Can anyone plese tell me about the { mathamatically closed but geomatrically open traverse }

this is kind of open traversiong but i have a confusion in mathamatcly .plesea i need your opinion ./

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A closed traverse is one that creates a closed polygon in shape and must be adjusted mathematically to make the geometry of the polygon true. An open traverse begins on a vector with two known coordinates that establish a control bearing and closes on one as well. The adjustment is made holding the begin and end vector. This traverse is typically a jagged line. Thus open and closed traverse.

A closed traverse is one which either closes back upon itself ( a loop traverse ) or one where the relative position of the closing leg is known ~ that is to say, the direction and positions of the two ends of a traverse, which does not close back upon itself, are previously known before beginning the work.  One may adjust out angular and distance errors in this scenario.

An open traverse is one where the relative position of the closing leg is not previously known when starting the work.  This is the least desirable situation, but may be effective if safeguards are taken ~ for example, closing the horizon on each setup or taking several redundant sets of angles at each setup.  One cannot adjust the open traverse, but must rely upon the care taken in the performance of the work. Running a traverse along a mine gallery is an example of this type of 'open traverse'

Dear Mr. Najar,

Both types of traverse surveys require accurate (or assumed) coordinates for the first and last points surveyed.

The loop traverse used one point for both functions.

An open traverse uses two.

Otherwise they are identical.


Dear J. Anthony Cavell

Thanks for your  comment i was really in need of this ,but having some little more confusion in my mind .As i am new to this job some qustions are still roaming round my head.

Thanks \



Sounds like you may still not have the answer you are looking for ...

Technology is a BEAST we can conquer together :)

Just guessing here ... you need to be very specific on just what it is you are doing and where the "mathematically closed but geometrically open" came from, software, your data collector when you adjust your traverse, something someone said, a text book  or ...???

If you are dealing with a NETWORK - then we're all going down the wrong path to try and help....

So let me expand on some of the answers you already have been given, presuming you are still LOOKING...

If it software that is causing your question, the following may help.  

When you traverse to a known point you get a coordinate and thus what software may refer to as a "mathematical closure", but it is still "geometrically open". You must turn the closing angle in order for the software to close out the bearings and adjust your angles, thus "geometrically open".  See attached image for figures showing a closing angle.

In the OPEN TRAVERSE figure - you begin by occupying B and back-sighting A, giving the software a coordinate to begin on , B, and an Azimuth or bearing, B to A ,to begin with.  then you traverse occupying 1, 2, 3, and 4.  While sitting on 4 you tie C and have coordinate closure (mathematical closure) but you will not yet have a geometrical closure because you have not measured another known course.  You need to Occupy C and turn the closing angle to D to get a closing bearing so the software can adjust your angles and give a geometrical closure.

In the CLOSED TRAVERSE figure - you begin by occupying 2, back sight 1 and turn to 3, again giving the software the coordinate of 2 to start on and the bearing 2 to 1 for an azimuth.  you then traverse by occupying 3, 4, 5, and 6.  When set up on 6, you tie 1 again and have a coordinate closure or mathematical closure, but angles are open  still so you will not yet have a geometrical closure because you have not measured another known course.  You need to Occupy 1, back sight 6 and turn to 2 to get a closing angle and bearing so the software can adjust your angles and provide a geometrical closure.


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