I've traversed from one point, in two directions, ending at a common point. But to begin the work of closing the combined traverse, I need a closed traverse. So, what I did, was assumed the end point of the first was the beginning of the second, and plotted all of the metes and bounds as if I had traversed backwards, all the way to the POB.
I question this approach, because I haven't measured the angle at the final point between the two traverses. (The angular closure of the combination is huge...about 47' shy of 1260 degrees (9 points). I think I need to occupy the final point, and measure the next to last points in either direction. Is that the proper way to "stitch together" two or more open traverses. I'm finding nothing in my reading about this.
Is there a "right" way to do this? I'd upload the plat, but I'm having trouble uploading jpegs for some reason.
Your method of combining sounds reasonable. It doesn't matter what order you actually measured the angles and distances. You have enough data to close the figure and do some checks if you measured 9 distances and 8 angles.
If you are adjusting by something like compass rule, start calculating the traverse at the point where you have no angle, with assumed coordinates for it and assumed bearing to the next point. If you need to translate or rotate everything later to match one of the points and/or lines real values it isn't hard.
Another check angle at the other point would be nice, but not mathematically necessary to get a solution. For 9 points there are 18 coordinate values. You get to arbitrarily pick three values: two coordinates for a point (whichever point you want) and one other value such as a bearing or one coordinate of the next point. That leaves 15 unknowns. By measuring 9 distances and 8 angles you have 17 equations in 15 unknowns, or two check measurements.
However, you don't have enough angle measurements to do an angle check or adjustment independent of the length adjustments. You are calculating the last angle based on both angles and lengths. Length error will be indistinguishable from angle error.
If doing an adjustment by least squares, any additional measurements would help isolate blunders and improve the overall accuracy.
> You have enough data to close the figure and do some checks if you measured 9 distances and 8 angles.
I think this assumes that both traverses were started from coordinates on the same system. If, as I suspect, both were started from random coordinates, then without the angle at the connection point there's an infinite number of ways of joining them together (i.e. both traverses can rotate 360° around the connection point and still satisfy all the data).
If there are two missing angles, then what you say is true.
If he measured all but one angle (any one), then there is no huge ambiguity but any attempt at finding an angular closure will be affected by length errors. The coordinate systems can be unified without a problem.
If he would measure all 9 angles then he could do an angular closure check independent of length errors.
> If he measured all but one angle (any one), then there is no huge ambiguity but any attempt at finding an angular closure will be affected by length errors. The coordinate systems can be unified without a problem.
Perhaps I'm envisioning a different scenario than you are. Below is a graphic that represents the concept I have in mind:
At occupied stations the angle between the 2 adjacent points is measured, along with both distances. At unoccupied stations, only the angle and distance *to* that station are measured.
3 different possible configurations of Traverse 2 (the red one) are shown, but the number of possibilities is unlimited. Without a unified coordinate system to begin with, I don't understand how one can solve for the positions of the Traverse 2 stations except the one in common with Traverse 1.
What am I missing?
I think your diagram has 2 unoccupied points, where the far ends of the traverses are the same point seen from two different places, resulting in 2 different estimates of the position of one actual point. The closure error is the difference between those ends.
Two 2 unoccupied points, thus 2 unmeasured angles, was the first of my 3 cases mentioned above, where your conclusion is true, not the second case you quoted.
As a side note, you then need one more occupied point in one of the traverses to make 9 actual points.
Alternatively, your diagram could illustrate 9 actual points with 3 unoccupied stations (unmeasured angles) and one unmeasured distance, but that wouldn't be relevant to any of my listed cases or any interpretation I can come up with for the original post.
> I think your diagram has 2 unoccupied points, where the far ends of the traverses are the same point seen from two different places, resulting in 2 different estimates of the position of one actual point.
Got it -- I misread the original scenario, and didn't realize he started both traverses from the same point. I agree with your assessment.
Aye! A spirited discussion it is, lol. Glad you guys got that all figured out.
Yes, the "one point" that I started from was the same point in both traverses. My resulting closure from combining them though, really sucks, so I will go back and measure the "joining angle", along with distances, just to be sure that's not the problem.
I'm still finding rookie errors on at least one of the traverses (read SD rather than HD), so I'm just not confident that there aren't others as well. I may just do one whole half of the thing again. I know the compass rule can close anything, but that's not really the point here.
FYI, point number 3 is the joining point of the two traverses.
Add A Tie Check At Minimum
With such a bad closure you may well have a blunder. Blunders require a number of redundancies.
Your traverse distances are short so it is not much extra work.
Paul in PA
Add A Tie Check At Minimum
> With such a bad closure you may well have a blunder. Blunders require a number of redundancies.
>
Yes, and I suspect math. Whoever came up with the whole system of N, S, d/m/s, E,W bearings ought to be shot. What's wrong with plain old decimal azimuths? Add, subtract, do trig...you name it; easy.
At any rate, the suspected bad math brings up this question:
I've done these using Traversing by Angles to the Right, as opposed to Interior Angles, Deflection Angles, or Azimuths.
But now I understand that, if using a total station, traversing by Azimuths might, in fact, result in the least probability of computational errors. If I preset the azimuth on each back sight, then turn the angle, etc. would this not be the best way to do these traverses?
Remember, the assumptions are: Total Station, but 100% manual data recording. I understand it's a different ball game using a data collector.
Add A Tie Check At Minimum
I do my comps using azimuths and grads. No dms, no quadrants. Makes the math easier.
Add A Tie Check At Minimum
The biggest reason NOT to run in azimuths in my experience is that once you have eliminated blunders and then balanced your traverse, your sideshots all need to be rotated to the corrected backsight. If you are working with angles-to-the-right, you would merely turn off the adjusted back point.
This presumes that you are entering the traverse first and balancing the error out before entering the sideshots. That's what we did where I used to work. Fieldbook data in azimuths. Even though the old HP9815 calculator with the surveying program would have allowed the sideshots to have been entered and would have adjusted them along with the traverse, that was not the way the the folks I used to work with learned to use the computer.
Add A Tie Check At Minimum
Well, I don't actually enter azimuths, I enter angles (or directions). What I mean is that anytime I need to deal with an azimuth (or bearing), for example a backsight, I use azimuths rather than bearings.
So, whether cogo or adjustment software, angles in grads and distances in meters. If needed I can convert to dms and/or feet at the end for delivery to the client. Just press a button...
Add A Tie Check At Minimum
It was after I posted my reply that I realized that most people would not have managed the data entry part of the survey the way we did.
I had been working there a while before it dawned on me that we were not correcting the azimuths recorded in the field book to the adjusted back azimuth.
And yes, I understand getting away from using bearings for data entry wherever possible.
Merging Open Traverses Hints
I have a good track record merging multiple traverses. If I plan on using GPS as a part of a large job, I often set my GPS control under good sky, then tie through roadside monumentation and head through the woods. This is especially important in some areas where the farther you get in the less visible occupation to follow. Where possible I set 3 GPS points but will work from a pair if that is all the sky available. Already having my ultimate destination in the data collector gives more certainty of staying near where the evidence is supposed to be. Because I most often work alone as far as I get in on one day may sit there waiting for me to come in from one or two other directions.
When I get to an orphaned TP I have several choices. Assume on traverse one my last points were TP 101 and TP 105. I am coming from TP 213 and can see TP 105. I do a set and name it TP 105/223. I then stake to TP 101. It is amazing how often when you know where to are heading that you can end up so close to line, that a second traverse point can be seen. If so I do another set to TP 101/224. Next check is to stake to any monumented corner I shot from TP 105 for an additional check. Depending how comfortable I am with closeness I may backsight TP 105 and do a set to TP 213. This often occurs if it is near end of day and completing the next occupation is iffy. If I does no work out back in the office coming back out is an option.
Assume it is not that close to the end of day but there is little chance of setting up on another job or line and I could not get a shot at TP 101, then I move ahead to TP 105/223 and shoot TP 101/224. I then reset my instrument to occupy TP 105, backsight TP 101 and shoot TP 213/225. From TP 105 I also look for monumented corners shot from TP 213.
Don't be surprised if you check into a point only 0.02-0.03' off and when you occupy your tie point you are missing the farther TP by 0.15'. That kind of math can quickly point you to a loose set far far away.
On multi parcel surveys there is a good probability that I will be coming at this connection point from a third direction. In that case I almost always plan on hitting a pair of TPs from one setup to finish off the multi redundancy.
Doing the absolute minimum on a traverse is really a waste of your least squares adjustment.
Shooting corner monumentation from multiple TPs is also a good check. With only minor thought and awarenesss along the way you can easily double shoot 1 in 5 or 6 monuments or side GPS points as you go.
Lastly if none of the previous has presented the opportunity to you is the planned tie travers across the middle.
In heavily wooded areas you may do less than perfect GPS just to help you get started and not include it in your final adjustment. or include it with lots of sway room.
Paul in PA
I will hazard an educated guess that the error is in the angle at point 1.
The 141°05'10" should be 141°50'10". Your interior angles then add up real close.
Starting a traverse at point 1 and continuing clockwise using the shown interior angles (except the one at point 1) I get a misclosure of only 0.85' compared with starting the traverse any where else and including the interior angle at point 1 gives misclosures of 2.25' to 4.96'.
Plotting the traverse and constructing the perpendicular bisector to the closing course almost points to point 1.
If you suspect a slope distance might have been entered instead of a horizontal distance, you might want to remeasure points 2-3. That side is almost parallel to the closure vector.
If that distance was 37.7 ft, and I ignore the angle at point 4, everything else would check nicely with the one remaining check measurement. I'm not sure how to interpret all the angles since none are marked as unmeasured. Was 2-3 a steep incline with an elevation difference of 21 ft such that the horizontal would be that much smaller than slope ?
Merging Open Traverses Hints
Thanks all for the input.
I have a ton to learn, not the least of which is how to take clear, concise, field notes. I've spent two days looking for errors, but my notes are so crappy, they're almost useless. 05? 50? Could be either. Did I take consistent double readings, Left and Right? Sometimes, but not always. If I were my instructor (I am, sort of, with the help of the folks here), I'd give myself an "F", but in this case I'm going with a "D-", so long as I go out and do the whole thing again, start to finish, and re-plot. Target is less than a foot of closure, before any adjustments.
> If you suspect a slope distance might have been entered instead of a horizontal distance, you might want to remeasure points 2-3. That side is almost parallel to the closure vector.
>
> If that distance was 37.7 ft, and I ignore the angle at point 4, everything else would check nicely with the one remaining check measurement. I'm not sure how to interpret all the angles since none are marked as unmeasured. Was 2-3 a steep incline with an elevation difference of 21 ft such that the horizontal would be that much smaller than slope ?
Nope. Points 2 to 3 was a drop in elevation of 1.845' I had already fixed the slope problem (it was between the POB and 8).
As much as I'd like to believe it's all due to one errant measurement, I think I'll find at least 2 or 3, if not more.We'll see.
Good thing I'm not doing this for a living!
>
> FYI, point number 3 is the joining point of the two traverses.
That is the weakest area of your traverse, (short distances). A small angular error will magnify considerably from that short leg.
Get that closing angle and check your angle at point #1.