Error of Closure

I think I figured out my bad assumption and posted in the [msg=152286]other thread[/msg] an explanation that I believe is compatible with this excellent example.

Note that in this Compass Traverse, the angular closure is 0degrees 0minutes 0seconds...

sigh

Surveying by close-compass traverse

DDSM;-)

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> Those who have attended one of my Traverse Analysis classes know well that one of the fundamental rules of traverse data is that good closure doesn't mean very much. Other than revealing large blunders, error of closure is mostly meaningless.
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> Larry P

I can't agree that it is near meaningless; you are going too far with that statement. It is a good quality indicator.

I do know that it is far from being conclusive, though.

Stephen

Large closure error is proof that something is bad.
Small closure error is lack of proof of anything.

Neither one is proof... they are both evidence.

Small error of closure is evidence that your tribrach levels are in good adjustment, that your prism offsets are set correctly, that your total station is resolving angles to good precision, that your PPMs are set correctly, that you generally adhere to good field survey methods...

Stephen

> Large closure error is proof that something is bad.
> Small closure error is lack of proof of anything.

Well said Bill.

Larry P

> Neither one is proof... they are both evidence.
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> Small error of closure is evidence that your tribrach levels are in good adjustment, that your prism offsets are set correctly, that your total station is resolving angles to good precision, that your PPMs are set correctly, that you generally adhere to good field survey methods...
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> Stephen

Stephen,

I disagree with your conclusion. Unless and until you look at the closure at every traverse point, you can not conclude small error of closure means any of those things. As I partially demonstrated above, one data set can have both small error of closure and much larger error of closure. Have seen some data sets where the smallest error of closure (1 in 100,000 for example) is 5 or 6 times the largest error of closure (1 in 15,000 for example). Both these numbers from the same data set.

This is why I conclude, you can tell if there are gross blunders in the data set by looking at closure. More than that, looking at one closure number tells the user very little.

Larry P

Then we'll just have to agree to disagree, Mr. P. 😉

As I said, I see good closure as more of evidence than of proof, and that it should not be viewed as being conclusive.

But the data set you have shown and the one you mention (1:100,000 to 1:15,000) are outliers. I too have run the starting points along the traverse a few times and while the closing error changes at each station, usually they were fairly close to each other. Close to each other meaning, say 1:50,000 at best to 1:30,000 at worst.

I also have done some rough experimentation with traverses a few times. I have taken traverses with good closure and purposely introduced a little error into a station and then a little more. Each time I did so, the error of closure got higher and higher.

Not absolutely conclusive, but a pretty good indicator.

Stephen

I understand what you are saying, and I get the idea that someone shouldn't put all their eggs in the basket of "We closed better than 1:100,000". But I can't see how you can infer that it is meaningless. It is one element in your evaluation, and it is not an element to be ignored. As you have said yourself, you can look through all the closures at every point and sometimes find a busted angle. If you can find a busted angle, then you have to recognize that error of closure is of evidenciary (sp?) value. No, it doesn't prove your traverse, but it is good "evidence" that all the angles except the one you left out are very likely reasonable, as well as your distances.

Coupled with extra efforts at every setup to help spot blunders you have some pretty good values. I haven't run traverses in some time, but we always had several checks on the angles, whether we were "wrapping" angles, or turning off a fixed lower plate. When we turned off a fixed plate we would generally backsight close to zero and "close the horizon" but we would also throw one random angle at the backsight and turn to the foresight and subtract the difference to see if we are in the ballpark. Same with distances we would take several distances direct and inverted, in feet, but would switch the readout and read one distance in meters. We could spot those nasty one-foot busts or a busted degree (for instance). With time and experience (as I am sure you know) you learn different tricks to double-check yourself while in the field and not have to come in with some embarrassing results. I have had good luck in the past with consistent good "closures" good angular closures and lack of "busted" problems. I am not perfect, but I think I can speak from experience.

At the risk of being run out of romper room on a rail, I learned some time ago that if all one was interested in was the mathematical linear closing area, one could enter the calls from a closed-loop traverse, as in one that begins on point 1 and returns with a closing shot back to that same point of beginning - type the bearings and distances of the calls on pieces of paper and drop them in a hat and shake them up. Then draw the courses of the traverse out of the hat and enter them as a traverse in the order they come out of the bag and though the geometry of the resulting figure wouldn't resemble the actual traverse at all, it should still come back to the same closing point as if entered in correct order.

So if you don't mind, enlighten me if possible (not possible for you - but that I might possibly be enlightened) as to how changing the point of beginning from one vertex in the loop to another impacts the linear misclosure at that point. Why wouldn't the resulting misclosure and the ratio of precision be the same?

Jerry S.

I know it to be true by experience. Why don't you merely try it? Take a closure from a traverse before you balance the angles and mess with it. When you run the traverse from point one, back to point one, there is one angle not in the mix. If you run the traverse starting at point two, and using the angle at point one to close back in to point two, you are using one different piece of data....the angle at point one and no longer the angle at point two. JB Stahl had a pretty good explanation of it in his post on the earlier thread.

Note if you balance the angles first, you will have the same closure at every point you start from. Your theory works in that circumstance.

That's the way I used to find problems with a traverse. You can isolate a bad angle, although, it might take a few hours to figure it out.

These days there are more options to find errors.

and that is precisely the point. They were not talking about the LINEAR error of closure. Sone of the old timers and old school surveyors here thought that they were referring to the LINEAR error of closure. Basically, there wasn't a disagreement on the error of closure but a misunderstanding on what type of error of closure.

I always found that sniffing around for a bad angle in a traverse should start with the first set and then the last of the job. It is just the 'human' factor for various reasons that bad error are usually found at these set-ups from the rush to get going and the rush to get 'leaving'.

Error of Closure> OK Larry

I did make up a traverse and mis-closed by 0.15'.... I actually just created 5 lines and then made sure that one line missed closing by 0.15'

I ran the closure (no adjustment) three times, using a different starting point.

I annotated the interior angles and listed the distances to create my traverse file.

The closures were different, ever so slightly and the error was different, ever so slightly.
1) 0.14845' 1 in 17716
2) 0.14816' 1 in 17751
3) 0.14975 1 in 17563
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I see that you are RIGHT! (even though it does round to 0.15')

Dtp

Well, now I see the difference because I was not reckoning with the idea of omitting one of the turned angles. That is enough to account for the difference.

I worked for a surveyor in my other life who learned his surveying with a mountain transit and chain. When he got his first total station, it was a manual total station and he had his crews go from working in bearings to working in azimuths.

We would release the lower plate motion before picking up to move to the forward point and then plunge the scope with the azimuth from the previous forward traverse shot still in the instrument and collimate to the backsight target which when I started was a plumb bob string. Our idea of closing a traverse was to shot back either to the initial point or a sideshot which we lovingly referred to as point 1A to achieve closure.

Only after a few years of this madness did we add the seeming optional step of actually reoccupying that initial point and turning back in to the second traverse station. Armed with the additional information provided by knowing your angular misclosure as well as your linear misclosure allowed me to find angular errors using a different technique. Not foolproof but still fairly effective.

And yes, rereading my post above I know I should have said blunders, not errors because they were truly caused by the blunder of turning the upper motion on the horizontal plate rather than the lower motion when fine tuning to collimation of the backsight target.

I used the method of bisecting the line between the inital point and the closing point and throwing a 90° angle back toward the traverse. If there is only one angular blunder of that type I describe above, that perpendicular would point back through the traverse very near to the place where the goof up occurred, plus or minus the net error of the other traverse legs. It didn't work nearly so well when there were two or more such blunders. I tried very hard not to make those types of mistakes but I was usually juggling deeds, looking at evidence in addition to operating the instrument. It was a recipe for an occasional blunder, at least for me.

here's a shortcut:

take your direction of the error of closure, rotate it by 90, find the angle that this bisects, return that station. most likely culprit. geometry is fun, so go read Euclid's The Elements for more information.

Maybe someday: anymore we run control with static and do some checks with the robot. I never seem to need to worry about it these days. On tight construction jobs out comes the digital level and it closes so well even leveling is now automated.