Hello my friend I want to know the procedure and calculation involved in finding the excluded angle by repetition method

my observations are here  for OAB

TOTAL STATION AT 'O'  SITE AT A  I SET MY ANGLE TO 0d0'0" then I turned to B my angle is 207d55'14"

then I hold the angle 207d55'14", again I site to A then I free the angle then I turned to B again, my angle is


like this I repeat 5 set of values they are

0d0'0"             first site at A







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  • Here Raymond , this is standard Closing  The Horizon

     Inst@1          DIRECT                             REVERSED          

                   circle       angle                   circle                 angle               avg. ang

    BS 2 D  0.00-00                      BS 2 R 180.00-04

                               42.12-14                                        42.12-12             42.12-13 

    FS 3 D 42.12-14                      FS 3 R  222.12-16

                               59.56-16                                        59.56-14             59.56-15


    FS 4 D 102.08-30                    FS 4 R  282.08-30                

                               257.51-34                                      257.51-34            257.51-34

    FSBS 2 D 0.00-04               FSBS 2 R 180.00-04  


                                                                                                            - 360.00-00

                                                                                         misclosure     =  0.00-02

    Still this is only one example.

  • Hi Raymond, I will give you a link to a book, that you can read on line or download to pdf, The title is Elementary Surveying,Go to page 204 thru 209 to see different method of measuring Angles in repetitions with Total Stations.Closing the Horizon is a method used of turning angles around a point to obtain a check of their sum,which should equal 360 degrees.This can be done direct or direct then indirect or mixed, with two or more points, either way you complete the circle of 360 degrees with their averaged sums. They may or may not, let you download this book , but you can still read it on line. I can also send you some notes.

    this is Direct Method Closing the Horizon field notes this only a example of one.

    Inst. @PT 1

    BS 2 D       0.00-00

    FS 3 D       45.52-45              ANG. 45.52-45

                                                                          MEAN 45.52-50 INITIAL

    BS 2 D       90.00-10

    FS 3 D       135.53-05            ANG. 45.52-55

                                                                                             HORIZ MISCL 360.0008

    BS 3 D       0.00-05

    FS 2 D       314.07-20            ANG. 314.0715

                                                                           MEAN 314.07-18 

    BS 3 D       90.00-05

    FS 2 D       44.07-25             ANG. 314.07-20

    you could also do 4 reversed pointing with this using 180 and 270 degrees, then average them together, or mixed the direct with the indirect then average them. This example is acceptable if misclosure (10sec) is permissible . Notice i did not spend time to zero the gun. Data Collector may ask to send circle to gun.


    Also using a Data Collector this may be all, a different method used.

    • Mr Billy send  me pdf showing drawing representation

      • Yes Mr Billy I study  about the article link you send to me ........closing the horizon is very useful in triangulation process mainly in least square adjustment.

  • Yes Raymond, MR.Cavell is well known ,it is great that this site has someone of his academics to be a member ,and to give you his opinion and advice.Because of this site you get to talk to, as you say a expert, who will take the time to help you and you are on the other side of the world.Yes kudos to Mr. Cavell and all the rest of our members who reach out and help other surveyors .Yes Raymond i was just voicing my opinion of how great i thought his answers were. But like he told you are not gaining any higher precision By doing this.When all you need are several bearing, bearing intersections if you need a average,then average them,You are not trying to find or measure a exact angle,because this buoy is moving.Also there are many different types of angle repetitions, I prefer 3 direct and 3 indirect or closing the horizon with direct and reverse. The one you are using was use for transit like he said.This was done because they only read to 20 or 30 seconds Also when i did this, i used even number of sets like 2,4 and 6 and only recorded the first and the last for the average of the winding. Today 's total stations are not like yesterdays transits and you will not gain anything by doing this type of accumulation of angles.

    Mr. Cavell also mentioned  a good method of using 0,90 and 180 and 270,but keep in mind that your instrument has errors,anytime you are trying to be most accurate it's best to turn direct and then reverse and average the two.And then i still like closing the horizon.

  • Hi Raymond, I am glad you explained why you angles were so different,I had to asked myself , what on earth are you doing.Mr. Cavell you are correct about the Babylonians,they and the Sumerians of Mesopotamia came up with the base 60 math,even on the circle of 360 parts, and you get a A++ for everything else.

    Great Answers Mr.Cavell

  • I'm not sure exactly what you are asking. I don't see enough information to determine an excluded angle. In fact, unless I am mistaken, between point O, A, & B we can determine only one angle from this data.

    From your description it sounds like you are operating the total station (a theodolite) like a transit with a Vernier, often called "winding up the angle". The total of the added angles is divided by the number of turns to arrive at the recorded angle.

    I calculate the observation this way.
      000° 00' 00"
      207° 55' 14"
      415° 28' 58"
      623° 22' 09"
      831° 06' 18"
     1039° 01' 11"
      207° 48' 14" observed  ((1039° 01' 11")/5)
      000° 09' 17" Std. Dev.

    (Note: the deviations between reading seems unusually varied with a standard deviation of over 9 arc minutes.)

    A preferred method is to use the instrument as a directional theodolite. One doesn't "set" the backsight precisely but rather simply near zero, turn and record, then backsight near 90°, turn and record - repeat with backsights at 180° & 270°. Determine the magnitude of each turn by subtracting the backsight from the foresight and calculate a simple average of those.

    Without a Vernier using the repeating method gains no precision. Using the recommended theodolite method compensates for eccentricities of the circle.

    Had there also been distances measured one could calculate the triangle with one angle and two sides and from that result deduce the other two angles.


    • After all the discussion, I think I've determined an improved technique for you to use to locate your buoys.

      Forget repetition, because with the large movement it will take many, many observations to come up with a comfortable number to pin your hat on and the buoys' movements eliminate making any practical use of direct and reverse measures.

      I recommend first that you establish two control points, O1 & O2, some distance apart but with good geometry to the two buoys.

      Occupy O1 and backsight on O2 and observe the right edge of buoy A until you believe you have captured its furthest excursion to the right, AR. Record that angle.

      Repeat the process except site the left side of the buoy until you capture its left most excursion, AL.. Record that angle. (If you wish to repeat these two steps feel free to do so)

      Average the two angles and call it A.

      Repeat the above process for buoy B getting BR, BL and their average, B.

      Now occupy point O2 and repeat the whole process again (except O1 is now your backsight).

      Using the baseline O1-O2 you should be able to calculate the triangles AO1B & AO2B as well as the distance and azimuth from A to B.

      Let me know how it works.


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