--- title: "Triangulation; EDM principle for trilateration sides" subject: "Surveying I" chapter: 8 key: "semester_3/surveying_i:triangulation-and-edm-principle-trilateration" source: https://www.bctengineer.com/q/semester_3/surveying_i/triangulation-and-edm-principle-trilateration site: BCT Engineering --- # Triangulation; EDM principle for trilateration sides Surveying I · Chapter 8: Triangulation and Trilateration - Asked in: 2080 Bhadra, 2+3 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/triangulation-and-edm-principle-trilateration - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-8 ## Question What is triangulation and trilateration? Describe the principle used in EDM for measuring the sides of a trilateration figure. ## Short answer Triangulation measures a baseline and angles, computing sides by the sine rule. Trilateration measures all sides by EDM and computes angles by the cosine rule. EDM works by transmitting a modulated wave to a reflector, measuring the phase shift of the returned signal. Distance = ½(nλ + Δλ). Integer ambiguity is solved using multiple frequencies, and atmospheric corrections are applied. ## Answer **Triangulation** is a method of horizontal control survey in which control stations are fixed at the vertices of a chain or net of triangles. One side (the **base line**) is measured very accurately, all the angles of the triangles are measured, and the lengths of the other sides are computed with the sine rule. **Trilateration** is the method in which the lengths of **all the sides** of the triangles are measured directly with an EDM (electromagnetic distance measuring) instrument, and the angles are computed from the sides using the cosine rule. #### Principle of EDM for measuring a side An EDM instrument sends out a modulated electromagnetic wave (infrared, light or microwave) from one end of the line to a reflector (prism) at the other end. The wave returns to the instrument, and the distance is found from the **phase difference** between the transmitted and the received signals. If the wavelength of the modulated wave is $\lambda$, the double path (to the reflector and back) contains $n$ whole waves and a part wave $\Delta\lambda$: $$ 2D = n\lambda + \Delta\lambda \quad\Rightarrow\quad D = \frac{1}{2}\left(n\lambda + \frac{\phi}{2\pi}\,\lambda\right) $$ where $\phi$ is the measured phase difference (angle). The instrument measures $\phi$ accurately, so $\Delta\lambda$ is known, while the integer $n$ is resolved by using several modulation frequencies (a coarse frequency to give approximate distance and finer ones for precise value). The velocity of the wave depends on temperature, pressure and humidity, so meteorological corrections are applied. Alternatively, in a pulse instrument, the time $t$ taken by a pulse for the double path gives $D = \frac{c\,t}{2}$. ```text EDM ====== modulated wave =====> reflector (prism) unit <===== reflected wave ==== phase difference -> distance D ``` Typical accuracy is $\pm (3\text{ to }5\ \text{mm} + 1\text{ to }2\ \text{ppm})$. The sides of the trilateration figure are measured this way, and the angles are computed with the cosine rule. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. On what principle does an EDM measure distance? A. Counting steps B. Phase difference between transmitted and received modulated waves C. Optical parallax D. Magnetic bearing Answer: B. The modulated wave is reflected by a prism and the phase difference gives the part wavelength, so the distance. (Key point: EDM principle) 2. What is the relation between distance D and wavelength for the double path? A. D = n lambda + delta lambda B. D = 2 n lambda C. 2D = n lambda + delta lambda D. D = lambda/2 only Answer: C. The wave travels to the reflector and back, so 2D contains n whole waves plus a part wave. (Key point: Double path formula) 3. How is the integer number n of whole waves determined? A. By guessing B. By measuring angles C. By using a longer tape D. Using several modulation frequencies, coarse first then finer Answer: D. Coarse frequency gives approximate distance and finer frequencies refine it. (Key point: Resolving ambiguity) 4. Why are temperature, pressure and humidity recorded in EDM work? A. They change wave velocity, so corrections are applied B. They change the colour of the prism C. They affect only angles D. They are not needed Answer: A. Wave velocity in air depends on atmospheric conditions. (Key point: Meteorological correction) ## Related in Surveying I - [Triangulation principle; 1st order trilateration](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangulation-principle-first-order-trilateration) — Surveying I, chapter 8 - [Principle of triangulation and trilateration](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aprinciple-triangulation-trilateration-note) — Surveying I, chapter 8 - [Principles of EDM measuring distances](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aedm-principles) — Surveying I, chapter 2, asked 12× - [Triangulation versus trilateration](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangulation-vs-trilateration) — Surveying I, chapter 8, asked 7× - [Triangulation, trilateration; specifications](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangulation-trilateration-specifications) — Surveying I, chapter 8, asked 5× - [Trilateration over triangulation; primary specs](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atrilateration-advantages-primary-triangulation) — Surveying I, chapter 8 ## Related in other subjects - [EDM principle and ECM metal removal rate](https://www.bctengineer.com/question.md?key=semester_4%2Fmanufacturing_and_production_processes%3Aedm-ecm-principle-mrr-numerical) — Manufacturing and Production Processes, chapter 8