Question

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). 

Hint:

With control points fixed, the datum is defined; count only the coordinate unknowns of new points. Then \(r=m-u\) (angles, distances, directions each count as one observation).

Answer 1

Redundancy (degrees of freedom) in a network adjustment is \[ r = m - u, \] where \(m\) is the number of independent observations and \(u\) is the number of unknown parameters being estimated after fixing the datum.
Here points \(A,B\) are fixed (coordinates known). Unknowns are the coordinates of \(C\) and \(D\): \(x_C,y_C,x_D,y_D⇒ u=4\).
Observations measured: all \(8\) internal angles and \(5\) sides \((BC,CD,DA,AC,BD)⇒ m=8+5=13\).
Therefore, \[ r = m-u = 13-4 = 9. \] \[ \boxed{9} \]