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Research Paper (National Research Council of Canada. Division of Building
Research); no. DBR-RP-278, 1966-01
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A fire problem in aircraft accident investigation
A N A L ~ ~ z E D
AIRCRAFT
VESTIGATION
Research Paper No. 278
,f the
Division 'ding Research
Price 10 cents
CANADIAN
AERONAUTI
Volume 12, No. 1
National Research Council
the wrec1;agc of cr,lslied aircraft, fr'~grlle~lts are often to sllow sign3 of fire, and it may be of great importance erlnlne whether fire preceded or followed the crash. If a rtain number of fire-marked fragments should be found to on co one another, this ~ l l a y be due to chance or to marlting fore fracture. Thls study provides a nleans of estimatirrg the probability of given configurations on the hypothe\is of random distributio11 of the marked pieces.
s important part of the task of accounting for an ircraft accident lies in atte~upting to determine ther any part of the aircraft was on fire before it
.
Survivors or a flight recorder might be able er this question, but if there are no survivors or e record is defective, some difficulty may arise.If spilled fuel burnecl on the ground, it may be fficult to tell whether inarlts of burning found on recltage are due to this or \vhether they appcared fore impact. T h e high speed and heavy fuel loads of dern aircraft may result in a multitude of fragments and many fires distributed ovcr thc impact area.
Some guidance in this probleni is givcn by official manuals on accident investigation'. In certain circum- stances, conclusions may bc drawn from the proximity of marked pieces to one another in a reconstruction of the aircraft. Such conclusions have hitherto becn a mattcr of judgment, but a recent accident has providcd an opportunity to ailalyze the problem, and this has re- sulted in the development of a method that, when cir- cumstances permit its use, will permit judgment t o bc assisted by calculation. It is thought that the result may t)e of value to investigators of futurc accidents, and nxly perhaps have other applications.
In what follows, thc adjective "marlted" applied to a fragment of wreckage will mean that it is burned, fused, or clearly fire- or smoke-marltcd. Clean frac- tures on a marked fragment are normally an indication of marlting before impact, but their absence does not prove the contrary bccause the same fragmcnt may have been marlted both bcfore and after i r n ~ a c t . Thus no conclusions can justly be drawn from a single frag- ment or from a nurnber of unrelated fragments.
It is the standard practicc of investigators to rccord the co-ordinates of the location from which such a iReceived 19th July, 1965
'Division of Buildiilg Research
fragment is recovered, and to detenninc as exactly as possiblc its place on the aircraft. Drastic measures may on occasion be necessary in the recovery operation, but if a fragment is further fractured during recovery the fact can usually be demonstrated. Experiment' has shown that the marks of fire are tenacious enough to survive burial in wet clay and subsequent washing with watcr hoses.
Subjcct to various qualifications, two
inay be statcd. If a number of n~arked fragments from different parts of an aircraft are found at one location and unn~arltcd fragments have been found elsewhere, it is an indication of ground fire; conversely, if marlted fragments from one part of the aircraft are found at several separate locations and unmarked fragments are also found, it is an indication of marlting before impact. A qualification of the second proposition is that fuel distributed by impact may collect and burn in l~ollo\vs in the ground or in dished fragments, so that a number of clean fragments from one part of the air- craft might conceivably becomc marked at several diffcrcnt ground locations. T h c subsccluent rcconstruc- tion would secm to give an untrue indication of fire in that particular part of the aircraft. Thus a Froup of marltcd pieccs, contiguous in thc rcconstruct~on, may be duc either to marlting before impact or to chancc or random causcs. T h e probability of a random group- ing can bc estimatcd statistically, as will be sho~vn; if it is lo~v, it is evidcncc in favour of marlting before fracture.
Suppose that a tcam of investigators has assembled a reconstruction of the aircraft from thc fragments as well as circumstances permit. Each marlted fragment that docs not bcar clear signs of ground firc supplies a hint, and by itsclf only a vcry slight hint, that perhaps it was lnarlted bcfore impact. If in the reconstruction several such pieces abut on one another' without inter-
vening clean fragments, however, the indication be- comes a strong one. T h e character of edges produced by fractures of aluminun~ alloy sheets, particularly the thiclt sheets uscd for wings, is such as t o lcavc no doubt ~vhcther two pieccs match, and this ltind of evidence is durable enough to survive nluch rough handling.
T h e practical problem is, with economy of time and labour, to read the message that the ~vrecltage is carrying and to assess, quantitatively if possible, how
strong is any indication found. Without requiring that a place in thc reconstruction be found for every fragment, and with much less labour than this would require, a search can be made for groups of marlted pieces that fit together. T h e procedure demands dili- gence, but no especial ingenuity. First the marlted pieces are separated from the rest and classified as t o general position on the aircraft, for example, b y surfacc finish and rivct spacing. Those parts that are smolte marlted from normal operation of the aircraft, such as thrust reversal buckets, would naturally be excluded. In such regions as wing surfaces, thick- ness may be continually graduated from root to tip. By classification on such indications as this, the search is narrou.ed to a number of piles separated so that all thc pieces that can possibly fit together are in the same pile. When no further brealtdowil can be made, the pieces in each pile arc tried edge to edge \\>it11 one another. If this worlc results in the assembly of a group of pieces numerous enough to be significant in the light of this analysis, the next step is to compare the cdges of the group with those of all clean pieccs in comparable categories. If one clean piece adjoins the group it will disqualify it as evidence of fire before rupture, unless therc is some special explanation. NOIMENCLATURE
c, s Constants in empirical expression for F ,
F,
Nuinber of grotlps of g contig-uous pieces, irrespec- tive of marlungg Number of co~ltiguous pieccs in a group
G Number of groups of contiguous marked pieces in one replicatioil
7n Proportion of fragments rccovered and found t o
be marltcd
N A4ean over all fragments of thc lumber of "neigh- t)ours", i.e. fragments having edges in common ~ v i t h a given fragment
p
I'robability of a particular configurationQ , Eapcctcd nuinbcr of groups cach having g con- tiguous marked pieccs
t Sun1 of probabilities cqual to or less than /I
ANALYSIS
T o interpret the findings of the search for marked groups, thc statistical null hypothesis that they ma!. be due to random causcs, i.c. chance, is examined.
Suppose that an area of surface is fractured into a large number, F,, of fragments; that a substantial nu11-r- ber of these are recovered, enabling an estimate to bc made of F,; and that a proportion n 7 of F , is both re- covered and found to be marked b y fire. Let the num- bcr of marlted pieces recovered be Q,.
QI = ~ I I F ~ (1)
Suppose that, on the average, each fragmcnt would abut on N neighbouring fragments if they had becn found. On the random hypothesis, the Q, marked pieces will have Q,N neighbours, of which mQIN will also be marlted. IVith this ilumbcr of pieces participat- ing, the expected number of marked pairs must be
E { Q ~ } = nlQIh7/2 (2)
In every case to w h i c l ~ this analysis is applicd it should be possible to find roughly this number of
0 1 2 3 4 5 6 7 8 9
P I E C E S P E R G R O U P
Figure 1
Some grollp counts
marlted pairs. If many Inore than this are found, doubt is cast upon the random hypotl~esis.
T h e number of pairs, marlted or not, that could have been made up fro111 the F , fragments, if they had all been found, is
13~- sul)stitution in Eq. ( 2 ) from Eqs. ( I ) and ( 3 ) :
A Inore general rcsult of which Eqs. ( 1) and (4) ,lrc special cases may now be derived. Consider the Ii, possible contiguous combinations of g pieccs selected out of the total availablc, i.e. F,. (But for the contiguity condition, F , \ ~ o u l d be
F 1 ! / g ! ( F 1 - g ) !
Onll- some of thc con~binations nrc contiguous how- ever.) Each of the g picces \\rill have a probability ?)/
of being both marlccd and recovcrcd, and if the distri- bution of marlting is random the probability that any one combination will be fully recovered with inarlting on each piece is 711" Thus the number of marlted groups
of 8 pieces that can be expected is
N o sinlplc method of estimating F , has been found. T h e method that has becn adopted is t o count groups for a 11umber of arbitrarily drawn random patterns and endeavour to relate the counts to the readily observable pararnetcrs of the patterns. Approximate empirical formulae for F , may be found thereby.
T h c actual counting of the possible contiguous combinations of g pieces within each arbitrary pattern was performed by a computer program. Some notes on this are given in Appendix A. A study of the counts (see Figure 1) reveals that, for a given pattern con- taining many more than g pieces, the ratio of F , to
F,,-,, is roughly constant, but passcs through a maxi- mum that will be called s.
ACTUAI. A S D CALCULATED NUMBER
or: GROUPS I N A PATTERX
A11 acccptat)lc appro~iination is providcd by
F, = (Fl7(g-l) (6 )
whcrc c is a constant, 0.7.
T h c ratio s sccms to be a function of thc numbcr of picccs in the pattcrn, of the number of ncighbours averagcd over every picce, and of \vhether the surfacc is a closed one. hTo simplc gcneralization has been found that fits all thc observations. For the prcsent pur- pose, ho\vevcr, whcre a conservativc figure is needcd, i.e. a high one, it is rcasonablc to take thc highest s valuc so far found for a random pattcrn; this is 3.6.
Eq. (6) ma!- be illustrated by comparison with an actual count for a pattern of 20 picces taltcn from a report by Jones' (see Table 1).
If chancc alone govcrns, and if in each of a long series of replications the mean cspected number of contiguous groups of g nlarltcd pieces is Q,, then the
Poisson scrics yields a probability for a replication containing G such groups
Q," CAI,( - Q,), G! ( 7 )
BJ- way of illustration, considcr an invcstigation in \vhich 60 markcd fragnlcnts arc rccovcrcd of an esti- n~ated 2000 fragnlcnts. F , from Eq. ( 6 ) and (I,from Eq. ( 5 ) arc givcn in Table 7 , together with thc pro- t)abilitics of finding G groups for G from 0 to 5 . From this tablc it ma!- be inferred that thc most probablc ilumbcr of groups of 3 or more nlarltcd pieces is zero; that the most probahle number of groups of 2 markcd pieces is 4; and that the most probablc number of singlc pieces is much grcatcr than 4.
Given that a certain unliltely configuration of markcd picces has a probability
p,
thc probability of random occurrence of a configuration as unlikely as this is t , the sum of thc probabilities of all possible configurations equal to or less thanp.
-
1
EstimatedAs thc probability that no groups of g picccs will be present is
evp( - Q,) (8)
the probability of no groups of g, and no groups of
g
+
1 or more is the product of a11 infinitc scries of similar terms -- Coun tccl---
F2 F3 FI F5 FoF7 groups of 2 Hcnce thc prot)at)ility of somc, i.c. one or illorc o r morc picces, is
Error per cen 1 50 181 653 2350 8460 30500
and t)ccausc Eq. ( 6 ) , thc appro\imation adoptcd for
F,,
leads to Q, .- c / ~ , ( . s I I I ~ / . s (11) it follo\t.s that 5 1 173 615 2037 5956 14845Continuing thc example already givcn, this quantity is tabulated in thc last column of Tablc 2.
T h e possiblc crplanatioils of thc unlikely configura- tions of marked pieccs supposcd to hare been observed are as follows: - 2 +5
+
6+
15 +42 +lo5 (a) chance,( b ) marlting beforc fracture, ( c ) othcr causes.
Category (c) includes such eiplanations as that the configuration resulted from sccondary fracture of a singlc fragment that had becn n~arlted as it flew through the air after primary fracture. All category ( c ) cxplanations are considercd to depcnd 011 remotc
possibilities. If so, and if thc probability t of arriving by chancc at a configuration as unlil;ely as the obscrved one is found by the reasoning above to be a small quantity, thcn the possibility (b), that the fragmcnts
11 crc nlarlted beforc fracture, rnust not be disregarded.
If t is of the order of unity, however, the observed facts can bc ascribed t o chancc, and no evidcncc will have bcen found of marking before rupture.
QUALIFICATIONS
It is not suggested that investigators should cvcr rely on this method alonc. T h e most that can be claimed is that where, a priori, doubt exists, this
Italics indicate the most probablc number of groups of each size.
group g r o ~ l p s marlced probability
.! ? F, Q, t Evpcctccl number I'robabilil!. of G = -- Piece5 Per S ~ m l m e d N u m l ~ c r of contiguous
recovered than small ones, and that marlting
may make a piece more, or perhaps less, liltely received their marl<ing 1)cfore fracture. to be recovered; and
ACKNOWLEDGEMENTS
ten1 is sufficiently accurate.
combinatorial aspects of the problem.
ciation are well established' and need not be described 1961.
here. It will suffice t o remarl< that ,quadrat bound- ( 2 ) Gwih, S. - Private c o m m ~ ~ n i c ~ ~ t i o n , aries on a surface of graduated thickness, such as the OT rALV.1.
wings of certain aircraft, could well be drawn t o co- ( 3 ) Jones, F. H. - Aircraft Accideilt Ii~cestignti incide with loci of constant thickness, thus avoiding the
necessity for precise location of a fragment of which (+) ~1,,,,, 11, -4, E, - ~ ~~ ~ ~ ~Dirta, ~J l ~ l i~ ~ l~ ~ ~~ i ~ ~ ~i ~ ~ ~
only the thickness is known. LOYLIOX, 1961.
APPENDIX
A
COUNTINGPWOCEDUREFORCONTIGUOUSGROUPS Given a drawing of a fracture pattern, the pieces are numbered from one upwards and this number is regarded as a name for each piece. A table is then pre- pared with all the names in the left hand column, and against each the names of all those pieces that have a common edge with it. Tlds is known as the joins list. For any group of pieces, a joins list may be compiled from the joins lists of individual pieces. These lists arc manually punched on cards, which are read as data t)y the computer programs.
Three different techniques for counting groups, .A, B and C, were developed, and each was independently programmed. In Method A, using "chain develop- ment", each tiille a piece was joined t o a forming group its (vacant) joins werc inspected and the nest piece selected from them. In Method B, "radial develop- ment", each time a joins list was formed it was a list of all the joins of the group. In both these methods only contiguous groups were formed, most of them many times over, especially with Method B. Different types
werc for~lied different numbers of times, so that each type had to be identified before it was counted.
In Method C, each of the possible co~llbinations of the pieces \\us fornled only once, whether it was con- tiguous or not. T h e test for contiguity consisted in I~uilding up the largest contiguous group possible with- in each combination. If this group ended by coinciding with the combination, it was counted as contiguous, otherwise not.
,\/Lethod X was unsatisfactory, 1)ecause it could not form all the possible groups. ( T h e simplest example of this is a group where three pieces join a central piece without joining one another.) Both Methods B and C gave correct counts. C was faster, but Method B was useful, because it could be used for a cluick check of the data and \\lould detect errors in the joins table that C would not.
Programs written in SDS 920 Fortran are available. _Anyone who needs a pattern counted is invited t o con- sult the author.
