Course code BūvZ3135

Credit points 12

Geodesy I

Total Hours in Course324

Number of hours for lectures56

Number of hours for seminars and practical classes16

Number of hours for laboratory classes56

Independent study hours196

Date of course confirmation23.03.2020

Responsible UnitInstitute of Land Management and Geodesy

Course developers

author prof.

Armands Celms

Dr. sc. ing.

author prof.

Natālija Sergejeva

Dr. math.

author Matemātikas un fizikas institūts

Svetlana Atslēga

Dr. math.

author reserch

Zanda Gavare

Dr. phys.

author lect.

Vita Celmiņa


Course abstract

Students acquire knowledge of the type and size of the Earth, coordinate systems used in geodesy, types of geodesic measurement, mathematical processing and evaluation of measurement accuracy, representation of the earth's surface in plans and maps, surveying methods, and topographic surveying, and can display graphically the results of measurements.

Geodetic Instrument Course
During the course, the students get acquainted with the most important geometrical and optical regularities, which are the basis of making geodesic instruments. Familiarize with optical and digital instruments and other measuring instruments used in geodesy. The structure and principles of geodetic instruments are practically learned. The classification of geodetic instruments by application, structure and precision parameters is acquired. Students practice field testing of geodetic instruments and other measuring tools.

Mathematical part of the study course deals to the elements of differential and integral calculus of single-valued functions and their applications. This part of the course provides the knowledge necessary for successful completion of other courses.

Physics part is giving an overview of fundamental laws that are essential to problem solving in engineering sciences, with emphasis on electromagnetics and optics. Course consists of lectures, practical exercises and laboratory workshops. During the lectures, students are introduced to theory and ways of describing physical phenomena by mathematical laws. Practical exercises provide for acquiring skills in solving physical problems.
During laboratory workshops, students deal with hands-on exercises where they measure, process and analyse various data readings. By completing the course of physics, students obtain a knowledge, which is necessary for proper understanding of physical aspects of the information gained within their major specialty courses, thus increasing specialist’s competence and providing for extra opportunities on job market.

Learning outcomes and their assessment

After completing the course, student:
1. Know types of geodetic measurements and their execution, surveying methods and mathematical processing of geodetic measurements - can list and describe different types of geodetic measurements.
2. Can apply the acquired theoretical knowledge in practice - evaluate the accuracy of the obtained measurements, process the measurement results and draw up situations, terrain, and topographic plan, draw up the measurement logs, plans, profiles, and other documents according to the requirements. The student demonstrates his / her skills in independently developed laboratory works.
3. Is capable independently acquire, select and analyze the information necessary for performing the geodetic works, to make decisions according to their competence and to solve the problems related to the work to be performed - which is evaluated during the development of laboratory work. The student understands professional ethics, can evaluate the impact of his / her professional activity on the environment and society.

Geodetic Instrument Course
After completing the course, student:
1. Know and understand most important geometrical and optical regularities, which underlie the constructive structure of geodesic instruments - can independently disassemble and assemble geodetic instruments
2. Acquire basic principles of digital instruments, is capable to choose geodetic instruments of appropriate accuracy according to the set purpose of work. Can evaluate the classification of optical and digital geodetic instruments, their construction and testing methods.
3. Can carry out field inspections of geodetic instruments and other measuring instruments. The student demonstrates practical ability to evaluate the technical condition of geodesic tools and other measuring tools and their compliance with the set requirements.

By the successful completion of this study course part, student:
1. Know differentiation of functions, indefinite and definite integrals, applications of derivative and definite integrals. Knowledge is assessed during the test.
2. Can perform calculation of derivatives, using derivative calculation the extreme values of function, finding indefinite integrals, using definite integrals finding the area enclosed between two or more curves volume of solid, understanding of relevant concepts and regularities. Skills are assessed during tests and practical work.
3. Can perform evaluation of intermediate results of calculations and professional evaluation and interpretation of final results. Competences are assessed during tests and practical work

After completing the course, student:
1. Knows and understands the regularities discussed in the course of physics and understands their real applicability for describing the processes considered in their specialty. The knowledge is assessed in laboratory works and tests.
2. Can perform measurements of physical quantities and apply knowledge in calculation for their branch of research, summarize and analytically describe the results. – The skills are assessed in laboratory works.

3. Is able to evaluate results of measurements and calculations, problem solving and understand what influence their professional activities have on environment. – The competence is assessed in laboratory works and tests.

Course Content(Calendar)

Full-time studies:
1. Introduction to the subject of geodesy. The subject of geodesy, its tasks, historical development and importance in the national economy. Connection of geodesy with other sciences. (2h)
2. Earth shape and size, the reference ellipsoid, horizontal distances and angles, maps, plans, and profiles. Absolute and relative errors of measurements. Operations with approximate numbers. (3h)
3. The orientation of the coordinate system and lines. Geographic and orthogonal coordinate systems. Latvian coordinate system LKS 92. Coordinate networks. Determination of orthogonal and geographical coordinates of points on the map. (3h)
4. Preparation of a situation plan. (3h)
5. Simple steps and methods of horizontal surveying. The concept of the horizontal survey. (3h)
6. Measurements of horizontal angles. Principles of measurement of horizontal angles. (3h)
7. Measurements of vertical angles. Principle of measuring vertical angles. (3h)
8. Theodolite traverse and polygons, mathematical processing of theodolite traverse. Theodolite traverses and polygons, their connection to the points of the geodetic support network. (3h)
Test 1 (1h)
9. Determination of areas. Area determination methods, their comparative evaluation. (2h)
10. Types and elevations of point heights. Ellipsoidal height. Orthometric height. Normal height. Relative height. Elevation. Height systems. (3h)
11. Geometric leveling. Types of leveling. (3h)
12. Methods of determining the height of a point. Mathematical treatment of leveling results. (3h)
13. Calculations in the leveling log. Longitudinal profile compilation. Design in profile. (3h)
14. Surface leveling methods. Terrain. General information about depicting terrain in plans and maps. (3h)
15. Tachymetry. Measurement of slope angles. Tachymetry log processing. (3h)
16. Preparation of topographic plan. Tasks in the topographic plan. (3h)
Test 2 (1h)

Geodetic instrument course
1. Course content, course requirements, literature, and normative basis. Historical development of geodetic instruments. (1h)
2. Classification and division of geodetic instruments. (2h)
3. Construction, testing, and regulation of optical theodolites. (2h)
4. Construction, testing, and adjustment of optical levelers. (2h)
5. Digital levelers. Levelers with rotating laser beam. (2h)
6. Direct distance measuring tools and their testing. (2h)
7. Optical rangefinders, their construction, and tests. (2h)
8. Construction, inspection, and adjustment of an optical square. (2h)
Test 1 (1h)
9. Construction and testing of the total station. (2h)
10. Construction and testing of digital levelers. (2h)
11. GNSS receivers, their construction, and testing. Structure diagram of GNSS receivers. (1h)
12. Photogrammetric equipment. (2h)
13. Laser scanning equipment. (2h)
14. Use of unmanned aerial vehicles in remote sensing measurements. (2h)
15. Test benches, procedures, and requirements for geodetic instruments. (2h)
16. Normative documents and standards regulating the conformity of geodetic instruments with the measurement requirements. (2h)
Test 2 (1h)

1. Basic Derivation Rules. Derivative of Composite Functions. - 4h
2. Applications of Derivatives. - 2h
3. Integration Rules. Substitution Rule For Indefinite Integrals - 4h
4. Definite integral. Newton – Leibniz formula. - 2h
5. Applications of Definite Integrals for Area Between Curves and Volume of Solids of Revolution. - 3h
Test - 1h

1. Magnetic field in the vacuum. Parameters characterizing magnetic field (strength, flux density). Biot-Savart law and its application in magnetic field calculations. - 2h
2. Ampere’s law and its application in magnetic field calculations. -1h
3. Magnetic flux, Gauss’s law in magnetism. Magnetic force on current-carrying wire and charged particle. -1h
4. Magnetic field of Earth. Magnetism in matter. Ampere’s law for magnetic field in matter. – 3 h
5. Electromagnetic induction. Faraday’s law of induction. Lenz’s law. Self-inductance. Inductance. – 3 h
6. Alternating-current circuits. Harmonic oscillations, damped and driven oscillations. Resonance. - 2h
7. Fundamentals of Maxwell’s electromagnetic theory. Electromagnetic waves and their properties. Electromagnetic spectrum. - 2h
1st test. Electromagnetism. – 1 h
8. Light and its parameters (speed, wavelength, frequency). Laws of light reflection and refraction. - 2h
9. Lenses, their parameters. The lens formula. Construction of image formed by lenses. Errors of lenses. Microscope and telescope ray tracing. - 3h
10. Dispersion of light. Ray tracing in prism, minimum deviation angle. - 2h
11. Interference of light. Optical path. Spatial coherence and temporal coherence. - 2h
12. Applications of interference: thin films, anti-reflection coatings. - 2h
13. Diffraction of light. Resolving power of optical devices. - 2h
14. Polarization of light. Malus’s law. Brewster’s angle. Birefringence. - 1h
15. Absorption of light. Lambert’s law. Optical phenomena in Earth’s atmosphere. - 1h

16. Propagation of electromagnetic waves in the atmosphere (phenomenon of refraction in the troposphere and ionosphere). - 1h
2nd test. Geometrical and wave optics. – 1 h

Part-time studies:

All topics specified for full-time studies are implemented, but the number of contact hours is 1/2 of the specified number of hours

Requirements for awarding credit points

Each section ends with a grade, the result is calculated as the weighted average
A written exam that ends with a mark.
Develop and defend laboratory works, pass 2 tests, the results of which form an accumulative assessment.

Geodetic instrument course
Written test that ends with a mark.
The resulting mark is formed by:
- test on theoretical knowledge acquired during the course;
- practical assignment according to the topics of the study course laboratory works and homework.
All laboratory works, tests and homework must be passed.

Must be passed two independent works and written test.

In order to pass the physics part, all tests must be written and the laboratory works must be developed and defended.

Description of the organization and tasks of students’ independent work

Students are required to complete two homework assignments independently, following the requirements defined in the lectures:
1. homework. Describe the rationale for setting up the coordinate reference system (volume of at least 15 pages, submit electronically, present)
2. homework. Presentation of terrain elements analysis for a given territory. (Presentation size at least 10 slides)

Geodetic instrument course
Students are required to complete two homework assignments independently, following the requirements defined in the lectures:
1. homework. Study of the development of geodetic instruments and description of specific groups of instruments (volume at least 12 pages, submitted electronically, presented);
2. homework. Elaboration of an example of a geodesic measuring procedure (according to the instrument systems considered in the study process) and selection of geodesic instruments according to the assigned work type (Presentation size at least 10 slides)

The following independent works must be completed:
Independent work 1: Derivatives of functions
Independent work 2: Integrals and their applications

Study of methodical literature and lecture materials in preparation for tests, completion of calculations of laboratory works developed during classes and preparation for defense of laboratory works.

Criteria for Evaluating Learning Outcomes

There are 2 tests during the semester. Each test consists of theoretical questions and practical tasks. You can earn up to 20 points for each test. The student is allowed to take the exam if both tests have been written successfully. If the student has obtained 20.5 points and more in both tests, you can receive the entry without taking the exam with the grade in the table or take it to improve the exam grade.
Exam score according to points:
16.5 - 20 mediocre - 5
20.5 - 24 almost good - 6
24.5 - 28 good - 7
28.5 - 32 very good - 8
32.5 - 36 excellent - 9
36.5 - 40 outstanding - 10

Geodetic instrument course
The assessment of the study course depends on the assessment of the theoretical questions and the solution of the test, and the cumulative assessment of the study course tests and homework. All planned laboratory work must be completed and credited. Lecture attendance must be at least 75% of the total.
A student can successfully pass the test or exam if at least 50% of the test questions are answered correctly.
Students who have at least 7 in the control course of this study course may not pass the theoretical test and mark the arithmetic mean of the tests in the course as the theoretical test.
The final grade is calculated as the arithmetic mean of the final test assignments and the average grade in the semester, which is calculated as the arithmetic mean of the grade tests and homework.

Both independent works must be passed (all tasks are completed correctly) and the final test score must be at least 4.

Knowledge control in physics: 1) Theory tests – 2; 2) Laboratory works (development and defence) – 4.
Each test shall be evaluated by 0-10 points. In order to pass the physics part, all tests must be written and the laboratory works must be developed and defended, and total 50% of the maximum possible points must be obtained.

Compulsory reading

1. B.Helfriča, I., Bīmane, M. Kronbergs, U. Zuments. Latvijas Ģeotelpiskās informācijas aģentūra. Rīga, 2007. 262 lpp.
2. Helfriča B. Mērniecība: mācību līdzeklis. 1.-3. daļa. Jelgava, 2004-.

Ģeodēzijas instrumentu mācība
1. B.Helfriča, I., Bīmane, M. Kronbergs, U. Zuments. Latvijas Ģeotelpiskās informācijas aģentūra. Rīga, 2007. 262 lpp.
2. Žagars J., Zvirgzds J., Kaminskis J. Globālās navigāciju satelītu sistēmas (GNSS). Ventspils: Ventspils Augstskola, 2014. 231 lpp.
3. Handbook of Global Navigation Satellite Systems. P.Teunissen, O.Montenbruck (Editors). Springer International Publishing AG, 2017. 1335 p.
1. Volodko I. Augstākā matemātika. I daļa. Rīga: Zvaigzne ABC, 2007. 294 lpp.
1. Fizika. A. Valtera red. Rīga: Zvaigzne, 1992. 733 lpp.
2. Fizika visiem.

Further reading

1. Freijs V., Jakubovskis O., Kronbergs M., Zuments U. Ģeodēzija. V. Freijs, O. Jakubovskis, M. Kronbergs, U. Zuments. Rīga: Zvaigzne, 1993. 383 lpp. Ir LLU FB ~ 100 eks.
2. Horizontālā uzmērīšana. Metodiskie norādījumi. Sast. I. Bīmane, M. Kronbergs. LLU. Zemes ierīcības un ģeodēzijas katedra. Jelgava: Latvijas Lauksaimniecības universitāte, 2012. 32 lpp. Ir LLU FB 25 eks.
3. Nivelēšana. Metodiskie norādījumi. LLU. Ģeodēzijas katedra; sast. B. Helfriča. Jelgava, 1995. 21 lpp. Ir LLU FB 5 eks.

Ģeodēzijas instrumentu mācība
1. Strang G., Borre K. Linear algebra, geodesy and GPS. Wellesley, MA: Wellesley, Cambridge Press, 1997. Nav lielākajās b-kās. Pieejams:
2. Nivelēšanas I, II un III klases nivelēšanas instrukcija. LR VZD. Rīga, 2001. 96 lpp. Nav lielākajās b-kās
3. Gravity, Geoid and Height Systems. Proceedings of the IAG Symposium GGHS2012, October 9-12, 2012, Venice, Italy. Edited by U. Marti. 348 p. Nav Latvijas lielākajās b-kās.
4. 4. Horizontālā uzmērīšana. Metodiskie norādījumi. Sast. I. Bīmane, M. Kronbergs. LLU. Zemes ierīcības un ģeodēzijas katedra. Jelgava: Latvijas Lauksaimniecības universitāte, 2012. 32 lpp. Ir LLU FB 25 eks.

1. Uzdevumu krājums augstākajā matemātikā. Dz. Bože, L. Biezā, B. Siliņa, A. Strence. Rīga: Zvaigzne, 2001. 332 lpp. Ir LLU FB ~ 300 eks.

1. Jansone M., Kalnača A. u.c. Uzdevumu krājums vispārīgajā fizikā. M. Jansone, A. Kalnača u.c. Rīga: RTU, 2000. 247 lpp.
2. Grabovskis R. Fizika. Rīga: Zvaigzne, 1983. 646 lpp.
3. Tipler P. A., Mosca G. Physics for Scientists and Engineers. 6th edition. New York, NY: Macmillan Education; W. H. Freeman and Company, 2008. 1172 p.

Periodicals and other sources

Ģeodēzija, Ģeodēzijas instrumentu mācība


In professional higher education bachelor study program “Land Management and Surveying” full-time studies and part-time studies