r1EASE~ TECHNICAL INrORtI.ATlvN CENTRE $OR EST FIRE RESEARCH INSTITUn:
CANADA
Department of Forestry
1\ COST ANALYSIS OF A LOOKOUT -
AIRCRAFT FOP.EST FIRE DETECTION SYSTEM
by
P.R. Kourtz
(Pro.iect F-54l
Nanuscript for proposed departmental publicption
(Ple!,-se do not quote from thi.s text)
Oxf. Cl.,ss. 432.23:671
O+~ t "1"'<1-
l~ay, 1965
65-H-6
A Cost Analysis of a Lookout Aircraft Forest Fire Detect jon System
Introduction
For many years fixed lookouts h~ve been the basis of almost
every forest protect'on agencies' detection system. Recentl~, li~ht air
craft have been used to supplement the t01 .. er system in areas i!lacteqllstely
protected. However, because of rising looko'lt costs and the sllccess of
the aircraft, some forest protection agencies are cons~dering abandoning
m~ny or all of their lookouts in favour of a lookout-aircraft or all
aircraft detection system.
There 3re adva)'"ltae;es ard disadvantages to systems l"€ly:1ng Mainly
on lookouts or to systems relying mainly "n aircrAft. Up until now, an
argument could have been presented to make ei thE:'r system arrear the best.
i-!owever, such an argument .... ,'QuId rave been based rk1.inly on opinions since
ob,lective facts concernine; efficiencjps a)'"ld costs werA rot <lvailable.
The aim of this report is to describe a technique to ob,1ectively
analyse t.he cost of a co,.,bincd lookout-aircraft det.ection system so that
the combination th'lt re511lt,~ in t!-f' 10h'Pst detection cost may be determined.
It must be kept in mind t.rlat tbis 'l.nalysis does not consider \>Ihether one
system is more efficient in detect:i.ng f:ires tJan 'l.notherj it only deals
with +he "out-C'f-pocket!1 cOc;ts trat "'ill result from a certain decision.
The anal;vsis is based on the assumption that fires "'ill be detected
equally well by either system giving the same coverage.
The technique invc-Ived the simulation of' vaIi.ou~ controllable
inputs jn. a simple mathernati cal model that deterMined the cost of detecUor'.
The rlata from an existing rr.anagenent unit iolere used to demonstrate the use
of thp model.
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Development of the Model
Tre Basjc Assumptions
For this analysis, assumptions were rMde on "'rich tpf' model was
based. Tre assur:Jptions FeTe:
a) Cost, rather than ,qbility to detect fires, wns tre basic par.9-
!':leter.
b) Tr:€ area covered by eacr lookout Has liMited hy vi.sibility and
topograph::. n'e overlap ;"ettveen lookouts "'a::'- subtracted from
the +.otal ()f the i'1dividnal lookout areas to e:ive the total
nrea of the district covered by lookouts.
c) Lookout costs ir.cluded the observers! \"ar:cs, all maintenance
costs, derreciaticn charp€s for the to"'cr, cabin and other
facjlit~es such as roads, docks and ro~unjcations .
d) Lookout costs cor-t:inued reg,qrdless cf the Dan,eer Index for
evpry day 0" t.'e fire season.
e) All costs \·'ere linear . (For exar.ple , Lf' the f1umr:"r 0" lookouts
...,ere doubled, p"'" costs for the lookouts '·'ere 1oubled).
r) T}-'e .<t~rcr.<tft covered a strip tr.e ,.d.dth of which ,.'.<ts a multiple
of thp lookout visibility .
g) The nUMber o~ air patrols required each d.<tv ~epended on the
D"lnger Index . During one air p"ltrol every point in the area
that W8.S to r.e cevered by "ireraft \,'::)'5 covered once.
h) A h.rf::;e fra,ction of t ~e aren U~at. ''''J.f'' not covered bv lookout,s
was covered by aircr~ft .
j) naily visibilities r'l.ngerl "r0!'l anI" to f'ifteen miles. (In
rC'llity, vjsit:ilit'" often eycpeds fi "te, !"I rnilf>s. However, it
is doubtf'll if rJ snall fire could he detect.ed at a distance
g!"ea1.er than fi"" c·'n r:lilps) .
•
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Tre Hodel
The d<iily cost of a lookout-aircraft rletec""io'1 s,vste"1 may be
eyvres;,o::od as:
(A Flv) F N R + L C
H V S
\);ere:
A i~ the total '1.re.oJ. of tre mA.Jlar,er''Cn'!" unit in square miles
L is the numhf'r of lookout~ in use
V is the lookout visibilitv in milE"s
Hv is the arl;'8 covered by L lookout~ during a vis;hi.lH:v of V miles
F is thp. largE'! f!"l.eb on of tpp are" r.ot cover~d hv lookout~ that is
covered by 1ircr~ft
N is' r.e rlu;tl~('I' of3.ircraf't pat.rol~ rf":(uiT<.:d pach day
R is the hourly rate crarged for ~re ircr"f't, ril!')t ~T'1d observer
M is the multiple of V V--'1~ det.err:rinf'd U'e;trjp ' .... idtr· ("overed b"
the aircraft
S is t.he sref~d of the aircrJft in l"-,j Ip.~ ~r rOU!'
C is thE -laHy cost of 3. lockout
and ""here:
(A - Pl v) F
"'I
t'VS
(A p~ v l F!\
nvs
(A :-.LV ~ FNH MVS
LC
is tre r'::l"'ai.r j !1g are:'!. not c(WrI'cd bv the L lookouts
d1JriJ".g V v~ :;ibilit;> t,h1.t must be covered bV the
aircraft
is the stri p ~'ridth cov'?red bv the aircraft
if; tj-,P. '1r"'!l eover'O'd 1:1:,> thE- Air(,l'"Ilf't, each r.our
is H~ numbe>r of ho!ll's re'1uired t.o COver the pA.trol
::tr"'l II! times eaer dA.Y
is ';.:--;i; dail~, '.'8st of L lookouts .
An c:xa"lple srowi!11" ~!- e USf; of tb" ,ooe1 may he seen on fl8~ 6
The model was uSBd to stud.v t/'";e eft'r;c+s of variolls va' ups or
the variables on ar.r.u'3.1 'ktect~ on costs. Since visihi.lit" varied fron
day to day an1 the nUMher of days 'n each DanRer Indey class and fire
season varied from :''''ar to "p8.r,'1ver3.ges ",(;Ore not 'l~ed . Inst.oad, jaily
det(.ction costs Wf'rf' calcula~ed krol\in£! ead" rlav's D.qnl'pr IJ"In<;x C'lpd
visib~lity. An an"wll dctf?ction cost was fourd hy sunning tre d.'l.ily
detectj on costs,
Application to Fi.eld [,ata
To study th" f'ffl~ct,s of '.he cont,rollable ar>d non-cont.rollable
Verillbles on annual net,f'ction costs, field d-'J.tCl f::-om an e:xisting manC'l'!:emf'nt
unit wr:re used.
Th .... , mar~~eTOC:nt llnit ras an
presertly protected by 16 lookouts.
al'C'a of 5, 15P S'1llarp "1ile5 N')d is
The 16 lookout,s Here lj~ted in order
of value to f.hF- d,~tectj on s'.'ster.. VOl}U" ''':IS 5ub.~p('~.5.vel:v :iet,er""ined
cased or::
"1) Fire; ~1'I7-1.rrl in tr.t" area
h) The pote!"- ial nUl'"''bpr of -rires
c) AreH sep.n
V1.1ue to U." rJ.·,t· ction system l,'~S th"- criterjon used to determine
the looy-outs U-'1.t T.rere c0r"ij.=:red ClS non-operrtti.nr: "rr t\'e sil"lulRtion .
The least valuf,ble 10okC'u' 5 1;'~_re t'l.ken O'J.t of tl-je lookout system first .
Are"!. seen mapc; "er0 .<tv<lih.hlc- for all 100kolltS. These were
reducr:d to a s(,;lle 1 i~·ch 0: 6 mil,:-,s ard arrF!.nfF'd on a comnogite r.1!lp . A
planimeter Has used to ~"'tpnnjry tre 'lreil. thClt L':l.ch A.driitional tower,
~3y.en ~n r:>rdcr of valup, ad':ed to the total '11"'-<1 cOVi'!'ed by lookouts for
visibilitit.s randnt" frr:'r:. (mE' to f'iftp"r. :,dl~·s . A table ",r~s th"n construct
e:! shm-cing F!.rp.as cow'red for ewry '!='ossibl·' co"'b~naHon of Land V. Fro",
this tabl!" v3111"s of Ply "-ere take'"! .
fo."tiT'la·E'~ (It' q'f' ·,u"'lber of p-~trols tf.at would bt:' rlown for each
Dan~cr Index clA.~~ d'ly ;'Ier·~ "1ad··.
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D":'Ige:r Ind.,.,y Clas~ ~;o. of Patrols r.IPr Day (N)
j-Jig!
Norte ra. tf'
2.5
1.5 0.5 (\ . 0
The fradians ,"11],-)1." f0J' <viritjoYl'3.1 patrols (lver higl ri!'lY -'JrE"'1s.
n'~ r.;stir 'It{",~; of r.unher of p!ltrol~ rr-'l'lired "or f'03ch Danger
Index class dav tl:1.t ;,rer'" )":i,je c01'respcndcd cl"sely +.0 tre theorical
numbers n :uireci1 ·kt'.minr-;r/ by t.,e tech!y'lUe
I1Scred1Jl_~ng f,ir('r.:l'~t for i"orf'st Fj_::e r)etf'ct~onn
rourl:! Rate
Cub $17.00
":> ~sr.·, 172 12 . '
C~~sn-'l 180 42. ('''l
df's('rjred j n ... he report 11
(8 ) Sneed (s) 0,
100
12 "
Tl":f> l:ourly r1~" (R) :i.r.clw!."j Ul<; CQ'·t of -'-hl::- 'lircr'l.ft, rilot "ni an bourlv
crarl,e of J,2.()C for ].n obsp.:'v'-r.
0.) RO'id ~:--lrl tl''1il "'0'1~3t'"'~;ction costs
b) ~:ted nnri gu;-,- ~,')~~ s
c) Sr€:ctic~ c'·sts
ri) Cupol'l. coo;ts
E;) r;,:;b'::": ('os~_s ~,C111Cir:r: .r'lr,,~tur'" 'L':'"l \:"€''''~ils
,.\ r" :"'J'lUr;:i. 'qtionl" ,,(I' i.p!OCrt C0St~
p) ,,_J !~. ''1t '"'?.rc"" (",)",t-
)-:) .'I·;r>r' .,~ rb."lv .... "'ll!. n1.iti ',0 t~· 1()0kout ob~I';'~"vr>!".
II ~.o\lr+z, .r. 1)61;.. ,cl ;:::J.i'tr. aircr:d't f'r.!· l'Tr.o;t fi~·.'.' r1f't~rtiC'r:. D<.:rt. ···f F'ore3try, Mi"'eo No. f4-~-17, Ottawa.
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Fror:l om' ,··eat:her !Otat:i.on in <-I.e l"''l.n'l.p'~r1f'''''!t, unit five years of
daily D~nr-;er Inde;)' ~nd vi::ih:llity rl::lta ... !ere obtr>jT)p.d. Tris nata was used
to st ..... dy hoV! U' "l:lri.ou<; values of tJ .. p contrcll·J.hle vRriahles affected
the ~n'1i{eJrert U1,~_t IS detection costs for H,osr yf''lrs .
Annual Detection Costs Based on t.h(~ Five> Years of Actual Dl3.ta
Bl"'f)d 0:'1 thA fivE' ,y<:",r5 of dEdlv D"inger Index ""nct vi sib~lity
data, rtnnual d,·tedj on costs \-!ere calcu11t<rl. f'or:
a) L v1.1u(·s frorr. 0 to 16
b) F values "rom 0 . 6 to 1.0
c) H anr! 5 v,31u0:" of 17 . 00 ·:mrl 8'> , '~?(lO arc! 100, ann. 42.00
and 115 r,,"s~ctivelv
d) M V1.1Uf·~1 of 1.0, 1. 5 ~nd 2.G
/,n E'x" ... '1pIA of 1. dail-: 'ietection cost. cr;lculat.inn usin~ dat"!
from the IT:;.,.nageP'f. r:t unit fo110\':5:
On ,Iune 5, 1964, t he vi 51 'hoD ity I.,.as 1 S f"'ilcs ami the Da~n:er
Ind~:x \0.''::> 11 'I-::i ~r.) .
v Ii
A
C
](
:-;
L
F
N
P2, • ".
15 (f'ror:1 A-c(uQ:l fir-1M ·hta)
~ . 5 ("i'·,ce Dangpr InMpy Hi'l,S High)
515 1 C:::ons t.:tr1t.)
12 . ~( (cl"lnst 1.:,\t)
~ 'I2JiO (a:rcraft ,q~6Ul"1Prl to be ~ CcssnC'l 172)
100 ,aircraf't 1.ssWoe-l t.o hp a CeSS'18 172)
2 ('lssumed,thps·- L'ere thp tHO '"'lost va11;ab1e
to\ofPr'S :i r: th-' :::·".mt- ('(:"1C nt unit)
e,g (':ls.~:.lI'lpd)
1 . 5 (~~~;urc'-:'rl.)
1206 (f!"'or rre00u~1v con1'1t.ructed table) .
The det~ctic:1 cost for June 5, 1964:, based on +".A;'f''lssumrtions was:
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(A - Ply) FUR + LC MVS
(5] jP - 1206l (0 .9) (2 . 5) (32) + (2) (12 RO) = $15206 (1. 5 (15) (100) • .
Sinc..? t!'1(' (~p,~l:: cu:-t 8'lU3t-ion hF\d to b<! solVl"d sevrrill hundred
thousand tiflif.'~ to riP'€'r!:1].nC' the <3!,nu·ll d(>t.cctjon costs for all the Many
corrtinations of t.h ("C'ntroll'"thle v'lh.al:'li- s, ,}->( probleM 1"'-3~ rrograJT!l'led into
a computeT .
R.esults OV.~"~ned Using the Fjve Years of ,\ctu8.1 D"tta
F
TiJ.llF I
Avo rag<o "nnui'll f).,t,O::C'L"ion C-::,,,t5 llndf'!"' Si:-:1ul:3t:ed CondHi cns (i.f=2)
lhlr'lber of Lookcuts
R o 1 4 p 12 16
(.6 17 85 Q,"92 IO,P:22 17 , 695 26 , 525 36 , OlQ 1,.5 , 774
C. 6 32 lOO 14,067 lo,,761~ 22 ,107 30, C93 39,rl1 48 , 41!3
0 ._6 ___ "~2~~1~1~5 __ ~16~.~'~5L) __ ~1~7~,~62~7~~2s3~,~7~69L-_J~1~,~4s23L-~4~O~,~1~42~~4~9w,~4~1'
0.7 17 B;: ~G,2r;7 12,19') 18,921 27 ,109 )6 ,850 46,509
0 . 7 .12 100 16,412 1 0 .,961 24;06~ 32 , 202 40, 144 49,493
~D~. ~7 __ ~4~2~_1~J~5L---"~q,~~~·1~~/~:",,11'"4~_?~6~,~00~7 __ ,""~" L,~2~1~3~~4~2S'L0~6~1~-L50~'w7~5~4
r: ~ :7 "5 11,72" P',"~ 20,146 2P,525 37,682 47 , 24.3
O.~ '32 1(0 14)':"56 20,15 P 26,C29 33 , 230 41 , 676 50, 767
O.R 42 1:5 21,407 22,641 28 ,245 35 ,003 43 , 1~n 52 ,095
C.9 17 ~ 13,188 14.941 21,372 29,505 3R , 114 47, 977
0.9 ":12 IGC 21,101 72,354 ??,9P9 14,7<;);9 43,007 51 , 942
~O~. Q::.. __ -",42,,--,,1.'·,L) __ -,,21"-, 'LG",2·~2 __ --,,2",5~, Ie ~c, Vl __ ,,,,6~. 7L9",3,--~4",4 ... ,,,62929_",5",3,,,,4 .. ,,,,6 1.0 17 85 :1.,653 lO,33'i 24 , ;'15(~ 12 , 055 40, 756 50 , 010
1.0 32 lCO ?;',/..,.45 JLI,)'l 29 , 950 36 , 167 lt4. , 33A 53 , 117
42 :1~. __ ---,2"5",,,,-7~8 ____ 2'!..L~55 '-12 1 721~--2.3::.AL! 5"8"2,-__ "4,,,6,,,, 2",1,,8,---".54,,-,-, 7L7:J.7
From Tat-IE. I' t C~tTl l''-' SCP!l. .. rl"!t:
11.) :c., '"I- 1 r81'Q.rd18s:" or" t,hf· r , R ,1.'"1d .s v:i1ues tha.t we r e u s ed , Fl.ll
-:;."y·rr'"lft det"ctjo'1 r"~uli..f'r~ in P~I )m,rvst ;:>venge annual detection
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b) n~tt;C'ti0n co"ts ".·lill rc r",duccd con3i.rl"r:,bly by w:;j ng r~L=!tj vely
1 :S~ "ypm<;:iv,,:, 51o'''·~r 'lircr::l.ft thaI" ",('Ire eYJ)('no;jve, fa ~t€r
.<tircraft .
c) The P v'.,.~ ')':~ chosen <>;re"ltJy "f·~·:cti.d +,b0 r;o~t of oet"!cti.on .
i'roh"bly t), :-'lost reaJis+ic v~lLe~: of F AY'! c]"'''e to 0.9 . A
valu, of 1 . 0 01' eVI.n grp':lter ','oulrl nf)t he unrf:tlson;>hlc if there
\.rt"'n~ nuc!; ovc-rlrmpirJ[' of fligU, stdps .
It ~/:\~ .'lSsuf"l,:,d i:l T"hle I tr,1t th'- "ri dtr of' !"·trir covered by the
airCFift ~·I-1.S t .. dcc He v;,·:h'ility . r},j" 1~~;u.)'l1pt';(m ','1" Tl'-'rhaps to'"
cptilT_i3tic . T~!t-;lE' II p"vr~ th- 'ovrrtl.!!e 3~'n'lal .;(t· .... ction C05+S based on
+.he five Y€1.rs of lctu"ll ~l"_"- f:)r ~trip \·,jdt!-~ nf 1 . 0 V, loS V ::l.nd
::?0 V for "l. F' v<tlu~ I"'\f " . 9 .
'T .bl F II
Avpragt: :.nnua1 Detect; Or. C')~t,s UndE"r Si:l'u}."lted CO'1diti.o,,~ (F 0.9)
::U11.her of Lookouts
H R S n 1 4 g 12 16 1.0 17 P5 26,176 ';17,'29'": 32,402 38,327 46 , 002 54 , 5R1 l.0 32 100 I~'? ,;);~12 l..2,12) 45 , 637 4>',912 54 , 986 62 , 508 1.0 !±2 1l~ ItS::- .V6 ~7,711 2° ,6?2 22,901 2",}72 62 .~96
1.5 17 P5 1'7, SQ4 19,·J59 2'5,04s) 12,446 l..1,010 50,177 1.5 32 10( ?-1.:-;'c, :2;: . ~f44 31 J Q"2 J~, 503 46, q99 55,462
1.2 ;:t? 112 ,22 1 1.1.0 32.662 :7 I l2"" "" ,162 ~2 . 22L 27 . ~2:l 2.0 17 85 1; ,100 14,941 21 . ??2 2Q,505 3R , 514 47,977 2.r 12 100 ?1,10 1 22,J";L. 27,9g9 14,789 43,007 51 , 942 2.0 !.2 112 2!:J.I OP' 2~1147 2),4<, l6,'121 44 .622 2:l . ~16
,\ Rcen 'n T;ib1· II, ··hen th, strip widtr to'·"lS l.QV and the
'lircraft co~t \.,7l.~ -2 . t>f' or l.,.2. "do11"rs 1.n hour, i.t 'o/a::; chp8.p:!r tr
maint"lin on(~ lo()Y'"',ut.. T}'-;f-' l'ost re£tli,t.i c st.r" p t,r:Ldtl. i::; nroh11.bl;V close
to 1 . 'JV i1.nd for H,is ",..;-jt.r. "lr. 'lll ~ 3.ircr'lf't system '..rq~ less f'ypensivp
than ~\ny cOT;\hinat) or. :)1' lookout s ~...nd3ir"r"rt .
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st:oIVn in T"Ible n.
TIllE ~II cos~ 2 L;'1r!er C:ir.'ul'lt~rl Cord'< t:iOr!5
(F = ('.9 ; R = )) . 00; S = 100; :,1", 1.5)
th:d'er 0' Lookouts _._--_., ---- --~.---
Y·'ar C j ______ 4, P 12 16
1960 H,'!')6 '12,-/06 37 , 901 4'< , '1'7'; )1,11 Q 59 , 280
1961 'l.(1, 36~ '11,14 -'Fl -"h <. , ,01" 49,7'7 57.706 1962 ?~JC5? 20,7f,2 25 J %2 31 , "'4{ 'H' J 5)-~ 47 ,0:'9
1963 ';)",3'19 211,7l.:3 34,(29 1,(" J ("\95 4Q;,2C8 57,302 '964 , ' 1..,,0:
I '- JG l 822 3~,:308 4CIr)~·P 4" ,~6? 55 ,98}
From T'1.bJr.> J!I "t C'l.n t.~ ~,een "':.~;a+ ':r_p deter;t~'n ('n'~ts for 19f.2 were far
belo~,' +,"',P '-'vel''''!!/'! of t" f' o+/.",!" fo~r ye'<rs. In 'm \ttemrt 1,0 e;"Tl'l.in this
v·~rirt+io,. Table 11.' ,,;:~s cors--rlJct~d.
-- --!·.nJ"'1Jal DetectioTl I',qy? of Dq.vs of Dn,"s of SeB.50n
Ye'lr Co~t ~'" Eytr"'~"" f-li.eh Moderate Lendh
1960 31,896 ? 23 76 192 191,1 lO,jf)5 0 lS 70 194 1962 20, 1',2 2c 01 196 1 '1!S" 27 J r.?7lJ 7 tJ ,4 213 1 '~6L jC I~Q() J ' 57 68 21~
~htr>lt '>n t !-:('- ~t.;;-:-l pr n'~ :h_:'~ 'n +.r.e F):tre!l'P1.!1rl ':~gIo. Dqnger
r.aex ~);'!3",eF ;.n~ or. ",-.,,,~c~ l"'~rt.',-. , 0r:E' ".' )ul':! PYJX'"t 1960 to ! <''lve the
:;West 1e+,ectin COot 'u;-i 1-;'6L '''a f".ve th:: ~~~".e"t. . P.o~·'ever, t~is is
" For •• G; I' r .?z R 32 ; lOO ; M 1.5
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not the case . T/-.f' nurr,er of d'l.'"s in eacr Dam~er Ir.dey C),1.<;,3 1.nc the
seascn len~tl do nct. "'T pear to be directly r-:-l;>.t.fO-d to detpr.ti,?n costs.
Ta:-le V .,hov:> thr> effect of v;sitility on dail~; ie~,ect~on CMt.S .
TABLE V
The ~f!'('ct of Visib~ lit;! or, Dail,\' Det.ect' ':'1'1 Costs
~o. of D<1.ys of netection Costs for Visibilit,v Detr'c' ~ n Cost :"':oderate D!lrfl'pr l'ode:r<lt,e Daf'ger Days (~'iles) " For :-jud e r~J t e n"lV • 1960 191-:-: 1060 1962 R
15 ?9.03 34 48 3,367 . 02 4,753 .44 14 IG6.); (; (, f.,?,f... . 6A 636 . 66 13 114" )'.' 0 1 114 . 27 12 ];'3.79 L 1 71..(2.74 123.79 11 135 . C5 1 0 13' . 05 10 IhY . S'O 7 7 1,(119 . °5 1 , 03 Q . 85
9 165.C6 1 r J6< .06 q 1,°5.69 " 2 17] , 1 0 371.3g 7 212.21 1 1 6'6 . 61 212 . 21 6 ')47.5r: ? 2 49'.16 49< . 16 5 297.10 1 1 "9J. )0 297 .10 4 '<'71.37 0 1 371 . 17
3 495.17 4 0 1,90:0.6,0:
2 '7.:.2.75 0 0
1 1,485 . 50 7 1 10 , )9" . 50 1 ,4~
TOT/,I -h ',I} 20, Q60 . OJ 9,900 . 73
fro"" '::,b1e V it, ('''''n be :;epr, ',1-1.+ de",ert.ion costs gre"l.t1"
incre'ise as
.:~ Frr L
: !:p
" ,
!1u:-:ber of 101·.' vis::t-ility d1..v:: : !"'cr",1.C'Cs .
32.CO : 100;
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were u~~pj d"'<i )"nt '~;::lldE' tr.e extre;nes in con<i'+,i(''1'" "J",1.t '-:oulrl r'gsult
R. reli',blc ·,'st','d.f; J' ~r:(' "l.v'C'r""'gE' 'lr;:lJ?l rif>t,:>~'" T. C'lst Rrd r:.n~e of
'lrnua1 v'ri'1.+-1o!:c: fJ\ 1'+ tl;:i~ E!.ver.q··..." and t,r,ll~ r""ve ""or" ~r:f'orrfltion
onw~lr.r t ha,
Index ~~,t~ rA I'P), ·.·~i. ;-'".tever, :""_,:-",t f("r~·t rl'nff'C'+i.on '1.p:t~r.c:ip5 have
"tn jnsufl'ld_ent :"," 'JI j "'!f thE: rcql:i;'t:d dat'l . Tr; everr"I'PE' t,hi~ problpm,
The Oat." iron) .'1.1:, lon :~et~,0d
T~.' fiv' 'e~!'S 0f 'Jc+\\",1 visihilit:: nnd D'1,.,~pr Index delta were
)j~t,~d c~' L·,rw,r I'1d~y l'l':'d~'PS C:.m -Ji,-jl'i]~tjp."". P"r R?e" Danc"'!' lndey
----------
Lew ~~~rl.f'.;·'t.e F i &"11 F.:xtrerne 12 . 2 ' , _ 4,
, P.l 16. 1
l' \
, , I) . L. 6,0 2 , ~_ --- !±.,.'L
It. .IIi;."'''' "tj'1i' +c, note 1,l,'l.t. '\s +)--" D"nr'er In'f>:x in('re"l.sf'd ,
"',he- v·'-.ibj] 't,'{ ''T,)''lr"w'r~, G"n('r'i.1~:", thf' l'P'IerSf' '''' t.h(' ropul;,_r conception .
n0'.'fpv'r, t",n: "nr", fr':;:r em' I:-.."~t,i('lllnr '1.1""1 ':inn I""!'l'! nrt rE'T'resent
"
, ~ 1 10\-' 'f,)_,,,, -':it_ e rigr Ext rene
I,vg, ;:' " r' ,v'" . 0,
?P , '--j ~(;. 7 <:,~ , 9 :"'O . C 8. 5 ,-.1' -, ,:lr
-;tand:lrd ;';pvi-:;.tior. "), 5 12, Q ll~ . H, . (l 5. 2
- 12 -
Tr.e nUMr·l"'T of d~ys in ~ach DClneer Index class W!3.S sinulated for
multiplying tr;PT"I t:iFRS thp stend-:;rd 'ieVi'itlO'1S Tor u v:- ~<t'
Index classes and adiing the products try thr: aver'lre nw..her of da:vs in the
appropriate Dflr.'?;er I!1dex cl;:ssf's. A?; eT"T"Ipl<> 1: shmtn 11'"' Ttl.~lp VI.
T;.:3LE VI
Sir.:ulati0n rd' t: p rJlJr!hf'r of D""5 "in Ep_cl- D-"rwer IJ"1rley Cl"lsS for Hp nU YeAr
1
D'l.oger I ndFJx Cl-:l.sS
Nil
Low
Moderate t-~ _'0..
Extreme
2 J Sti'lrrlarrl Randomly Sdccted Dcv· :ttion n"rF'~l n~v~ 'ttE'
~.5 - D.414
12.9 + C" . r6c 14.0 - 0.691 1, n + l.P9
5 . 2 + r.902
4 Avg . No . ()f
D,ys l_~'r Yn{lr
2R . 9
56 .7 5~ , 9
40.C () . 5
Total ntur.t:-f" r of -\1 y3 ir. the nU f:!.-re se"lson
5 Sj~uIRted No . of Days per Year (2x})+4
24
58
46
59 1;
200
This method F'nS~re5 th·,t there "''i11 b!: ,,:()od~ t'"ld, "'.ver"ge, long "'Ind short
fire S€1l.S0:1S .)11"'11"1r to those -,h",.t have ocC'urred in the t"JA.st.
Tt:c vj~ihjlitv for e;J('r. d,·y in e,'u'r. Oltn9'er Inn<?)f class W8,S
determined ir n imilar M8nner . kn ex~~le 's ~hown in T~ble VIr
Day No.
1
2
3
;:..5
,,6
T"BlE VII
SifT'ulA.tion of :J,ily Vi~i:-,:ilH;ps "l" the Hoder"te D'lnp,er IndAx Cl . .,ss fur t: e nth YeA.r
SLn,d -ird ft;-j,r -lJmly Sel ('oct,ed ;~vg. V"isiVJjt.:<-, Devi 'it ion :-Jol':-,,<'ll Devi 'l."':t: ~ for :·'oier~te D;;nf'f'r
6.0 - 1.71..3 14.3
" , C. 713 .. .. + r . 168 " " .. .. - l.n3 " " + 0 . 020 ..
Simulated Vi.sibilitI
4
19
15
7
1"
- 13 -
7r.~reforE', this d'l.t.'1. sicnulabon neU.od provided. v,'\lu<;!s for V,
N, ~nd se'l.son lenl;'th. 'I'\'"e input d'lt"l. 'ind +.re d~:tll ~:i!Tlul"l.+~:ior method
WeI'''' prcgr"".Jmed int:"' "l. c0nrUt.er for U-p pt;:>,,!'ose of rietcrminin'" "l.verage
annual detect ion C(:sts ar,d q l'lE'A.sure of dis,!=ersio""! 1'or' '!arious values of
the controJl.<tble v~.ri"hle5. Tr,e value.:; of -I-~jP inrut vqr; '1ble~ are given
below:
L
R
C
V
5,15li (const'tr,t)
0, 1, 2, 3, 4, 5, 10, 16
100 (cOn'3ti-(nt)
'32 (constR.nt)
12.80 (constR.nt)
Determined b:v rl"t,\ sim~;l"!tion ("isitili-l-i",s of 16 J'!1ilef' or A.l,ove h!ere reduced to 15 rrdlps)
N De~ erminf'Od ry Ii'lta f"irr.ull'ltion
PI v ~e":erYT)ired frof!'. rreviousl,V constructed
t"-1:-1e kno"'in~ p,eif"h"rmined v'Jlues of L 3nd V.
F C.9 (constqrt)
:.5 (cons'l:af't)
The computeT' sir--.ulated d.qt"l for 100 fj re <:;f>1.~ons "ll"d c'llculated
the :lv~r·1.ge Clr.nualieted,j on costs and stami,'ird 1PV1"ltion5 ror :111 COffi
hinatio)1s of 't.8 controll"ble v"lriRbles. _~or A"lch combin3tion of variAbles
'J. new set of IGO-ye1.r d'lta ',"t8 Sirr.lll'l.ted 3.nd on]y sl;'ason If"nl!,ths between
150 and 230 dl.l.y~ ;.,jere 'lcceptect.
TABLE VIII
Comparison of the Re~ultp Obt:l:!.npj '.15i1"'>" tb~ Inc :'('·1.rs of SiT'lulated DRta find U;e llesults Oht.qinf'd 11sir'li the P~vr; Y(:.1.rs of Actul'l.l Data *
r~umr:t; r of Lookouts
0 1 2 < 4 5 10 , 16 n.verag~ Annu.:tl COStS (3imu- 26,48') ?6,J93 ;'>'" ,6ee. 29',953 3C ,~69 31,932 3~,558 50,287 lated Data}
Sto.'-d;,:rd Devj"!.t 'on 4,657 4,161 4,2::>3 4,638 4,4$4, 4,624 4,978 6,093 (S';mulated Det .,)
Aver.2ee Annu::!l Cost 2~,134 26,994 3L,121 32,035 33,872 35,238 42,932 55,462 (Actual D'l.t'l'1
* For F ~ 0.9; i'l 1. 5; R ~ <2.00; S ~ lor
- 14 -
Results usinlS the sif'lulatect d1.t'l. indic.,tC'd 1;.1-!l.t an Rverage of
$96 a ye::J.r would be saved if one lookout w;:t'" 0p0r-.tJ,d ('omr~1red veith an
all-3.ircr·,ft ",yster"l, but it js doubt""ul if this ·jjfrE'renc€ if' significant.
However, it is signific"l.nt .j.r'!t -I:hf' use of "tn O'tll-'lircr"l.ft or mostly
etll-aircr1.ft ~ysterr will result in the Im·:cst 'lVpr·"It':€ 1.nnu.'11 detection
cost.
/, Ci"refHl examination of the dA.t"l. ;;ir'1ulation method reveals
several possiblp. W! Rknesses:
a) It aSSUITS t.h'1t tt.ere -; s a norMP..l rli strihl1t~ nn (If J1urnber of
days in eac~ D1.nger Index class.
b) It "lSSum8S +j-,at f-here is a nOJ""1al distri'rution of d.qil.v
vi~il iH ties. (T~ere were suf"icient r11.h. to test t~i6 aSf'umption
and results ,.hnwed th<,t <-he d~stritution '."Il'" not nor~.ql. Tr.:is
probably "'esulted from +,)-e in'lbility of ohserv!;'rs to accurq+.ely
measure visibility eSp:'ci'llly dt:.rinp p;ood vif'ibjlit.v conditions .
Most of Hi::; difficulty could be overcome by '>clect.inp A. low-er
maximum vi.sibility f'ucr .::.s 12 miles .
c) TI-;e '"'.'..lr.-:b8r of d'lY~ in "I D3.nger Indcy cl't~'> "''1S co.,sidered to
be irrlq:endent of th(' nurr,her of ·i<l75 :in the re~ining Danp:er Index
classps during ~ny given ye.qr .
Ii) It \'[IS "'ClsulY'~d th,gt eacr. day!" vis;bility Has independent of
the previous do.y.3 ! visibility .
It is not known hrw incorrect these ~ssu1"'lption~ 9.r .... or how rr.uch they
influence U,e results~ h"..lt beCc1Use tre rp~ult ~ tlSiN' sj.mulated data were
simiJ,.!" to tre reSl11ts t;sing ,'letu",} 1'lta, :it nror-"I.b1:v ;s safe. to conclude
that the da.t,l Simulation :r:e"':..hod is '.It.;ite reI tahlc.
Conclusinnr.
Result S obt'1.inf:'d ·lsing +re fi ve ye,rt' of :t.ctu'll d,tli and the
sif!".ul·tied daV> indicate for t.he 'l.r'?R studied f"h'1t :
- 15 -
~) Tre USE' of '.'!.n ',ll-<tjrcr:.:;rt or ""ostly 1.Jl-"I.'T('r , ft detection
system viII result. 'j tr.t' Im,-,('C'¥ .nnu'll d~t(!ction co~ts.
:;.) D,·tecUon co~tc:; "ll} Of'! l"'''8uc(>d con~irl,'!'''..rly (:ly usirg
rel'lti'lf'ly lr,ss cX!'f'nsjve, slow<':,r 'lircr",ft t 1.n mer''' e:rpensive,
f: sh.'l' ~ircr~ft.
c) T> (" }. r,y<'st. non-cor,t,rolL:.':le fpc+,or'lff ctinp' '1.11-,ql.rcr'lft
det(ction cos· '1 is d1.ily vit,-ibilit:'. It inf'}UI~rc"3 'lnmnl detection
costs mu~h mOlT t~i'm S~"'son lerwi:r. or rll'"lrr'" nf d'1ys in ~~I.ch Danger
Ir.dnx C11'15S.
Th: d:-tt,q simul'lT1on net hod rrov-i r1 p'r. r"'su] t'" simn'}r to the
T(;51l1t:: obt.,jnr,d from t\.e f-ivr- :lE'"jrS of act,u'1.1 d:-tt1.. T]11B technique
m:.y he "'['pli.ed jn :-tT'~'\~ \o'her" li"'-I1'" of tr", r'"quir.-.d chi,;;o. Rrf' 3v:-tilable
to obt~dn Cln C!:ltimRte of 'i,," ?.v~:r::"e co"t n' rj,t""ct'C:1 1.rct +)-c 1"mge o'
like ly flr:nll"'} v', ri :lti ons .
'1',_ rr- :in 3c'I"r-,1 c·-p,J:rp;;sps in UP. "i-1l1,tinn b~crniC1u~ :
1.) TI-p rr.r)("l~l in ~+" pre~e'1t. fan ~1.ke" no ',110''':1''':('1''5 for the
1.dd',j.ion'1 rl€=t c-l-ior '·"Tlir'-. rt:; riur'np: lo·.,..-jnf' o'!"'l·r'ltjorc;.
1ftr,r l:i.'f.tr.5nl"" st.or~", or rillrj''': t.irr3 of i.n('r"'9.~:erl forRst use by
the pllbl'r .
b) V'111';(:"; nf F <"inri l·i ;CT' liffic1.:1t t('l ''''''''''Se· 'l"'!d 'llso the> one
md ' ... visibility r] 'lsses ,"'1" t '0 fin"O , To ()VFTC-Orne thE'~e nroble"1s
'\('twll p-:troJs ('')'j '~ tr lii.id C'lt fer 11.TPer vi<:'hllity C1·1.5<:'<>S .
TJ-'is ',,'o'lld r~'(vide '1;1' vltrol 1~,,,t'lnrp,,, ;')f'r\ U',uc: daily "!:iT ratrol
coc:t"l lvojc\inl" t~(O ""~'=>f" ity "'0 d;rectl/ .o,.-t;r..qte wl.h:u; f'or F and M.
(') 'i~hir. 'l )'l.r.." ,o>'!'C '1 , ,.,.' c:- "IS t~"It ",+ ;:j.nd, it, "'auld DC nossihle
... ) r,'~Vt ,t +,1, ~"!":f' t',-if:' s"'1f' .... "l RTr,"!.!,. 1t vcr'V rI' ;f'('rf'!1t lev!'ls of
f';rf. '!"r"IH' . 1',,_ i~' t., e d'\~ ly r., 1:'2:,,~.i..or ~. ,·t on the d1.tll "ror.! one
\Oit:<l.tl,f'r ""','1t.'on ( ~ '.'- co icr:t -i, -1.)-." ~y'''-pl''') F.,i.f!r.t :'i"s':lt tn Cl. l'i!'ge
e:-rcr. TI-.':~ rrot-·l·'t;] ~("1l'1 hF nvercofl1E. by divirl'n" tre T"'ln.<t(fe~,..,t
- 16 -
C llculi:!ti!lf dllil:: s;'tection c('sts f'OT ~ndividl1'11 "cetors. D.,il'l
det'}ction costs "or thF- '-'In.<!geY':fnt unit w:ul"'! b~ 01", SUMo of t .... e
d'.il.v dptecticr: C051,S .
d) The tt~chrd'1uP "5 'U~~S t,r~,t t:-ere1.rE' pnnUP'h 1ircr",f+ 13.v'lil
at-;lf> t fill t~p r1trol requin:~T'lel1ts erl.ch d.:.:",. P.o"'CVf'~J cturin~
VF:ry low v'i "'iIi itv d~i~1S +,r.i.~ is '!~r" 1 ikely r>ot po~s~.hle for most
forest prct,C'''' i 'n 1.f":>ncie::,.
The sirnJl -:tion tpc:h)1inue described in +hj., ri:-port provides , for
~ frlrt.i CilIa'!' !H"''', '1 metr'od ...to~:t.'irhr trF) effect;, of V'1rious .,.lteTl'latives
on dete('tJon~ truf' '\ ~trod to dehr"11!"lro ",h, l'-'1st expensive
detpctio~ystem.
t.
