MOUNTAIN PHOTO ORIENTATION

JAGDISH NANAVATI

TIME AND AGAIN we come across instances of climbers who make a claim of ascent of a certain peak, and yet they do not know where exactly they have been. An ascent of mountain x is claimed whilst actually they were on mountain y. Even on the same mountain a claim of reaching a summit may turn out to be an ascent of a lower point on the same mountain, which may be mistaken as the summit.

Such errors take place primarily due to lack of sufficient preliminary homework before embarking on the expedition. Absence of ground study during the expedition is another contributing factor. To avoid such errors advance collection of information and detailed study of the region through maps, photographs and previous accounts cannot be over emphasised. Important locations in the mountain area should be spotted on the survey map after checking the bearings carefully. On return from the expedition, the photographs taken could be studied with the survey maps to establish the locations of the other points from where they were taken. Such studies are fruitful to the climbers themselves as it leads to better understanding of the region visited.¹

At the outset it must be stated that what is being described in this note is the very elementary principle on the subject of photo orientation. The methods mentioned do not boast of any fine degree of accuracy which is needed in map making and surveying. These are best left to the experts in the field. However, mountaineers and trekkers are satisfied with reports of elevation and distances which are expressed correctly within say 50 ft in the matter of elevation and quarter of a mile in distances. Maps used are generally half inch to one mile scale with 200 ft contour interval. Such descriptions of the routes would be of sufficient guidelines for the readers and others to follow.

In this note we are concerned with the methods to discover the inter-relationship which exists between the vertical image on a photograph and the physical features as recorded on a survey map and through these inter-relationships determine the location from where the given photograph was taken.

It is assumed that the principles of map reading are fully grasped. However certain relevant aspects may be recapitulated "here.

A map can be defined as a diagram showing the details and features which exist on ground. It is a representation on paper of a certain area of land. The survey map also aims to indicate the shape and topographic composition of the ground. It is a miniature representation of selected features recorded through the language of signs, The meanings of these signs are generally given at the bottom of a map. These are few and once familiar one can read a map like a book and obtain information on the terrain, distances, heights, and so on.

Scale: A map is a representation of a vast area on a small piece of paper. Therefore one has to restrict the quantity of information reduced on the given span of paper. Relatively speaking, the larger the scale the greater the details contained and the easier it is for establishing a meaningful co-relationship with a photograph of that region. The scale of one inch to two miles is the minimum requirement for such a purpose.

Contours: On a survey map there are series of irregular looking curved lines with some figures shown on them at certain places. These are contour lines, which are merely lines joining points on ground of the same altitude, as indicated by the figures. The contour lines not only show altitude but indicate the shapes of the ground features. By practice one can visualise the shapes of these features by looking at the contours and thus co-relate them on a photograph.

Intervisibility: The contours also indicate the intervisibility between two points on ground. This is determined by plotting a section of ground between the points on a graph paper. It can also be determined by simple mathematical formulae:

Point D would be visible from Pt A provided the height of any point at distance AB does not exceed the height at the line of sight at Pt E.

Ground position: It is best to determine one's position on the ground with the aid of a survey map and record the same on it. The location of camera position would thus be established.

The ground position can be read from the map by

1. laying the map and co-relating with visible physical features,
2. by reading bearings of known physical features with the use of a prismatic compass and then plotting the location on the map by working out the back bearings.

Just as a map is a representation of ground on a small span of paper, a photograph records the image of the ground from a given camera position. In the case of a photo of a mountain region, the camera records vertical images, as affected by distances between the camera and the objects and the camera tilt. Unlike the map, the photo taken by a camera does not represent a diagram in uniform scale, since the image of objects is affected by both the distances from the camera position and the tilt of the camera itself.

Perspective denotes relative sizes and shape of objects recorded by the camera on a plane surface of the negative. Perspective is altered by moving the camera closer or away from the objects; similarly perspective is affected by raising or lowering the camera and tilting the camera forwards or backwards. If the focal length of the lens on the camera is changed without moving the camera location there is no change in perspective. But if thet camera position is altered, the perspective is immediately altered. (See Fig. 1, 2, 3, and 4)

Camera lenses with varying focal length have specific angle of view which is usually expressed for the diagonal length of the negative. The angle can be obtained for the horizontal dimension, or worked out from the figure given for the diagonal. A particular lens of 50 mm focal length on a 35 mm camera would accept a view of 45° diagonally, 39° horizontal and 27° vertically. Lens maker's data may be referred for each type of lens and camera.

Thus the full view of the negative would record a known span which could be used for determining bearings provided the camera was levelled when taking the photo. Preferably, use a stand with level indicators. Whilst on location select two well separated bearings from within a particular camera view. For example one may be due north i.e., 360° and the other 20°. The bearings should be selected in such a manner that there are two prominent objects cutting the respective bearings, say a and b on 360° and x and y on 20°.

If the photo was taken with camera levelled the objects a and b would fall on one vertical line on the photo and the objects x and y on another, both vertical lines being parallel on the photo and representing 360° and 20° bearings.

When such a photo is suitably enlarged and placed under a transparent graph sheet with same number of vertical and horizontal divisions as respective angles of view, the lines would indicate horizontal and vertical angles from the camera location. The horizontal centre line would represent the level line.

It will be seen that to avoid distortion of the image, the camera should be as levelled as possible. Special cameras (photo-theodolites) are fitted with elaborate levelling devices. However, it is not difficult to obtain photographs with camera held in a reasonably levelled position. If the horizon is visible, positioning the same in the horizontal centre line of the view finder will ensure a levelled photograph.

Assuming that the photograph is taken with camera levelled, each vertical line on the photo would represent a bearing in the same way as seen through a prismatic compass. In other words, each object falling on such a vertical line on a photograph would have the same bearing. A levelled photo is thus a true record of bearings and can be used for identifying various points with the use of a survey map. Such a photo will also have a horizon line (whether actually visible or not) which denotes points of equal altitude as that of the camera position. This aspect of the horizon line will not be affected by the tilt or the distances between features of equal heights and the camera. (Except for minor variation due to the factor of curvature of earth and refraction of light, which can be determined with reference to a table of calculations given in a survey book.) (See fig. 5)

Keeping in mind the above elementary principles of map reading and the nature of the photographic image, we may now turn to methods of determining the camera position of a given photograph, with the aid of a survey map. It would be helpful to collect photographs of the region taken from various locations. This would assist in identifying important features. Mark on the photograph and the survey map all such features which could be identified, e.g. peaks, spurs, valleys, ranges, glaciers etc. Mark on the photograph the heights of identified points as given on the map. Notice the horizontal space between the points/peaks identified (Greater the horizontal space, greater the angle or the difference of bearings). Notice the vertical space between horizontal lines cutting various points/peaks. (Greater the vertical space does not indicate more relative height or altitude except for points of equal distance from the camera position.)

Having marked the identifications of points on the photograph and the survey map it may be possible to select sets of identified points (preferably of varying distances) on the photograph falling on respective vertical lines (each representing a bearing). Join sets of such common points on the survey map and project them to the point of convergence, indicating the camera position.

Identification of points on a photo may reveal that point 'A’ of 13,000 ft in the distance appears on the photo lower than a nearby point ‘C^’ of 10,000 ft altitude. (Fig. 3) This indicates that the camera position was lower than the altitude of point 'C.

To illustrate the actual identification of camera position, we may turn to a photo of the Nilkantha range published in the Himalayan Journal Vol. XVIII opp. p. 104, taken by J. A. Jackson whilst his party was attempting a peak Pt 20,330 ft in the Bangneu Bamak region, which they named as 'Avalanche Peak*. (See Panorama I) The photo was taken en route after climbing above Camp 2 (17,000 ft) on the glacier. However, the exact location or its height was not indicated in the article, Identified common points are marked on both the photo and the Sketch map respectively. (See Fig. 6 and Panorama I) It will be noticed that no two identified points fall in a vertical line on the photograph. Hence direct converging lines pointing to the camera position at their intersection point cannot be drawn on the map. However, from a preliminary examination of the photo it can be safely concluded that the camera position lies demarcated within a triangular boundary of OE'J' shown on the sketch map. This is evident from the following:

1. In the photo, Pt D is to the left of Pt E. As such the camera position should be to the east of line OE' extended from DE.
2. The photo shows only 1/3 of the southwest ridge from west col H leading to Pt L, as Pt J blocks the view. Even Pt K 20,000 ft on the^HL ridge is not visible. Thus the camera position would lie somewhere to the west of the line OJ' extended from LJ on the map.
3. In the photo, since Pt E 18,200 + ft appears higher than Pt D 19,000 ft, the camera position cannot be higher than the altitude of E i.e., 18,200 + say, 200 ft (contour interval) = 18,400 ft. (E's height is denoted by 18,200 ft contour only)
4. The extended lines from DE and LJ cut at O. The contour line for 18,400 ft may bej joined between the lines OE' and OJ' forming a triangle OE'J' within which the camera position must lie.

Points B, F and J are three relatively well fixed identified points on the map and their relative position on the photo represents the co-relation in their horizontal angles from the view point. A supplementary counter check was afforded by points E and H, although these are not intersected points denoted by spot heights.

On careful examination of a series of alternative positions within the triangular boundary OE'J' and co-relating horizontal angles to photographic dispersions of various points, an estimated camera position x could be fixed which is found generally satisfactory. It is estimated that the camera position would be within a radius of half a furlong from position x marked on the map. Reading from the contour lines, the altitude of the position x is indicated to be 18,000 + ft.

Independent of the contour indication the altitude of the position x (and thus a location on a slope) can be worked out independently by the following method:

(a) The photo shows Pt J (18,870 ft) and F (Nilkantha, 21,640 ft) at almost identical horizontal line, or at nearly identical angles of elevation along their respective lines of sight. The altitude of the camera position can be calculated since the altitude of F and J and their respective distances can be read from the survey map. Correction for curvature/refraction has been applied to the distances to Pts J and F. i.e. yj=1.5 ft and zf= 28.15 ft.

The camera position x would be at an altitude of say, 18,075 ft.

Thus it could be safely concluded that the camera position for Jackson's photo was located about 7 miles north of Nilkantha on the southern slopes of Avalanche Peak, at an altitude of about 18,075 ft, within a very small margin of variation.

The above exercise was towards determining the camera position and altitude on a slope whilst climbing a known mountain.

One also comes across summit photographs claimed to have been taken from a mountain x, whilst on closer examination of the summit photos on the same lines as above, indicate that the climbers were on another mountain y. Such gross errors generally take place due to lack of adequate ground study or faulty map reading. However, determining the camera location of summit photographs would be easier than the one from a mountain slope. A summit, by its very nature, is a high single point. Converging lines drawn on map from identified points would lead to the true mountain or the summit climbed.

An expedition claiming to have made the first ascent of Sudarshan 21,350 ft in 1972 had taken a number of photographs from the summit showing adjoining peaks. However, Sudarshan itself was seen in one of the summit photo. The climbers mistook it as Matri 22,050 ft! Clearly there was a case of mis-identification of peaks seen as well as the peak climbed. Matri is only 700 ft (213 m) higher than Sudarshan and at distance of 15,421 ft (4700 m) from Sudarshan. The vertical angle between two points on a survey map can be calculated based on the horizontal distances and the difference of height between two points in question. Such an exercise reveals that Matri should have made a low vertical angle of 2° 36' only from Sudarshan. However, the vertical angle made by the peak as seen in the summit photo, was indeed higher. A reflection on this aspect alone would have indicated to the climbers that the peak seen could not have been Matri, and thus they could not have been on the summit of Sudarshan. From the other excellent summit photos it was easy to establish that the climbers were actually on peak Koteshwar 19,800 + ft which is c 1500 ft lower and 1.5 miles southeast of Sudarshan thus rendering it on the photo to be at a larger vertical angle (fig, 7).

In fairness to the expedition it must be stated that when the errors were pointed out to the leader and followed by discussions, he accepted the correct position and withdrew the claim of the ascent of Sudarshan.

Another expedition had claimed the first ascent of Swargarohini I 6252 m in 1977. A good description of the route and photographs were also given, including location of camps. On a visit to the area in 1984, the coordinates of peaks as seen in the photos together with descriptions of routes were studied on ground which indicated clearly that they had climbed Swargarohini IV 5966 m.

It appears that the climbers had misjudged the location of their base camp to be under Swargarohini I, when they were actually towards Swargarohini IV, after turning a prominent spur down from the main massif of I.

The ascent of Swargarohini IV was indeed a creditable climb. This misidentification was immediately appreciated by the leader when it was shown to him.

It was unfortunate that such an agreement could not be achieved on a mistaken claim of the ascent of Matri 22,050 ft by a women's team in 1962. The climbers entered Thelu Bamak and reached Pt 19,690 ft at its head (See Fig. 7 Map), what is now known as Thelu Peak. They announced it to be the first ascent of Matri I In spite of showing the contradiction in their descriptions of the route and the fact that Matri is unapproachable from Thelu Bamak, the leader refused to recognise the error. Notions of false prestige prevented recognition of the truth.²

The camera position for Jackson's photo was located by interpreting the co-relations of indentified points on the photo and the survey map. The camera position can be verified by another fascinating method i.e., by picturisation of the scene on a graph paper by interpreting the heights and distances from an assumed location on the map.

A fine illustration is the sketch in this journal (p. 64) prepared by Arun Samant. This sketch of the Bandarpunch basin is not an imaginary one. It is actually developed by applying the basic principles described earlier on the nature of photographic image in relation to the view from a camera location.

A camera was assumed to be placed at 10,000 m altitude in midair above Bali Pass (map p. 64) and vertically tilted at an angle of 20° downward looking at the Bandarpunch basin. On the contour map about forty prominent points were selected scattered over the main ridges, boundaries of glacier, icefalls etc., which would fall-within the visual cone of the camera, having horizontal dispersion of —20° to +20° (40° in all) and vertical dispersion of —10° to +10° (20° in all) in relation to the optical axis of the lens. On the map each of the forty points were joined to the point of the assumed camera location at 10,000 m in mid-air over Bali Pass (i.e. in plan). Thus horizontal co-ordinates of each point in terms of degrees could be read from the map. Similarly, vertical co-ordinates in term of degrees were calculated trigonometrically by finding dip of each point below camera position at 10,000 m, to the contours shown on map for the forty selected points, and their respective horizontal distances from the camera position.

By adopting a suitable scale between degrees and linear distances (i.e. 1° = 5 mm), all the forty points were plotted on a graph paper. By joining these forty points appropriately the sketch was then completed, with certain details added by map reading. The sketch clearly represents the view the camera would have taken if placed in mid-air at an assumed location and altitude.

Similar map-developed sketch can be made from a terrestrial location x and compared with the actual photograph said to have been taken from such a point. The sketch and the photo would be identical if both the locations are the same. If not, the photo was taken from a location other than the one from where the sketch was developed.

We may turn back to Jackson's photo of Nilkantha range. It was found that the photo of Nilkantha was taken from a long distance of about 7 miles and a high elevation of about 18,075 ft. It revealed Nilkantha's northface and the west ridge in a good perspective view. This section of the photo was enlarged and placed on a graph paper to produce a photo-chart 'A' which enabled estimates of altitude of the mountain's various physical features within a small margin of error (in terms of heights in mountaineering estimates). (Panorama J)

The horizontal distances from the camera position to the summit of Nilkantha F, a prominent feature G on the west ridge, and the west col H, were measured from the survey map to be 6 miles 7| furlongs, 6 miles 7| furlongs and 7 miles 1/16 furlongs respectively.* A line joining the summit F and the west col H (FH) is nearly normal to the line of sight from the camera position x (^xFH = 91.5°). The photo thus revealed the true nature of the gradient of the west ridge without undue distortion. Since the difference in altitudes of two extreme points on the west ridge, the summit 21,640 ft and west col about 17,900 ft, were known, a linear interpolated scale was obtained along the west ridge FH, Since the distance between the west ridge (FH) and the camera, position (x) was very large (xF = 36,712.5 ft, xH = 37,001,25 ft) in relation to the height (3750 ft) interpolated, the results of linear interpolation are uniformly reliable.

As the altitude of the camera position was estimated at about 13,075 ft, the horizontal line at a distance of 6 miles 7| furlongs would be at an elevation of about 18,075 ft + 28 ft (correction due to curvature of earth/refraction) = 18,103 ft. Thus the approximate horizontal plane line PL on the photo chart cutting at about 18,103 ft, reveals points of similar altitude as that of the camera position x, subject to corrections for curvature/refraction at a given distance.

The scale on the photo-chart 'A' is linearly applied over the line FH. Points on the north face of Nilkantha are nearer to the camera position x. As such the horizontal lines drawn from selected points on the north face to the scale line FH would indicate a slightly inflated altitude, provided the points are above the horizontal plane line PL. The degree of such inflated altitude will depend upon the combined factor of the respective elevation of the selected points and their distances from the camera position x. Calculation reveal that the following selected points on the xF line and elsewhere would show variations as under:

 

* 6 miles 7-5/8 furlongs = .36,712.5 ft = 11,190 m

6 miles 7-3/8 furlongs « 36,547.5 ft = 11,140 m

7 miles 1/16 furlongs = 37,001.25 ft = 11,278 m

 

The variations above the horizontal line PL to points west of line x'F will be under 50 ft. The scale FH is well applicable to the west ridge as the maximum variation is shown by the variation for the point G i.e. 15 ft. Other points on the west ridge are closer to the line FH thus narrowing the variations still further.

It may be pointed out that the height of Pt G on the west ridge was shown by a circular] contour of 20,400 ft indicating it to be somewhat higher than that (contour intervals 200 ft). However the photochart has revealed its altitude to be at 20,171 ft which was subsequently confirmed.

The above examination of the photochart Illustrates the use a mountaineer can make of suitable photographs for determining locations and estimate altitude of various physical features on a mountain.

The scope of this note does not permit the full exposition of the controversy raised by the claim in 1961 of the first ascent of Nilkantha.³ This must await another occasion. However, certain comments must be mentioned very briefly as important issues were raised as a direct result of revelations through the photochart A.

The second Inquiry Committee⁴ which went into the claims of the Indian Nilkantha Expedition 1961,⁵ had got the Survey of India to prepare a special 1:10,000 scale map with 100 ft contour interval. By examination of vertical aerial photograph of Nilkantha, with stereoplotting instruments, the heights of important features on the mountain were given by the Committee as seen below and may be compared with those shown by the photochart:

 

* It may be noted that the scale on the photochart was obtained by linear interpolation of difference of altitude between the summit 21,640 ft and approximate height of west col at 17,900 ft (in the absence of spot height). Now, taking the west col at 17,960 ft the heights obtained from the revised scale for respective points above, will indicate altitude figures in closer proximity to those given by the special survey.

However, for the purpose of a mountaineering account the altitude estimates of features and locations nearing 50 ft plus or minus are quite satisfactory. The methods and safeguards adopted to prepare the photochart 'A' can be profitably used by climbers. It is a sad commentary on the Indian Nilkantha Expedition 1961 that their original expedition account would have us believe Hump V (Pt G) to be above 21,350 ft and that too after claiming the first ascent of the peak by a summit party of a member and two Sherpas! The climbers¹ admittedly had poor conception of the true perspective of the mountain and the route they had set on to climb, although they had with them half inch survey map. The trained eyes of an army captain and other officers ought not to take more than five minutes to grasp the true significance of the contours on the summit ridge and the relative altitude of crucial point G.

The Enquiry Committee explains:

'None of the members of the expedition could provide the correct heights of the different campsi as the expedition carried neither altimeter nor maps beyond the base camp.' No study even after the return ?

It was only after the photochart A was sent by this author to the sponsors* together with detailed comments pointing out serious errors, that the altitude of the expedition's camps got drastically deflated in successively revised versions, in an attempt to explain serious contradictions whilst still maintaining the claim of the ascent having been made. The crucial last Camp 5, originally given at 21,200 ft by the leader, dropped to 20,600 ft under the first inquiry by a Survey Officer*⁵, and then to 19,970 ft in the last version given out by the second Inquiry Committee. The site of Camp 5 was taken by the Committee at a point 230 ft below the ridge near Hump V (Pt G) as shown on the photograph (of the mountain) by the leader. The Inquiry Committee estimated the height to be 19,970 ft at that site. No photographs were available to establish location of Camp 5 or indeed of the so-called summit climb. Weather was atrocious. The summit film roll got exposed whilst removing from the camera at Camp 5. It said: 'No conclusive photographs of Camp 5 or beyond were available.' Although expressedly unconvinced by the summit account given by the lone member*, the Inquiry Committee charitably gave the benefit of doubt to the summit party on nonconclusive grounds.** At the same time it went out of its way to recommend another attempt for next year i.e, 1964, which incidentally never took place, under IMF banner.⁷

Commenting on the report of the Inquiry Committee, the Alpine Journal, London (Vol 69 May 1964 No. 308 p. 145) stated:

'The Committee... ('s) support of the claim is hedged round with certain qualifications that strike one awkwardly...... certainly the report of the committee tends to give the reader the impression of being one of those 'smoothing-over* committee reports that one knows so well; on the one hand, commending Mr Nanavati for having drawn attention to errors, and on the other trying to avoid saying that the claim to have made the ascent cannot be accepted. Their final recommendation, that another Nilkantha Expedition be set on foot, sounds very much like a tacit admission of not being quite satisfied, though giving Mr Sharma the benefit of all doubts.

'All things considered, one is, a little surprised at the committee's findings and wonders* if it might not have been better had they merely recorded a 'non-proven' decision, which the coming expedition could confirm or otherwise.'—unquote

The story of Nilkantha Expedition 1961 is apparently a classic example of how not to conduct an expedition.⁸ The Inquiry Committee goes on to list such do's and don'ts and finally to top it all, to 'recommend the Survey of India...... to attach some........ surveyors to expeditions to peaks of comparatively lesser known topography'. In the context of its reference does the Committee suggests Nilkantha as one such? Six previous attempts had taken place before 1961 with their accounts published in the Himalayan Journal and elsewhere and an excellent half inch survey map published years ago. Nilkantha is almost in the backyard of Badrinath ! Do one really need a surveyor on Nilkantha to read maps and mark heights on the routes for sahibs to see ?

It may be said that photo orientation falls within the technical realms of the science and craft of photo surveying and map making. However with elementary understanding of the survey maps and the nature of photographic image, even a lay climber can also derive valuable data by applying their co-relations and obtaining greater insight into the topography of the mountain world.

REFERENCES

1. Himalayan Journal Vol 32 p. 128, 'On Claiming Peaks' by S. S. Mehta.
2. The Climbers Club Bulletin (Bombay) No. 8, April 1964, p. 12 'Matri Affair by Jagdish Nanavati.
3. Himalayan Journal Vol XXIV, p. 148 note. Also, 'Nilkantha — Still Unelimbec!?' by Jagdish Nanavati, November 1963, a typed script study, 70 pages.
4. Col B. S. Jaswal, Chairman (1963), summary, Himalayan Journal Vol XXIV, p. 150.
5. Led by Capt Narinder Kumar.
6. Major N. B. Nayar, Survey of India (1962), Directorate of Military Survey. Major Nayar had completely ignored the photo chart 'A' offhand. A detailed separate note on photo-altitude chart was sent by this author to Mr P. C. Sen Gupta, an ex-officer Survey of India 1914-50, also Air Survey Company of India, 1950-60 and author of 'How to Map the Earth'.
   Mr Sen Gupta observed*. 'I had the pleasure of going through your paper and workings for the heights in order to test the accuracy of the (photo) Altitude Chart (A) and for the location of the camera-position on Map (II). The results are uniformly good’.
   ‘ . . . There is no justifiable reason to ignore examination of the workings for the preparation of the photo-chart. I found it very interesting, and have reasons enough to consider my labour as well rewarded, especially because of their origination from one who cannot be expected to have dealt with the matter so efficiently, not being in our line of experience and observation, and more because the plotting has been done extremely carefully with a view to get to reliable results'
   A professor of the University of Roorkee, had also independently found the methods adopted for the photo-chart 'A' as quite sound.
   The fallacies of Major Nayar's Report having been exposed, the Indian Mountaineering Foundation was compelled to appoint the second Inquiry Committee which came up with another expedition version.
7. Himalayan Club Newsletter No. 30, p. 23, reports an ascent of Nilkantha by J&ado Tibetan Border Police team on 3 June 1974 led by £. P. Gfenna. No details were published.
8. The Climbers Club Bulletin (Bombay) No. 2 August 1963, p. 9, contains an excellent exposition on the subject, 'Rules of the Game' by Ashoka Madgavkar.

 

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