Convergent, Iterative Optimization of Solutions – Why Solving some Problems is Easier Said than Done

For some problems the challenge is not to identify the solution. The real challenge is working out how to put the solution in place. Anyone who has setup a theodolite will understand what I mean. The solution is simple to describe. Position a precision optical measuring device so that it is; perfectly level, at a reasonable height for operation and directly above a predefined mark. Sounds easy, but given a tripod and a theodolite most untrained surveyors will take hours and usually give up in frustration. The problem is that there are too many degrees of freedom in the system. Everything is interdependent. Make one small adjustment here and it knocks things way out of whack there!

The secret is to follow a procedure that is based on a strategy. There are many variations on the procedure, but they all rely on the same strategy. Establish an initial, sub-optimal, solution that is configured to allow for as much adjustment as possible. Adjust this preliminary configuration gradually refining the setup until it finally meets the requirements.

The following are the most succinct instructions I could find after a google search for “setting up a theodolite”. I took these instructions from here

Setting Up the Tripod

(doing this correctly will save a lot of time and frustration in subsequent adjustments!!)

Extend the tripod legs to a proper length (around shoulder height), and set the tripod approximately over the marked survey point. The tripod head should be levelled (use horizontal objects as references), and each leg should make approximately a 70 angle with the ground. Feel free to lift the tripod and redo the above if necessary. Avoid having a tripod leg coming at you; that might cause some inconvenience.

Carefully take the theodolite out of the carrying case, and remember how it was fitted in the box so that you know how to put it back later. Mount it on the tripod, and fasten the tripod screw. Make sure the tribrach base and the tripod head (both triangular) are parallel and share the same centroid to permit maximum translation in any direction, which will be needed later on. Remove the lens cap, put it back into the carrying case, and close the box.

Setting Up the Theodolite

1 Rough Centering
Secure the front tripod leg. Hold and move the two other legs to roughly center the theodolite by locating the ground mark via the optical plummet. Use your right foot placed near the mark as a guide; see Fig. 1. Secure the tripod legs when done.

2 Rough Levelling (use the circular bubble as the guide)
By adjusting the length of one tripod leg at a time while keeping the other two still, the circular bubble can be levelled without causing disturbance to the previously accomplished centering (check the optical plummet to see this is true).

3 Precise Levelling (use the plate bubble as the guide)
Rotate the theodolite until its plate bubble is parallel to any two footscrews (A and B), then adjust A and B to center the bubble. The left thumb rule applies as usual (bubble will travel in direction of left thumb). Now rotate the theodolite body by 90, and center the bubble with the third footscrew (C) only. Repeat this procedure for each 90 revolution of the instrument until the bubble is centered for all four positions. Now check the optical plummet: adjustment of the footscrews has probably disturbed the centering.

4 Precise Centering
Loosen the tripod screw, and slowly translate (do not rotate) the theodolite around until it is exactly centered over the survey point, then tighten the screw.

5 Repeat 3 and 4 until levelling and centering are both accomplished precisely.

Some generalized lessons can be drawn from this procedure. When faced with a complex problem that has an obvious solution always consider how the solution will be put in place. If the solution comprises many interdependent sub-components use a convergent, iterative optimization process. Put the part of the system with the largest scope for adjustment in place first and set all configuration parameters to the middle of their range before starting to make adjustments. Monitor the size of successive adjustments; they should get smaller as the procedure progresses. If they start to get larger at any point this is a danger sign. Don’t worry if early configuration is very imprecise

use your right foot as a mark

Make accommodations early in the process for flexibility that may be needed later.

Make sure the tribrach base and the tripod head (both triangular) are parallel and share the same centroid to permit maximum translation in any direction, which will be needed later on

Avoid having a tripod leg coming at you; that might cause some inconvenience [when using the theodolite].

Understand that the best procedure may be non-trivial and not obvious to the novice. Ask someone who has done it before how they did it and what they would do different next time. If you come across one of these situations beware, some things really are easier said than done.

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