GATE Geomatics Engineering Section I Flashcards

24 sample cards from the Section I deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. Give the stadia (tacheometric) distance formula for a horizontal sight.

   $$D = K\,s + C$$ where $D$ is horizontal distance, $s$ is the staff intercept (top minus bottom stadia readings), $K$ is the multiplying constant (usually $100$), and $C$ is the additive constant (often $\approx 0$ for internal-focusing instruments).

2. Give the tacheometric formulas for horizontal distance and vertical height with an inclined sight (angle $\theta$, staff held vertical).

   $$D = K\,s\cos^{2}\theta + C\cos\theta$$ $$V = K\,s\,\frac{\sin 2\theta}{2} + C\sin\theta$$ where $D$ is horizontal distance, $V$ is vertical height between instrument axis and central hair, $s$ is staff intercept, and $\theta$ is the vertical angle.

3. What is trigonometric levelling?

   An indirect method of determining the difference in elevation between points using measured vertical (zenith/altitude) angles and horizontal or slope distances, applying trigonometry, used in hilly terrain where direct levelling is impractical.

4. Give the basic formula for height difference in trigonometric levelling for a vertical angle $\alpha$ over horizontal distance $D$.

   $$V = D\tan\alpha$$ where $V$ is the height of the object above the instrument axis. The RL of the point is then $RL = RL_{\text{instrument axis}} + V$ (plus curvature/refraction correction over long sights).

5. What is traversing in surveying?

   A method of control surveying consisting of a series of connected lines (a traverse) whose lengths and directions (bearings/angles) are measured, to establish the relative positions (coordinates) of the traverse stations.

6. Differentiate a closed traverse from an open traverse.

   A closed traverse starts and ends at the same point (loop) or between two known points, allowing checks on accuracy (angular and linear closure). An open traverse does not return or close on a known point, so it cannot be checked and is used only when unavoidable (e.g. roads, rivers).

7. Define latitude and departure of a traverse line.

   For a line of length $L$ and WCB $\theta$: Latitude (N–S component) $= L\cos\theta$ and Departure (E–W component) $= L\sin\theta$. North latitudes and East departures are positive; South and West are negative.

8. What is the condition for a closed traverse to be geometrically closed, and what is closing error?

   For a closed traverse $\sum \text{Latitude} = 0$ and $\sum \text{Departure} = 0$. The closing error $e = \sqrt{(\sum L)^{2} + (\sum D)^{2}}$, where $\sum L$ and $\sum D$ are the residual sums of latitudes and departures.

9. State Bowditch's (compass) rule for traverse adjustment.

   Correction to a line's latitude (or departure) is proportional to its length: $$\text{Correction to latitude of a line} = -\sum L \times \frac{l}{\sum l}$$ where $l$ is the line length and $\sum l$ the perimeter. Used when angular and linear measurements are of equal precision.

10. What is triangulation?

    A control survey method in which the area is covered by a network of connected triangles. One side (baseline) and all angles are measured precisely; the remaining sides are computed using the sine rule. It provides horizontal control over large areas.

11. What is trilateration?

    A control survey method in which the lengths of all sides of a network of triangles are measured (using EDM) and the angles are computed trigonometrically. It is the distance-based counterpart of triangulation.

12. Compare triangulation and trilateration.

    Triangulation measures angles (plus a baseline) and computes sides; trilateration measures all sides (distances) and computes angles. Trilateration became practical with EDM. Modern practice often uses a combined triangulation-trilateration network for strong, well-checked control.

13. In triangulation, how is an unknown side computed from the baseline using the sine rule?

    With baseline $a$ opposite angle $A$, an unknown side $b$ opposite angle $B$ is $$b = a\,\frac{\sin B}{\sin A}.$$ All angles of each triangle are measured and the sine rule propagates lengths through the network.

14. What are the orders/classes of triangulation based on precision?

    First (primary/highest precision, longest sides for national/geodetic control), Second (secondary), and Third (tertiary, for local detail) order. Precision is judged by average triangular closure and baseline accuracy, decreasing from first to third order.

15. Classify aerial photographs based on the camera axis orientation.

    Vertical photographs (optical axis truly vertical, tilt $< 3^\circ$), tilted photographs (small unintentional tilt), and oblique photographs (axis intentionally inclined). Obliques are further divided into low oblique (horizon not shown) and high oblique (horizon shown).

16. What is the difference between a vertical and an oblique aerial photograph?

    A vertical photo is taken with the camera axis pointing (nearly) straight down, approximating a map and useful for measurement. An oblique photo is taken with the axis tilted, covering more area but with variable scale and perspective distortion.

17. What is the difference between a low oblique and a high oblique photograph?

    A low oblique photograph does not show the horizon (camera tilted modestly), while a high oblique photograph shows the horizon and a large area. Both have scale that varies across the image.

18. Define flying height in aerial photography.

    Flying height ($H$) is the vertical height of the aircraft/camera above the chosen datum (often MSL). The height above the ground/terrain is $H - h$, where $h$ is the average terrain elevation above datum.

19. Give the scale of a vertical aerial photograph over flat terrain.

    $$\text{Scale} = \frac{f}{H - h}$$ where $f$ is the camera focal length, $H$ is the flying height above datum, and $h$ is the terrain elevation above datum. Equivalently scale $= \frac{\text{photo distance}}{\text{ground distance}}$.

20. How does terrain elevation affect the scale of a vertical aerial photograph?

    Scale increases for higher ground (smaller $H-h$) and decreases for lower ground (larger $H-h$), since scale $=\frac{f}{H-h}$. Thus a single vertical photo has variable scale unless the terrain is perfectly flat.

21. If focal length $f$ and photo/ground distances are known, how is flying height $H$ found over flat ground at elevation $h$?

    From scale $=\frac{f}{H-h}=\frac{\text{photo distance}}{\text{ground distance}}$, rearrange to $$H = h + f\,\frac{\text{ground distance}}{\text{photo distance}}.$$

22. What is relief displacement in a vertical aerial photograph?

    The radial shift of an image point caused by the object's elevation above datum; tall objects lean outward from the principal point (nadir). It is given by $$d = \frac{r\,h}{H}$$ where $r$ is the radial distance of the image from the centre, $h$ the object height, and $H$ the flying height above the base.

23. What is the contour interval and how is it related to map scale?

    Contour interval is the constant vertical distance between successive contour lines. It is generally smaller for large-scale maps and flat ground, and larger for small-scale maps and steep/hilly terrain, balancing detail against clarity.

24. What does a graphical (linear) scale on a map provide that an RF does not?

    A graphical scale is a line subdivided to show ground distances directly, and it remains valid even if the map is photographically enlarged or reduced (it scales with the map), whereas the printed RF would become incorrect after such resizing.

What this deck covers

Section I flashcards FAQ