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(civl102)[2003](f)quizB-solutions~PPSpider^_10056.pdf
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CIVL 102 Fall 2003 Quiz 1 Solution

1. Resection was performed using control triangle R, Q and S whose coordinates and internal angles are as shown. Assuming the measured angles R-P-S and S-P-Q are free of any errors, determine the E, N coordinates of P to the nearest 0.001m; show calculations in the space below.



Correct answer (20 points):
Stating Tienstra formula (see notes Ch. 3), even with wrong #s: 10 points

Applying Tienstra formula:
RSP=134341 version:
(EP, NP ) = (189.168 mE, 39.618 mN) (5 points each; full marks for 0.01 m)

RSP=152350 version:
(EP, NP ) = (191.578 mE, 72.736 mN) (5 points each; full marks for 0.01 m)


For questions 2-5, please circle the correct answer. A correct answer will receive 20 marks, and any wrong answer will receive a deduction of 10 marks.

For a closed traverse with 3 sides only, there would be no redundant measurements, and hence the conditional adjustment method cannot be applied.
Correct answer (20 points): False
* 3 angles and 2 length (not including baseline) can be measured while 2 coordinates (x and y of unknown point) need to be found, hence the redundancy is again (5 C 2 =) 3. We can proceed with conditional adjustment as usual requiring the angles to sum to 180 degrees while the E and N misclosures each vanishes.

In the least-squares adjustment of closed traverses, what units would the diagonal terms in the weight matrix carry?
Correct answer (20 points): Half in m-2 and half in (degrees)-2
* For traverses, the SSR is a dimensionless quantity. Hence, the units in, say, squared distance residual (m2) must be cancelled by the weights units, which must be in m-2.

In a triangulation survey involving angles only, suppose the weight of an angle i is 106 times bigger than that of all other angles j (ji). What would you expect as the result of least squares adjustment of the survey?
Correct answer (20 points):The adjusted value of i would remain almost unchanged from its observed value.
* This will make the residual zero (adjusted = observed) to prevent the large weight from swelling the SSR (which we want to minimize).

Consider the following closed-loop traverse with baseline A-B. All the labeled angles and plan distances were measured by means of traversing, and they all contained small random errors.


Suppose you have a software that can minimize a function of several variables, but CANNOT handle any constraints on the variables, i.e. it works just like the Excel Solver but without the Add constraints capability. Can you use it to adjust this traverse by least squares and get correct results?
Correct answer: Yes, (10 points) and the variables to use are:
EC, NC (10 points) or any two L or/and (10 points)
* The three constraint equations let you eliminate three variables among the five thetas and Ls. Then you have the minimal set of variables, say, L1 and L2. But using t