of a second, so there is no flicker of tearing from video frame fly-back.
The analysis of the pairs of NAC films from the 1992 experiments presents a number of considerable challenges from the viewpoint of software development. These include the simple problem of finding a useful display of the two sequences, identification and matching of fragments in each, storage and indexing of the very large numbers of images involved, and manipulation of the huge amount of data which will be collected from each film sequence. A rough estimate based upon an inspection of a few test images suggests that up to 500 fragments can be usefully studied in each film sequence (left and right cameras); that is to say approximately 1000 fragment tracks for each shot, with associated rotation and size measurements. These fragments then need to be matched, that is, fragment trajectory x in the left hand view must be tied to trajectory x' in the right hand view, in order to determine the true three-dimensional velocity of the fragment.
The majority of problems have been solved and incorporated into a program called HV-3, the natural progression from HV-2. Alongside the expected problems and challenges, several unexpected complications have arisen. The problems and solutions are described in this chapter. No significant results have yet been collected using HV-3, but sufficient progress has been made in the research programme, in the form of software development, to warrant the inclusion of this chapter within the thesis.
Digitisation of the 1992 NAC film, and subsequent calibration of the system, have been carried out in an almost identical fashion to that used in analysing the 1989 films (see Sections 4.3 and 4.4 respectively), and using the same software without modification in the case of the digitisation. This chapter describes only the significant developments made in the 3D analysis and serves as limited documentation for the (as yet incomplete) HV-3 program.
Development of the HV-3 program, for analysis of the three-dimensional data from our impact experiments, began in November 1992. The first version, numbered version 0.0, was simply written to test screen layouts for the simultaneous study of two film sequences. Various arrangements were tried, including a high-resolution display which allowed both images to be viewed in full on the same screen. This system gave the impression that it would be very difficult to work with, because the separate views were too small. Given that the analysis of the 1989 single-camera data had been perfectly acceptable in terms of image size, the same resolution of display was adopted for HV-3 with a split screen showing half of each view, as shown in Figs 5.4 and 5.5 in the previous chapter. These two views can be scrolled smoothly up and down using the mouse, allowing fragments to be tracked across the entire image in each case. Since it forms the most basic element of the analysis, some time was spent optimising the graphics routines for this. The screen is now redrawn, with both images, in less than of a second, so there is no flicker of tearing from video frame fly-back.
Up to 800 frames per camera, per shot will eventually have been digitised following the 1992 experiments - this corresponds to 2 seconds of film and allows time for fragments to fall back into the field of view if their vertical velocity component is less than ~10 m s-1. This extended data has not yet been used but it is hoped that a parabolic curve fit (possibly taking into account air resistance) will allow fragments to be identified after leaving and re-appearing at the top of the view.
In the 2D analysis program HV-2, a record was kept (within the data file for each shot) of all digitised images which had been recorded. This list was then compared to those offered by the user (for example, on floppy disc) at run time. The HV-3 program, on the other hand, cannot be run from floppy disc and is designed to use a hard disc or CD-ROM drive as the image source. When run, the program quickly scans the hard disc or CD for available images and works within the range found. Images and image directories are expected to conform to a specific format, which must of course be valid on any of the possible file systems. Our CD-ROMs are produced to ISO-9660 format, one aspect of which is that the individual directory and file names must be no longer than 8 characters and these characters must all be upper case. For image files the format used is S_C_FFF where S is the shot number, C the camera and FFF the frame number after detonation of the contact charge; an example is 6_1_055, which would be shot 6, camera 1, frame 55 (frame numbering effectively starts at 000, with frame 000 being immediately before detonation). The expected hard disc or CD-ROM file structure is shown in Fig. 6.1 with some example files indicated. This figure in fact shows the structure of our first in-house CD-ROM, entitled IANS_CDR_01, which holds all 1989 image data as well as shot 6 from the 1992 campaign.
Figure 6.1: The file structure expected by HV-3. Files in these paths are automatically picked up by HV-3 and made available for analysis. The actual position of the HYPERVEL directory within the file system is not defined, and can be set by the user.
As can bee seen from Fig. 6.1, files are initially grouped according to the camera, then into blocks of 50 in order to not exceed the current Acorn ADFS directory limit of 77 files, if the images need to be stored on a hard disc. The directory limit within ISO-9660 is 255 files, still less than the 800 images maximum which could be required. Having worked with this arrangement for some time, it is clear that the CD access times could have been reduced by putting simultaneous frames together on the disc - i.e. using something like 6_1_055A and 6_1_055B for the two camera views at frame number 55 and putting the in the same directory. As it is, the CD drive needs to read the two files from significantly different places on the disc, considerably slowing down any animated display.
Although different keys are now used, fragment tracking in HV-3 is very similar to that in HV-2 (see Section 3.6.3). The most significant difference is that fragments in principle appear in both left and right views. This is catered for by maintaining two three-dimensional arrays, one of which holds x position data and the other y position data. These arrays are fx%(i,f,c) and fy%(i,f,c) where i is the image number, f the fragment number and c the camera. In order to minimise the amount of storage required for the fragment positions, unmatched fragments are overlapped - that is to say, array values corresponding to fragment f in one camera do not necessarily correspond to the fragment with index f in the other camera. This means that another array must be maintained with fmax entries, indicating whether a particular fragment index corresponds to a matched fragment. This complicated process is all handled automatically by the software.
Figure 6.2: An example screen (with the background images 'killed') from the HV-3 program, showing the tracked fragment positions in image 20 for each view. Image pair 20 is shown fully in Fig. 5.5. Each identified fragment is indicated here by a small box, and numerically matched fragments are connected by straight lines. These are not necessarily the same fragment in each view (see text).
The process of matching fragments between views is carried out by matching approximate rotational rates of known fragments. To date this has not yielded many matches but only a small proportion of fragments - 40 in fact - have been tracked. Using the fragment rotation as an identifier avoids the problems of the 2D nature of each separate view, since rotation can be accurately measured from only one film as was done with HV-2. In principle this technique will allow more consistent matches to be made as more fragments are tracked, and the fragment size and flight time can also be used as soon as they are available. Fragment spin rate is measured using a system which is almost identical to that used previously, with the necessary extension that two values of the rotation time are held for each fragment index - i.e. the observed spin rate in each view. These values will not usually be the same until fragments have been matched and the necessary trajectory data copied between array columns.
Assuming that a fragment can be tracked in both left and right film sequences, it is straightforward to calculate the position in 3D space based upon its position in each of our two views. We start by considering the co-ordinates of the fragment in each view, as shown in Fig. 6.3.
Figure 6.3: Co-ordinate labelling for the 3D location of a fragment (indicated here by a grey circle) in the two camera views. Co-ordinates are initially measured from the bottom left of each view.
Since we know the distance of the NAC cameras from the table, we can calculate the angular width and height of the field of view by considering the angular width of the target table (we assume an image aspect ratio of 1:1). We can then calculate the angular position of the fragment in the left and right hand views.
The two NAC cameras form an equilateral triangle (of side length 12.0 ± 0.1 m) with the target table, and a second triangle with the fragment under investigation -this second triangle is indicated in Fig. 6.4.
Figure 6.4: Triangulation of a fragment F based upon its position in each NAC frame. The vector 
and angles a1 and a2 are known.
The angular position of the fragment in each view allows us to calculate the unit vectors from each camera to this fragment. These unit vectors are labelled 
and 
and can be used to find the value of a0 in Fig. 6.4. since
which allows us to then use the sine rule to determine the other unknowns in Fig 6.4:
thus uniquely defining 
and 
, being the distance of the fragment from camera 1 and camera 2 respectively.
This system has not yet been used to measure the 3D position or velocity of any fragments in the 1992 experiments. Nevertheless, the foundations have been laid for a complete analysis of the twin-camera experiments, and this will hopefully be possible in the near future. Assuming that the HV-3 program is developed further and allows full analysis of the 1992 experiments, we will be in the position of having an unprecedented amount of data on an estimated 4000 fragments, across a variety of target structures. It remains to be seen what differences, if any, will be found between the homogeneous and pre-fractured targets, but there will certainly not be a shortage of data with which to make comparisons.