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Traverse Closure in Cave Surveying

by D.J. IRWIN and R.D. STENNER.

The several years it has taken to survey St. Cuthbert’s Swallet (1) have taught the authors a great deal about some of the less publicised aspects of cave surveying.  It has also resulted in the accumulation of a considerable body of data concerning cave survey precision.  We encountered problems which the cave surveying literature to date had not dealt with, and we feel that our findings will be of assistance to other surveyors.  This article is concerned primarily with the closing of traverses and this involves of necessity a discussion on compass calibration and the precision to be expected in a cave survey.

At some time, a surveyor will find that he has surveyed a part of the cave by a circular route which finishes at a part which has already been surveyed.  The circular traverse which starts and finishes at the same point is known as a closed traverse.  In many cases, the surveyor will find that there are occasions when several of these closed traverses have been made.  One may say “So what!” but generally, when the calculations have been made, the surveyor will find that - instead of the traverse ending at a point which coincides exactly with the start or with a previous survey point, it will have a slightly different value of the co-ordinates.  This failure to close is known as the traverse closing error.  It will be obvious that two different points in space cannot represent the same survey station, and thus they must be made to ‘close’.  Various methods for closing such a traverse have been discussed elsewhere (2) and so we shall only mention the methods in passing and dwell on the recommended procedure.

Problems really occur when one is faced with a number of closed traverses as shown symbolically in figure (i).  Whereas one can easily close a single or double traverse, the maze type looks and is more complex, Ellis attempts to show how this type of network can be closed, and states ‘…the first thing is to make a subjective assessment, and if any of the traverses are thought to be more accurate than others, then they can be closed first and the others closed on to them.  If all the traverses are of the same expected accuracy, the method favoured by the author is to close the outer traverse and then the inner traverses successively.’ (3).  As the surveying unit is now in general use on Mendip, there is little need to lower the survey grading below the requirements of C.R.G. Grade 6 and so one will have to think of all the traverses as being of the same expected accuracy - or so one would think!  From the results of the St. Cuthbert’s survey, both of the authors have shown beyond doubt that errors will be found in the most unlikely places.  One might think that, because of the difficulty of caving through boulder ruckles that the survey line would display the same lowering of standards for that part of the survey; but it was found that this was not so.  Surveying through such passages tended to make the surveyors more careful perhaps. At any rate, most of the errors occurred in parts of the cave where surveying was easiest.  As a result, it is not possible to assess the accuracy of any section of the survey line simply by relating it to a particular type of cave passage.

At the outset of the St. Cuthbert’s survey, we followed the recommendations current at the time by closing all the traverses as soon as they were completed during the field work data collecting.  These were termed the individual traverses, and then each passage junction to passage junction co-ordinates were joined up in various ways to 'hunt' for any obvious error.  Several errors were found and the offending lines were omitted for all later checks. As the number of traverses increased, subsequently covering the whole cave, this procedure became extremely complex and cumbersome.  However, the St. Cuthbert’s survey network was closed by this method and any section of the framework suspected of containing gross errors was either re-surveyed or fed in to the network at a later date.  Once the main traverse was closed, the remaining sections of the cave were closed in order of accuracy.  Without the help of computers, and only working from notebooks and desk calculators, this process took many hours of work running into a period of just under two years involving 1,500 man-hours!  This procedure caused a considerable amount of unnecessary resurveying. During the later stages of this work, it was found that the northern section of the cave (New and Old Routes) had an exceptionally large error.  This had not been discovered previously as it had compensated with a similar error in the Coral Chamber area, and so had gone unnoticed.  This was due to the fact the closing of the individual traverses was dominant in, the calculations, any other method having been discarded on the advice of other surveyors of considerably more experience than either of the authors.

This discovery of an error in the northern section of the cave showed the unreliability of using traverse closure errors the check the precision of various parts of the survey. It then became obvious that both the authors had missed a very simple way of assessing - with reasonable accuracy - any line survey section in the network.

Because any two stations in the cave must have the same coordinate changes between them irrespective of route chosen, we were able to tabulate the coordinate changes and see at a glance those which obviously contained errors of some form.  An example from the Rocky Boulder Series will demonstrate this procedure fully later in the text.  Although the St. Cuthbert’s survey was not closed using the tabular method (because the main traverse had already been established) the method was used to check our work.  The experience of a complicated network now enables the authors to recommend the following procedures, which will make it unnecessary for any other surveyors to fall into the frustrating difficulties and time-wasting problems that we met with the St. Cuthbert’s survey.

Willcox states that ‘...the core of the problem lies in discovering all the possible closed traverses for a network….’ (4).  In the case of St. Cuthbert’s, this would number 1.5 x 1013 (or 150 million million – Ed.) traverses and when repeat surveys are considered, the number would rise to 1.0 x 1030.  Obviously, another procedure must be looked for!

Why Does A Closed Traverse Not Close?

With the usual instruments used for cave surveying - a liquid damped compass~ a clinometer and a measuring tape, one cannot read the instruments accurately enough to collect precise readings.  All the readings obtained will be approximations.  For example, the compass card is normally graduated in 1 degree divisions, and when sighting through the eyepiece it is not possible to obtain a value better than ¼ of a degree.  Even this value is optimistic and will depend largely on the individual compass. Similarly, the clinometer readings will be of the same order of accuracy and if a good commercial tape is used, measurements will be to the nearest 1" or 0.1 ft.  The catenary effect may be ignored providing the tape is pulled taut before taking the reading. (5).

The greatest source of error is not, however, the readings of the individual instruments, since - provided the reading of the instruments themselves and the actual instruments are consistent, such errors will largely compensate, and with the type of survey we are considering, the Station Position Error can be ignored.  It is thus necessary to consider errors due to factors other than reading the instruments and to station positioning.

Compass Calibration

When a survey is made over a number of trips during which the compass calibration will have changed or, more importantly, when using more than one compass, then care in the compass calibration becomes of crucial importance. In fact under these circumstances, calibration errors can become larger than systematic errors.  Judging by correspondence in caving publications in recent years, calibrating a compass has not been felt to be necessary by some surveyors, but the importance is easy to demonstrate.

First, the theory. Figure (ii) shows the systematic error predicted by Warburton (6) to be statistically probable in a Grade 6 survey with an average leg length of 15 ft.  Also shown are the positional errors caused by 10 and 0.50 calibration errors. It must be noted that whereas the distance axis for the systematic error represents the slope distance of the survey, that for the calibration error shows the plan distance between a point and the start of the survey.

Consider two surveys made with different compasses that both start from the same station ‘close’ at a second point with a plan distance of 1,000 ft. from the origin.  If each of the surveys contains 1,500 ft. (slope distance) of survey line, then the systematic error would be expected to be 9.4 ft.  The error due to a 10 difference in calibration will be 17 ft. and if the error is 50, the total error will be 85 ft.  Since the readings given by two different compasses can be greater than 50, failure to calibrate a compass can introduce tremendous errors into a survey.

Now, from theory to practice.  When the St. Cuthbert’s preliminary survey was being compiled in 1962, Ellis was using the results of several surveyors, using different compasses calibrated (or not calibrated!) in different ways.  It is hardly surprising that he did not find it easy to combine the survey.  More recently, discrepancies were noted between three different surveys of the Rabbit Warren Extension.  Each end of this series is marked, as far as the survey is concerned, by stations which are part of a large network of passages, the co-ordinates of which can be taken as being substantially correct.  A survey by Irwin (7a) and by Ellis (7b) disagreed by a considerable distance when calculated from the same origin in the Rabbit Warren.  When these surveys were compared with Ellis's earlier calculations (1958) the difference was even more pronounced at 22 ft.  The differences are, in fact, due to calibration differences between the compasses used.  It has been shown that the site used by Ellis to calibrate his compass for the 1962 survey is subject to a large magnetic discrepancy due to buried steelwork. Irwin’s survey was used because it is consistent with the calibration used for the rest of the cave.  When the two Ellis surveys are corrected for differences in calibration, the three surveys are very nearly coincident.

Compass calibration errors cannot be avoided entirely, and the need for extreme care is shown by the fact that the closure errors (Fig iii) are slightly greater than those predicted by Warburton (6) which can be attributed to the unavoidable small errors in calibration.

To sum up, the traverse errors reported in figures (iiia, and iiib) are possible only with great care in compass calibration, when more than one compass is used.

If a single compass is used and the survey is completed very quickly, better closures may be recorded on paper but, whatever closure errors the surveyor reports, without proper calibration procedures the North arrow and hence the alignment of the whole survey will be uncertain.  The surveyor may be unaware of the problem, but anyone who, at a later date, has to survey an extension will certainly find more than his fair share of problems.

Expected Traverse Closure Error For A Grade Six Survey

In 1963, Warburton (6) published two articles in the W.C.C Journal discussing the accuracy of a cave survey, and produced theoretical curves to enable the surveyor to assess the expected accuracy in terms of closure error for any length of traverse. As these curves were based on certain assumptions, they can obviously be used only as a rough and ready guide. They do not allow for human failure in introducing gross errors into the survey and neither the do they allow for the approximate readings gathered from the instruments nor take into consideration the inaccuracies produced by poor calibration.  For the first time ever, a curve is published based on a set of traverses gained from the St. Cuthbert’s survey all to C.R.G. grade 6 and from them on can show from practical experience the expected closure error for a given traverse length. 

Closing A Single Traverse

If the co-ordinates for each station and the end points of the traverse are known, closure of the traverse can take place.  Assume that the beginning of the traverse has the known co-ordinates of E = 0.00, N = 0.00, Ht. = 0.00 but the end co-ordinate differences are N = -1.20, E = +3.60 Ht = -1.80, and there are twenty legs giving a total traverse length of 620 ft., then the traverse closure error is:-

Horizontal error:  = 3.79

Vertical error                                          = 1 .80

To close the traverse, each leg co-ordinate has to be the method shown on page 7:-

Station 1.

N = x

E = y

H = z

Station 2.

N = x +

E = y -

H = z +

Station 3.

N = x +

E = y -

H = z +

&c.

&c.

 

&c.

Thus the final station will have the full errors applied as corrections and will thus be equal to station 1.  The traverse will then close.

SIMPLE MULTIPLE TRAVERSE

If, as in Figure (iv) below, the circular traverse ABC is already closed by the method described, but a further traverse represented by the line ADB exists, then this can be closed on to the existing traverse by a similar method.

Figure (iv)

Editor’s Note:    Owing to the later receipt of material of a more immediate nature, the remainder of this article has been put back to the February issue of the B.B., in which it will be concluded.