In the following figure, A and B are fixed points with known plane rectangular coordinates. C and D are the new points in the control survey whose coordinates are to be determined. For this network, the surveyor has measured all 8 internal angles (1 to 8) and 5 sides BC, CD, DA, AC and BD. The value of redundancy (r) for the given figure will be equal to ____________ (In integer).
1. Given Data:
Number of measured internal angles = 8
Number of measured sides ($BC, CD, DA, AC, BD$) = 5
Fixed points with known coordinates = 2 (Points $A$ and $B$)
New points to be determined = 2 (Points $C$ and $D$)
2. Formula for Redundancy ($r$):
Redundancy ($r$) is calculated as the difference between the total number of independent observations ($n$) and the total number of unknown parameters ($u$) required to define the network coordinates.
$r = n - u$
3. Step-by-Step Calculation:
Step 3.1: Calculate total observations ($n$)
$n = (\text{number of angles}) + (\text{number of sides})$
$n = 8 + 5 = 13$
Step 3.2: Calculate total unknown parameters ($u$)
In a 2D plane survey, each new point has two unknown coordinates ($x$ and $y$).
$u = 2 \times (\text{number of new points})$
$u = 2 \times 2 = 4$
Step 3.3: Calculate the value of redundancy ($r$)
$r = 13 - 4$
$r = 9$
Final Answer:
The value of redundancy ($r$) for the given figure is 9.
Important Questions from Triangulation
In the triangulation network shown in the figure, $b$ and $g$ are the observed lengths of the baselines, while 1 to 18 are the observed interior angles. The number of redundant observations is __________ (Answer in integer).
- In a triangulation exercise, the horizontal distance between two points P and Q was found to be 12380.56 m. The average elevation along the line PQ was 748.82 m above the reference ellipsoid. The reduced horizontal distance between P and Q over the reference ellipsoid is _______ m (Rounded off to two decimal places).
Consider the radius of Earth to be 6378 km. - Which of the following statements is/are CORRECT?
Which of the following triangles are well conditioned and may be suitable for control establishment using triangulation?
Triangle Interior Angles I $90^\circ$, $45^\circ$, $45^\circ$ II $130^\circ$, $25^\circ$, $25^\circ$ III $110^\circ$, $35^\circ$, $35^\circ$ IV $110^\circ$, $45^\circ$, $25^\circ$
