survey.

State that horizontal taping means thatmeasurements are taken directly fromthe tape as the tape is held in ahorizontal position. Computations arenot used in this method.

Explain that the tape is stretcheddirectly on the ground when the groundis level and fairly smooth.

1. Taping on level ground Demonstrate on the chalkboard howground features affect taping. Theseconditions may require that the tapebe elevated from the ground the samedistance at both ends with the tapeheld between the waist and knees.(Ref. A, pp. 124-125)

2. Taping on unevenground

Show how the tape graduations are pro-jected to the ground with a plumb bob.

Sketch some uneven ground conditionson the chalkboard. Show the way oneend of the tape is placed on the ground(at the higher end) with the other end

16

HIGHWAY SURVEYING Measuring Distances


being raised from the ground until thetape is level. This is done either byestimation or the use of a hand level.(Ref. A, pp. 126-127)

B. Slope taping State that slope taping is done bymeasuring on the ground and then usingcalculations.

Indicate the mathematics involved inreducing a slope measurement to ahorizontal distance. (Ref. A, pp.128-130)

III. Duties of Tapemen (or Chain- Point out that the head tapeman alwaysmen) carries the zero end of the tape.

A. Taping

B. Marking and checking

Describe the procedure for measuringone station, which equals 100 ft. ofline. Explain how the rear tapemanaligns the head tapeman. At thispoint the alignment is important toenable the instrument man to set thenew line exactly.

Tell the students that the proper ten-sion on the tape is either estimated,or gaged with a spring balance. Thisis always done by the head tapeman.

Explain that the rear tapeman plumbsthe 100-ft. graduation mark with theplumb bob 1/8 in. above the point.Then the head tapeman clears a smallarea for the taping pin. Followingthis, the head tapeman waits for asignal from the rear tapeman and dipsthe tape about 1/4 in., touching theground with the plumb bob.

Show how the head tapeman pins the newdistance and then checks the locationwith a second measurement.

C. Taping uphill and downhill Tell the class how tapemen work uphilland downhill. The head tapeman checksto maintain a horizontal line when thetaping operation advances downhill.The rear tapeman checks for horizontalalignment when the taping advancesuphill.

17

HIGHWAY SURVEYING

CONTENT OUTLINE

D. Determining stationfractions

E. Breaking tape

Measuring Distances


Explain that when the end of the lineis reached, the last distance measuredwill usually be a fraction of the100-ft. tape.

Describe the method of reading fractions.The rear tapeman holds a full-footgraduation over his point. Thisparticular graduation is the one whichwill bring the subgraduations at thezero end of the tape over the end-poillt of the line. The head tapemanthen rolls the plumb bob cord alongthe subgraduations with his thumbuntil his plumb bob is directly overthe end point.

Describe (by means of a sketch) theprocess of breaking tape in makingseveral horizontal measurements on asteep slope or on very uneven ground.

Stress the importance of notekeepingto insure that small partial measure-ments are not lost.

IV. Errors and Mistakes in Taping Remind the students that (as explainedin Lesson 2) inaccuracies in measure-ment can result from both errors andmistakes.

A. Principal errors in taping Point out that there are seven prin-(or chaining) cipal sources of error in linear

measurements made with a tape. Theseerrors, which include both systematicand random errors, are listed andexplained below.

1. Tape of incorrectlength

2. Tape not horizontal

Explain that a tape of incorrectlength causes a systematic error.This can be practically eliminated bycomparing with the standard tape andapplying a correction. Note that thetype of error discussed here iscumulative. (Ref. A, p. 131; Ref. B,p. 23)

Refer to the conversion from slopedistance to horizontal distance. Showhow the error, when the measuring tape

18

HIGHWAY SURVEYING

CONTENT OUTLINE

Measuring Distances


is not horizontal, is equal to

h2

2s

where: s = the slope distance betweenthe two given points

h = the vertical distancebetween the two points

(Ref. A, p. 131; Ref. B, p. 23)

This error is cumulative and alwayspositive. It can be eliminated by useof a hand level.

3. Changes in temperature State that a steel tape will contin-ually change in length because oftemperature changes. Discuss coeffi-cient of expansion briefly.

4. Incorrect tension

5. Sag

Demonstrate how a correction is com-puted by the formula. (In the formulathe length of tape, the coefficientof expansion, and the change in tem-perature are multiplied together.)(Ref. A, pp. 132-133; Ref. B, p. 24)

Caution the students that errors dueto temperature change are cumulative.

State that a tension error is not ofgreat importance when a reasonableestimate of tension is made. This typeof error is negligible except in pre-cise work. Tension can be computed bya formula. (Ref. A, pp. 132,137;Ref. B, p. 24) Tension errors takenall together tend to be compensating.

Explain that sag affects any measure-ment where the tape is suspended fromthe two ends. (The tape assumes theshape of a catenary.) The sag causesthe 1-..orizontal distance between thetwo ends to be shorter than the lengthof the tape. Sag error is cumulativeand can be computed by f.,rmula. (Ref.

A, pp. 132,135; Ref. B, p. 25)

19

HIGHWAY SURVEYING

CONTENT OUTLINE

6. Incorrect alignment

7. Tape not straight

B. Other errors in taping

C. Mistakes in taping

Measuring Distances


Demonstrate the error when one or bothof the taping pins are placed oneither side of the correct taping line.(Ref. A, p. 131; Ref. B, p. 26)

hs 2

Show how the formula can be used2

to compute the error when one end ofthe tape is off line. Mention thatthis error is cumulative and positive,but almost negligible.

Point out that some parts of the tapemay be out of line because of grass orbrush in the way. The error caused bythis condition is systematic andvariable; it is cumulative and positive.(Ref. A, p. 131; Ref. B, p. 26)

Other errors, which perhaps occur lessfrequently, are random errors. Theyinclude the following (Ref. B, p. 29):

1. Deflection of the plumb bob bywind

2. Failure to place the taping pinon the point where the plumb bobtouches the ground

3. Failure to steady the plumb bob

Explain that mistakes (due to poorjudgment or carelessness) which occurcommonly in taping (Ref. A, p. 140)include the following:

20

1. Adding or dropping a full tapelength

2. Adding a foot

3. Using the wrong mark on the tapefor zero or 100

4. Reading a number wrongly upsidedown

5. Mentally transposing figures

HIGHWAY SURVEYING

CONTENT OUTLINE

V.

Measuring Distances


6. Not calling numbers clearly

7. Not calling a decimal point

Importance of Accurate Measure- Tell the class that all efforts shouldments be made to obtain accurate measurements.

The success of the survey and subse-quent application are directly dependentupon accuracy.

A. Precision needed in taping Point out that accurate measurementsare obtained by careful and precisetaping, with the proper corrections.Explain the importance of accuratemeasurements by showing how they willbe used. (Ref. A, pp. 138-140; Ref.B, pp. 29-30)

1. Standard tape forcorrection

B. Usual practice in taping

1. Limits of precision

Explain that a tape whose actual lengthdiffers from its marked length can becalibrated against a standard tape.Each office usually has one standardtape, used for calibration and for noother purpose. When a tape used inactual surveying is compared to thestandard, the correction needed isdetermined. This correction is thenapplied to all measurements made withthis tape.

State that accuracy of angular measure-ment and linear measurement should becompatible. If the angles are roughlymeasured, it is wasted effort to mea-sure a line to thousandths of a foot.

Describe the usual practice in tapingthrough broken country. The procedureis to take measurements with the tapehorizontal, break tape, and applytension by estimation. No allowancesfor sag or temperature are made.

Explain that although many errors maybe made, the more - significant errorswhich commonly occur are:

21

1. Tape not level

2. Sag in tape

HIGHWAY SURVEYING

CONTENT OUTLINE

Measuring Distances


3. Variation in temperature

4. Poor plumbing

Assume possible values for the fourerrors and show that the total errorcould range from plus 0.44 ft. toplus 0.96 ft. per 1000 ft. of line.This gives limits of precision rangingfrom 1 part in 2300 to 1 part in 1000.

Note that 1 part in 5000 would beconsidered excellent taping.

State that the measured length of aline is nearly always considerablylonger than the true length.

QUESTIONS FOR REVIEW1. If the Geodimeter can measure distance so accurately, why is it not

used by everyone?

2. How is a tape set horizontally when a measurement is made?

3. How much tension is placed on a standard tape when calibratinganother tape?

4. How does an increase in temperature affect the measured length of aline?

5. If a distance is measured with the tape incorrectly aligned, is theerror significant?

6. List five mistakes which can be made in taping a distance.

7. What degree of accuracy would be considered excellent taping?

8. How does the measured length of a line compare with the true lengthin usual practice?

9. Who checks for horizontal when the taping operation advances downhill?

10. In your estimation which of the four common errors is most significant?

ASSIGNMENT1. Solve problems 1, 2, 3, 6, 7, 13, and 16 on pages 145 and 146 of

Ref. A.

2. Read pages 151-173 in Ref. A.

22

Lesson 4

LEVELINGOBJECTIVES

1. To provide pertinent information about the leveling process2. To teach the class the use and care of the level


I. Use of Leveling in Surveying Explain to the class that leveling isused to obtain elevations of objectsin the process of surveying. Levelingis also used to control the grade inconstruction surveys.

A. Definition

B. Curvature and refraction

1. Effect on leveling

2. Correction formula

Define leveling as the operation per-formed to determine the elevation ofa point, and the difference in elevationbetween two points. (Ref. B,,p. 32)

State that in leveling, the effects ofcurvature of the earth and atmosphericrefraction must be taken into account.(Ref. A, pp. 151-152; Ref. B, pp. 32-33)

Sketch the earth and show a levelinginstrument taking a horizontal sighting.The sketch will show how the curvatureof the earth affects an elevation.

Describe the effect of refraction asa downward bent ray of light whichcounteracts about one-seventh of thecurvature effect.

Present the empirical formula whichcorrects for the combined effect ofcurvature and refraction:

h' = 0.021 M2

where: h' = combined effect of earth's

23

HIGHWAY SURVEYING Leveling


II. Methods of MeasuringElevation

A. Barometric leveling

curvature and atmosphericrefraction, in feet

M = distance from the point oftangency (station of theobserver), in thousands offeet

Explain that differences in elevationcan be found by barometric, indirect,stadia, and direct leveling. (Ref. A,p. 152)

Describe briefly how elevation is de-termined with the aneroid barometer.Critical factors are the sensitivityof the instrument and the complicationsof the weather. (Ref. A, pp. 156-158;Ref. B, pp. 35-38)

Point out that barometric leveling isnot used in the construction of high-ways. This method is used mainly onexploratory or reconnaissance surveyswhere differences in elevation arelarge.

B. Indirect or trigonometric State that indirect leveling is oftenleveling called trigonometric leveling. Differ-

ence in elevation between two pointscan be determined by measuring thevertical angle from one point to theother and the horizontal distance be-tween them. The difference in elevationis then computed by the use of trig-onometry. Sketch an example of thison the chalkboard. (Ref. A, p. 154;Ref. B, p. 33)

1. Correction needed Remind the class that the effects ofcurvature and refraction must be cor-rected when the horizontal distance ismore than 1,000 ft. This correctionmust be applied to readings taken byindirect levelings as well as thosetaken by some of the other methods.

Tell the class that this effect can beeliminated by sighting from both endsof the line and using the average ofthe differences in elevation.

24



State that indirect leveling is notused very much in highway work.

C. Stadia leveling

D. Direct leveling

1. Application

2. Demonstration

III. The Level

Point out that stadia leveling is donewith a transit and is a rapid means ofleveling. This method is only moder-ately precise. (Ref. B, p. 35)

Make a brief comparison between stadialeveling and indirect (or trigonometric)leveling.

Inform the class that direct levelingis the most accurate method used todetermine the difference in elevationbetween two points on the earth's sur-face. (Ref. A, pp. 153-156; Ref. B,p. 34)

Draw a sketch on the chalkboard, showing a level set up between points Aand B, and discuss the following:

1. Location of the level

2. Reading the rod

3. Difference in rod readings

4. Elevation at B when elevation atA is known

5. Ignoring ground elevation wherelevel stands

Set up a level at one end of the class-room and have the students find differ-ences in elevation between variousobjects.

Assign a given elevation to an objectand ask the class to compute theelevation of other objects.

Stress the fact that this basic operationis the most important element inleveling.

Point out that the engineer's levelused in the classroom is a typicalinstrument for leveling.

25

HIGHWAY SURVEYING

CONTENT OUTLINE

A. Description

B. Kinds of levels

1. The dumpy level

Leveling


Indicate that the level consists of atelescope with a very accurate spiritlevel attached to the telescope long-itudinally. (Ref. A, p. 158; Ref. B,p. 38)

Show the students that the telescopeis supported at the ends of a straightbar, firmly fixed at the center to theaxis on which it revolves. This axisand the optical axis of the telescopeare perpendicular to each other. Theentire level is supported on a tripod.

Explain that the two main types oflevel are the dumpy level and the wyelevel (also written as Y-level). Theself-leveling level and the Locke handlevel are also used frequently and arediscussed below.

Exhibit the dumpy level, pointing outthe telescope and its rigid connectionto the level bar. (Ref. A, p. 159;Ref. B, pp. 42-44)

a. Description Name and describe the parts of thedumpy level:

1. Telescope--about 30 or 40 diametersof magnification. The opticalaxis is perpendicular to the axisof the center spindle.

2. Spirit level--axis parallel tothe axis of the telescope. Theupper surface of the spirit leveltube is round to form a circularcurve longitudinally. The sensi-tivity of the spirit level in-creases with the radius of thecurve. This sensitivity ismeasured by the angle (given inseconds) through which it must betilted to make the bubble moveone scale division.

3. Cross bar--telescope support

26



2. The wye level

4. Capstan-headed screws--used toadjust the spirit level in avertical direction only

5. Spindle--revolves in the socketof the leveling head

6. Foot plate--threaded to fit thetripod head

7. Clamp--holds the collar on thesocket

8. Tangent screw or slow-motionscrew

9. Leveling screws -- usually four,but use of three is becoming morecommon

10. Tripod--either fixed or adjustable

11. Sunshade--protects from directrays of sun

12. Vertical and horizontal cross-hairs--alignment and reading hairs

13. Crosshair adjusting screws

14. Focusing screw and eyepiece

Show the students the wye level andexplain the differences between it andthe dumpy level. (Ref. A, pp. 160-161;Ref. B, pp. 38-42)

a. Differences in The wye level differs as follows:construction

1. Its telescope can be removed andturned end for end.

2. It has Y-shaped supports for thetelescope, called wyes.

3. It has capstan-headed nuts toraise and lower the wyes.

b. Advantages and Comparison of the dumpy and wye levels:disadvantages

27



1. The dumpy level is simple in con-struction and has few parts. Thewye level, however, has the dis-advantage of having many parts.

2. The wye level can be adjusted byone man. The dumpy level is ata disadvantage in this respect,since it requires two men foradjustments.

3. The dumpy level requires few ad-justments and they last for alonger time.

4. Overall, the dumpy level is themore popular of the two. The wyelevel is slowly passing out ofuse in the United States.

3. The self-leveling level Exhibit a self-leveling level and showthe class how rapidly it can be set up.(Ref. A, pp. 163-165; Ref. B, pp. 44-45)

4. The Locke hand level

Point out the bull's-eye bubble (in thecircular spirit level) and mention thatit centers very quickly.

Refer to other characteristics of thislevel such as its light weight andoverall size. Another feature is thatit has only three leveling screws.

Show the Locke hand level and allowthe students to use it on a 6-footrule to find eye height. (Ref. A,p. 165; Ref. B, p. 47)

Describe the hand level as a brass tubewith a small level tube mounted on thetop. A 45° mirror enables the user totell when the main tube is horizontal.

Explain that most hand levels do notmagnify and can be used only for roughleveling and short distances. Othertypes are available which magnify 2or 4 times.

28



IV. The Leveling Rod

A. Types

1. The Philadelphia rod

a. The vernier

Tell the class that leveling rods aregraduated wooden rods used in measuringdifferences in elevation.

State that there are two types ofleveling rod. One is the target rod(read by the rodman). The other typeis the self-reading rod (sometimescalled a speaking rod) which is readdirectly by the instrument man. (Ref.

A, p. 171; Ref. B, pp. 48-51)

Point out that the limit for theaccurate reading of a self-reading rodis 400 feet. Beyond this distance atarget rod is used.

Exhibit the Philadelphia rod and statethat it is the most commonly used rod.Describe its parts:

1. Front face and rear face

2. Brass sleeves

3. High and low rod sections

4. Clamp

5. Target

Explain the graduations of the rod.Draw a large sketch on the chalkboardshowing how readings are made.

Mention that the Philadelphia rod canbe used both as a self-reading rod anda target rod.

Describe the waving of the rod andexplain its purpose. (Ref. A, p. 172)

Pass the target to the students for aclose inspection and ask them to notethe small vernier scale.

State that the vernier is a device forreading a scale to a finer degree thanthe smallest division on the scale.(Ref. A, pp. 27-29; Ref. B, pp. 51-53)

29



Explain that in the vernier the lengthof a division is slightly less than adivision on the main scale of the rod.

V. Bench Marks

A. Bench mark leveling

1. Marking and recording

2. Coordinating old andnew plans

Sketch the vernier of the levelingrod target on the chalkboard.

Mention that this vernier is 0.09 ft.long and is divided into 10 parts;each part is thus .1 x 0.09 or0.009 ft.

Explain how to read the vernier andgive the class printed examples ofdifferent readings.

Describe least count (fineness ofreading). (Ref. A, pp. 27-28)

Explain that bench marks are permanentor semipermanent marked points ofknown elevation. (Ref. A, p. 185;Ref. B, p. 54)

State that bench mark leveling is de-termining the elevations of a seriesof bench marks, placed in the vicinityof a construction project by the sur-vey party.

Point out that a bench mark in thefield should always be marked, andshould also be described in the notes.Both the bench mark and the notes arevaluable for later reference.

State that if a new system of benchmarks is placed, the point of originshould be at a standard, known benchmark. The U.S. Coast and GeodeticSurvey has such a system of benches.This system assures that old and newplans for highways and components areon the same datum.

QUESTIONS FOR REVIEW1. Describe the process of leveling.

2. Is it possible that a 1-mile sighting could result in a 3-incherror because of the effects of curvature and refraction?

30

HIGHWAY SURVEYING

3. Which type of level is the most popular?

4. Give one distinct advantage of the wye level.

S. Which leveling rod is most commonly used?

Leveling

6. Why is a target rod used rather than a self-reading rod on a levelsighting of more than 400 ft.?

7. Briefly explain the use of a .vernier.

8. What is least count?

9. Describe a bench mark and explain its use.

10. What is meant by waving the rod?

ASSIGNMENT1. Solve problems 1-6, and 13 on pages 181 and 182 of Ref. A.

2. Study pages 185 -197 and 213-227 in Ref. A.

31

Lesson S

LEVELING (continued)OBJECTIVES

1. To study the purposes of leveling in highway engineering2. To explain and describe the kind of leveling used for each of these

purposes3. To describe the procedures for .leveling

CONTENT OUTLINE

I. Leveling in HighwayEngineering

II. Types of Leveling


State that highway engineering usessurvey leveling in numerous phases ofdesign and construction. The mainapplications are:

1. Establishing bench marks

2. Specifying the profile (theelevation at frequent points)along the centerline of a highway

3. Determining the shape of theground on both side. of thecenterline

4... Delineating the surface config-uration of a piece of land

Explain that the above applicationsare accomplished by specific types ofleveling identified as follows (keyedby matching numbers to paragraphsabove):

32

1. Differential leveling

2. Profile leveling

3. Cross-section leveling

4. Leveling for a plot plan



A. Differential leveling

1. General steps inleveling

The elevations in all four of thesetypes are usually obtained by directleveling.

Draw a sketch on the chalkboard indi-cating uneven ground; the examplesshown in the textbooks may be used.(Ref. A, pp. 186-189; Ref. B, pp. 57-60) Define differential leveling asthe operation of determining theelevations of points some distanceapart.

Using the sketch, illustrate the gen-eral steps in finding elevations indifferential leveling by use of directleveling:

33

1. Begin work at a bench mark (whoseelevation is known). Record thiselevation.

2. From the bench mark, select apoint (in the direction the sur-vey is to move) and set up theinstrument at that point.

3. Take a reading (called a back-sight) on a leveling rod at thebench mark. From that readingdetermine the elevation at theline of sight of the level. Thisis the height of instrument orH.I.

4. From the leveling instrument,pick a firm point (a large stone,a concrete object, a tree root)in the direction the survey is tomove. This point will be aturning point or T.P.

5. Take a reading (called a foresight)on a rod at the T.P. Determinethe elevation of the T.P.

6. Pick another point from the T.P.(in the direction the survey isto go) and move the instrument tothat point.



7. At the new location, take a back-sight on a rod held a'. the T.P.From this reading determine thenew H.I. of the level.

8. Select another T.P. With thelevel at the same location as inthe previous step, take a fore-sight on the new T.P. and deter-mine its elevation.

9. Repeat steps 6, 7, and 8 untilanother bench mark is reached.The elevation shown on this benchmark will provide a check on thesteps taken so far.

2. Procedure applicable to State that the procedure describedother aspects of high- above can be continued to determineway engineering any number of T.P.'s and bench marks

required. It can also be used (withsome variation) for profile leveling,for cross-section leveling, and forleveling a plot plan.

B. Profile leveling

1. General procedures

Define profile leveling as the processof obtaining the elevations of pointsalong a continuous line. (Ref. A,pp. 213-215; Ref. B, pp. 72-82)

Note that the principal difference be-tween differential and profile level-ing is in the number of foresights andbacksights taken.

Mention that the continuous linefollowed in profile leveling could bea centerline for a highway, railroad,sewer line, canal, or sidewalk. Thiscenterline may b a straight line, aseries of straight lines connected bycurves, or a broken straight line.This is sometimes called a traverseline.

Explain that before the elevations ofpoints are determined, the centerlineis marked off on the ground. The num-ber of markings depends on the topo-graphy of the area. If the terrain is

34

HIGHWAY-SURVEYING Leveling


rough the line is marked off in 25-ft.sections; in rolling country, 50-ft.sections; in flat: areas, only at fullstations, that every 100 ft.

State that where the slope changesradically, the elevation should bedetermined at each point of radicalchange. This should be done even ifsuch a point does not fall on a marklike a 25- or 50-ft. mark. Examplesof radical changes in slope are thepeak and the bottom of a hill.

Draw a sketch on the chalkboard, show-ing a centerline marked off. This willgive an elevation view of the center-line.

2. Field procedures Outline the steps in the field procedurefor profile leveling:

1. Set up the level near the be-ginning of the centerline.

2. Take a read'ng on a bench markand record it.

3. Add the reading to the elevationof the bench mark to obtain theH.I.

4. Take a reading at station 0 + 00and record it. This is called arod reading or a Yod shot.

5. Subtract the rod reading from theH.I. to obtain the elevation ofstation 0 + 00. If 50-ft. markshave been set up on the center-line, the elevation of station0 + 50 would be the next shot.

6. Continue to take rod shots alongthe profile until the view isobstructed.

7. Select a T.P. and take a rod read-ing on it.

35



8. Mark this in the notes as T.P.No. 1 avid describe its position.

C. Cross-section leveling

1. Purpose of crossprofile

9. Subtract the reading on the T.P.from the H.I. to establish theelevation of the T.P.

10, Move the instrument along thecenterline, back sighting on therod at T.P. No. 1. Add the rodreading to the elevation ofT.P. No. 1 to get the new H.I.

11. Continue finding elevations onpoints along the centerline untilthe view is again obstructed.

12. Repeat steps 7 through 11 as manytimes as needed to complete theprofile.

Tell the class that the survey mustend at a bench mark so that a checkcan be made.

State that all rod readings taken onthe ground are usually read to thenearest tenth of an inch. Readingstaken on turning points and oil benchmarks are read to the nearest hundredthof an inch.

Explain that the DOT design officeneeds data concerning the shape of theground on both sides of the centerline.The data is used for location studiesand earthwork estimates. Cross profilesare run at right-angles to the center-line. (Ref. A, pp. 215-218)

Tell the class that the length of asection in the centerline depends onthe topography. A cross profile ismade at each section mark along thecenterline. Thus, if a section ismarked every 50 ft., then a crossprofile is taken every 50 ft. Thecross profile extends to the right andto the left of the centerline.

36



Explain that a modern highway uses alarge right-of-way. To get enoughwidth, the cross profile may have toextend as much as 200 ft. to the rightand to the left of the centerline.

2. Field procedures Indicate to the class the field pro-cedure for cross-section leveling:

1. Assume that the 50-ft. points aremarked off on the reference line(the centerline, in this case).Set up the level in the vicinityof the beginning station. Findthe H.I. by reading a rod on abench mark and record the H.I.

2. Use a right-angle prism and extendthe line at the 50-ft. mark to theright of the reference line.

3. Send the rodman to the right; holdhim on line by usc. of a right-angle prism at the station point.Note that the rodman carries thelevel rod and the zero end of a200-ft. cloth tape.

4. Let the tape pass through yourhands and read the distance whenthe rodman stops for an elevationreading.

5. Have the rodman stop for a readingat all changes of slope; (demon-strate with a sketch). The levelrod faces to the instrument atevery stop. Have the instrumentman read the rod and call outthe reading. The man at thestation point calls out the dis-t.nwe.

6. Tell the notekeeper to record theinformation at the proper station,under the proper H.I. These noteswill be studied in a later session.

7. When enough shots have been takenon the right side of the reference

37

HIGHWAY SURVEYING

CONTENT OUTLINE

Leveling


line, repeat the procedure on theleft side of the line.

3. Cross-section leveling Compare cross-section leveling withcompared with profile profile leveling. Show that taking aleveling shot at a station point or at zero on

the tape is a point on the profile ofthe reference line.

4. Effect of movinginstrument

D. Leveling for a plot plan

State that when one cross section isfinished, the instrument is moved alongthe reference line to the next sectionmark. Here another cross section ismade.

Tell the class that if a portion of across section cannot be made from agiven position, the instrument must bemoved. The notes must then clearlyshow that the remaining portion of thecross section was done from a newposition.

Mention that this work will be reviewedin Lesson 14.

Explain that for some problems it isnecessary to know the surface shape ofa piece of land. Examples of applica-tions are: drainage, irrigation,earthwork, location and constructionof buildings. The procedure for de-termining surface shape is:

38

1. Sketch the method of dividing anarea. A rectangular grid systemis established with distances be-tween lines of 10, 25, 50, or100 ft., depending on the topo-graphy.

2. Stakes are set in the ground atthe intersections of the gridlines. Each stake is labeledwith a letter and a number.

3. Leveling is done (on the stakes)the same as for profile leveling.Usually more shots are taken fromone position of the level than forprofile work.



III. Detailed Procedures inLeveling

A. Setting up the level

4. Rod readings are taken at eachstake and also whenever a breakin the slope of the ground occursbetween stakes. The position ofeach break is measured from thestakes and recorded.

Explain to the students that the gen-eral approach to determining elevationswas covered previously in this unit.Additional details necessary forleveling are given below.

State the steps for setting up thelevel (Ref. A, pp. 171-173; Ref. B,pp. 55-57) as follows:

39

1. Spread the legs of the tripod andplace them so that the footplateis approximately level. Pusheach leg firmly into the ground.

2. Loosen two adjacent levelingscrews.

3. Turn the telescope so it ispositioned over a pair of oppositeleveling screws.

4. Adjust the level until the bubblecrosses the center of the tube.

5. Turn the telescope so it ispositioned over the other pair ofleveling screws.

6. Bring the bubble to within twodivisions of the center.

7. Repeat the bubble adjustment overthe first pair of opposite level-ing screws.

8. Check the bubble for both direc-tions, carefully adjusting onescrew for a final position.

9. Note that when one screw istightened and the other loosened,the bubble will move in the di-rection of the tightened screw.



Caution the students that after theinstrument is leveled it should betouched only when necessary. Evenwalking around the tripod may unbalancethe level.

B. Handling the rod Explain how the rod should be handled:

1. Hold the rod vertically and plumbon the bench mark or the turningpoint.

2. Place the rod so its face isperpendicular to the line ofsight as nearly as possible.

Tell the class that a rod that is ex-tended should never be carried aboutexcept for immediate use. Alwaysclose the rod when there is no need tokeep it extended.

C. Reading the rod Point out the steps for the instrumentman in reading the rod:

D. Bench mark leveling

1. Height of instrument(H.I.)

1. Focus the telescope on the rod.

2. Check the bubble and read the rod.

3. Check the bubble again and recordthe rod reading.

4. Signal "all right" to rod man.

State that additional details neededfor a full understanding of the level-ing procedure are as follows:

40

1. To find the height of the levelinginstrument at its first location,add the backsight reading to theelevation of the bench mark. (A

backsight is often called a plussight.)

In the same way, find the H.I. forany other location of the levelinginstrument. This is done byadding the backsight reading tothe elevation of the point onwhich the reading is taken.

HIGHWAY SURVEYING

CONTENT OUTLINE

2. Elevation of T.P.

Leveling


2. To find the elevation of a turningpoint subtract the foresight (orminus sight) from the H.I.

3. Foresight distance to 3. When determining the location ofequal backsight dis- a leveling instrument or a turningtance point, make the backsight distance

equal to the foresight distance.This procedure will cancel instru-ment errors. (Ref. A, p. 188)

4. Accuracy assured byrerun

4. To assure accuracy in leveling,make the run over again from theoriginal starting point but usedifferent turning points. Anotherway is to make the run in reverse.

QUESTIONS FOR REVIEW1. Explain differential leveling and give an example.

2. Describe a turning point.

3. What is a good method of checking a level run?

4. What is profile leveling?

5. In differential leveling how would the lack of a beginning elevationaffect the work?

6. When would a grid system for taking level readings be used?

7. What part of cross-sectioning is profile leveling?

ASSIGNMENT1. Solve problems 13, 14, and 15 on pages 209-210 of 12,:- A.

2. Study pages 173-181 and 197-207 in Ref. A.

41

Lesson 6

LEVELING (continued)OBJECTIVES

1. To inform the class about a method of notetaking2. To instruct the class in the use and care of leveling instruments3. To describe errors in leveling and adjustments on instruments


I. Field Notes Tell the class that there are variousways to take notes. Show the samplenotes in the texts. (Ref. A, pp. 189 -191; Ref. B, pp. 60-61)

A. Preliminary survey

1. Standard system

2. Bench mark leveling

Describe the system used by the StateDepartment of Transportation. In thissystem notes begin at the bottom ofthe sheet and work up the sheet as thestations increase. The notes areusually placed on the left-hand sideof the notebook.

Pass out prints of a typical benchmask leveling run and point out thefollowing facts:

42

1. The sheet of paper has coordinateruling and also has six columnsfor information.

2. The columns, from left to right,are for: station, description,backsight, heieit of instrument,foresight, and elevation.

3. The point of beginning (B.M. 1)has its description next to itwith its elevation in the lastcolumn.

HIGHWAY SURVEYING

CONTENT OUTLINE

3. Profile levels

a. Left-hand sheet

b. Right-hand sheet

Leveling


4. Above the first line of infor-mation in the third column is thebacksight (marked, as usual, witha plus sign). Next to it on thesame horizontal line in thefourth column is the height ofinstrument.

5. The first turning point or T.P.1 is found above this line ofinformation with its descriptionin column two. The foresight,on the same horizontal line, isin the fifth column (marked, asusual, with a minus sign).

State that in the preliminary surveythe profile levels are placed in thesame type of coordinate notebook asfor bench mark leveling.

Pass out one left-hand sheet and oneright-hand sheet, with a typical cross-sectioning problem printed on them.

Show how the point of beginning, B.M.1 (with description), is on the bottomat the left; its elevation is on theright-hand edge.

Point out that the backsight, markedplus, is shown slightly above and tothe right of the notation B.M. 1. TheH.I. is in relatively large, heavyfigures in the middle of the sheet.

State that cross-sectioning will beginat station 0 + 00 from this setup ofthe level.

Note that the station notations arewritten on the heavy coordinate lines.

Tell the students that the first rodreadings for station 0 + 00 will beplaced on the right-hand sheet, di-rectly across from the stationnotation 0 + 00.

43



Explain that in the center of thesheet, just below the heavy coordinateline, a zero indicates that a rodreading was taken at the station markof 0 + 00.

4. Reciprocal leveling

B. Notes for resurvey work

State that a small dash line over thezero shows the rod reading written onthe heavy coordinate line.

Point out that as rod readings aretaken to the right of the base line,the notes follow the right. Thedistance from the base line is writtenbeneath the coordinate line and therod readings on the coordinate line.

Add that when the rod readings aretaken to the left of the base line,the notes proceed to the left of thezero notation. All rod readings areon the right-hand sheet.

Explain that there may be a lack ofspace on the line for the notes, tothe left or to the right. If thisoccurs the station 0 + 00 is continuedto one large coordinate square above.

Tell the students that many stationscan be cross-profiled from the sameH.I. The H.I. is then carried to thenext sheet and written in large, heavyfigures at the bottom of the sheet.

Show by sketch how difficult it is tokeep the backsights equal to the fore-sights in leveling across such ob-stacles as a river or a ravine. (Ref.

A, p. 197; Ref. B, p. 68)

Explain that the difference in ele-vation is obtained by two sets ofobservations, one on each side of theobstacle. The mean of the two obser-vations is used.

Mention that after design is completedand just before construction starts,the centerline of the route isestablished and cross-sectioned.

44

HIGHWAY SURVEYING

CONTENT OUTLINE

C. Electronic data sheets

Leveling


Show samples of the hardbound booksused for notes.

Pass out prints of the new electronicdata sheets. These show bench markleveling and profile-leveling infor-mation. Explain that these sheets weredesigned to be used with the BurroughsB-5500 computer.

1. These sheets are used the same asordinary coordinate sheets.

2. The left side of the sheet hassix columns for a level run.

3. If the base line is used, thecenterline notation is crossedout.

4. These sheets are weatherproof,strong, reproducible, and concise.

D. Proof of level notes End a sheet of level notes with theH.I. at the top of the sheet.

II. Signals

Begin the next sheet with the sameH.I. at the bottom.

Show how elevations are checked. Thedifference in elevation between twobench marks should equal the differenceof the sum of the backsights and thesum of the foresights. (Ref. B, p. 61)

Inform the class that the observer andthe rodman should always be in constantcommunication. (Ref. A, p. 39; Ref.B, p. 57)

A. Standard signals Demonstrate the signals used to com-municate with the rodman:

1. An upward movement or a raisingof the hand signals the raisingof the target.

2. A downward movement or loweringof the hand signals a lowering ofthe target.

45



3. A circle of the hand signalsclamping of the target.

III. Errors in Leveling

4. The signal for plumbing the rodis a raised arm leaning in thedirection the rod should go.

5. A wave of both hands signals"All right."

6. The observer signals a foresightby holding one arm verticallyabove his head

7...TO-igiablish a turning point, theinstrument man waves his arm ina circle above his head.

8. When the rodman is ready to setthe rod on a bench or on a turn-ing point, he holds the levelrod horizontally over his head.The rod is then brought down onthe point.

9. The signal given to wave the rodis to move one arm from side toside above the head.

List the principal sources of errorsin leveling on the chalkboard. (Ref.

A, pp. 198-201; Ref. B, p. 68)

A. Common errors 1. Instrument defects

B. Instrument errors

2. Faulty manipulation of level orrod

3. Errors in sighting

4. Mistakes in reading the rod

5. Mistakes in recording or computing

6. Natural errors

7. Personal errors

State that there may be numerous in-strument errors; the most common oneis I'mperfect adjustment of the level.

46

HIGHWAY SURVEYING

CONTENT OUTLINE

1. Imperfect adjustment

2. Telescope condition

C. Manipulation errors

D. Settlement errors

E. Sighting errors

F. Mistakes in rod reading

Leveling


Show by sketch the errors caused byimperfect adjustment of the level.IndLate how the balancing of back-siglItF and foresights eliminates theerrer.

Explain that a worn telescope willgive faulty readings, especially whenthe objective lens moves to an inclinedposition.

Tell the class that careful instrumentusers will check the bubble before andafter each reading.

Demonstrate the possibility of a highrod reading being taken. This iscaused by the upper section not beingcompletely extended.

Demonstrate on a sketch the error inthe foresight if the level tripodsettles into the ground between abacksight and a foresight.

Point out that the same condition mayoccur when the turning point is not asolid point.

Explain parallax. This is a relativemovement of the image of the level rodwith respect to the crosshairs as theobserv,Ir's eye is moved. Stress thatthis is caused by improper focusingof the objective lens.

Let the class observe a fuzzy cross-hair and allow the students to adjustthe eyepiece until the hairs are clearand distinct.

State that the plumbness of the rodcan be checked by the vertical cross-hair.

Emphasize that the most common mistakeis to misread the numbe..! of feet ortenths.

47



G. Co.putation

H. Errors due to naturalsources

1. Extreme refraction

Call attention to two very common mis-takes in recording: transposingfigures, and interchanging the back-sight with the foresight.

Remind the class that only one back-sight is ever taken from each positionof the level, and that any otherreading must be a foresight.

Point out the importance of checkingthe computations on each page of notesbefore proceeding to the next page.

Recall the cause of error resultingfrom curvature and refraction: 0.002ft. in a 300-ft. sight.

Tell the class of the extreme refractiveerrors that could occur during themiddle of a hot day.

2. Precaution against sun Caution the class to attempt to keepthe level shaded. The sun causes un-even expansion of different parts ofthe instrument which will cause thebubble to move.

Personal errors

J. Limit on errors

State that there may be inherent con-ditions in an individual that may causepersonal errors. An example is defec-tive vision of the observer which mayresult in a consistently low or highreading.

State that if care is used in leveling,most of the errors will be random.(Ref. A, p. 201; Ref. B, p. 68)

Point out that the error in any lineis proportional to the square root ofthe number of setups.

1. Order-of-error formula List the allowable errors within thespecific classifications. The dif-ference in feet between two runs shouldnot exceed a constant times the squareroot of M, where M is the distance inmiles.

48



1. First order--allowable error of0.017 times the square root of M

2. Second order--allowable error of0.035 times the square root of M

3. Third order--allowable error of0.05 times the square root of M

4. Fourth order--allowable errorgreater than the first three

IV. Adjustments of the Level

A. Wye level

1. Crosshairs

Inform the class that running a lineof levels for construction work shouldbe at least second order work. Forprofile leveling 0.1 times the squareroot of M is generally used.

Describe the adjustments of the levelas being subject to the principle ofreversion. Reversing the position ofthe instrument doubles the error.(Ref. A, pp. 173-181; Ref. B, pp. 603-607)

Show the capstan-headed screws or nutswhich control the crosshairs and those.which control the bubble tube.

Caution the class to make all adjust-ments in a careful manner. Repeat alladjustments until the instrument is insatisfactory operating condition.

Remind the class how the constructionof the wye ZeveZ is different from thedumpy level. Although the trend is touse the dumpy level, it is best toknow the adjustments of the wye levelalso.

Explain that when the wye level is inadjustment and leveled, the horizontalcrosshair should be truly horizontal.The intersection of the vertical andhorizontal crosshairs should be apoint on the optical axis of the tele-scope.

49

HIGHWAY SURVEYING

CONTENT OUTLINE

2. Line of sight

3. The bubble tube

4. The wyes

Leveling


Point out that the line of sight ofthe telescope should be parallel withthe axis of the wye rings. This ischecked by loosening the clips andsighting a point. If after rotatingthe telescope 180° in the wyes, thecrosshair intersection is still on thepoint, the telescope is in adjustment.

Explain how the upper and lower capstanscrews for the crosshairs move thehorizontal line for adjustment. Showhow the side capstan screws are turnedto move the vertical line.

State that the axis of the bubble tubeshould be in the same plane as the lineof sight and parallel to it.

Demonstrate this adjustment and showhow the level bubble is centered whenthe telescope is revolved in the wyes.If the bubble is off center, adjust itlaterally by means of the capstanscrew on the side of one end of thebubble tube. Replace the telescope inits initial position and adjust theleveling screws of the level. If thebubble is off center, make the sameadjustment again.

Describe the second step by taking thetelescope out of the wyes and placingit with the ends reversed. If thebubble is off center, adjust the bubbleby means of the capstan nuts at oneend of the level tube, until it ishalfway to center. Repeat until thebubble remains on center.

Explain that the reason for adjustingthe wyes is to hold the bubble tubeperpendicular to the vertical axis ofthe level.

Show that this adjustment requiresleveling over one pair of level screwsand then over the other pair. Thetelescope is then revolved 180° on thevertical axis and turned end for end.

50



B. Dumpy level

If the bubble is off center, it shouldbe brought halfway back by means ofthe capstan nuts at the ends of thecrossbar. After centering the levelagain with the leveling screws, theadjustment should be rechecked.

State that there are fewer adjustmentson the dumpy level than on the wyelevel because there are fewer parts.

1. Crosshairs Point out that the crosshair adjustmentis the same as for the wye level.

2. Bubble tube

3. Line of sight

C. Self-leveling level

Explain that the bubble tube adjustmentmakes the level tube perpendicular tothe vertical axis of rotation. Thisis done so that when the instrumentis leveled, the bubble will remain inthe center as the telescope is revolved.

Show that the bubble tube in the dumpylevel is the same as in the wye levelwith one exception. The capstan screwsused on the dumpy level are on theright-hand end of the level tube.

Tell the class that the line of sightmust be parallel to the axis of thelevel tube.

Describe by sketches the operationcalled the peg method. This is usedto test whether the line of sightcoincides with the optical axis.

Note that the only adjustment on theself-leveling level is done by thepeg method. The horizontal crosshairis moved by means of a single capstanscrew. This is hidden from sight underthe cap at the eyepiece end.

QUESTIONS FOR REVIEW1. In leveling why are the backsights marked with a plus sign?

2. In any level run what is the relationship between the difference ofany two bench marks and the difference of the sum of the backsightsand the sum of the foresights?

51


3. What is the signal for establishing a turning point?

4. How does a worn telescope affect the accuracy of readings?

5. If 25 readings of a rod are taken from one position of the level,how many of these readings can be backsights?

6. What is the expected error in any line of levels?

7. Construction line levels should be what order of work?

8. What is the principle of reversion?

9. Describe the process of reciprocal leveling.

10. Explain the method by which the line of sight is made parallel tothe axis of the level tube.

ASSIGNMENT1. Solve problems 1-12 on pages 207-209 of Ref. A.

2. Study Chapter 12, pages 254-275 of Ref. A.

52

Lesson 7

MEASUREMENT OF ANGLES AND DIRECTIONSOBJECTIVES

1. To provide information on measuring angles and directions2. To :furnish the information for orienting a point, line, or survey


I. Location of Points Remind the class that the purpose ofa survey is to determine the locationsof points on or near the surface ofthe earth. (Ref. A, p. 254)

A. Fixed location

B. Definition of direction

Show that the location of a point isfixed if any one of the following isknown:

1. Direction and distance from aknown point

2. Direction from two known points

3. Distances from two known points

4. Direction from one known pointand distance from another knownpoint

Point out that the direction of anyline as defined by two points is de-termined by horizontal angular measure-ment between the line and some refer-ence line. This applies to a horizontalprojection (plan view).

Add that for vertical projection thedirection of one point with respect toanother can also be defined. Thedirection is defined by the verticalangle between the plane of the horizonand the line joining the two points.

53

HIGHWAY SURVEYING

CONTENT OUTLINE

C. Definition of an angle

D. Reference

1. Fixed reference

2. Meridian line

II. True Meridian

A. Convergence

B. Amount of convergence

Measurement of Angles and Directions


Show that the angle between two pointsis the horizontal angle between linespassing through the two points andconverging at a third point.

State that the vertical angle to apoint is its angle of elevation ordepression from the horizontal. Thiscan be positive or negative.

Explain how lines about a point arereferenced to each other. (Ref. A,pp. 254-255)

Point out that a line can be describedaccording to a fixed line of reference(base line). This can be any line ofa survey or an imaginary line.

Call the fixed line of reference ameridian. Describe this meridian asan assumed meridian if it is arbitrarilychosen without regard for the compass.

Call it a true meridian if it passesthrough the geographical poles of theearth as a true north and south line.Call it a magnetic meridian if it isparallel with the magnetic lines offorce of the earth. (Ref. A, p. 255;Ref. B, p. 114)

Explain that the direction of the truemeridian is always the same for anygiven point on earth. (Ref. A, p. 255)Add that this true meridian is estab-lished by an astronomical observationsuch as a sunshot.

Tell the class that true meridians onthe surface of the earth are lines ofgeographic longitude. They convergetoward the North and South Poles.

Show by use of a globe that the twofactors affecting amount of convergenceof two meridians in a given vicinityare:

54

1. The distance north or south ofthe equator

HIGHWAY SURVEYING

CONTENT OUTLINE

C. Grid meridian

III. Magnetic Meridian

A. Variations



2. The difference in longitude be-tween the two meridians

State that a grid meridian is eitherassumed or true. This is a referencemeridian with which all other meridiansin the area are considered to beparallel. (Ref. B, p. 115) Pointout the grids on an ordinary geodeticmap.

State that the direction of a magneticmeridian is that taken by a freelysuspended magnetic needle. The di-rection of the magnetic needle definesthe magnetic meridian at a certainlocation at a specific time. Unlikethe true meridian, whose direction isalways fixed, the magnetic meridianvaries from time to time. (Ref. A,pp. 255-256; Ref. B, p. 114)

Explain that there are many causesfor variation in the magnetic meridiandirection. (Ref. A, p. 258; Ref. B,pp. 125-128)

1. Change of magnetic pole Tell the class that there is a con-tinual shift of the earth's magneticpoles. The north magnetic pole is inthe vicinity of latitude 74° north,longitude 101° west, in McClintockSound, north of Hudson Bay, Canada.The south magnetic pole is south ofSydney, Australia, about 1800 milesfrom the geographical South Pole. Thelatitude and longitude of the southmagnetic pole is 68° south and 144°east; this shows that the poles arenot directly opposite.

2. Secular change Point out that shifting of the magneticpoles causes a secular change. Thisis unpredictable and can be chartedonly from past performances.

Compare the shifting to a pendulummoving from west to east every 150years and then moving back in theother direction. The greatest speedis in the middle of the cycle.

55

HIGHWAY SURVEYING

CONTENT OUTLINE

3. Annual variation

4. Local disturbance

5. Magnetic storms

6. Erratic action of thelines of force

B. Magnetic dip

C. Magnetic declination



Add that secular change also createsan annual variation which is a minorswing of about 1 minute per year.

Explain that local attraction anddisturbances due to geodetic or man-made causes also create variations.

Tell the class that many factors affectthe lines of magnetic force which de-termine the direction the magneticneedle will take. These are: magneticstorms, sunspot activity, the auroraborealis (aurora australis in theSouthern Hemisphere), cosmic rayactivity, and ionospheric activity.

Remind the class that the needle doesnot point to the magnetic pole butlines up with the lines of force ofthe earth.

State that on the 100° meridian in theUnited States, the magnetic pole is duenorth. However, the compass points10° or more to the east of true north.

Point out the extreme change fromMaine, (where the compass points 22°west of true north) to the State ofWashington, (where it points 24° eastof true north).

Describe magnetic dip, which is 0° atthe magnetic equator and 90° at themagnetic pole. (Ref. A, p. 256; Ref.B, p. 123) The magnetic needle of thecompass must be counterweighted tooffset this effect.

Define the angle between the truemeridian and the magnetic meridian asthe magnetic declination. (Ref. A,

p. 256; Ref. B, p. 125)

Use colored chalk and show on thechalkboard the two types of declina-tion. State that if the needle pointseast of the true meridian, the declina-tion is east. If the needle points

56

HIGHWAY SURVEYING

CONTENT OUTLINE

D. Isogonic chart



west of the true meridian, thedeclination is west.

Distribute isogonic charts (availablefrom the United States Coast andGeodetic Survey), which show lines ofequal declination in the United Statesfor a given year. (Ref. A, pp. 256-257; Ref. B, pp. 126-127)

1. Agonic line Explain the agonic line as the line ofzero declination.

IV. Azimuth of a Line

A. Basis

B. Forward azimuth

C. Back azimuth

Define the azimuth of a line on theground as the horizontal angle betweena meridian and the line, measured ina clockwise direction. (Ref. A, pp.260-262; Ref. B, pp. 115-116)

Tell the class that in astronomy andin geodetic work the azimuth of a lineis measured from the south meridian.In surveying, azimuth is measured fromthe north meridian. Give exampleswith line references from true north.

Assume a magnetic declination and askthe class to convert the true azimuthto a magnetic azimuth.

Point out that a stated azimuth isunderstood to be a line directed froman original point to a terminal point.This is called a forward azimuth.

Explain that if the forward azimuth isunder 180°, we must add 180° to findthe back azimuth. If the forward azi-muth is greater than 180°, subtract180° to find the back azimuth.

V. Bearing of a Line State that the bearing of a line givesthe direction of the line with respectto the reference meridian. (Ref. A,p. 260; Ref. B, pp. 117-118)

Repeat to the class that the azimuthof a line is an angle measured in adefinite direction from the referencemeridian. The angle can run from 0°to 360°.

57

HIGHWAY SURVEYING

CONTENT OUTLINE

A. Size and direction

B. Types of bearings



State that the bearing of a line isnever greater than 90°. It indicateswhether the angle is measured fromthe north or south, and whether it ismeasured toward the east or west.

Ask the class what they think a backbearing would be. Give examples oflines and compute both bearings andazimuths.

Add that a bearing may be either true,magnetic, assumed, or grid, dependingupon the type of meridian used.

Note that when the bearing of a lineis north and parallel to the meridian,it is called due north. If it is eastand perpendicular to the meridian, itis called due east.

VI. Relationship Between Bearing Reiterate that the true azimuth differsand Azimuth from the magnetic azimuth. The dif-

ference is the magnitude of themagnetic declination at the time andplace of the reading.

VII. The Horizontal Angle

Explain that if the magnetic declina-tion is east of true north, all mag-netic azimuths will be Jess thancorresponding true azimuths by theamount of magnetic declination. Ifthe magnetic declination is west oftrue north, then the magnetic azimuthwill be larger than the correspondingtrue azimuth by the amount of magneticdeclination.

Emphasize to the students that con-versions between true and magneticdirections are best made by means ofthe azimuths.

Define horizontal angle as an angleformed by two intersecting verticalplanes. The vertical planes intersectalong a vertical line which containsthe vertex of the angle. (Ref. A, p.264; Ref. B, pp. 131-132)

58

HIGHWAY SURVEYING Measurement of Angles and Directions


Mention that in surveying, the instru-ment measuring this horizontal angleoccupies the position at the vertex.

A. Direction Explain to the class that a horizontalangle has a direction or sense.If measured to the light, it is con-sidered clockwise; to the left,counterclockwise.

B. Deflection angles Explain with a sketch that a deflectionangle in surveying is the angle madeby a foresight with a prolongation ofa backsight. (Ref. A, p. 262)

C. Interior angles

D. Traverse

1. Traverse features

a. Transit points

1. In a closed polygon the algebraicsum of the deflection angles is360°. This is true when theright deflection angles are con-sidered opposite the leftdeflection angles.

2. If the bearing of any line isknown and the deflection anglesare observed, the bearings ofall the lines may be computed.

Tell the class that the sum of theinterior angles in a closed polygon isequal to 180° (n-2), where n equals thenumber of sides of the polygon. (Ref.

A, p. 262)

Define a traverse as a succession ofstraight lines connecting a successionof established points along t. `a routeof a survey. (Ref. A, pp. 26,-263and 331-338)

The points defining the traverse linesare called transit points or transitstations.

b. Distance The distances are measured along thelines.

c. Change of direction An angular measurement is made at allchanges in direction.

59

HIGHWAY SURVEYING

CONTENT OUTLINE

d. Closed traverse

e. Open traverse

2. Purposes

QUESTIONS FOR REVIEW1. How is direction defined?



A closed traverse forms a closedfigure,. This type affords a mathe-matical check by use of geometry.

If a traverse is not intended to close,it is called an open traverse or routetraverse. Also:

1. This is the type used in routesurveying OT highway work.

2. This traverse is run by measuringangles to the right. An appli-cation will be covered in alater lesson.

3. There is no mathematical check onthe fiold measurements. The onlychecks would be made by tying intoanother established line or takinga sunshot at the beginning andend of the traverse.

Point out that traverse surveys areused for many purposes to determineor establish:

1. Positions of existing boundarymarkers

2. Boundary lines

3. Area

4. Control for mapping

5. Ground control for photogrammetricmapping

6. Control for earthwork problems

7. Cor-xol in locating objects

2. Is the location of a point fixed if distances from two known pointsare given?

3. Describe a base Zine.

60

HIGHWAY SURVEYING Measurement of Angles and Directions

4. What is a grid meridian?

5. What causes variations in the direction of a magnetic meridian?

6. Does a compass needle point to the magnetic North Pole of the earth?Explain.

7. What is magnetic dip?

8. Differentiate between an isogonic line and an agonic line.

9. Define an azimuth of a line.

10. Compare an azimuth of a line with a bearing of the sam6 line.

11. In measuring a horizontal angle, where should the instrument measuringthe angle be located?

12. Describe a deflection angle.

ASSIGNMENT1. Solve problems 1-14 on pages 274-276 of Ref. A.


61

Lesson 8

THE TRANSITOBJECTIVES

1. To provide basic information about the construction of the transit2. To instruct the class on the use of the transit


I. The Transit Tell the students that the engineer'stransit (surveyor's transit) is aninstrument of great versatility.

A. Application Mention that the transit has many uses.It is used to measure and lay offhorizontal angles and directions, tomeasure vertical angles, to determinedifferences in elevation, and to pro-long lines and determine distances.(Ref. A, pp. 279-284; Ref. B, pp. 136-142)

B. Description of the instru- Point out that this universal instrumentment has a telescope which permits long and

accurate sighting.

State that the transit has a horizontalcircle usually graduated in half de-grees. High precision work requiresgraduations of 20' or 15'.

Explain that the verniers used forreading the horizontal and verticalcircles of the transit are based onthe same principle as the verniers forthe target rod.

Add that the compass box is used toobserve magnetic bearings.

Show the spirit leveling tube on thetelescope. This helps to measurevertical angles accurately and allowsthe transit to be used as a level.

62

HIGHWAY SURVEYING

CONTENT OUTLINE

C. Parts of the transit

1. Alidade

2. Horizontal limb

3. Level head assembly

D. Functions of transitsections

The Transit


State that the transit is made up ofthree subassemblies: alidade, hori-Zontal limb, and leveling headassembly.

Show pictures or diagrams of the un-assembled transit.

Point out that the alidade consists ofa circular cover plate equipped withtwo level vials at right angles to eachother. The plate is rigidly connectedto a solid conical shaft called theinner spindle. This section alsocontains the verniers for the hori-zontal circle, the frames which supportthe telescope (standards), the verticalcircle with vernier, the compass box,and the telescope with its level vial.

Show that the horizontal limb is themiddle section which is rigidly at-tached to a hollow conical shaft calledthe outer spindle. The outer spindlereceives the inner spindle of thealidade.

Point out the upper clamp and statethat this prevents rotation of theinner spindle within the outer spindle.Also, on the face of the horizontallimb, there is a graduated horizontalcircle.

Explain that the piece with the fourleveling screws is the spider and itholds the outer spindle. Under thespider is the bottom plate which screwson the tripod and supports the levelingscrews.

Show that the lower clamp preventsrotation of the outer spindle.

Indicate that there are essentiallythree groups of operations in the useof the transit. These affect the tele-scope, the spindles, and the hori-zontal circles and verniers.

63

HIGHWAY SURVEYING

CONTENT OUTLINE

1. Telescope

a. Construction

2. Vertical circle andvernier

3. Spindles

a. Clamped instrument

, The Transit


Describe the telescope of the transitas being similar to the scope of theengineer's level. It is shorter inlength but it has an objective lens,focusing wheel, crosshairs, and eye-piece. (Ref. A, p. 283)

Note that the telescope is attached tothe horizontal axis and can be held inany inclination with a vertical clamp.It can be moved slowly in a verticalplane with the vertical tangent screw.

Explain that by turning the eyepiecewe can regulate the sharpness of thecrosshairs.

Indicate that the vertical circle isrigidly connected to the transverseaxis of the telescope and that it movesas the telescope is raised or depressed.It may be clamped in a fixed positionby its clamp, then moved slowly by itstangent screws. (Ref. B, pp. 141-142)

Show that the vernier on the verticalcircle has a least count of one minute.

Explain that the vertical circle shouldread 00 when the telescope is hori-zontal. If it does not read 00, anindex error exists which must be ac-counted for. (Ref. A, p. 296)

Note that the quality of rotation iswhat gives the transit its name, aLatin derivative which means to crossor pass over.

Adc that the inner and outer spindlesprovide the rotation of the alidadeand the limb about the vertical axisof th'e instrument.

Point out the status of the transitwith both the upper and lower clampsin the clamped position. Neither thealdade which contains the vernier northe limb which contains the graduatedhorizontal circle can move.

64

HIGHWAY SURVEYING

CONTENT OUTLINE

b. Upper motion clamp

c. Lower motion clamp

The Transit


Explain the status of the transit whenthe upper cZamp is locked and thelower clamp is free. The outer spindleis free to rotate and this permits thealidade and the limb to move as oneunit.

Show the effect with the lower clamplocked and the upper clamp loose. Thealidade can rotate but the horizontallimb remains fixed. As the alidadewith the vernier moves around the edgeof the fixed graduated circle, thereading on the circle changes.

d. Slow motion rotation Inform the class that for slow motionaction, both the upper and lower clampsare equipped with tangent screws.

4. Horizontal circle andvernier

a. Graduations

b. Verniers

(1) Vernier design

Remind the class that the horizontalcircle is located on the periphery ofthe upper surface of the horizontallimb. (Ref. A, pp. 284-285; Ref. B,pp. 139-141)

Show on the chalkboard the differenttypes of graduations such as 30', 20',and 10'.

Mention that the circle is numberedboth clockwise and counterclockwise sothat we can read the angles in eitherdirection.

Note that on the horizontal circlethere are two verniers (A and B)exactly 180° apart.

Point out the location of the vernier.The outer edge of each vernier is incontact with the inner edge of thehorizontal circle.

Remind the class that regardless ofshape (either straight or curved) avernier is always constructed andread in the same manner.

Describe the design of the transitvernier as compared to that of thelevel rod.

65

HIGHWAY SURVEYING The Transit


(2) Reading thevernier

(.3) Class exercise

(4) Precaution

II. Using the Transit

A. Preliminary procedure

State that the double vernier isgraduated clockwise on one side forthe numbers increasing clockwise andgraduated counterclockwise on theother side for the numbers increasingcounterclockwise.

Explain that if the horizontal circleis divided into 30' portions and thereare 30 spaces on the vernier, theleast count is 30'/30 or 1'. If thehorizontal circle is divided into 20'units and there are 40 spaces on thevernier, the least count is 20'/40or 1/2' or 30".

Note that the instruments used in theexample are 1' and 30" transitsrespectively.

State that any vernier is read by:

(1) Noting the graduation on the circlebeyond the vernier index (2) adding tothe value of that graduation the valueof the vernier graduation which coin-cides with a circle graduation. Thereading should always be in the di-rection in which the circle is increas-ing.

Ask the students to take vernier read-ings on the instrument,

Caution the class to always use amagnifyin7, glass for vernier readings.

Stress that the basic formation ofgood working habits will lead to suc-cess in the use of the transit. (Ref.

A, pp. 290-291; Ref. B, pp. 142-144)

Advise the class that all stEns in theprocecure should be done in thefollowing order. Add that a fixed se-quence of operations becomes secondnature:

1. Placing the transit on 1. Adjust the friction of the tripodthe tripod legs at the tripod head.

66



2. Set up the tripod with the legswell spread and pressed firmlyinto the ground.

2. Carrying the transit

3. Setting the transitover a point

3. Place each tripod toe in an in-denture or crevice, if on a hardsurface.

4. Remove the instrument from thecase, lifting it by the base.

5. Remove the dust cap from theobjective lens and replace itwith the sunshade.

Hold the transit and tripod on Lheshoulder in a horizontal position. Theinstrument should be to the rear, andbalanced to carry the weight of thearm.

67

1. On an incline, stand about 2 ft.downhill, facing the point overwhich the transit is to be setup.

2. Seize two legs and place thethird leg on the ground about2 ft. uphill from the point.

3. Pull the other two legs outwardand backward. Place legs on theground so the footplate is nearlylevel.

4. If the ground is level, the legsare spaced equidistant from thepoint so the footplate is nearlylevel,

5. Attach the plumb bob to the hookof the instrument by using asliding knot in the cord. (Drawa sketch of the sliding knot andshow the class how to tie it.)

6. Center the instrument on thefootplate.



7. Move the instrument withoutchanging the relative positionof the tripod legs so the plumbbob hangs within 2 or 3 in. ofthe point.

4. Precautions

B. Measuring a horizontalangle

8. Push each leg firmly into theground.

9. Raise or lower the plumb bob untilit hangs about 1 in. above thepoint.

10. Choose the leg that is most nearlyon the opposite side of the pointfrom the plumb bob. Push thisleg farther into the ground ormove it outward and then push itinto the ground, until the plumbbob is exactly opposite a secondleg.

11. Move the second leg until theplumb bob comes within 1/4 in.of the point.

12. Loosen two adjusting screws.This loosens all leveling screws.

13. Level the instrument roughly with-out setting the screws tighter.

14. Turn the instrument until theplate levels are in line withpairs of opposite leveling screws.Turn the leveling screws.

15. Slide the head until the plumbbob is over the point.

16. Level the instrument by graduallytightening the leveling screws.

Stress the importance of not touchingthe instrument after it has been setup, except to operate it.

Explain that when measuring a horizontalangle both the upper and lower clampsare loosened and the horizontal limb

68



1. Setting the "A" vernierat zero degrees forconvenience

2. Pointing the instrument

a. The backsight

b. The foresight

c. The angle

rotated.. The standards are held untilthe zero graduation on the circle isalmost coincident with the index ofthe vernier. (Ref. A, pp. 291-292;Ref. B, pp. 144-145)

State that the A vernier can be setat zero by clamping the upper motionand turning the upper tangent screwto make the zero graduation with thevernier index. The vernier nearestthe upper clamp and tangent screw isknown as the A vernier.

Mention that in pointing the instrumentonly one horizontal clamp is free. Thelower clamp is free when starting topoint on the first side of the angleand the upper clamp when pointing tothe other side of the angle.

Remind the class that the lower motionis free so the telescope can be aimedat the first range pole..

State that to make the backsight, thelower motion is clamped and the ob-jective lens is focused. The verticalcrosshair is then brought on the sightrod with the lower tangent screw.

Note-that the instrument is now com-pletely locked and the circle readingis 00 and 0'.

Inform the class of the procedure formaking the foresight:

1. Loc3en the upper clamp and rotatethe alidade clockwise on itsvertical axis until the telescopeis aimed at the second sight rod.

2. Clamp the upper motion and bringthe vertical crosshair in on therod with the upper tangent screw.

State that the angle turned is now onthe horizontal circle, which is thedifference between the initial readingof zero and the final reading.

69

HIGHWAY SURVEYING

CONTENT OUTLINE

3. Synchronization oflines and planes

4. Maladjustment of thetransit

The Transit


Describe the various components of thetransit as lines and planes (Ref. B,pp. 145-147) :

1. The line of sight is normal tothe horizontal axis.

2. The horizontal axis is normal tothe vertical axis.

3. The vertical axis is normal tothe plane containing the hori-zontal 'Arcle.

4. The line of sight is parallel tothe axis of the telescope bubbletube.

5. The axis of the plate levels liein a plane parallel to the hori-zontal circle.

6. The optical center of the objectivelens is parallel to the line ofsight.

7. The inner spindle and outerspindle must be concentric.

8. The horizontal circle and verniersmust be concentric.

9. A line joining the indices of theA and B verniers must pass throughthe center of the horizontalcircle.

Caution the class that a transit isnever in perfect adjustment. There isalways some adjustment required. (Ref.

B, pp. 145-148)

a. Methods of reducing State that there are two methods thaterror we can use to eliminate errors caused

by maladjustment: double-centeringand reading both the A and E verniers,

(1) Double-centering Advise the class that of the two cor-rective methods double-centering ismore important. This method is also

70

HIGHWAY SURVEYING

CONTENT OUTLINE

(2) Angles by rep-etition

C. Running open traverse

The Transit


called double- sighting. (Ref. A, p.296; Ref. B, pp. 145-146)

Describe double-centering as the pro-cedure of making a measurement of anangle once with the telescope in anerect position and once with the tele-scope in the inverted or plungedposition. The mean value of the read-ings is used.

Point out that plunging the telescopeis the act of turning the telescopeabout its transverse axis. The tele-scope bubble vial is on top of thetelescope.

Stress that double-centering eliminatespersonal errors and instrumental errorsand increases the accuracy of themeasurement.

Tell the class that we can also reduceerrors when measuring angles, by rep-etition. Half of the readings aremade with the telescope plunged andthe mean value of the readings is used.(Ref. A, pp. 292-295)

Draw a sketch on the chalkboari of abase line run and letter the transitpoints, starting with A.

Describe to the class the steps in-volved in running an open traverse:

71

1. Assume that the line AB, the firstleg of the base line, has a mag-netic azimuth or a true bearing(by solar observation).

2. Set up the transit at B and back-sight at A with the horizontalcircle set at zero. The lowermotion should be clamped andupper motion free.

3. Turn a clockwise angle to C, andtake the first reading. Lock theupper motion, releasing the lowermotion.



4. Plunge the telescope and back-sight at A.

I. "Angles-to-the-right"

5. Release the upper motion and clampthe lower motion. Turn clockwiseto C, taking the second reading;this is cumulative.

6. Move the telescope to the erectposition, lock the upper motion.Release the lower motion, andbacksight at A.

7. Turn the telescope clockwise toC, taking the third reading(cumulative). Plunge the tele-scope and backsight at A.

8. Release the upper motion, clampthe lower motion, turn clockwiseto C. Take the last and fourthreading.-

9. Divide the four readings by 4and use the mean value.

Label the above method (an open traverse)angles-to-the-right. This expressionis used by the New York State Depart-ment of Transportation.

QUESTIONS FOR REVIEW1. Name the tnree subassemblies of the transit.

2. Describe the alidade.

3. How is the sharpness of the crosshairs regulated?

4. When the lover clamp is locked, what portion of the transit isimmobili zed?

5. Explain index of error.

6. When the upper clamp is locked and lower clamp is free, what motionis possible in the transit?

7. What is the least count if the horizontal circle is divided into 20'units and there are 30 spaces on the vernier?

72

HIGHWAY SURVEYING

8. Describe briefly how the sliding knot is made.

9. Explain briefly the procedure for measuring an angle.

.10. What is meant by plunging the telescope?

11. Why are angles measured by repetition?

The Transit

12. What is the most important rule to remember when reading a vernieron the horizontal circles of the transit?

ASSIGNMENTJ. Solve problems 1-4, 7, and 8 on pages 320-321 in Ref. A.

2. Study Chapter 13, pages 298-320, and Chapter 14, pages 326-347 inRef. A.

73

Lesson 9

THE TRANSIT (continued)OBJECTIVES

1. To describe sources of errors in angles2. To teach the adjustments of the transit3. Tc describe field operation with the transit

CONTENT OUTLINE

I. Sources of Errors in TransitALIgles

A. Instrumental errors andcorrections

1. Errors in measurementof angles


Describe the sources of errors as beingil!strumental, personal, or natural.

Note that all instrumental errors are.systematic. (Ref. A, pp. 312-317;Ref. B, pp. 154-157)

Point out that when the line of sightis not parallel to the telescope level,an error is introduced in the measure-mPT-- of vertical angles.

Show that this error is eliminated byreading a vertical angle with the tele-scope direct and reversed. This pro-cedure also eliminates any errorarising from the displacement of thevertical circle vernier from itscorrect position.

Tell the class that most instrtaentalerrors can be eliminated by taking themean of two angles. One observationcan be made with the telescope directand the other with the telescope in-verted. The following are examplesof possible errors:

74

1. The optical axis of the telescopeshould be parallel with the move-ment of the objective lens whenit is being focused. If thiscondition does not exist an error



2. Error of eccentricity

B. Personal errors

will be introduced in the measure-ment of a horizontal angle. Thiswill be especially true when thebacksight or foresight stationsare at different distances fromthe transit.

2. The line of sight must be per-pendicular to the horizontal axisof the transit. If not, an errorwill be found when the backsightand foresight points are atdifferent elevations.

3. The horizontal axis must be per-pendicular to the vertical axis.If not, an error is created whenthe backsight and foresightpoints are at different elevations.

Mention that if the plate bubbles areout of adjustment, the vertical axisis not truly vertical when the bubblesare centered. Eliminate this error byleveling both bubbles, turning thetelescope 180° and bringing bothbubbles halfway back to center.

Note that the A and B verniers shouldbe 180° apart. If they are not, areading should be made on both ver-niers and the mean value used.

State that personal errors are intro-duced by the instrument man and, hisrodman. These are always more seriouswhen short sights are used; they arecumulative. Some causes of personalerror are: (Ref. A, pp. 317-318; Ref.B, pp. 156-157)

75

1. Failure to have instrumentcentered over station point

2. Bad pointing of the telescope onthe target

3. Failure co give sight exactly onpoint


CONTENT OUTLINE.

C. Natural errors

D. Errors not otherwiseclassified


4. Failure to use a magnifying glasson the vernier

S. imperfect focusing of the tele-scope

6. Failure to center the platebubbles exactly

Describe natural errors as being dueto weather or soil conditions (Ref.A, pp. 318-319):

1. Wind vibrating transit or swingingplumb bob

2. Heat from the sun causing unequalexpansion of parts

3. Settling of tripod legs due toboggy ground or thawing soil

4. Refractive errors due to atmos-pheric conditions

Point out:that there are personal mis-takes not classified as personal errors.These are blunders and are called bustsin the field. (Ref. B, pp. 157-158):

1. Forgetting to level instrument

2. Turning the wrong tangent screw

3. Transposing digits in recording

4. Dropping full 20', 30', or 40'from a vernier reading

5. Reading the wrong circle

6. Recording a small vertical anglewith the wrong algebraic sign

7. Sighting on the wrong target

Precision of Angular Measure- Note that the accuracy required in thements measurement of horizontal angles is

largely determined by the purpose ofthe survey. (Ref. A, pp. 319-320;Ref. B, pp. 170-173)

76

HIGHWAY SURVEYING

CONTENT OUTLINE

A. Allowable angular error

1. Results desired

2. Probable error

The Transit


Explain that if the allowable linearerror in a distance L is d, the cor-responding angular error, e, can bec-mputed from the relation:

tan e =

Show that when distances are measuredto 1/500, the angles need only bemeasured to 5'. If distances aremeasured to 1/5000, the angles needonly be measured to 30". And if dis-tances are measured to 1/10,000 theangles reed only be measured to 20".

Note that the probable error in thedirection of any line in a traverse,with respect to any other line, maybe expected to vary as the squareroot of the number of setups betweenthe two lines.

3. Indeterminate precision Remind the class that unless a traverseis closed or begins and ends at knownpoints, the precision is indeterminate.If proper procedures are followed,there will be reasonable assurancethat the accuracy will not fall belowa fixed standard.

4. Limits for traversing Explain that in highway work the re-quired precision must have imposedlimits. The angular error of closureshould not exceed 30" times the squareroot of n, where n is the number of-observations. The total linear errorof closure should not exceed 1/5000.

III. Adjustments of the Transit State that in order for a transit tofunction properly and accurately itmust be kept in perfect adjustment atall times. (Ref. A, pp. 307-310)

A. To eliminate parallax Describe the procedure for eliminatingparallax (Ref. B, p. 608) :

77

I

1. Sight through the telescope andfocus the eyepiece on the cross-hairs.



2. Focus objective lens on a clearlydefined target about 300 ft.away.

3. Turn the objective focusing pinionslowly backward and forward, atthe same time moving your eyefrom side to side.

4. Observe for apparent lateralmovement between the image andthe crosshairs.

5. Stop focusing at the point whereno lateral displacement occurs.Disregard sharpness of image andcrosshairs as this is the pointof no parallax.

6. Refocus the eyepiece if the imageis not sharp. It will be foundthat the crosshairs will be moredistinct.

B. To make the vertical cross- Note that the line of collimation ishair perpendicular to the the optical line of sight passingtelescope axis through the optical center of the lens

and the intersection of the crosshairs.To make the vertical crosshair perpen-dicular to the telescope axis do thefollowing (Ref. A, p. 307):

1. Sight through the telescope andset one end of the vertical cross-hair on a sharply defined point,A.

2. Elevate or depress the telescopeso the vertical crosshair tracesover the point.

3. If coincidence is not present,loosen all four capstan screwson the crosshair ring.

4. Move the crosshair zing around inthe proper direction. Check andcontinue to adjust until thevertical crosshair is in exactcoincidence with a point, as thetelescope is moved up and down.

78

HIGHWAY SURVEYING

CONTENT OUTLINE

C. To make the plane of col-limation of the verticalcrosshair perpendicularto the telescope axis

D. To make telescope axisperpendicular to verticalaxis or spindle

The Transit


5. Tighten the capstan screws andcheck again.

Describe the procedure for making theplane of collimation of the verticalcrosshair perpendicular to the tele-scope axis (Ref. A, pp. 310-311):

1. Set up the transit and sight thevertical crosshair on point A,about 300 ft. away from thetransit.

2. Plunge the telescope and setpoint B at approximately the samedistance away from the transit.

3. Leave the telescope in the plungedposition and rotate the instrumentto 'sight again or, A.

4. Plunge the telescope and setpoint C along the same line aspoints A and B. This point willnot fall on point B if the in-strument is off adjustment.

5. Take one-quarter of the distancefrom points B to C and set pointE on the same line.

6. Turn the horizontal screws on thecrosshair ring until the verticalcrosshair is set on point E.

7. Set on A and repeat operationsuntil points B and C coincide.

Describe the procedure for making thetelescope axis perpendicular to thevertical axis, or spindle (Ref. A, pp.308-34):

79

1. Set up the transit and sight onhigh point A.

2. Depress the telescope and setpoint B on the ground.

3. Rotate the instrument 180° andsight back on A.

HIGHWAY SURVEYING

CONTENT OUTLINE

The Transit


4. Depress the telescope again andset point C.

5. Take one-half of the distancefrom points B to C and set pointD so that BD is equal to DC.

6. Raise or lower the right end ofthe telescope axis until thevertical crosshair intersectspoint D.

E. To make axis of telescope Explain that making the axis of thelevel parallel to the line telescope level parallel to the lineof sight of sight requires the same adjustment

as for the dumpy level. (Ref. A, p.310)

Proceed with this check, using thetwo-peg adjustment.

Note that when the line of sight isset on the proper rod iading, thecorrection is made by raising orlowering one end of the level tubeuntil the bubble is centered.

F. To make the plate bubble Describe the procedure for making thetube axis perpendicular plate bubble tube axis perpendicularto the vertical axis or to the vertical axis or spindle (Ref.

spindle A, p. 308):

1. Set up the transit. Rotate thetransit plate so each bubble tubeis over a pair of leveling screws.

2. Bring the plate bubbles to thecenter of both tubes.

3. Turn the plate 180° in azimuth.

4. Note how far the bubbles movefrom the center.

5. Raise or lower the tube until thebubbles come halfway back tocenter.

6. Repeat until turning the instrumentin any direction will not affectthe bub.:.

80


CONTENT OUTLINE

G. To make vertical circleread zero when line ofcollimation is hori-zontal

IV. Field Operation with Transit

A. Prolonging a straight line

B. Balancing-in


Describe the procedure for making thevertical circle read zero when the lineof collimation is horizontal (Ref. A,p. 310)

1, Level up the transit using thetelescope level.

2. Inspect the vernier and verticalcircle to see if the zeroscoincide.

3. If they do not coincide, loosenscrews and shift vernier untilthe zeros do coincide.

Tell the class that many field operationsare performed with the transit.

Show how prolonging a straight lineinvolves the simple procedure ofplunging the telescope. (Ref. A, p.298)

Point out that if the instrument isout of adustment, the method ofdouble-centering must be used. (Ref.

B, p. 183)

Define balancing-in as the procedureused when two ends of a line are notintervisible but both e-ads can be seenfrom an intermediate point. (Ref. A,p. 302; Ref. B, p. 185)

Show by sketch that the instrument isset at the intermediate point, sightedat A, plunged, and sighted at B.

Explain that the distance between theforesight and point B is estimated.The instrument is set up a proportionaldistance from the two points in aneffort to be on the line. This is re-peated until the instrument can beplaCed exactly on the line by slidingthe transit on the footplate.

C. Running random lines Show on the chalkboard the procedureif point B is not visible from point

81



A or from any intermediate point. Arandom line may be run from point Ato a point where point B may be seen.(Ref. A, pp. 302-303; Ref. B, pp, 185-186)

D. Finding the intersectionof two straight lines

Indicate that the angle between therandom line and AB can be computed bytrigonometry.

Explain by use of a sketch that theintersection of two straight lines isfound by using straddle stakes andstring. (Ref. A, p. 304; Ref. B, pp.186-187)

E. Prolonging a line past an State that obstacles such as heavyobstacle timber, houses, or buildings which

cannot be removed until constructionbegins prevent direct extension of aline. We can, however, use methodsto overcome the obstacles.

1. Offset method Describe the offset line. This utilizesa perpendicular offset distance fromthe line, a right angle turn whichplaces the line parallel to the originalline, and a perpendicular offset backto the original line. (Ref. A, p. 300;Ref. B, pp. 187-188)

Note that short sights are criticaland difficult to use in this procedure.

2. Deflection angle method Point out that another method utilizesan isosceles triangle. In this tri-angle we use small base angles andeven-foot legs. (Ref. A, p. 301)

Show that when an obstacle is encoun-tered, a small deflection angle (a)is turned off the desired line. Thenan even numbered distance (such as100 ft.) is taped.

1. Set transit at the 100 ft. mark.Turn a deflection angle (2 a)in the opposite direction.

82



F. Setting parallel lines

G. Measuring an angle whentransit cannot be set atthe vertex

H. Application of triangu-lation

1. Solving with trigo-nometric tables

2. Solving without trigo-nometric tables

2. Measure the same distance (100ft.) on this line, establishin3a point on the original line.

State that the offset principle canbe used to set two lines parallel toeach other. (Ref. B, p. 188)

Tell the class that two offsets aregeometrically sufficient but thatthree offsets are desired.

Stress the use of geometry. Show thatparallel lines can be set by makingthe alternate interior angles equal.

Explain that it is sometimes impossibleto set the transit at an intersectionof building walls or fence lines.(Ref. A, p. 305)

Sketch an intersection of fence linesand show how offset lines to eachfence are set by swing offsets.

Point out that the transit is placedat the intersection of the offsetlines and th-. angle is turned betweenthe offset lines.

Explain the process of determining aninaccessible distance (such as acrossa body of water) by the use of trigo-nometry. (Ref. A, p. 304)

Show that with two setups of the transit,two angles are measured and one dis-tance taped. This enables the unknownside to be computed by the use oftrigonometric functions.

Mention that if tables are not available,a second method may be used whichinvolves simple arithmetic.

Show by sketch the layout of twosimilar triangles. Turn a 90° anglefrom the inaccessible point to a pointon the working side of the obstacle.(See sketch in Ref. A, p, 30A.) No

83



other angles are turned but two measure-ments are made.

I. Plotting by radiation

J. Plotting by intersection

K. Plotting by resection

Describe plotting by radiation. Thisis a procedure in which the transitis set up at a convenient point andthe horizontal angle and distance toeach desired object is observed.(Ref. A, p. 329)

Emphasize the importance of intersectionin connection with the location ofobjects which must be defined accu-rately. (Ref. A, p. 330)

Explain the procedure of plotting byintersection. This method uses a baseline or any convenient line of a knowndistance. Angles to the objects areobserved from both ends of the baseline.

Add that the base line becomes theknown side of a triangle. The objectis at the vertex of the triangle, andboth measured angles adjacent to thebase line are known.

Point out that the triangles can becomputed for distances which arenecessary for plotting.

Caution the class that well-shapedtriangles should be used with :eason-ably sized angles.

Describe this variation of intersection.This is a method of setting the transitin an unknown location and determiningthe location of the transit by sightingon points of known location. (Ref. A,

p. 331)

QUESTIONS FOR REVIEW1. Name three sources of error which may occur in the use of the transit.

2. How are most instrumental errots eliminated?

3. How is an error of eccentricity eliminated?

84


4. Give three types of personal errors which are prevalent in themeasurement of angles.

5. List three types of natural errors which could affect the measure-ment of angles.

6. What is the probable error in the direction of any line in atraverse with respect to any other line in the same traverse?

7. What is allowable in highway work with respect to the angular errorof closure?

8. What is allowable in highway work with respect to the linear errorof closure?

9. Describe parallax.

U. Explain the position of the line of collimation in the telescope.

11. Why is the two-peg test made?

12. What is the procedure of balancing-in?

13. How can a line be prolonged past an obstacle?

14. Describe how an angle may be measured when the transit cannot beplaced at the vertex of the angle.

15. Differentiate between the procedures of radiation and intersection.

16. In using the principle of resection what factor is not known?

ASSIGNMENT1. Solve problems 9-19 on page 321 of Ref. A.

2. Study Chapter 13, pages 295-298; Chapter 15, pages 350-375; Chapter16, pages 415-417; and Chapter 18, pages 454-461, all in Ref. A.

85

lassos to

THE TRAVERSE AND STADIA SIIRVIITINGOBJECTIVES

1. To teach the computation of the traverse2. To show how to use the State Coordinate System3. To introduce the fundamentals of stadia surveying


I. The Traverse Point out to the class that while theopen traverse provides no mathematicalcheck on field measurements, theclosed traverse does follow the lawsof geometry. (Ref. A, pp. 331-334;Ref. B, pp. 192-194)

A. Traverse construction State that a traverse may be run:

B. Interior angle traverse

1. Angular error

1. By design (a perimeter of a givenarea)

2. By coincidence (intersections ofbase lines and sidelines of openbase line surveys)

Show how a certainrun with sidelinesline at some pointsome other point.closure.

base line could bethat leave the baseand then return atThis provides

Explain that in the interior angle'traverse the interior angles and hori-zontal distances are first measured.Thena check is made with the formula180° (n-2) on the sum of the angles.(n is the number of sides of thetraverse.) (Ref. B, pp. 194-197)

Point out that in a traverse of n sidesthere is a limit on the closure of themeasured angles. This should not

86

HIGHWAY SURVEYING The Traverse and Stadia Surveying


exceed the least count of the vernierof the transit times the square rootof n.

2. Bearings Mention that only one azimuth may beknown at the beginning of the traverse.

Check the students' knowledge aboutdetermining the azimuths for all thelines in the traverse and for con-verting them into bearings.

C. Deflection angle traverse Show by sketch the deflection angletraverse that closes on its point oforigin. (Ref. A, pp. 334-335; Ref.B, pp. 197-202)

1. Angular error Mention the check for angular errorthat must be made before the bearingsare computed for the sides. Thedifference between the sum of theright deflection angles and the sumof the left deflection angles mustequal 360°.

D. Adjustment of angular error Repeat that by using the formula 180°(n-2) the total error in anOes may befound for any closed traverse. (Ref.

B, p. 195)

1. General distribution

2. Other distributions

Indicate that since all angles aremeasured under similar conditions, theusual procedure is to distribute thetotal error equally. (Ref. A, pp.458-459)

Stress that distribution is done im-mediately after discovering the totalangular error and before any otheradjustment is made.

Add that judgmci.t may be used in dis-tributing total angular error. If

some angle are measured between veryshort ,ides, the error may be withinthose angles.

Describe distribution if repeatedmeasurements yield angles above theaccuracy of the instrument, such as

87

HIGHWAY SURVEYING

CONTENT OUTLINE

E. Traverse computation

1. Distribution of totalerror

The Traverse and Stadia Surveying


readings to 20" on a 1' transit. Theerror may be distributed within thosearithmetically derived angles.

Emphasize that the result of the fieldwork in executing a traverse is aseries of connected lines of knowndirection and length. (Ref. B, pp.209-210)

Note that the first step in the traversecomputation is the distribution of thetotal angular error:

2. Computation of bearings Tell the class that bearings are nextcomputed so that each line has a di-

...mg

rection relative to the others.

3. Linear errors Point out that errors may exist in themeasured lines which would tend toalter the shape of the traverse. A

system of latitudes and departures isused to discover discrepancies.

4. Adjustment of the tra- State that after the latitudes andverse departures are computed, the error of

closure is found and the survey isbalanced.

II. Rectangular Coordinates

A. Origin

B. Projections

Describe the coordinate axis for anyline as a reference meridian (true,magnetic, or assumed). Also, describea line at right angles to the meridianas a reference parallel. (Ref. A, p.454)

Show that the intersection of theselines marks the origin and that anybearing may be plotted in its properquadrant.

Explain what is to be done when thelength and direction of a line areknown. The length of its orthographicprojection upon the meridian and uponthe parallel is computed. (Ref. A,pp. 455-456; pp. 210-211)

1. Latitudes Show that the projection of a line ABon the meridian is termed the latitude

88



of the line. This is found by multi-plyinn distance AB by the cosine ofthe bearing angle.

2. Departures

C. Computations

1. Data form

2. Class problem

Note that if a line has a northerlybearing, its latitude is designated asnorth, or positive. If the line hasa southerly bearing, its latitude isdesignated as south, or negative.

Show that the projection of a line ABon the parallel is called the departureof the line. Departure is found bymultiplying AB by the sine of thebearing angle.

Note that if a line has an easterlybearing, its departure is designatedas east, or positive. If the line hasa westerly bearing, its departure isdesignated as west, or negative.

Emphasize that in computing a traverse,care must be exercised to worksystematically.

Draw the form used for computation onthe chalkboard and give the class asimple example with four courses.(Ref. B, p. 212)

Work out a problem on the chalkboard.Emphasize the observance of signs andthe placement of the proper functionof each angle in its proper position.

Set up the problem so that errorsare incorporated. For example, thelatitudes and the departures can con-tain a difference in their plus andminus sums. Elicit the nece3saryc- rrections from class members.

D. Summaticn of latitudes and Indicate that in any closed traversedepartures the sum of the north latitudes should

equal the sum of the south latitudes.Also the sum of the east departuresshould equal the sum of the westdepartures. (Ref. B, pp. 213-216)

89


CONTENT OUTLINE TEACHING POINTS AND TECHNI'UES

Tell the class that there is no pos-sible means of determining the truemagnitude of angle and distance errorswhich occur throughout the traverse.

1. Compass rule

a. Errors

State that some surveyors wrongly dis-tribute the error in accordance withtheir own estimation of the field con-ditions. There are several rules fordistribution of errors which will pro-duce a mathematically closed diagram.

Explain that in order to reconcile anyadjustments in the measurements of asurvey some assumptions must be made.(Ref. A, pp. 459-460; Ref. B, p. 217)

1. The errors in traversing areaccidental and, therefore, varywith the square root of thelengths of the sides. This makesthe corrections to each sideproportional to its length.

2. The effects of the errors inangular measurement are consistentwith the effects of errors intaping.

b. Definition Define the compass rule:

2. Transit rule

1. Latitude of any course:

correction to be appliedtotal correction in latitude

length of courselength of traverse

2. Departure of any course:

Forractioili_total correction in departure

length of courselength of traverse

Explain the assumptions on which thetransit rule is based (Ref. A, pp.459-460; Ref. B, p. 217):

91

HIGHWAY SURVEYING

CONTENT OUTLINE



I. The errors in traversing areaccidental.

2. The angular measurements are moreprecise than the taping measure-ments.

a. Definition Define the transit rule as follows(Ref. A, p. 459):

3. Problem

III. Location by RectangularCoordinates

A. Axes

1. Latitude of any course:

correction to be appliedtotal error in latitude

=latitude of course

arithmetical sum of all thelatitudes

2. Departure of any course:

correction to be appliedtotal error in departure

departure of coursearithmetical sum of all the

departures

Note that the transit rule is merelya rule of thumb which does not applysuccessfully in all cases.

Use the compass rule on the sampleproblem used to demonstrate how tocompute latitudes and departures andthen balance the survey.

Show how the length of each side andits bearing is adjusted.

Amplify the previous explanation ofrectangular coordinates. Describe thecoordinates of a point as the distancesmeasured to the point from a pair ofmutually perpendicular axes. (Ref. A,pp. 454-455; Ref. 13, pp. 221-222)

State that the distance from the X-axis is the Y coordinate of the point.The distance from Y-axis is the Xcoordinate of the point.

92

HIGHWAY SURVEYING

CONTENT OUTLINE

B. Plane surveying

C. Positive quantities

D. Computations

IV. New York State,CoordinateSystem



Mention that in the United States thenorth part of the meridian on whichthe survey is based is the positiveY-axis. A line perpendicular to thismeridian through an assumed origin isthe X-axis. Note that the X-axis ispositive in an easterly direction.

Give an example, showing the coordinatesof several points.

Tell the class that usually the co-ordinates of all the points in thesurvey are made positive quantities.This is done by placing the originfar enough south and west.

State that before the coordinates ofthe points in a traverse can be com-puted, the coordinates of at leastone point in the traverse must heknown. (Ref. A, pp. 463-468)

Show that the coordinates of stationB are computed when the coordinatesof station A are known in the line AB.

1. The Y coordinate of station B isdetermined by adding (or subtrac-ting) the latitude of line AB tothe Y coordinate of station A.

2. The X coordinate of station B isdetermined by adding (or subtrac-ting) the departure of line AB tothe X coordinate of station A.

Point out that the bearings and dis-tances of the lines can be computed bythe simple trigonometric functions ofright triangles. This can be done ifthe coordinates of the points areknown.

Mention that the methods of plane sur-veying are based on the assumptionthat all distances and directions areprojected onto a horizontal plane sur-face. This surface is tangent to thesurface of the earth at one point

93



within the area of the survey. Statecoordinate systems provide one set ofplane rectangular coordinates toserve the whole area of a small stateor a portion of the area of a largestate. (Ref. A, pp. 415-417; Ref. B,pp. 340-341)

A. Limits of a system

B. Geodetic surveying

Explain that in two independent surveysthe measurements in each survey arereferred to two different horizontalplanes which do not coincide. (Ref.B, pp. 342-345)

Point out the effect of convergency ofthe meridian. If the Y-axis of a planecoordinate system for each of the twosurveys is assumed to be parallel tothe true meridian, then even the Y-axesof the two systems are not parallelwith one another.

State that in any system the fartheraway measurements are made from thepoint of tangency, the more will thedistances and angles as measured onthe ground differ from the correspondingdistances and angles projected on ahorizontal plane. When this conditionbecomes intolerable, the limits ofplane surveying have been reached.

Advise the class that the methods usedin precise geodetic surveying are de-signed for the spheroidal surface ofthe earth. Angles in triangles areconsidered to be spherical. Coordinatesof points are computed with referencesto parallels of latitude and meridiansof longitude. This is done by usingangles computed near the center of theearth rather than distances.

Add that geodetic surveying does nothave the limitations of plane surveyingand that precise work may be done overlarge areas of land. Precise work ofthis type is more complex and moreexpensive.

94



C. United States Coast andGeodetic Survey

D. State systems

1. Highway control

E. Application of a statecoordinate system

1. Types of projections

Mention that much of this work iscovered in Unit Ii of this series,"Highway Drawing."

Mention that for a century the U.S.Coast and Geodetic survey has beenestablishing horizontal control monu-ments. These take the form of tri-angulation, traverse, and intersectionstations, and are placed only afterprecise geodetic surveying.

Note that all the control points in thecountry bear a definite relationshipto each other--all refer to one commonspheroidal surface. (Ref. B, p. 341)

Explain that state coordinate systemshave been devised to allow methods ofplane surveying to be used over a greatdistance in any direction. This en-ables precision to be maintained equalto that of geodetic surveying.

Point out that precision is of greatimportance in highway surveying becausea highway often covers a long distance.With the coordinate system, each endof the highway can be tied, forming aclosed traverse.

Explain that because of the transfor-mation from the spheroidal surface ofthe earth to one horizontal plane,there are varying applications to astate system:

1. If the state is small, it can beembraced in one projection.

2. If the state is large, it can bedivided into zones broken alongcounty lines.

a. Transverse MercatOr Describe the transverse Mercator pro-jection as employing a cylindricalsurface. The axis is normal to theearth's axis of rotation and intersects

95



b. Lambert conformal

the surface of the earth along twoellipses. These ellipses are equi-distant from a meridian plane throughthe center of the area to be projected(Ref. B, pp. 346-349):

1. This causes distortions in aneast-west direction. It is thusused for states or zones havingshort east-west dimensions, suchas Vermont.

2. New York State adopted its co-ordinate system on July 1, 1939.The State was divided into fourzones, three of which are trans-verse Mercator projections.

3. The East, Central, and West zoneshave central meridians of 74°20'W., 76°35' W., and 78°35' W.,respectively. The origin of co-ordinates is at the intersectionof each of these meridians withthe parallel 40°00' N.

4. Each of these origins is given byx = 500,0C° ft. and y = 0 ft.

Describe the Lambert conformal pro-jection which employs a conical sur-face. Its axis coincides with theearth's axis of rotation and inter-sects the surface of the earth alongtwo parallels of latitude. Theseparallels are approximately equidistantfrom a parallel lying in the center ofthe area to be projected. (Ref. B, pp.357-360):

96

1. This causes distortion in a north-south direction. It is thus usedfor states or zones having shortnorth-south dimensions likeTennessee.

2. The fourth zone of New York State(Long Island) is a Lambert con-formal projection.


CONTENT OUTLINE

2. Actual error

3. Geodetic and gridazimuths

F. Advantages of a statecoordinate system


3. The origin of coordinates is atthe intersection of the meridian74°00' W. and the parallel 40°30'N. at x = 2,000,000 ft. and y =100,000 ft.

Mention that if the east-west distancesin the transverse Mercator projectionand the north-south distances in theLambert projection are limited to 158miles, the distortions would not begreater than 1/10,000.

Tell the class that when a survey isplaced on a system of plane rectangularcoordinates, all bearing and azimuthsare referred to the same meridian.Characteristics of the survey are(Ref. B, p. 345):

1. The system is rectangular. All

grid north and south lines areparallel to the central meridian.

2. The convergence of meridianscauses a difference in the gridbearing and geodetic bearing ofa line. The difference increaseswith the latit,,de and the distanceaway from the central meridian.

3. The difference between the gridazimuth and the geodetic azimuthof a line is indicated by thesymbol 8 (theta) on the Lambertgrid. On the transverse Mercatorgrid the difference is indicatedby the symbol Va (delta alpha).

List the following advantages in usingthe State Coordinate System (Ref. B,pp. 372-373):

97

1. Standardizes and unifies surveys

2. Increases the permanency of sur-veys

3. Provides more accurate results

HIGHWAY SURVEYING

CONTENT OUTLINE



4. Reduces cost of survey work

5. Insures better records

6. Prevents mistakes

7. Allows lost points to be replaced

8. Conforms maps of the same location

9. Provides less expensive photo-grammetric mapping

V. Stadia Surveying Define the term stadia surveying asthe method of obtaining horizontaldistances and differences in elevation.This is accomplished with the opticalgeometry of the lens, the crosshairsof the *.elescope, and the transitreading of the vertical circle. (Ref.

A, pp, 350-358; Ref. B, p. 413)

A. Procedure Explain that this is a process by whichthe angle at the instrument is measuredby observing two points on a graduatedrod.

Note that stadia surveying is usedwhen low accuracy is permitted.

B. Principle of transit ,tadia Point out that the transit telescopemeasurements is equipped with three horizontal

crosshairs; the upper and lower hairsare called the stadia hairs. (Ref. A,pp. 354-357)

Draw a sketch on the chalkboard, showingthe telescope, the lens, the focalpoint, and the rod.

1. Space between the stadia Call the distance between the uppercrosshairs and the lower hairs i.

2. Laws of optics Discuss the laws of optics. Explainthat a ray of light parallel to theoptical axis of a lens will passthrough the principal focus of the lenson the opposite side. (Ref. A, pp.354-355; Ref. B, pp. 413-416)

98

HIGHWAY SURVEYING

CONTENT OUTLINE

3. Focal length

4. Stadia interval



Show this point on tha sketch as pointF. Show the distance from the centerof the lens to F as the focal lengthof the lens, f. This is constant fora given lens.

Explain that a ray of light will bebent at the bottom of the lens, passthrough F, and strike the rod at apoint B, above the optical axis.Similarly a ray of light will be bentat the top of the lens, pass throughF, and strike the rod at a point A,below the optical axis.

Mention that this distance AB on therod is called s or stadia interval.It is found by subtracting the stadiahair reading at A from the stadia hairreading at B.

Find by similar triangles that thedistance R (from F to the rod) is equalto the focal length (f), over thestadia hair spacing (i), times thestadia interval:

R =fs

5. Stadia interval factor State that the ratio f/i is called thestadia interval factor, or K, whichdefines R as Ks.

Note that the manufacturers of mostinstruments space the stadia hairs sothat K is equal to 100.

6. Total horizontal distance Show on the sketch how the total hori-zontal distance D, from the centerlineof the telescope to the rod is derived.This consists of R (from focal pointto rod), plus f (the focal length fromfocal point to lens), plus c (from lensto centerline of instrument).

7. Stadia equation for a Add that c is variable and negligible

horizontal line of sight so that the term f + c is called stadia

constant C. This defines the totaldistance D as equal to R + C or Ks + C.

99



VI. T.nclined Line of Sight

A. Geometry of line of sight

B. The vertical angle

C. Tables

1. Use of tables

VII. Difference in Elevation Be-tween Two Points

State that the stadia constant C isprinted on the box which houses thetransit. It varies from 0.6 to 1.4but in the new type of internalfocusing telescope it is always equalto 1.00.

Conclude that since D = Ks + C, thestadia interval read on the rod ismultiplied by 100. Then the constantis added for a horizontal distance.

Emphasize that this is applicable onlywhen the line of sight is inclinedless than 30.

Advise the class chat the inclinedmeasurements _.re more frequent thanthe horizo:Ical ones. (Ref. A, pp.356-358; Ref. B, pp. 416-419)

now by sketch that the inclined stadiameasurement must be reduced geometricallyto find the horizontal distance,H.

Describe briefly the geometry of thisconversion. Also describe the differ-ence in elevation between the centerof the telescope and the middle cross-hair reading,V.

Stress that the inclined angle ismeasured on the vertical circle of thetransit.

Explain that the compfl*ations for eachinclined sight are ,dious task andtables are used t' ,..cilitate the work.

(7ef. A, Table ( pp. 959-966; Ref. B,Table A, pp. 643-650)

Set up an example for the class anddemonstrate the use of the stadiatables.

Explain to the class the significancecf the vertical distance, V, found inthe tables or by computation. Thisvalue comprises the distance from thecenterline of the telescope to the

100



middle crosshair reading. This is notthe true difference in elevation be-tween the ground level at the transitand the ground level at the rod. (Ref.

A, pp. 363-365; Ref. B, pp. 420-422)

A. Total difference inelevation

B. Rapid procedure

Identify the elements that make up thetotal difference in elevation. Thedifference is the distance from thecenterline of the telescope to theground, or H.I., plus the verticaldistance, V, minus the-middle rodreading (distance from reading on rodto the ground under the rod).

Stress to the class that this differ-ence in elevation is the H,I. minus V,minus rod reading, if the verticalangle is negative.

Explain that if the middle crosshairis set on the rod at the H.I. ele-vation, then the vertical distance, V,is the difference in elevation.

QUESTIONS FOR REVIEW1. What is the sum of all of the interior angles of a closed traverse?

2. Explain what is meant by a field execution of a traverse.

3. What is the projection of a Zine on the meridian?

4. How is the projection of a Zine on the meridian found?

5. What is the mathematical summation of latitudes and departures?

6. Describe the linear error of closure.

7. Define closure precision.

8. What is the compass rule as used to balance a survey?

9. What is the transit rule as used to balance a survey?

10. Compare the compass rule with the transit rule.

11. How is it possible to avoid the use of a negative coordinate whenestablishing a plane coordinate system?

101

HIGHWAY SU1tVEY1N6 The Traverse and Stadia Surveying

12. Explain how the United States Coast and Geodetic Survey system,utilizing one common spheroidal surface, can be reconciled with theState Coordinate System.

13. What is the maximum distance in miles which limits the distortion toless than 1/10,000 in the State Coordinate System?

14. Name six advantages of a state coordinate system.

15. Describe what is meant by stadia interval.

16. What is the stadia constant of an internal focusing telescope?

17. How can the true difference in elevation be determined when usingstadia?

ASSIGNMENT1. Solve problems 1-4, 7, and 8 on pages 375-376 of Ref. A.

2. Solve problems 1, 2, 4, 8, and 11 on pages 474-476 of Ref. A.



102

Lesson 11

PRINCIPLES OF FIELD ASTRONOMYOBJECTIVES

1. To provide the student with the fundamentals of field astronomy2. To teach the students how to locate the true bearing or azimuth of

a line


I. Introduction to Field Astronomy State that a knowledge of practicalastronomy is necessary for determininglatitude, time, longitude, and azimuth.(Ref. A, pp. 502-521; Ref. B, p. 375)

A. Application

B. Scope

C. Relationship of stars toearth

Tell the class that astronomy is usedto determine the absolute location ofa point and the absolute direction ofa line. Absolute location is thelatitude and longitude. Absolutedirection is true north or truemeridian.

Mention that a complete coverage offield astronomy is beyond the scope ofthis course. But the information pre-sented here will enable the studentto perform certain field operations.These include the securing of thecorrect standard time and a trueazimuth from solar observations.

Explain that time, latitude, longitude,and true azimuth may also be determinedfrom observations of certain stars.

Point out that the various heavenlybodies are assumed to be located on thesurface of a sphere of infinite radius.The center of the earth is the centerof the celestial sphere.

103

HIGHWAY SURVEYING Principles of Field Astronomy

CONTENT OUTLINE

D. Definitions of terms

1. Celestial poles

2. Celestial equator

3. Zenith

4. Vertical circle


Draw a sketch of the celestial sphereon the chalkboard. Place the earthat its center. (Ref. B, pp. 376-380)Describe the terms that apply to fieldastronomy:

The two points of contact made on thecelestial sphere when the line of theearth's axis of rotation is extendedin both directions.

The intersection of the celestialsphere with a plane passing throughthe center of the earth, perpendicularto the axis of rotation.

The extension of a vertical line at anypoint on the surface of the earth. It

intersects the upper portion of thecelestial sphere at the zenith and thelower portion of the celestial sphereat the nadir.

A great circle (with full diameter ofthe celestial sphere) passing throughthe zenith and the nadir.

5. Meridian plane A plane passing through the celestialpoles.

6. Meridian One of the intersections of a meridianplane with the celestial sphere.(Degrees of longitude are measuredeast and west of Greenwich.)

7. Hour circle A great circle passing through thenorth and south celestial poles.

8. Horizon The intersection of the celestialsphere with a plane that passes throughthe center of the earth, perpendicularto a vertical line.

9. Azimuth (of a heavenly The angular distance measured alongbody) the horizon from the south point of

the meridian to the vertical circlethrough the heavenly body. The azimuthis positive when measured clockwise.

104



10. Altitude (of a heavenly The angular distance measured upwardbody) from the horizon along a vertical

circle. The co-altitude or zenithdistance is equal to 90° miLus thealtitude.

11. Latitude

12. Declination

The angular distance measured alongthe meridian from the equator towardthe zenith of a given point. Latitudesnorth of the equator are consideredpositive. Those south of the equatorare negative. The symbol for latituueis the Greek letter phi (cP) .

The angular distance measured from theequator to a body along the hour circlethrough the body. If the body is northof the equator, the declination ispositive. If it is south, the decli-nation is negative. The symbol fordeclination is the Greek small letterdelta CS).

13. Transit The transit of a heavenly body is itspath over the observer's meridian.

14. Refraction The angular increase in apparentaltitude due to the refraction oflight. Refraction correction is alwaysnegative and is a maximum when thealtitude is small.

15. Correction for parallax A small angular increase in the apparentaltitude of a heavenly body to allowfor the fact that the observations aremade at the surface of the earth in-stead of at its center.

16. Ephemeris The annual report of the behavior ofthe sun and the more important starsused in field astronomy.

Pass out copies of the ephemeris anddiscuss some items found in the booklet:

1. Information about the parts ofsurveying instruments

2. Use of the instruments

105

HIGHWAY SURVEYING

CONTENT OUTLINE

a. Source or ephemeris

(1) Publications

b. Cost

c. Time

(1) True solar time

Principles of Field Astronomy


3. Miscellaneous data

4. Trigonometric functions

5. Concept of celestial observations

6. Daily calendar for the currentyear, listing the sun's apparentdeclination for each day with thedifference in declination for onehour

7. The question of time for each day

8. Tables of refraction and parallax

9. Tables for the sun's semidiameter

Advise the class that several companieswhich make survey equipment publish anephemeris. These are generally givenas an advertisement.

Mention that the official ephemerispublished by the U.S. Department ofthe Interior sells for about 30 cents.

Inform the class that there are twokinds of time involved in solar ob-servations. (Ref. A, pp. 521-527;Ref. B, pp. 380-383)

Describe a true solar day (apparentsolar day) as the interval of time be-tween two successive lower transitsof the sun's center over a givenmeridian.

Point out that successive lower transitsvary day to day. There are two reasonsfor this -- 1. The plane of the earth'sorbit is oblique. 2. The earth'sangular velocity about the sun in itselliptical orbit varies. If we kep,:

time in accordance with this, it wouldbe very confusing.

106



(2) Mean solar time Stress that mean solar time overcomesthe erratic pattern of true or apparent .

solar time. This is true because itis the interval of time between twosuccessive lower transits of the meansun over the same meridian.

Tell the class that mean solar time isbased on a fictitious sun which travelsat a uniform rate along the equator.Sometimes it leads the true or apparentsun, sometimes it lags.

State that mean solar time at any in-stant for a given meridian is the hourangle of the mean sun, referred to thesame meridian, plus 12 hours. At mid-night the hour angle of the mean sunis 12 hours. At mean solar noon thehour angle of the mean sun is zero hour.

(3) Equation of time Describe the equation of time as thedifference between apparent solar timeand mean solar time. Its value foreach day of the year is listed in theephemeris. (Ref. A, p. 523)

(4) Standard time Emphasize that standard time is themean standard time referred to inmeridians, 15° apart. This is measuredfrom Greenwich, which is at zero de-grees longitude. (Ref. A, p. 527;Ref.. B, p. 381)

Show that the meridians are 1 hourapart in time. Eastern standard timeis the time of the 75th meridian westof Greenwich.

Point out that the standard time re-ferred to the Greenwich meridian iscalled Greenwich civil time (GCT), oruniversal time.

(5) Local time Define local time as that based on theobserver's meridian. (Ref. B, p. 382)

Show that local civil time (LCT) isbased on mean solar time. It is thehour angle of the mean sun measured fromthe local meridian, plus 12 hours.

107



Remind the class that local apparenttime (LAT) is based on the true (ap-parent) sun and is the hour angle ofthis sun plus 12 hours.

Point out that when the sun's actualcenter is on the observer's meridian,it is local apparent noon.

Give some examples in time. At a cer-tain instant the time is 10:42 a.m.,Pacific standard time, and the placeis at longitude 121°33'20" wherestandard time is based on the 120thmeridian. (Ref. A, pp. 525-527):

1. Local civil time is earlier byan amount equal to 1°33'20" or6m 13.3s. (m = minutes of time,and s = seconds of time.)

2. Conversions from degrees, minutes,and seconds to hours, minutes, andseconds is based on:

360° = 24h1° = 4m

1' = 4s1" = 0.067s

3. Local civil time at longitude)21°33'20" is 10:35:46.7 a.m.

Give other examples of time analysis.

II, Solar Observation Explain that the purpose of solar ob-servation is to obtain informationabout the position of the sun inaltitude and azimut., (referred to aline on earth). This data is requiredso the true azimuth of the line onearth may be determined.

A. Observations on the sun Mention that the altitude of the sunis measured on the vertical circle ofthe transit and that the azimuth ismeasured on the horizontal circle.(Ref. A, pp. 530-546; Ref. B, pp. 383-389)

1. Difficulties Note the difficulty in setting thecrosshairs directly on the center of

108



2. Standard practice

the sun (unless a special reticule isavailable). The crosshairs are madetangent to the edges of the sun, withthe necessary correction added or sub-tracted to achieve a reading to thecenter of the sun.

State that in the morning hours thesun is rising, so the lower edge orlimb is observed for altitude. Duringthe afternoon hours the altitude ofthe sun is decreasing, so the upperlimb is observed. Throughout the daythe sun is moving from east to westand the east limb is observed forazimuth.

Stress that all three observations aremade on the trailing limb.

B. Procedure Describe the procedure for observingthe sun:

1. Set Itp and leve l the transit andpoint the telescope in the hori-zontal direction of the sun.(Ref. A, p. 532; Ref. B, pp. 385-389)

2. Center the telescope bubble andcheck the vertical circle forany index error.

3. Raise the telescope and point itat the sun without actually lookingthrough the telescope. (Eyes maybe damaged unless the telescopeis equipped with a prismatic eye-piece or special solar attachments.)

4. Hold a white card about 3 or 4in. behind the eyepiece and movethe telescope in altitude andazimuth until a circular shadowis cast on the card.

5. Focus the crosshairs until theyare visible on the card. Thenfocus the telescope to make theimage of the sun clear and sharpon the card.

109

HIGHWAY SURVEYING

CONTENT OUTLINE

I. Error caution



Remind the class that the image of anerecting telescope will be upside downon the card. The lower edge of thesun's image is actually the upper limbof the sun. The left edge of the sun'simage is the eastern limb of theactual sun.

C. Tangency of the crosshairs Make some sketches for the morning andafternoon sun and show how the cros-hairs are brought tangent to the properlimbs of the sun. (Ref. B, p. 388)

1. Diameter in minutes

2. Correction

D. Multiple readings needed

Mention that the diameter of the sunis 32' and its semidiameter (about)16') is listed for different times ofthe year in the ephemeris.

Point out that the vertical angle iscorrected for index error, parallax,and refraction before the semidiameteris ,added (morning) or subtracted(afternoon).

Note the condition when the verticalcrosshair is placed tangent to theeastern limb. The horizontal circlereads too small by an amount equal tothe semidiameter times the secant ofh, the altitude or vertical angle.

Give some examples, using definitedays so that exact corrections may befound in the ephemeris.

Explain that several observationsshould be taken in rapid succession toobtain multiple readings. The valuesof the vertical and horizontal anglesand the time of each shot are recorded.(Ref. B, p. 388)

Stress the fact that the watch timeshould be noted to the nearest secondwhether the watch is correct or not.

Show that the horizontal and verticalangles are plotted on left and rightcoordinates in a graph, against thetime on the abscissa. A mean vilue istaken from this graph.

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HIGHWAY SURVEYING

CONTENT OUTLINE

III. Latitude and Longitude



Emphasize that both the latitude andlongitude can be scaled quite accuratelyfrom a large scale topographical map.The latitude can be computed from de-termining the difference in time be-tween the unknown point and some pointof known longitude. (Use, for example,radio time signals from the NavalObservatory at Washington, D.C.)(Ref. A, pp. 537-539; Ref. B. p. 395)

Determination of Standard Time Caution the class that although theprime purpose of astronomical obser-vations is the determination of thetrue azimuth of a line, it may benecessary to know the standard timewithin one or two seconds. (Ref. A,pp. 542-545)

A. By transit of the sun

B. By altitude of the sun

1. Watch error

2. Hour angle

a. Formula

State that the exact time may be de-termined by noting the instant thesun's center passes the meridian.(Ref. A, p. 542; Ref, B, p. 390)

Add that the time may also be deter-mined from the altitude of the sun atany instant. (Ref. B, p. 391)

Point out that this determination oftime will measure the amount of errorin watch time.

Remind the class that the center ofthe sun cannot be located. Thereforea reading is made on the lower limb inthe morning, and upper limb in theafternoon. The observed angle iscorrected for index error, refraction,parallax, and semidiameter of the sun.

State that the following formula isused for determining the hour angle,which can be converted:

cos t =sin h - sin (I) sin 6

cos 61) cos 6

b. Terms Give the meaning of each letter:

1. The hour angle is t.

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HIGHWAY SURVEYING

CONTENT OUTLINE

c. Cautions

d. Class problem

Principles of Field Astronomy'


2. The latitude is (P.

3. The declination obtained from theephemeris is 6.

4. The corrected altitude is h.

5. The polar distance, or 90° -is p.

Note that the approximate time must beknown so the declination may be ob-tained from the ephemeris. If thetime used or estimated varies too farfrom the correct time, the operationmust be done again.

Ad'Ase the class that the best resultsale obtained when the observed altitudeis about 20° and the time is one hourbefore noon or one hour after noon.

Work out a problem on the chalkboardand have the students find the requiredinformation from their copies of theephemeris. Use logarithms unless adesk computer is available.

V. Solar Observations for Azimuth Indicate that the azimuth of a line maybe determined whenever the time isknown to within one or two minutes.This is done by measuring the horizontalangle from the line to the sun's centerand then measuring the altitude of thesun's center. (Ref. A, pp. 539-542;Ref. B, pp. 401-409)

A. Mean values Impress upon the class that eightmeasurements are taken, four with thetelescope direct and four with it re-versed, all in quick succession. Thiswill give results reliable to 15",using a 30" transit.

B. Procedure for solar Describe the procedure for makingobservations solar observations for azimuth:

1. Set up and level the transit overpoint A. Level the telescope, andrecord any index error on the

112



vertical. circle. Set horizontalcircle to read 0°00'00", and takea backsight on point B. (Draw asketch on the chalkboard, showingthe pattern of this procedure.)

C. Formula for azimuth

2. Loosen upper clamp and point thetelescope at the sun, obtainingan image on a white card.

3. Take four observations in thismanner, recording the horizontalangle, the vertical angle, andthe time at the instant oftangency.

4. Reverse the telescope and repeatthe procedure described above.

5. Loosen upper clamp and backsightto transit point B, checking outwith 180°00'00" on the horizontalcircle.

6. Correct the horizontal and verticalangles and plot against time formean values.

7. Reject any readings which areobviously wrong.

Tell the class that there are severalformulas. The following formula willbe used in this class to determine theazimuth of the sun:

tan 11Z =/sin (s4) sin (s-h)

cos s cos (s-p)

Give the meaning of each letter:

1. The azimuth of the sun, measuredfrom the north, is Z.

2. The latitude is (I).

3. The corrected altitude is h.

4. The declination taken fromephemeris is S.

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HIGHWAY SURVEYING

CONTENT OUTLINE

D. Observations

E. Problem



5. The quantity 1/2 (q) + h + p) is s.

6. The polar distance, or 90° - 6,is p.

Note that the best results are obtainedwhen the observations aral made between8:00 a.m. and 10:00 a.m. or between2:00 p.m. and 4:00 p.m.

Stress that the solution of the equationfurnishes Z, the azimuth of the sunfrom true north.

Show by sketch how the true azimuthof the line AB is found.

Distribute a completely worked-outproblem on any standard working form.Follow through the steps of the problemwith the students. (Ref. A, p. 540;Ref. B, p. 406)

QUESTIONS FOR REVIEW1. What are the celestial poles?

2. What point is exactly opposite the zenith?

3. Describe the azimuth of a heavenly body (star or sun).

4. Explain what declination is.

5. Why does refraction affect a transit reading?

6. Why does the phenomenon of parallax require a correction?

7. Describe a true solar day.

8. What is the equation of time?

9. What is the difference between standard time and local time?

10. Why is the lower edge of the sun's image actually the upper limb ofthe sun when using the transit in a solar observation?

11. How is the time determined from the altitude of the sun at anyinstant?

12. If the horizontal angle from a base line to the center of the sun ismeasured, and if the altitude of the center of the sun is known, whatcan be computed at a given time?

114



2. Solve problems 2-4, 6, 9, 15, and 17 on pages 567 and 568 of Ref. A.


115

Lesson 12

HORIZONTAL CURVATUREOBJECTIVES

1. To familiarize the student with the geometry of horizontal curvatureand its use in highway alignment

2. To describe the compound curve, the reverse curve, and the spiralcurve


I. Horizontal Alignment Define horizontal alignment as a linewhich consists of straight linesconnected by curves. (Ref. A, pp.714-715; Ref. B, pp. 269-270)

A. Change of direction

B. Tangents

C. Point of tangency

D. Curves

Point out that if a highway wereconstructed from terminal A to ter-minal B, it is improbable that thesepoints could be connected with astraight line.

Tell the students that because of manyconditions (deep swamps, mountains,bodies of water, housing developments),it becomes necessary to changedirection for highway design.

Indicate that sections of straightlines are tangent to the change ofdirection or curves.

Note that at a designated point on thetangent an abrupt change occurs frommoving in a straight line to moving ina circle.

State tl,at there are many ways toachieve a change in direction from thetangent. The most widely used methodinvolves the use of a simple circularcurve.

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HIGHWAY SURVEYING Horizontal Curvature


II. Nomenclature

Draw a sketch on the chalkboard,showing. two tangents connected witha simple curve. Use colored chalkon all sketches.

Advise the class that in introducingthe simple curve many new expressionswill be used but no new geometry willbe encountered.

Emphasize that the stationing of aroute progresses around a curve in thesame manner that it does on the tan-gents. As shown on all plans, thestationing will increase from left toright.

A. Point of curvature Make an appropriate sketch on thechalkboard, mark the point where thecircular curve begins and call it thepoint of curvature, or P.C.

B. Point of tangency Call the point where the curve endsthe point of tangency, or P.T.

C. Point of intersection

D. Tangent distance

E. Center of curvature

F. Radius

G. Length of curve

Identify the point of intersection(P.I,) of the two tangents as thevertex of the tangents.

Point out that the distance along thetangent from P.C. to P.I. is the tan-gent distance, T. This is equal tothe distance along the tangent fromP.I. to P.T.

Draw radii perpendicular to the tan-gents at P.C. and P.T. which will inter-sect at point 0 (the center ofcurvature),

Mark the radii of the curve, R. Theseare at right angles to the tangents atthe ends of the curve.

Show the distance along the curve asL (the length of curve). This ismeasured along the curve from P.C. toP.T.

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HIGHWAY SURVEYING

CONTENT OUTLINE

H. Long chord

I. External distance

J. Middle ordinate

K. Deflection angle

III. Degree of Curve

A. Sharpness of curve

B. Radius of 10 curve

Horizontal Curvature


Draw a straight line from P.C. to P.T.Call this the long chord, C.

Connect the vertex (P.I.) to the radiiat 0 (the center of curvature).

Call the distance from P.I. to thecurve, measured along this radial line,the external distance, or E.

Call the distance from the long chord,C, to the middle of the curve, measuredalong this same radial line, themiddle ordinate, or M.

Name the deflection angle between thetangents, the intersection angle, A(delta). This is equal to the anglebetween the radii at the point ofcurvature, O.

Describe the degree of curve as theangle at the center subtended by anarc 100 ft. long. This is called D.(Ref. A, p. 715; Ref. B, p. 271)

Explain that sharpness can be expressedeither by the degree of curvature orby the length of radius--the sharperthe curve, the shorter the radius.

Compute the length of radius of a 10curve. See Figure 1.

118

Figure 1RADIUS OF A 1° CURVE



Repeat that by definition the angleat the center is 10 when the subtendedarc is 100 ft. By proportion:

10100' 100

3677 2ffR Circumference

Solving for R:

(100') (360°)R 5729.58'

1° (2Tr)

State that 5730 ft. is used as thelength of radius for a 1° curve.

C. Relationship between thedeflection angle and thedegree of curvature

Inform the class that the tangent dis-tance indicates the relationship be-tween A and D. Use Figure 2 to showthis relationship and leave the figureon the chalkboard for future referencein derivations. (Ref. A, pp. 716-718)

0

Figure 2DERIVATION OF ELEMENTS OF THE SIMPLE CURVE

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HIGHWAY SURVEYING

CONTENT OUTLINE

1. Derivation

2. Relationship of A, D,and T



Derive the equation for the tangentdistance:

T= R tan -IL

2

Sketch Figure 3 on the chalkboard andshow the relationship between the de-flection angle, the degree of curvature,and the tangent distance.

Figure 3RELATIONSHIP OF A, D, AND T

3. Computations for T Compute the tangent distance for 1°and 3° curves, using a deflectionangle of 53°.

Solution forR = 5730'

D = 1°,

A 53T = R tan -2.= 5730 x tan -2--

= 5730 x 0.5 = 2865'

A = 53, =Solution for

R = 1910'D 3°,

AT = R tan .2- = 1910 x 0.5 = 955'

120



4. Computations for L

IV. Formulas

Indicate that when D = 1°, 1° of thecentral angle subtends an arc of 100ft. Therefore, 53° of the centralangle will subtend an arc of 5300 ft.,which equals L.

Add that when D = 3°, 3° of the centralangle will subtend an arc of 100 ft.,so 53° of central angle will subtendan arc of

53 x 100 = 1767' = L3

Point out that in this formula

100AL = or by geometry:

53° L= and L = 5300'

Note that the delta angle is alwaysconverted into decimals of a degree,from minutes and seconds.

Derive the equation for the externaldistance from triangle AOV inFigure 2:

cosA

R E'R + E

A2 +cos

E =A R.

cos 7

Derive the equation for the middleordinate distance. From triangle AOF:

OF = R cosA*

'

OF + FD = R;2

FD = R - OF = R R cos 2 = M.

Derive the equation for the long chord:

A AFSin = AF = 11 AB

121

AB is the long chord.



AAF = R sin .2-

A. Problem

A2AF = 2R sin = C

2

Explain that the usual informationthat is available is the location ofthe tangents and the deflection angleof the tangents. These are constant,but the degree of curve to be used isvariable and will depend on standards.

State that the most common error madein computing curve data is in thestationing of the curve; the stationingto the P.I. is known (distance alongthe tangent). Show that the stationingmust backtrack from the P.I. to theP.C., and then proceed around thecurve.

Set up a problem on the chalkboard andfind the stations of the P.C. and P.T.,the external distance, the middleordinate, and the long chord. Given:At station 30 + 00 of a centerline, itis decided to change direction by53°, using a 3° curve.

Make a sketch and show each element asit is computed:

A = 53°; D =

T = R tanA

=2

573030; R =

=

1910'

955'

=

(1910)(0.5)

100A (100)L = 1767'

D 3

P.I. is at station 30+00Tangent distance - 9+55

P.C. 20+45

L +17+67P.T. 38+1f

122

M = R - R cosA

= 1910 - 1910 x 0.8952

M = 1910 - 1710 = 200'



E R =1910

R =.895cos .2A-

V. Field Layout

A. Procedure

2135 - 1910 = 225'

C = 2R sinA

2 x 1910 x 0.446 = 1710'

State that when the curve data iscomplete, the curve must be locatedin the field.

Point out that the most conv(ientmethod of locating points on a cir-cular curve is by means of deflectionangles from the tangent.

Describe the procedure for locatingpoints on a circular curve in thefield:

1. Set up and level the transit atthe P.I.

2. Use the transit to sight alongthe tangents, measuring the tan-gent distance off on both theback tangent and the forward tan-gent. (Ref. A, pp. 718-721;pp. 274-276)

3. Bisect the interior angle at theP.I. and set in the midpoint ofthe curve. This is done bymeasuring off the external dis-tance from the P.I. to the curvealong the bisector of the interiorangle.

4. Move the transit to the P.C. ofthe curve. Locate the points onthe curve by turning off the com-puted deflection angles from thetangent.

B. Computation of deflection Refer to Figure 2 and set the deltaangles angle equal to 30° for computation of

deflection angles. (Ref. B, pp. 273-274)

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HIGHWAY SURVEYING

CONTENT OUTLINE

1. Pf,rivation

2. Concept

3. The P.C.



Consider the triangle ABV, formed bythe long chord from P.C. to P.T., thetangent from P.C. to P.I. and the tan-gent from P.I. to P.T.

Establish that if the delta angle is30°, the angle at V, the interior anglebetween the tangents, must be 150°.

Add that if the angle at V is 150°,the angles at A and at B must equal30°. Since the angle at A equals theangle at B, they must each be 15°.

Assume that the transit is set up atpoint 0, the center of curvature. Thetotal deflection from P.C. to P.T.would be 30°.

Reiterate that when the transit is atthe P.C., the total deflection to P.T.is 15°, that is, angle A.

Conclude that any deflection with thetransit at P.C. is one-half of whatthe deflection would be to the samepoint if the transit were at point 0.

Assume that the transit is at point 0,sighted at the P.C., and an angle equalto D is turned. An arc of 100 ft.would be subtended along the curve.If the transit is at the P.C., an angleof only 1/21) would be turned to subtend

an arc of 100 ft.

Stipulate that to establish pointsevery 100 ft. on the curve, the transitis set up at the P.C. and deflectionsof 1/2D are turned. The first deflectionof zD is for the first 100 ft.., then

plus ZD is added for the second100 ft., etc. For each succeeding100 ft. add zD to the previous angle.

State that in most cases the P.C. willnot be at a full station. If thiscondition exists it may be necessaryto compute the deflection to the firsteven station instead of a full 100 ft.

124



Outline a direct proportion method ofcomputation: e.g., if the P.C. is atstation 12 + 60, the first deflectionis made to station 13 + 00, or for adistance of 40 ft. Use 40/100 of thefull deflection, which is %D.

C. Computing deflection

Offer another method--the computationof the odd deflection in minutes. Usethe formula 0.3 cD, where c is the sub-chord, or 40 ft., and D is the degreeof curvature.

Note that in most cases the curve isstaked out in 50-ft. intervals. Forthis interval the deflection is 1/41).

Proceed to show the class a typicalproblem. Set up the deflections fora 400-ft. curve when delta is 8°, Dis 2°, the P.C. is at station 44, andthe P.T. is at station 48:

1. Set the transit at the P.C., andsight at the P.I.

2. The first deflection is to station45 and is equal to D/2 or 1°.

3. The second deflection is tostation 46 and is equal to D/2plus D/2 or 2°.

4. The third deflection is to station47 and is equal to D/2 plus D/2plus D/2 or 3°.

5. The fourth deflection is tostation 48, the P.T., and is equalto D/2 plus D/2 plus D/2 plus D/2or 4°.

Show that the last deflection tostation 48, the P.T., is 11 of thedelta angle, or 8/2 or 4°. This stepis a check on the work.

Give the class another exercise. Tellthem to find the deflections to stakeout the curve every 50 ft. Given:

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HIGHWAY SURVEYING

CONTENT OUTLINE



A = 54°20'; D = 7°40'

L = 708.70

P.C. is at station 121 + 56.35

P.T. is at station 128 + 65.05

Sub-chords--122 + 00.00 - 121 +56.33 = 43.65

0.3 c D (0.3)(43.65)(7.67) =100.4' = 1°40.4'

128 + 65.05 - 128 + 50.00 = 15.05"

0.3 c D = (0.3)(15.05)(7.67) =34.6'

D/2 = 3°50' and D/4 = 1°55'

P.C. station 121 + 56.35122 + 00.00 = 1°40.4'122 + 50.00 = 3°35.4'123 + 00.00 = 5°30.4'123 + 50.00 = 7°25.4'124 + 00.00 = 9°20.4'124 + 50.00 = 11°15.4'125 + 00.00 = 13°10.4'125 + 50.00 = 15°05.4'126 + 00.00 = 17°00.4'126 + 50.00 = 18°55.4'127 + 00.00 = 20°50.4'127 + 50.00 = 22°45.4'128 + 00.00 = 24°40.4'128 + 50.00 = 26°35.4'128 + 65.05 = 27°10'

Check deflection to P.T. at station128 + 65.05 or (0.3)(708.70)(7.67) =1630' = 27°10'

orA

=54°20'7

227°10'

D. Transit setups on the curve State that because of obstacles it isoften impractical or impossible to runall of a given curve with the transitat the P.C. (Ref. A, p. 721; Ref. B,p. 277)

126



Explain the procedure for running acurve when all of the curve cannot bestaked from the P.C.:

VI. Compound Curve

1. Compute the deflections as foruse at the P.C.

2. Set up at any point on the curve.Backsight (with the telescope in-verted) at the last transitstation with the vernier readingthe deflection for the pointsighted (as computed under 1above).

3. To locate other points, plungethe telescope. Use the deflectionangles for the next point aspreviously computed for use atthe P.C.

Note that when the point used as abacksight is the P.C., the backsightvernier reading is zero.

Define the compound curve as a curveformed by two simple curves that haveone common tangent and a common pointof tangency. Both curves lie on thesame side of the common tangent.(Ref. B, p. 289)

A. Point of compound curvature Add that the point of common tangency(where the two curves join) is calledthe P.C.C., or the point of compoundcurvature.

Tell the class that the compound curveis not the best way to change direction.It is used whenever the topographymakes it impossible to use a simplecurve. It is also used whenever adesign must be revised.

Mention that the compound curve issometimes used to correct a conditionwhere two simple curves are connectedby a short tangent. This is known asa broken back curve.

127



VII. Reverse Curve Define the reverse curve as a curveformed by two simple curves that havea common tangent and a common pointof tangency. Both curves lie on op-posite sides of the common tangent.(Ref. B, p. 290)

VIII. Spiral Curve

A. Uses of the spiral

Draw a sketch showing a typical reversecurve.

Emphasize that the reverse curve isundesirable in design although someuses do exist. The reverse curve isused for the connecting two paralleltangents and in some highway crossovers.

Point out that a very popular use ofthis type of curvature is made by therailroads in slow-moving spurs. How-ever, a short tangent is usuallyplaced between the curves.

Define the spiral curve as a cubicparabola used to provide a transition(horizontally) from the tangent to thecircular portion of a curve.

Tell the class that the use of thespiral curve is questionable on themodern highway. With the advent ofthe 11- and 12-ft. lane, the demandfor the spiral has dwindled. (Ref. A,pp. 724-726; Ref. B, pp. 291-292)

Note that in the ordinary curve thechange of direction is made abruptlyat the P.C. On a highway curve avehicle is traveling on a tangent andat the P.C. it is traveling on a curve.

Point out that this type of curve isused extensively in foreign countrieswhere economy dictates the width ofthe travel lane. The clothoid, orEuZer's spiral, is used instead of thecubic parabola. These curves are moredifficult to use and lay out in thefield, but they are more mathematicallyexact.

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HIGHWAY SURVEYING

CONTENT OUTLINE

B. The spiral illustrated



Draw a sketch of Figure 4 showing thecubic parabola. Explain that theradius of this curve is infinity.

Figure 4ELEMENTS OF THE SPIRAL CURVE

Show on an X-Y graph the most importantelements of the curve:

1. The degree of curvature of thespiral varies. The limits arefrom zero at the beginning (thetangent to the spiral) io themaximum of the circular curvewith which it is used.

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HIGHWAY SURVEYING

CONTENT OUTLINE



2. The offset y varies as the cubeof the length of spiral.

Draw a sketch of the spiral showingonly the major elements. Point outthat the spiral is rather complicatedand that only the rudiments will becovered.

Describe the parts of the curve usingsubscript s for the spiral and sub-script c for the circular curve.

Briefly note some of the relationshipsamong the parts.

C. Reasons for the use of the Explain the effect on steering. Thespiral impact of centrifugal force cannot be

absorbed instantly at the change ofdirection in the ordinary curve.

Point out that the vehicle attempts tomake its own path around the curve.At moderate speeds, mcst vehicles makethe transition within the confines ofthe normal lane width. At high speedsand on sharp curves, the transition ismade by hazardous banking or by goinginto the adjoining lane.

D. Advantages of the spiral Advise the class that the spiral pro-vides a natural, easy path to followbecause the centrifugal force isgradually increased or decreased. Thespiral:

1. Minimizes encroachment onadjacent lanes

2. Provides increased safety

Add as much information as time permitson the geometrical analysis of thespiral. Mention that there are 23items to be computed in the curve data.

QUESTIONS FOR REVIEW1. What is the easiest way to achieve a change in direction from a

tangent?

130


2. Identify the following notations used in horizontal curvature:

(a) P.I.

(e) P.T.

(b) P.C.

(f) R

(c) L

(g) E

(d) T

(h) M

3. Describe the degree of curve.

4. What is the radius of a 10 curve?

5. In stationing a curve why is it necessary to backtrack from the P.I.to the P.C. and then proceed arourd the curve to the P.T.?

6. What is the most convenient method of locating points on a curve?

7. Explain what is done when an obstacle prevents the location of anymore points from the P.C.

8. Define a compound curve.

9. Define a reverse curve.

10. What is the main reason for using a spiral curve?


2. Study pages 228-231 in Chapter 10 of Ref. A.

131

Lesson 13

VERTICAL CURVATUREOBJECTIVES

]. To instruct the student about the geometry of the vertical curve2. To instruct the student in the uses and computations of various

types of vertical curve


I. The Vertical Curve State that the vertical curve is anarc of a parabola. It is used becauseof

A. Classification

1. The gradual change in its direction

2. The ease in computing elevationsalong it

Compare the v-..rtical curve with thehorizontal curve for effecting agradual change between tangents. (Ref.

B, pp. 280-281)

Show by sketch how a vertical curverounds off the intersection of twograde tangents. This curve acts as atransition from one grade tangent toanother.

Tell the class that there are twoclassifications of vertical curve:the sag vertical and the crest vertical.

1. The sag vertical Sketch and explain the sag verticalwith these conditions:

1. A descending grade is followed byan ascending grade

2. A descending grade is followed bya flatter descending grade

132

HIGHWAY SURVEYING

CONTENT OUTLINE

2. The crest vertical

B. Controls

II. The Geometry of the Curve

A. Sketch

B. Nomenclature

1. Point of vertical inter-section

2. Point of vertical curva-ture

3. Point of vertical tan-gency

Vertical Curvature


3. An ascending grade is followed bya sharper ascending grade

Define the first grade line (on theleft in the sketch) as G1 and thesecond (on the right) as G2.

Emphasize that a downgrade is alwaysnegative and an upgrade is alwayspositive.

Explain and sketch the crest verticalwith these conditions:

1. An ascending grade 1.s followed bya descending grade

2. An ascending grade is followed bya flatter ascending grade

3. A descending grade is followed bya sharper descending grade

Mention that the design of verticalcurves is controlled by considerationsfor comfort and safety.

Indicate that the curvature adopted isthe parabola whose equation is y =axe + bx + c. (Ref. A, p. 229; Ref.B, pp. 281-284)

Draw Figure 5 on the chalkboard andidentify the various elements as theyare discussed.

Note that there is simplicity in usingthe parabola for curvature.

The point of vertical intersection ofthe grade tangents is the P.V.I.

The point where the vertical curvebegins is called the point of verticalcurvature or the P.V.C.

The point of vertical tangency is atthe end of the curve and is denotedas the P.V.T.

133

HIGHWAY SURVEYING Vertical Curvature

CONTENT OUTLINE TEACHING POINTS AND TECHNIQUES.

L *-1

Figure 5THE PARABOLA USED AS A VERTICAL CURVE

4. Symmetry

5. Center correction

6. Length of curve

Point d is halfway from c to t. Ifpoints c and t are at differentelevations, then point d is at themean of these elevations.

Point e is halfway from point a to d.

The distance from point a to e is thecenter correction, H, which is

Gl - G2 LH -

8 100

1. G1 - G2 is the algebraic differencein percent between the two grades.It is always expressed as apositive number and, later, willbe called A.

2. L is the length of the verticalcurve in feat.

L is the horizontal distance fromP.V.C. to the P.V.T., measured alongthe chord, and actually representsthe parabolic curve.

7. Vertical tangent offset The y distance is the vertical_distance-m-a-p6int-or the grade tangent to

a point on the curve.

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HIGHWAY SURVEYING

CONTENT OUTLINE

8. Horizontal distance

Vertical Curvature


The x distance is the horizontal dis-tance from one end of the verticalcurve to any point on the curve.

C. Computations for elevations Describe how the elevation of point Pon the curve is found. The elevationof a point vertically above or belowpoint P on the tangclt must first becomputed.

1. Point correction

III. Problems

A. Ordinary crest vertical

State that a correction is made whichis either subtracted or added to theelevation of the point on the tangent.Use the following formula for thecorrection to be applied to the tangentelevation for any point:

x 2Hy =

Advise the class that the best way tobecome familiar with the variationsof the vertical curve is to work outproblems.

Outline the following-problem and solveit in two ways: Given a vertical curveof 400 ft., the P.V.I. at station25 + 00 on the curve, at elevation98.25, with a +4% grade and a -2.6%grade. Find the elevation of stations24 + 25 and 25 + 00 on the curve.

1. Sketch Draw Figure 6 to depict the problem.

Compute the stations and elevationsof the P.V.C. and the P.V.T.

Find the center correction which willgive the elevation on the curve atstation 25 + 00. This correction is

GI - G2H

8x

4 - (-2.6) 4008

x100

3.30,

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HIGHWAY SURVEYING

CONTENT OUTLINE

P. V.C23 +00

Vertical Curvature


P.V.I.STATION 25+00

EL. 98.25

E L. 95.25STATION 24+25 EL. 94.95

P. V.T.27+00

2. Alternate method

Figure 6CREST VERTICAL

To get the elevation on the curve atstation 25 + 00:

98.25 - 3.30 = 94.95

Now find the correction to be subtractedfrom the tangent elevation at station24 + 25:

x2H (125)2

(3.30)

Y TIT p0012CT! L 2 J

= 1.29'

Then 95.25 - 1.29 = 93.96

which is the elevation on the curve atstation 24 + 25.

Draw Figureof analysis.

Compute theand the P.V.first gradeon the same

7 to show another method(Ref. B, pp. 284-285)

elevations of the P.V.C.T., and then extend thetangent, L/2 or 200 ft.,grade, which is 4%.

State that station 27 + 00 will be13.20 ft. higher than the elevation atstation 27 + 00, at the P.V.T.

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HIGHWAY SURVEYING

CONTENT OUTLINE

PV.C.

P V.1

STATION 25

Vertical Curvature


20°

010

0EL.98.25

I I I I I lit2

I I

0 iI

STATION 23

P.V.T.I I

STATION 27EL. 93.05

Figure 7ALTERNATE ANALYSIS OF THE CREST VERTICAL

Call the center point the half-pointof the vertical curve. From the lawsof the parabola, (1/2)2 x 13.2 is equal

to 3.30 (center correction).

Divide the total curve into 25-ft.segments (400/25, or 16 sections).Then station 24 + 25 is 5/16 of thetotal from station 23 + 00.

Point out that (5/16)2 x 13.2 is 1.29or that station 24 + 25 is 5/8 of thehalf curve. Then station 24 + 25 is(5/8)2 x 3.30, which is 1.29.

B. Problem on the sag vertical Recall to the students the appearanceof the sag vertical and outline thefollowing problem: Given a 600-ft.vertical curve on a +2% grade and a+5% grade. The P.V.I. is at station7 + 00 at elevation 42.50. Find theelevation at station 7 + 75 on thecurve.

1. Sketch Draw Figure 8 to depict the problem.

Compute the station and elevation atthe P.V.C. and P.V.T.

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HIGHWAY SURVEYING


Vertical Curvature

P.V.C.4 +00EL. 36.50

...-

EL.27. 50

4. 2. To "*"..

2. Alternate method

P.V.I.STATION 7+00EL. 42.50

Figure 8SAG VERTICAL

P. V. T.

10 +00EL. 57.50

Compute the center correction:

HGI - G2 L

8 x 100

+2 - (+5) 6008 100

2.25'

Compute the differential in elevationfrom the tangent to the carve atstation 7 + 75:

x2H (225)2(2.25)1.26'

Y (300)2L 2LLTJ

Find the elevation at station 7 + 75;this is 46.25.

Note that the elevation on the curveat station 7 + 75 is 46.25 plus 1.26,or 47.51.

Use an alternate method, either byextending the forward tangent backward,or extending the back tangent forward.

Divide the length into 24 parts.

138



Observe that the forward tangent,extended backward 300 ft. ends at anelevation 9 ft. lower than the P.V.C.For the correction required at station7 + 75, take (9/24)2 (parts from oneend) of 9 ft., or 1.26'.

Advise the class that (9/12)2 of thecenter correction (using half of thecurve) is also 1.26.

C. Problem set up in tables Mention that there are times when itis expedient to use a tabular form fora problem. Here is an example: Givena 1,000 foot vertical curve with a-5% grade meeting a +7% grade at station22 + 00, at elevation 432.00. Findthe elevation at each station on thecurve.

1. Sketch Draw a simple sketch of the problem.

Compute the center correction:

GI - G2 L AL8 x 100 800

(12) (1000)

80015.00

Compute the correction for station18 + 00 to use as a , :heck:

x2H (100)(15)0.6'

Y (500) 2

Lay out a table of four columns:stations, elevations on tangents,differential corrections, and ele-vations on the curve.

Fill in the first column by insertingthe stations and then computing thetangent elevations of those stations.

Make use of the parabolic law insteadof the formula, and compute thecorrections for each station, e.g.,station 18 + 00.

139



IV. Special Problems Emphasize that in many instancesvariations of the simple vertical curveare employed to solve special problems.

A. Low point Explain that it is very important tofind the low point of a sag verticalcurve. This applies especially fordrainage work or whenever a bridge isbuilt on a sag vertical. (Ref. A, p.231; Ref. B, pp. 286-287)

1, Sketch Draw Figure 9 to show a low pointproblem.

P.V.C.90+00EL.418.00

2. Problems

6\0

0

x 6-1

P. V.I.94+00

EL.400.00

Figure 9SAG VERTICAL(Low Point)

P V.T.98+00

EL.424.00

Outline the following problem: Givenan 800 ft. vertical curve with theP.V.I. at station 94 + 00 at elevation400.00. Grades are at -4.5% and +6.0%.Find the station and the elevation ofthe low point of this vertical curve.Use the following formula:

Grade of flatter gradient (L)x =

A

Note that this gives the station ofthe low point. If the length of curveis given in stations, the answer willbe in stations:

x = (4.5)(8) 3.43 stations15

140



Point out that the low point is 3.43stations, or 343 ft., beyond he P.V.C.(station 90 + 00), or at station93 + 43.

Find the elevation of the low pointby using the following formula:

x2 A

y = 7E; where x and L are stations

(3.43)2(10.5)Y = 16

Note that 7.71 ft. is the correctionto be added to the elevation on thetangent at station 93.43. This is402.56.

Note also that the elevation of thelow point is 402,56 plus 7.71 or410.27,

B. High point Show that the high point is computedin the same manner.

C. Unsymmetrical curves

1. Problem

Work out a simple problem for a highpoint.

Explain that there are times in highwaydesign when ordinary curves will notfit the field conditions.

Use an approach to an intersection asan example where it would be more ad-vantageous to use a vertical curvewith unequal tangents.

Call this curve an unsymmetricalvertical curve.

Outline the following problem: Giventwo grades intersecting at station41 + 00, one grade at +6%, the otherat -3%. Use a vertical curve of 600ft. composed of two sections, L1 of400 ft. and L2 of 200 ft. Find theelevation on the curve at station40 + 00 and at station 42 + 00.

2. Sketch Draw Figure 10 to show the problem.

141



P V. C.37 + 00

EL. 60.00

x 6

40+00

P.V.I.41+00

EL. 84.0042 +00

° P.V.T. 43. +001

EL. 78.00

x

Figure 10UNSYMMETRICAL VERTICAL

Find the center correction usingstations and decimals of stations in-stead of feet:

LI L2 A (4)(2)(9)H =2 6.0'2 (Li -77,2)- 2c4 + 2)

Find the elevation at station 40 + 00on the tangent. This is 78.00.

xl2H (3)2(6)

Y1 177 = 3.37'

78.00 - 3.37 = 74.63, elevation atstation 40 + 00, on the curve

Find the elevation at station 42 + 00on the curve. The tangent elevationis 81.00:

x22H (1)2(6)L2

Y2 = = - 1.5'

81.00 - 1.5 = 79.50, elevation onthe curve at station 42 + 00

QUESTIONS FOR REVIEW1. What type of curvature is used to effect a change in vertical

alignment?

2. Name three types of sag vertical curves.

3. Name three types of crest vertical curves.

142


4. Identify the following notations used in vertical curvatures:

(a) P.V.I. (b) P.V.C. (c) P.V.T.

(d) L (e) A

5. What distance is called the center correction?

6. How is it possible to compute a vertical curve problem without usingformulas?

7. Where would an unsymmetrical vertical curve be used?

ASSIGNMENT1. Give the following problem to the class to do at home: A P.V.I. is

at station 25 + 00 at an elevation of 880.00. The tangents are at+5% and a -4%. There exists a hold control on the vertical curvefor a railroad which is at station 26 + 00, elevation 873.0: Findthe length of curve.

HINT: Draw Figure 11 to explain the problem.

P.V. I.25+00

EL. 880.00

HOLD{STATION 26+001EL-Er/3.00

Figure 11PROBLEM USING A HOLD CONTROL

a. Note that the elevation at station 26 + 00 on the tangent is876.00, which makes y equal 3 ft.

b. Call the x distance, from the hold control at station 26 + 00 tothe right end of the curve, equal to L7- 100

X2H

2c. Use the formula y = Substitute the value of 7 - 100 for x

i

and solve for L. This is 600 ft.

2. Solve problem 6 on page 232 of Ref. A.

3. Study pages 680-709 in Chapter 26 of Ref. A.


143

Lesson 14

THE PRELIMINARY, CONSTRUCTION, ANDFINAL SURVEYS

OBJECTIVES1. To teach the student the basic elements that make up the preliminary

survey, the construction survey, and the final survey2. To identify the major differences in the procedures3. To show the sequential operation of the tiree surveys


I. The Pattern of the Designated Point out that in the design and con-Survey struction of a highway the survey is

actually the complete control. Thiscontrol extends from the inception ofan idea to the design plan, from thedrafting board to the field, and fromthe field to the finished highway.(Ref. A, pp. 682-686)

A. Types of survey Explain that there are essentiallythree basic types of survey: pre-liminary, construction, and final.

B. Similarities

Each one can be broken down intosmaller divisions.

Note that all these surveys havesimilar features.

1. Accuracy Tell the class that every survey mustbe accurate within the allowancesgiven.

2. Permanency State that all surveys are a part ofthe permanent record of a project.This record must be treated for per-manency in the field work and in therecording of the notes.

3. Relationship Stress the importance of the relation-ship of one type of survey to another.Surveys must be easily identified witheach other, because the preliminary

144

HIGHWAY SURVEYING Preliminary, Construction, and Final Surveys


II. The Preliminary Survey

survey controls the construction sur-vey, and the construction survey con-trols the final survey.

Explain that the preliminary surveyincludes all of the topographic in-formation concerning alignment of aproposed highway. (Ref. A, pp. 689-694)

A. The reconnaissance survey Point out that this survey precedesthe preliminary survey. It is the in-formal act of selecting the generallocation of a highway. (Ref. A, p.686)

1. Method

2. Description

B. The base line survey

Mention that the survey is made bywalking, riding, or flying over a givenarea. U.S. Coast and Geodetic Surveymaps and aerial photographs are usedas guides. The equipment used islimited to a 100-ft. tape, a hand level,and a compass.

Describe this survey as a rapid exam-ination made to indicate which align-ment would afford the best route.

Note that the base line survey iscommonly called the preliminary survey.We make this survey specifically tocollect information by measurement andobservations supported by notes.

Mention that this could incorporatethe reconnaissance survey by the sur-vey party running more than one baseline.

I. Equipment Advise the class that complete surveyingequipment is required for this work.

2. Extent of survey Indicate that all the topographic in-formation concerning the area issecured with cross-sections. This isrequired so that when the informationis plotted, it will be an accuraterepresentation of conditions in thefield. The designer can then determinenew alignment of grades, cutoffs,

145



3. Area

intersections, foundations, drainage,bridge design, right-of-way, and otherengineering features.

Point out that in the advance pro-graming cf a project, certain data issecured and computed concerningexisting and future traffic. Thisdata prescribes the classification ofthe highway that is needed. As soonas a proposed highway is classified,standards are available as to thewidth of right-of-way required.

State that the width of right-of-waydictates, in most cases, how far outat right angles from the base linethe survey will go. This is never ashorter distance than the necessaryright-of-way distance.

4. Techniques of the base Explain the use of the base line byline using a sketch. Point out that this

is merely a reference line to whiche\erything else is related.

Show that this line is used to providean exact picture of what is on theground.

Emphasize that by using a base line asa reference line, a centerline can beestablished from one point to anotherpoint. The centerline may fall on thebase line, close to it, or at a dis-tance from it. On occasion the center-line may cross the base line.

C. Procedure of the preliminary State that the very first step in thesurvey preliminary survey is the designation

of the path or line.

Secure all maps and plans of the areato use for reference.

1. Location on old a)ignment Indicate that if the proposed highwayis in the vicinity of an existing high-way, all record plans and right-of-way maps of highways should beobtained.

146

HIGHWAY SURVEYING

CONTENT OUTLINE

Preliminary,'.Construction, and Final Surveys


2. U.S. Geological Survey Study the U.S. Geological Surveymaps topographic maps of the area. Obtain

a list of all the official bench marksand triangulation points in thevicinity. These are shown in the U.S.Geological Survey files.

3. Base-line alignment

4. Orientation

5. Running the base line

Explain that if the program data re-quires that the proposed highwayfollow an old alignment, the base lineshould be run as close to the oldcenterline as possible. Use of theedge of the existing pavement as abase line would be ideal and wouldprovide a parallel reference line.

Suggest that it may be expedient torun the stationing as close as possibleto the old centerline stationing.

Remind the class that very often thebase line will cross the new center-line.

Show the class by means of sketcheshow the centerline stationing isequalized to the base-line stationing.

Establish a true north azimuth forthe base line at its beginning. Thisshould be checked every mile or two,and it must also be checked at theend of the line.

Point out that the base line is run ineven 100-ft. stations with all of thetransit points tied. This means thatall of the angle points and all ofthe points on Zine (P.O.L.) are tiedtogether.

Select points for ties which will re-main undisturbed for years. (This isnecessary because the highway may notbe built for many years.) The pointsshould be protected from traffic.Protection is also required againstmaintenance equipment, plows, mowingmachines, and children.

147



State that all transit points shouldbe tied to a minimum of three points,preferably four, and give reasons.

Paint the transit point stationingidentification on the nearest pole,tree, or rock for ease in location.

Indicate that the best procedure isto run the base line first, from be-ginning to end. Then the survey shouldreturn to the beginning and, pick upthe topography.

6. Location of topography Locate all the important availabletopography, either manmade or natural.This should be done by right angleoffsets from the base line or by anglesand distances from a transit point(radiation method).

List the topography generally located:

1. Buildings and houses

2. Culverts and bridges

3. Curbs, sidewalks, and edges ofpavements

4. Sewers, catchbasins, and manholes

5. Underground conduits, manholes

6. Water pipes, water valves, hydrants

7. Gas mains, gas valves, meter boxes

8. Trees, shrubs, hedges, orchards

9. Powerlines, towers, poles

10. Woods, swamps, gardens, cultivatedfields

11. Property lines, stone walls,property monuments, retaining walls

12. Rock outcrop, rock ledges

148

HIGHWAY SURVEYING

CONTENT OUTLINE

7. Level run

Preliminary, Construction, and Final Surveys


13. Intersecting roads, driveways

14. Names of property owners

15. Names of creeks and local namesof natural items and roads

Note that if a certain road classi-fication demanded 120 ft. of right-of-way, topography must be picked upto a point beyond this limit. It isa good policy to extend at least 150ft. on either side of the base line,unless the new centerline is forcedto follow a known line.

Begin a level run at a recognizedpoint of known elevation or at a U.S.

Geological Survey bench mark.

Establish bench marks in the vicinityof the base line, roughly 1,000 to2,000 ft. apart. These marks shouldbe closer together if the terrain isrough.

Stress the value of placing one ortwo benches close to the vicinity ofa proposed bridge.

Point out that an object which cannotchange elevation must be used for abench mark. If nothing is available,show how to cut a tree near the rootfor the mark.

Tell the class that if no trees, largestones, or foundations, etc. areavailable, large stakes should bedriven into the ground. These areused as a last resort and cannot beused after a winter's exposure.

Explain that the foresights shouldequal the backsights (both under 500ft.). All readings should be takento the nearest hundredth of a foot.

State that the level run can bechecked at a known elevation or at aU.S. Geological Survey bench mark.

149

HIGHWAY SURVEYING

CONTENT OUTLINE

8. Cross sections

D. Notes



Continue the level work by takingcross sections of the base line froma point well in advance of the pro-posed highway. The point should alsobe well ahead of the terminal point(1,000 to 1,500 ft.).

Sate that sections are taken every100 ft. when the ground features areuniform. Sections are taken every50 ft. if the ground becomes moreerratic.

Add that if the topography is rough,it may be necessary to secure crasssections at 25-ft. intervals or pos-sibly at 10-ft. intervals.

Advise the class that if any creek isencountered, it may be wise to take asideline and to cross section thecreek for 1,000 to 1,500 ft.

Show how a skewed section is taken atany point on the stationing. This isused to give a better picture of askewed culvert or some other oddfeature in the terrain.

Advise the class that the limits of across section should always exceed thelimits of the topography. The contoursof the area a distance away from thebase line could affect the drainagedesign.

Note that if cross sections are notrequired of intersecting streets,drives, and railroad facilities, aprofile must be taken.

Indicate the importance of securingthe elevations of pipe inverts, man-hole bottoms, elevations of highwatermarks, and elevations of ordinary highwater.

Exhibit some survey notebooks andpoint out that there are several methodsof recording. All of these follow thesame ,,,eneral pattern.

150

HIGHWAY SURVEYING

CONTENT OUTLINE

1. Transit notes

2. Level notes



Explain the method used to record thebase line run on ordinary, coordinatelooseleaf note paper.

Describe the system used to recordtopographic information and show howsketches assist the notes.

Explain the method used to recordcross section notes. Demonstrate whathappens when notes for back stationsare obtained from an H.I. in thevicinity of a forward station.

Indicate the importance of carryingforward the H.I.

Recommend a No. 3 pencil for notetaking. This is soft enough to beread easily, yet hard enough not tosmudge.

3. Latest type of note paper Exhibit the new type of note paperbeing used for both transit and levelnotes. This is the 81/2 x 11 in. vellumtype paper which fits into a 14-ringaluminum notebook.

Point out the following features ofthe paper and the form:

1. Toughness of the material in thepaper

2. Quality of reproduction

3. Space for sketches on the transitnote sheets

4. Decimal spacing of lines for quickchanges in scale when sketching

5. Uniformity from sheet to sheet(Every entry has a place.)

Distribute sheets to the class forexamination.

Indicate that the level note sheets're designed to be used in the

151


CONTENT OUTLINE . TEACHING POINTS AND TECHNIQUES

electronic engineering program forearthwork computation in the BurroughsB-5500.

4. Other records List the items which should be re-corded with the notes:

III. The Location Survey

A. Design information

1. Dated daily record of the partypersonnel

2. Dated daily record of the weather,including temperature, wind, etc.

3. List of symbols and abbreviationsused in the notes

4. List of all reference materialsused, such as utility companymaps, village records, town.records, etc.

Explain that the location survey isoften described as the constructionsurvey or stakeout. Actually thereis very little difference between thetwo. (Ref. A, pp. 697-700)

Remind the class that the preliminarysurvey information is used to designthe highway.

Show by sketch, a given base line andassume a designed centerline. Thismay or may not begin on the base line.Have the centerline either close to ora good distance away from the base line.

Explain that in the design there isalways a mathematical tie. This isbetween any point on the base line andany point on the centerline.

B. Location of the centerline State that the first step in the re-survey is to relocate the base line.The base line is run without takingany topography.

Add that the transit points should beretied beyond the limits of the con-struction if possible.

152

HIGHWAY SURVEYING

CONTENT OUTLINE

2. Slope stakes



line. Reiterate that this was thebasis for computing the earthwork.

Take a sample set of notes and draw across section from the data.

Point out that data on the location ofthe original ground and the positionof the base line are inked on thecross section drawing. The theoreticalposition of the proposed centerlineis penciled in.

State that the resurvey sections willbe taken at right angles to the newcenterline. This affords a bettercomparative picture of what will bechanged by the construction.

Remind the class that the period be-tween the preliminary survey and theresurvey could be any time from oneyear to three years or more. Takingthe resurvey sections in the abovemanner' eliminates one of the possibilitiesof claims in earthwork quantities.

Explain that the slope stakes are setat the point of intersection of theproposed fill slope or proposed cutslope with the original ground. Thesepoints are measured from the preliminarycross sections. Involved is the dis-tance from the new centerline to thetoe of slope or to the top of slope.This is the cut section on the leftand right of the centerline.

Note that these stakes are usuallyplaced on the left and right of thefull station centerline, but only onone side at the 50-ft. point.

Explain that stakes can be placed be-fore cross sectioning is done or duringthe cross sectioning process. Theelevation of the ground next to thestake and the elevation of the stakeitself are recorded.

154

HIGHWAY SURVEYING

CONTENT OUTLINE

1. The new centerline

2. Curves

3. Physical evidence

C. Resurvey levels

1. Cross sections



Point out that the next step is to layout the centerline. So far, thiscenterline exists only on paper.There is a precise relationship betweenthe base line and the centerline.

Indicate that the designed curves arestaked out as a part of the centerlinewith the P.C. and the P.T. usuallytied to the base line. The P.I. isalways tied to the base line.

Mention that these points should alsobe tied to some reference point inthe field.

Tell the class that the centerline ismarked by a lath at the 50-ft. points(25-ft. points on curves). The sta-tions are marked with blue keel onthe lath.

Repeat that whenever points such as acenterline station, a P.C., or a P.T.are referenced, the stakes should beoutside the construction limits.

Stress the importance of rerunninglevels and checking all of the benchmarks for location and elevation.

Point out that at this time the lo-cation of the centerline is known.All bench marks which will be destroyedby construction should be relocated tosome safe point. This should be asclose as possible to, but outside thelimits of construction.

Study all bridge plans so that newbenches may be placed in the bestpossible location for use at thebridge site.

Draw a sketch showing the relativeposition of the new centerline withthe base line.

Show now the preliminary cross sectionswere taken at right angles to the base

153



Mention that the stake is usually off-set from the actual point. This off-set is marked on the stake togetherwith the station mark.

D. The stakeout Recap the preliminary steps: Thecenterline has been staked, the benchmarks checked or relocated, and thenew cross sections taken.

Following these steps the major portionof the construction survey work con-sists of setting stakes for the guidanceand control of construction operations.(Ref. A, pp. 729-731)

1. Right-of-way Describe by sketch the operation ofstaking out the right-of-way.

2. Clearing and grubbing

3. Finishing stakes

Show several copies of typical right-of-way appropriation maps. Explainbriefly the principles of appropriatingproperty.

Advise that stakes are placed on thenew right-of-way line at every breakor angle point as indicated on theplans.

State that all right-of-way is tied tothe base line and not the centerline.

Add that a stake (marked R.O.W.) isdriven and a piece of red flag tiedon a piece of lath (witness marker).

Explain clearing and grubbing. Priorto this operation a marked lath shouldbe placed just outside the workinglimits but inside the right-of-way line.

Describe finishing stakes as earthworkstakes set for continuing survey workpertaining to grades.

Point out that after the rough gradingis finished, earthwork stakes areplaced. These are set in the center-line or on the shoulder line, or off-set a certain distance from the center-

155



4. Pavement stakes

E. Structure stakeout

line. Finishing stakes are placed bythe surveyor as requested by the con-tractor.

Note that this operation also ties inthe centerline.

Mention that these stakes are markedwith the amount of cut or fill neces-sary at the point affected.

Tell the class that pavement stakesare generally placed 2 ft. outside theedge of pavement. These are placedevery 50 ft. on both sides for tangents,and every 25 ft. on both sides forvertical and horizontal curves.

Stress the importance of tying in themajor lines of a bridge: e.g., thecenterline of bearings, the centerlineof a pier or an abutment, etc.

Point out that these stakes should befrom 100 to 300 ft. away from thestructure. Conditions in the vicinityof a bridge site are not conducive toretaining anything on the ground;therefore, it is a good idea to usedouble stakes for insurance. (Ref. A,pp. 734-736)

Describe the staking that would be re-quested for other portions of thebridge construction: e.g., footingalignments, pile driving patterns,alignment for piers and abutments, etc.

Note that throughout the bridge con-struction, elevations are given foreach phase of the work.

State that all alignments and gradesare given for the culverts in theproject.

Inform the class that in general thereis considerable reestablishment oflines, points, and grades throughoutthe entire construction project.

156



IV. The Final Survey State that the final survey occursafter construction and before the finalestimates for payment are made.

Impress on the class that the actualfinished centerline must be tied forthe preparations of record plans andfor office review of the project.

Note that the base line used for thissurvey is the finished centerline, andcross sections are taken from thisline.

Mention that the finished cross-sectioning is placed with colored inkon the preliminary cross sections.

Stress to the class the importance ofthe final survey. Earthwork quantitiesare paid for by a comparative differ-ential between the resurvey crosssections and the final cross sections.

Explain that all structures, manholes,drop inlets, sewer lines, pipe under-drains, etc. are recorded. The eleva-tions of culvert inverts are alsorecorded.

Add that pavements are measured andrecorded, with emphasis being placedon intersections.

Explain that the finished project maynot be exactly as designed. The finalsurvey serves as a check to show as-built conditions.

State that the original base line isalso retied and brass plugs are placedwhenever the transit points fall onnew pavement

V. Final Examination Note: It is recommended that theexamination at the end of this unit begiven at this time. Allow a maximumof 1 hour for its completion.Sufficient time must be reserved forcorrection of the answer paper: by thestudents.

157



Advise the students that the examinationis not for grading purposes. The examis intended to point out weak areas inthe understanding of the material.

Suggest that additional mastery ofhighway surveying will be gained bythe discussion that will follow theexamination.

Point out the desirability of retainingnotebooks and textbooks as sources ofreview for the future.

QUESTIONS FOR REVIEW1. What are the basic types of surveying in highway work?

2. What is the main difference between the reconnaissance survey andthe base line survey?

3. Explain briefly where a base line is run and how it is preserved forthe future.

4. How is topography located from the base line?

5. For what distance beyond the terminal points of a highway shouldcross sections be taken?

6. Why is it necessary to deviate from the right angle cross sectionwhen a road, a creek, or a railroad is intersected by the base line?

7. What is the first step in the resurvey?

8. From what line of reference are the resurvey cross sections run?

9. Explain why it is necessary to place slope stakes for the newcenterline?

10. What reference line is used for the final survey?

11. Why is the final survey especially important to the contractorbuilding the highway?

158

HIGHWAY SURVEYING Final Examination

PART I - TRUE OR FALSE STATEMENTS

INSTRUCTIONS: On the line provided, write the letter T if a statement istrue and F if the statement is false. (Correct answers areshown in the answer spaces.)

T 1.

T 2.

F 3.

F 4.

T 5.

F 6.

F 7.

T 8.

9.

T 10.

F 11.

12.

F 13.

T 14.

F 15.

In geodetic surveying the spheroidal surface of the earth isalways taken into account regardless of the area being mapped.

A vertical line is by definition a plumb line.

An instrument man who suffers from astigmatism could possiblymake a conditional error.

Both systematic errors and random errors follow laws of prob-ability.

The technique of subtense is comparable to stadia surveying.

The rear tapeman checks for horizontal positioning whenever thetaping operation advances downhill.

The most accurate method used to determine the difference in ele-vation between two points is barometric leveling.

The wye level has many more parts than the dumpy level.

The principle of the vernier is based on the fact that thelengths of the divisions on the vernier are slightly less thanthe lengths of the divisions cn the scale.

If the H.I. of a level is 875.50 and a foresight reading on aB.M. is 2.50, the elevation of the B.M. is 873.00.

The balancing of backsights and foresights eliminates errors inthe level.

The agonic line is also an isogonic line.

A transit is completely locked with the vertical crosshair seton a range pole. It is only necessary to free the lower motionand set the vertical crosshair on the second range pole in orderto measure a horizontal angle.

The latitude of a point on the surface of the earth is the angulardistance measured along the meridian from the equator to the ze-nith of the point.

A 1000-ft. vertical curve is placed on a grade of +5% and -4%,with the P.V.I. (elevation 200.00 ft.) at station 50 + 00. Theelevation of station 45 + 00 of the curve is 185.00 ft.

159

HTGHWAY SURVEYING Final Examination

T 16. With the transit at the center of curvature any deflection istwice what it would be to the same point if the transit were atthe P.C.

T 17. When the delta angle of a curve is 90°, the tangent distance isequal to the radius.

F 18. The mean solar time is based on the true solar day, or the inter-val of time between two successive lower transits of the sun'scenter over a meridian.

T 19. The direction of the side of error in a closure is denoted bythe angle whose tangent is equal to "the error in departures"divided by "the error in latitudes."

F 20. Parallax may be eliminated by using a longer sunshade on thetelescope.

PART II - FILL-IN STATEMENTS

INSTRUCTIONS: Complete the following statements. (The correct answers areshown in parentheses at the end of each statement.)

1. The limits of a cross-section should the limits of the topog-raphy obtained. (exceed)

2. The is equal to one-eighth cf the algebraic differ-ence in percent between two grades, times one-hundredth of the lengthof curve. (center correction)

3. The curve utilizes the geometry of the cubic parabola. (spiral)

4. The formula 0.3CD will furnish the total deflection from the P.C. tothe P.T. in . (minutes)

5. In a 1° curve, 1° of central angle will subtend an arc of ft. (100)

6. In general the measured length of a line is than the true

length. (longer)

7. If B.M. No. 6 is at 966.24 ft. and a rod is read at 6.24 ft., the H.I.is ft. (972.48)

8. The right angle prism is used primarily in leveling.

(cross section)

9. An ascending grade followed by a sharper ascending grade is avertical. (sag)

10. Magnetic dip is degrees at the magnetic pole. (90)

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11. In a closed polygon the algebraic sum of the deflection angles isdegrees when the right deflection angles are considered to be oppositethe left deflection angles. (360)

.2. The expression means to turn the transit telescope about itstransverse axis. (plunging)

13. The line of is the optical line of sight passing throughthe optical center of the telescope lens and the intersection of thecrosshairs. (collimation)

14. The procedure of observing a horizontal angle and the distances tomany objects from one position of the transit is called(radiation)

15. The limb of the sun is observed for azimuth. (east)

161


PART III - MATCHING

INSTRUCTIONS:

3

Write on each line providedexpression in Columnanswers are shown.)

Column A

B which

1.

2.

3.

4.

in Column A the number of theis best suited. (Correct

Columb B

New H.I.

Bearing angle cosine

Balancing a traverse

Long Island

Incorrect tape length

Least count

Turning point

Foresight

9

13

10

12A

R tan -2- 5. Swing offsets

2 Vernier 6. Triangulation

15 Parabola 7. Radiation

6 Inaccessible distance 8. Resection

17 Curvature and refraction 9. Latitude

19 R = 1910' 10. Lambert conformal projection

1 Systematic error 11. Celestial equator

8 Transit location unknown 12. Tangent distance

20 Sunshot 13. Compass rule

4 Minus sight 14. External distances

18 Index error 15. Vertical curve

16. Spiral curve

17. 0.021 M2

18. Vertical circle

19. D = 3°

20. True meridian

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PART IV - MULTIPLE CHOICE

INSTRUCTIONS: Read all possible answers and then place an X in the spacenext to the choice which most accurately answers the questionor completes the statement. (Correct answers are shown.)

1. In taping, which source of error would give the least amount of errorto a measurement?

(a) Variation in temperature(b) Sag in the tape(c) Errors in plumbing

X (d) Imperfect alignment

2. The perimeter of a traverse was measured as 9900.00 ft. in January ata temperature of 0° F. The line was checked in July at a temperatureof 90° F. What was the summer length of the line?

(a) 9900.00'(b) 9957.92'

X (c) 9894.25'(d) 9905.75'

3. What instrument is best used in stadia surveying?

(a) Dumpy levelX (b) Transit

(c) Wye level(d) Self-leveling level

4. If the rod reading on B.M. No. 19A at elevation 414.06 is 6.52', whatis the elevation of the top of the pedestal on a pier when the rodplaced there is read at 2.08'?

X (a) 418.50(b) 422.66(c) 405.46(d) 416.14

5. By the laws of probability the error in a line of levels can be ex-pected to be proportional to the of the number of setups.

(a) Square(b) Cube

X (c) Square root(d) Cube root

6. The instrument errors affecting the transit are:

X (a) Systematic(b) Accidental(c) Random(d) Personal

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7. The magnetic bearing of a line was found to be 520630'W in an areawhere the magnetic declination is 12°30'W. What is the true bearingof the line?

(a) S32°30'WX (b) S8°00'W

(c) S12°30'W----(d) 58°00'E

8. The true bearing of a line AB which lies on the agonic line is N17°45'W.What is the magnetic bearing of AB?

(a) N17°45'E(b) Due north

X (c) N17°45'W(d) Indeterminate

9. If the upper and lower clamps of a transit are locked and the horizon-tal circle reads 0°00'00", what would the horizontal circle read ifthe lower clamp was unlocked and the telescope turned one quadrant?

(a) 90°00'00"(b) 45°00'00"(c) 180°00'00"

X (d) 0°00'00"

10. Resectioning is actually the operation opposite from:

(a) RadiationX (b) Intersection

(c) Triangulation(d) Balancing-in

11. If the algebraic sum of the latitudes is +0.24 and the algebraic sumof the departures is -0.32, what is the linear error of closure?

(a) 0.56X (b) 0.40

(c) 0.08(d) 0.16

12. In problem 11 what is the direction of the closure?

(a) NortheastX (b) Northwest

(c) Southwest(d) Southeast

13. The stadia interval factor for most transits is:

(a) 1.00X (b) 100

(c) Variable(d) 1000

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14. At a certain instant the time is 9:45 a.m., Pacific Standard Time.The location is at longitude 128°50'50" Where standard time is basedon the 120th meridian. What is the local civil time?

(a) 9:13:00 a.m.(b) 10:20:23.4 a.m.(c) 10:13:00 a.m.

X (d) 9:09:36.6 a.m.

15. The azimuth of the sun (Z) is always measured:

X (a) From the north(b) From the south(c) Clockwise(d) Counterclockwise

16. The tangent distance is equal to the radius of a simple curve when A is:

(a) 30°(b) 45°

(c) 60°--a (d) 90°

17. The P.C. is at station 126 + 00, the P.T. is at station 136 + 00, andA is 36°. What is the deflection angle to the center of the curve?

(a) 18°

(b) 15°

(c) 12°

X (d) 9°

18. On a 600' vertical sag curve, the grades are -2% and +4% with the P.V.I.at station 50 + 00. What is the station of the low point?

(a) 47 + 00(b) 48 + 00

X (c) 49 + 00(d) 51 + 00

19. What information is marked on a slope stake?

(a) Amount of cut(b) Amount of fill

X (c) StationOffset

20. If the horizontal circle of a transit is divided into 10-minute unitsand there are 60 spaces in the vernier, the least count is:

X (a) 10 seconds(b) 12 seconds(c) 15 seconds(d) 20 seconds

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document resume ce 000 918 fimmano, ralph; kacharian, … · 2013-10-24 · document resume ed 086...

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