Lightning Hazards to Aircraft Fuel Tanks

l8 NACA TN 4326 APPENDIX A SYMBOLS coefficient in Fourier se rie s A a length of side of plate thickness of plate b capacity C c s pecific heat E voltage curren t I k thermal conductivity non - ne ga tiv e int eg ers Q quantity of heat resistance R T temperature t time t' time constant t ' u tempe rature at t rectan gul ar coordinates len g th of side of heated block depth of heated block Kr onecker symbol (defined in eq . (14) ) reference tem per ature ri se ( initial tem p erature of heate d block)

e

thermal diffus i vity NACA TN 4326 density p

differential operator ~ 2

20 NACA TN 4326 APPENDIX B HEAT FLOW IN A PLATE DUE TO LIGHTNING STROKE Introduction When a lightning stroke hits a metal plate, such as a structural mem"ber of an airplane, it may "burn through the plate or it may "burn out only a small pool of metal, causing a pitting of the plate. Of course, the worst damage is caused when a hole is "burned through the plate . The material on the "back side is then open to damage "by the arc; and, if a mem"ber such as a gas tank is involved, explOSion may result.

Even if the plate is not "burned through, there may "be a sufficiently great release of heat energy in the plate to lead to severe damage . The question is whether a large enough temperature rise may occur on the inner surface of the wall of a gas tank to initiate an explosion in the tank. This pro"blem in heat conduction is theoretically analyzed herein.

Theory Consider a metal plate in the form of a square of side a and of thickness "b, with a » "b. Take a rectangular set of coordinate axes with origin at the center point of one side of the plate, referred to as the inside surface . Orient the x,y-axes parallel to the sides of the plate, and the z-axis normal to the inside surface. The outside surface

of the plate then corresponds to the surface z = "b . The lightnin g stroke

will "be supposed to strike the outside surface of the plate at the point

(0,0,"b), directly OPPOSite the origin of coordinates ° of the . coordinate

system, and to release there a quantity of heat Q at time t = 0. The

pro"blem is to evaluate the temperature distribution on the inner surface of the plate as a function of time; in particular, the temperature at the point 0, which will be the hottest point on the inner surface.

Since this is a damage problem, it is "best to set the conditions on the analysis so that the temperature rise on the inner surface will be overestimated rather than underestimated. Therefore, the analysis is simplified by supposing that no heat is lost from the plate either by radiation or by co nduction to the air.

The heat - conduction equation (1)

°

N A CA TN 4326 is to be so l ved in the r eg i on - a a - < - x:s.

-

2 2 - a a -< ( 2 ) y 5. -

-

2 2 0< z < b with the bound ar y con di t i on s dT 0 at x= ±~ dx= dT_ 0 at y= ( 3) ±~

dy-

dT_ 0 at z = O,b

dz-

The fo l lowing fun ct i on s are speci a l so lutions of t he heat -c onduction equation ( l ) that sat i s f y t he boundary c o ndi t ion s ( 3 ): where l, m, an d n are non - ne g ative inte ge rs an d Next, these p ar ticular solutions are combined in suc h a m ann er t hat the initial con d i ti ons repre s entin g the heat so urce pr o duc ed on the out - side of the pl ate b y t he lightnin g stroke are s atisfied . For t h i s pur- pose the genera l solut i on f or the temper atur e at any poin t in the p late is formed : Let the tem per a tur e di s tribu t i on at t = 0 be known, s o t hat ( 7) T( x,y , z , O) = u ( x,y,z ) 22 NACA TN 4326 is a known function of the coordinates x,Y ,z in the plate . Combining equations ( 6) and ( 7) gives (8) In o rder to express the coefficients in this Fourier series in terms of the function u ( x,y,z ) , the symbol M[F ( x,y,z) ] is defined as the mean value of the function F(x,y,z) over the volume of the plate . That is, a

{ a/2 1 /2 {b F (x, y, z) dz dy dx

(9) M[ F(x, y, z )]

a/ 2 o

L - a / 2 J

where a b is the volume of the plate .

USing equation ( 8 ) and the usual metho ds of calculatin g the coeffi - cients in a Fourier se ries gives

M { u ( x,y,z) cos

The evaluation of the initial temperature distribution u(x,y,z) requires simulatin g the heatin g effect of the li g htnin g stroke in some suitable fashion . Suppose that at t = 0 an amount of heat Q is lib - erated in a small block of the plate defined by the conditions a.

- a - a. a - < -< X < - < -

- - 2

2 2 a - a - a.

~ < (11) - < - < y :5 - 2 2 2 2 b - b i3~z ~ The heat is thus liberated in the small block of dimensions a.,a.,i3 sit - uated on the outer surface of the plate, jus t opposite the point 0 on the plate . The material in this block will be raised to the uniform temperature NACA TN 4326 B= _ Q -

(12)

cpa 13 where c is the specific heat and p is the density of the metal . The function u(xJyJz) will be e~ual to B in this block and e~ual to zero outside it.

The coefficients A ~ mn f r om e~uation ( 10 ) can now be evaluated as follows: A =

(13)

1. mn For convenience of notation the Kr one c ker symbols are used:

l if

7, = 0 (14) 5~ 0 = J

{O

~ f 0

Carrying out the integrations indicated in e~uat i on (13) yields

! c : cos [(~' ) 0 + ~ )J dx ~ ~ . l Sin [(~ . ) ( a;a )] - sin [ (~. ) (a;~ J l

( :n ) sin ( ~!n ) cos (~ n )

o if 7, is odd

sin ( ~~

(_) ~ / 2

is even ~ na a 2a

(15)

NACA TN 4326

~ { ~ COS[~':)Z]aZ = ;. { Sin (n.) - Sin [n.~b~~)J}

( ;n ) sin \ ~~~ ) cos [nn ( 2~~~ ) ]

This yields the gene ral formula a. f3 -r . (I :r{a. ) . I m:rca. ) . ( P.:r{f3 ) e a b (_) [(7. +m)/2] +n SID \2;- SID \ "2a SID \"""1) 1 ] [ 1 ] [ 1 ] ( 7,:r{a. ) I m:rca. ) ( n:r{f3 ) ( 17) [ 2(1+07,,0) 2(1+~,O) 2(1+~,O) \ 2a \ 2a \T He re I and m have only even values, since by equation ( 15) the coef- ficient A will vanish if I or m is odd.

Imn The final solution of equation ( 6 ) for the tem perature distribution

in the plate fo r t ~ ° can be written as

T(x,y,z,t) = ~ <P(a, a. ;x,t)<P (a, a. ; y , t) \jf(b,~jz,t) (1 8 ) cpa. ~ where CD (_)I/ 2 sin (I n a.

~ cos [(I:l~ x + ~ TI

2a <P ( a, a. ; x, t) =

exp [_ ~ :) 2 ~

In a.

~(l + DI,O)

L

2a I =0,2,4, ..• (1 9 ) CD

sin ~ n~~ ~

(_)n ~ cos [(~ n l z J

\jf(b,~jz,t)

exp t ~~~ 2t J

1 nn~

L

2 ( 1 + Dn,O ) b n=0,1,2, ...

( 20 ) NACA TN 4326 If 7, is even,

cos [ (~n)0 + i )] = (-) 7,/2 cos (7,:X) (21)

so that the new summation index, p = 7,/2, can be introduced, which takes

all non -ne gative integral values, and formula (19) can be replaced by

If) ex> to a.

en cos

~ 2 rX2

a

sm ~:~) ex{ ~~x)" tJ <p(a,cx,;x,t)

""

-( 1

L + 07,,0)

a p=0,1, 2, ...

( 22) The formulas given represent the exact solution of the proposed problem. However, in view of the nature of the ap pl ications to be made of them, it is feasible to allow some simplifications .

The size of the plate is not very mater ial to the flow of the heat to the inside of the plate so lon g as the thickness is small compared with the breadth of the plate. It is therefore convenient to take the limit a-+ CID. In this case, <p ( a. ; x, t) lim <p( a,a.;x,t) ( 23) a -+ CID The series in equation (2 2) goes over into an in teg r al, and on working out the process the following solution is found:

sin S cos

( 24)

~(~;x,t) ~ ; 1:-

~ where s = pna./ a.

This function can be reduced to a more convenient form for numerical computations. Introduce the following notation (which is valid for t > 0):

~)~

(25)

\zx/t) ~

NACA TN 4326 Substitution into equation ( 24) yields (26 ) Now define the function (27 ) Making use of this abbreviation giv es from equation ( 26 ),

<p ( a ; x,t) = lJ + ~ \ - g( X - ~ \J

g( X

( 28 )

2 L \ 2X -It! \ 2X {t !

From equation (27), dg = 4 ( OO cos (2T]iJ.) exp (-iJ. ) diJ.

dT] ;( J 0

(29 ) on making use of formula 508 of Peirce's table of integrals (ref . 2 ) .

It is obvious f r om equa tion ( 27 ) also that g (O) = O. Equation ( 29 ) is

integrated directly as a differential equation : (30) This shows that the function g eT]) defined in e quation (27) is just the ordinary pr obabi lity integral and thus can be found tabulated in numeri - cal form .

NACA TN 4326 The following formula for the temperature distribution from the heat source (strictly speaking) in a plate of infinite breadth) is finally obtained: Q

T(x)y)z)t) = -- 2- <p( a ;x)t)<p(a;y)t)'I)r(b)l3; z)t) (31)

cpa 13 with the function <p( a ;x)t) defined by equation (28 ) and the function 'I)r(b)l3;z)t) defined by equation ( 20 ).

Discussion of Formula (31)

Formula ( 31) g ives the temperature distribu t ion throughout the plate

resulting from the heat source introduced by the lightning stroke. In applying the result) only the temperature distribution over the inner sur-

face needs to be known. This is obtained by setting z = 0 in equation

(31). For simplicity of notation) this temperature function is written

as follows: T(x)y)O;t) (32) The following formula results: (33)

TO(x)y;t) = ~ <p(a;x)t)<p(a;y)t)W(b)I3;O,t)

cpa 13 where) from equation (20), (34) 'I)r(b)I3;O,t) ----(1 + n=O) 1) Since the tem perature distribution TO(x)y;t) is expressed in equa- tion (33) as the product of two types of functions, it is convenient to examine the nature of each of these functions separately.

At the initial instant t = 0) conditions require that the whole of

the inner surface of the plate be at the uniform temperature taken to be T ~ O. Therefore, the following must be obtained from equation (34): (35) 28 NACA TN 4326 This is an alternating series of a type somewhat difficult to handle, since the terms do not diminish very rapidly in magnitude. There will be no attempt to prove ri g orously that the sum of the s eries is actually zero as is indicated in equation (35) .

It is apparent by inspection of equation (34) that as t -+ co the series converges rapidly to the value i3 (36) b Owing to the exponential nature of the summands in the series in their dependence on the time variable, the dominatin g term will be the one having the smallest exponent ; that is, the second member of the series,

since the first one (n = 0 ) does not depend on the time at all . There -

fore, the function given by equation (34) will start from zero at t = 0

and will r ise quickly to the final value i3/b practically like an expo - nential function with the time constant (37) Expressed in physical terms, this function determines the flow of heat from the initial heat source directly thr ough the thickness of the plate .

The time constant (37) can therefore be expected to be quite small for plates of ordinary thickness such as are used in the construction of aircraft .

For an aluminum plate, Thermal conductivity = k = 0 . 504 cal/(cm) (sec) (oC )

Specific heat = c = 0 . 217 cal/( g ) (oC)

DenSity = p 2 . 70 g/ cm From this information, the thermal diffusivity is 2 k 2/ x = - = O. 086 cm sec cp x = ~= 0. 93 cm/~

Taking b = ~ inch = 0 . 318 c e ntim et e r, t he ti me cons t ant is

19 . ) = 0 . 0 119 se c (38)

t' \0 . 9311: NACA TN 4326 The rise time of the temperature on the inner surface of the plate, di- rectly opposite the heat source, should thus be of the order of 12 milli- seconds. This result will not be particularly sensitive to the size of the initial heat source; that is, it does not depend greatly on the value of ~, since the expression (37) for t' does not involve this parameter.

The temperature at the pOint 0 shoul d have a maximum value, which is abou t (39) The initial rise of the temperature at the point 0 is determined by the flow of heat through the thickness of the plate, but its ultimate decline is g overned by the transverse flow of heat along the plate. This is expressed by the functions ~(~;x,t) and ~( ~ ;y,t), which, of course, have the same functional form.

From the initial conditions, the following is expected at t 0: if > ~/2 Ixl ~ ( ~ ;x,o) = (40)

{~

if < ~ / 2 Ixl It i s easy to show from equation (28) this is the that case, if it is noted from equation (30) that g (-Tj) = - g(Tj ) ( 41) g ( (0) = 1 The function ~(~;x,t) is roughly exponential in form and decays comparatively slowly in rel ation to the initial rapid rise of temperature at the point O. It is best shown in the form of gra phs drawn for special cases.

The analysis has assume d that the initial heat source has a square cross section and a depth ~ . In practice one will have little or no control over the exact shape of the region in which a lightning stroke develops heat in the plate; and on the whole one will proba bly find a circular or roughly elliptical spot. For p oints near the center of the spot and points away from the spot by distances large compared with the radius of the spot, the exact shape of the spot will be immaterial. For an exactly circular spot the analysis can be made in polar coordinates.

This analysis is discussed in a later section for completeness, but its use would require numerical wo rk with Bessel functions, which was not considered justifiable in view of the uncertainties in the data.

30 NACA TN 4326 Graphical Example In order to show the nature of the heat flow in the plate, a par tic - ular case is presented in g raphical form. Consider an aluminum plate with the following dimensi ons : Thickness = b = 0 . 318 cm ( 1/8") 0 . 5 cm Source size = 1 ; : (1/16 ") 0 . 159 cm The source is then assumed to be 0. 5 centimeter s~u ar e and extends half - way th ro ugh the pla te . Fr om the data g iv en in the prec e din g section for alum i num , the temperature of the so urce, for a gi ven heat input Q, lS initially

a = 10 . 3 Q (4 2 )

whe re Q is expressed in joules, and a is tn e temperature rise

above r oom temperature in de g rees centi g rade.

Tempera ture at poin t O. - The temperature at the poin t 0, which is on the inside of the plate just opposite t he center of the source, is considered first. Making use of e~uation (33) g ives

TO = TO(O,O;t)

a l~( ~ ; o,t )1 2x* (b,~;0,t) (4 3 ) The function *(b,b/2;O,t), which de te rmines the flow of heat th r ough the thi c kness of the plate, is pl ott ed in figure 26. It starts from zero and rises to 0 .5 , sin ce the flow of heat directly throu gh th e plate would double th e amount of heated metal and so wou l d l ower the temperature by a factor 0 . 5 . This function is plotted on a universal time scale as a functi on of tit ', where t' is d e fined by e~uation (37) .

The function ~ (0 . 5 ; O , t), which d et e rmin es th e flow of heat away from the po int 0 along the plate, is pl otte d in figure 27 . This gr aph starts at uni t y at t = 0 and diminishes c om par atively slowly to zero .

The composite result, g ivin g the tem per atur e at the p oint 0, is plotted as curve A in fig ure 28, which shows that the temperature at 0

rises to about a/4 a s its maxi mum value in about 20 millise c onds and

then falls rath er steep ly; in 1/10 second it is down to a /10 . This point wil l obviously be the hott est on the inside of the p la te, so that the rapidity with which it cools off will b e an important criterion governing th e firing of an exp losiv e ga s mixture that contacts th e sur - face here .

NACA TN 4326 31 Temperature at a neighboring p oint . - As an indication of the tem- peratures re a ched on the inside of the plate near the source point, the t e mp e rat ur e -t ime curv e has b ee n plott ed f or a po i nt 0 . 5 c e ntim et er from the p oi nt O. Th e cur ve is giv en a s cur ve B of fi g ur e 28. The t e mp e ra- tu r e at t his point ris e s slowly to only about 25 pe rc e nt o f th e maximum tem pe ratur e at 0 and th en falls slowly . Th e flow of he at alon g th e a lumi nu m p lat e is s o rapid that only th e points quit e ne ar th e initial so urc e a re h e ated to any gr e at ex t e nt .

Eff e ct of Cont i nuou s Sourc e I t has bee n a ss u me d in th e pr ev ious calculations that th e h e at sourc e

i s es t ablished instantaneously at time t = 0 and that only the tempera-

t ure distribution from this origin is si g nificant. In practice, the applica t ion of the heat will not be so instantaneous, but the source may be applied for some time and may vary from instant to instant in magni- t ude. Once the pr o blem of findin g the temperature distribution from an instantaneous source has been solved, it is possible to write the method of findin g it from a variable source, taking advantage of the linearity of the differential equation of heat conduction and of the boundary co ndi t ions.

First t he notation in which the result has been expressed will be revised. Instead of using the particular instant t = 0 as the t:ime of a pplic at ion of the source, this instant is indicated as t . Also, l suppose th at t he heat is supplied in an infinitesimal time interval dt , l

suc h tha t Q = q(tl)dt . Then, from equation (31) the temperature dis-

l t ribu t ion fol l owin g from this source at times t > tl would be given by t h e formula ( 44) Clearly, to find the temperature distribution from a set of sources operatin g in the past it is necessary only to sum (inte grate) expression (44) over all the sources that have been present. This yields the final formula: ( 45) I t is no t practicable to evaluate this expression by actual inte- g ration if the source function q ( tl) is ve ry complex . The best method NACA TN 4326 of handling it is probably by numerical and graphi c al means, ap p roximating the source function by a set of discrete sources .

Treatment of Infinite Plate in Cylindrical Coordinates The mathematical analysis of the heat flow in a plate has been car - ried out entirely in terms of Cartesian coordinates in the earlier sec - tions of this report . This has led to the use of a heat source in the form of a small rectangular parallelepiped . The reader may consider that it would be more sensible to use a heat source in the form of a small cylinder. This is ce r tainly correct in principle, and the procedure used has been one of convenience only . In this section the analysis is carried through for cylindrical polar coordinates with a cylindrical shape for the source and solved in terms of Bessel functions .

Using the usual cylindrical polar coordinates, with origin at the point 0, the heat - conduction e~uation takes the form o ( 46) Only cylindrically symmetric solutions need be considered, so that the temperature depends only on the distan ce from the center of the plate and not on the angular position around the source .

Fi r st, particular solutions of the differential e~uation (46) are sought which obey the boundary conditions of the problem . Here an in - finitely large plate is taken at the start, so that the boundary condi- tions reduce to the re~uirement that the solution be finite everywhere, and be Single - valued . There is to be no flow of heat from the surfaces of the plate, so that dT/oz = 0 at z = O,b .

Particular solutions satisfying these conditions are of the form (47) , .here A is an arbitrary real positive constant, and F(r) is a solu - tion of the differential e~uation d 1 d 2) () -- + - -+A Fr = 0 (48) ( dr2 r dr

The only solution of e~uation (48) that remains finite at r o (for

A -f 0) is

•

NACA TN 4326 33 (49 ) F(r) = constant x JO(A r) where J is the Bessel function of first kind of order zero.

O To satisfy the initial conditions these parti c ular solutions are combined linearly . The members in the variable z must be summed over

the non-negative integer n = 0}1}2 .. ' } while the radial solutions

must be integrated over the parameter \ . If the initial heat source is a small cylinder of radius a and depth ~} into which an amount of heat

Q is deposited at t = O} the result is

(50)

T(r}z}t) = - Q -"!.....::: 2- <p(a;r}t)"' ( b}~;z}t)

cplla ~ with

sin ~ nll~ ) [ 2 J

__ --'~'_ b ""-L.. _ exp _ (! _ n_ ll _X) t (51) '\jr(b}~;z}t) nlll3 \ b b which is identical with the function defi n ed in equation (20) . The func- tion <p(a;r}t) is of the form (52) where g(\) must be determined from the initial con d itions . Here the following is required : if r > a (53) <p(a;r}O) if r < a If (54) u(r) <p(a;r}O) Then} from equation (52)} (55) The inversion of this integra l equation fo r g ( \) wh en the left side is a known function gives NACA TN 4326 ( 56) Making use of the initial conditions (53) which define the function u(r )) in the present problem ( 57) This leads to the formula t

.(a;r, t) ~ !O~[!O a JO(' R)R dR ] JO(kr) exp( _, 2 ), d'

~ faa [!a~ JO(AR) JO (A r) exp( - ,2 t ), d ~ R dR (58)

It would be possible to make use of these formulas for the calcula- tion of the temperature distribution in the plate) but t he work would be greater than by the earlier method) without significant inc r ease in ac curacy of the re sult .

REFERENCES 1. Stout ) H. P .) and Jones) E.: The I g nition of Gaseous Explosive Media by Hot Wires . Third Symposium on Combustion and Flame Phenomena) The Williams & Wilkins Co .) 1949) pp. 329 - 336 .

2. Pei rce, B. 0 .: A Short Table of Inte g rals . Third ed.) Ginn and Company) 1929.

~ CJl ~ tI>- ~ N 0)

s;: o :x>

, I kv sec R wave AND 12 1 x 1

=

at generator, 0.0004 40,000 (I)x(t) 200

= 200 coulombs

amp amp EFFECT, THAT

=

ng-duration 200 200- duration rectangular current Lo back HEATING sec NERATORS E AIRCRAFT 2 R CR-5 G 10,000 10 kv criti- stroke ON x 10- at

=

-6 FORCES, 0 . 25 ~f value (C)X(E) damped 172,000 30 coulombs CURRENT

=

=

1/2 Secondary generator, LIGHTNING 3,000 3,000xlO 5,000-amp duration to cally SURGE I MECHANICAL sec OF kv 5 R NATURAL criti- l5xl04 r, o 10- x TYPES OF coulomb

at =

CURRENT, value 100.0 69,000 --- (C)X(E) ~f damped

= 0.5

xIO- generat THREE High-current tlon

=

PEAK a 1/2 EFFECTS 3 . 3 3.3 OF OF 100,000-amp dur to cally to FER S and charge TRAN REPRODUCE current

jOUle~

ased duration to COMPARISON ak dt, - pe rele ARGE erosion form heating H mechanical -8 ) effect, proportional C I. proportional of current, xlO 2 nergy wave

e fa"

elative TABLE amp nd

(R

( pitting proportional transfer square R effect, to Relative Peak a Relative force, NACA TN 4326 (a) Laboratory building and network.

Spherical mirror for 360 photographic recording of all lightning discharges in vicinity Loops pick up propagated 1l'j~p radio - interference High-voltage ~ impulse components the discharges test Altitude Storeroom chamber Library and Control room seminar room High- Laboratories current generator Darkroom --m-- -~~ Lightning High-current generator generators 6 million volts impulse -4::::::=~~~=~=~~~~f=!=~~~~\-- 100,000 amps.

1.5 million volts D.C.

generator (b) Cross section of laboratory showing test facilities.

Figure 1. - Lightning and Transients Research Institute laboratory for producing simulated lightning channel.

NACA TN 4326

o 50 100 ~ Sec

V---+J\/\J\r+"V\/\r>O--- -~

~ 100)~00 Amperes

o 50 100~ Sec

150 )000 Volts

h

~Amperes

o 10) 000 ~ Sec '1l~

8)000 Volts 20~ Amperes 7: o 50 )000 ~ sec 100)000

I

13.5 kv --<It==~

60 cps --- 15)000 Volts 3 Phase --4 100)000 10)000 ~ til 1)000 "' ~ Q) H ~ 20 )000 40)000 60)000 0 80)000 100)000 Time) micro sec Figure 2. - Composite waveform generators and resulting waveform.

NAcA TN 4326 C- 476l0 Figure 3 . - Environmental explosion chamber with integral wind tunnel .

NACA TN 43 26 3 9 High- .. - vol t age bushing r M easuring equipment "" l' , " \ '.

'I I W i nd-tunnel " , blowe r

'~\_' \

~ "

~ Camera

~

Sample t a nk Fi gure 4 . - Schematic diagram of envir o nmental explos i on chamber showing location of integral wind tunnel ) camera ) and measuring equipment.

NACA TN 4326

/'

,

~

r::.

H igh - volt ag e g enerator I , I I , I / ..

duct Fi gure 5 . - C on cr ete - bl ock p it for f ull - scale experimental setups t o control poss ible explosio n and fire hazards from ignited fuels during l abo r atory tests i n volving discharges to full - size fuel tanks .

i

NACA TN 4326 High-voltage ....--- bushing Environmental tank Fastax camera

)

to I p::j o \ Transparent insulating section Figure 6. - Environmental explosion tank for test setups with discharge to small fuel cells under different conditions of temperature, air velocity, and pressure.

NACA TN 4326 ____ Test plate F==::::;:::;;:::::;:::;;:::::;:::!

r-------------~ Multichannel recorder Amplif'iers Selector Cold junctions switch L..- ______ --l '------I Oscillograph Figure 7. - Block diagram of thermocouple system.

____ ...... C- 760 6 Figure 8. - Cross section through center of crater produced by laboratory discharge to 1/8-inch- thick aluminum plate.

NACA TN 4326 . 5 . 4 · 3 (!)

~ -....., ..!d ()

v

r\

oj . 2 P

"-

ill "- r"I

•

p:; I . 1

V

~

r--.

.......

</

-

o

-"

-

(a) Theoretical c ur ve .

. 5 ....

- Jr

i'o"" . 4

/

"\

.3

'\

\\.

/

. 2 ~~

V

~ .1 ........

""- ......

I ....

"'1-0 I o 1 10 . 01 . 1 . 001 Time, t, sec (b) Experimental curve .

Figure 9 . - Temperature - time curves for liB - inch - thick aluminum plate .

44 NACA TN 4326 0 . 038 S ec o Sec 0.004 Sec 0 .040 Sec 0 . 204 S ec 0 .010 S ec Figure 10 . - Photographic sequence of sample fuel-tank ignition by artificial-lightning discharge.

NACA TN 4326 o Sec 0 . 061 Sec 0 . 055 Sec 0 . 081 Sec 0 . 110 Sec 0 . 058 Se c 0 .120 S ec 0.060 Sec Figure 11. - Fuel - tank explosion by artifi cial-l ightning discharge with 300-mph windstream.

NACA TN 4326 Temperature indicator current generator Wind -tunnel section

o

Lucite Mixture tunnel indicator throat

camer::ndO

observer

o

Fire extinguisher' Cathode follower and oscilloscope for pressure measurement Figure 12. - Test arrangement for scale fuel-tank explosion studies.

NACA TN 4326 Figure 13. - Photomicrograph of cracks in fuel-tank wall where no direct puncture or explosion occurred.

NACA TN 4326 (a) Without windstream.

(b) With windstream.

Figure 14. - Spark showers from punctured aluminum sheet with and without windstream.

NACA TN 4326 (a) Holes burned in ends of wingtip tank cones by natural lightning.

C-46615

•

200-coulomb 30-coulomb 30-coulomb 30 coulombs long-duration with short pulse long-duration long-duration 200-amp peak 500-amp peak 4000-amp peak 150,000 amp (b) Holes burned in 2O-mil aluminum by laboratory-generated artificial discharges.

Figure 15. - Comparison of holes burned by natural and artificial lightning.

NACA TN 4326 (a) Puncture of 0.064-inch sheet (b) Erosion but no puncture in by standard 230-coulomb discharge. 0.OB1-inch sheet by standard discharge.

(c) Puncture of double-wall 0.040- (d) Puncture of 0.040-inch sheet inch sheet spaced l/B inch.

by 2O-coulomb discharge.

C-47614 (f) Erosion of 0.OB1-inch sheet (e) Puncture of 0.OB1-inch sheet with windstream and faulty discharge. with windstream and standard discharge.

Figure 16. - Erosion or puncture of fuel - tank aluminum alloys (shown half size) by artificial-lightning discharges.

NACA TN 4326 Figure 17. - Hole and pit marks on a wingtip fuel-tank tailcone caused by natural lightning.

C-47613 Figure 18. - Successive in - line displacements of holes burned by natural lightning in aD - mil aluminum air- craft skin as aircraft moved through discharge.

NACA TN 4326 CIl Q) 25 bll H III ..Q 0 20 'H

1:l

Q) () H 10 r-- r-- Q) P-< r 5 r--

1 n nnn I nn nnnnnn n nn n n n n n

0 6 8 10 -10 -8 - 6 - 4 - 2 0 C 2 0 0 50 F.

14 F 32 F Figure 19. - Variation of percentage of lig htning strokes to aircraft with temperature in U.S. flights.

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10 -

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o 24 26xl0 o 8 14 ).6 18 20 22 4 6 10 12 Altitude, ft Figure 20. - Variation of lightning strokes to aircraft with altitude in U.S.

flights; 123 incidents.

NACA TN 4326 l1) to (J) Fuselage nose ~

I

Fuselage misc.

I

Wing Aileron Elevator

I

Rudder

I

Propeller

I

Antenna

I

Inspection doors

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opened Compass of'f' ~ Mi sce l laneous

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o 15 25 30 5 10 20 Percent of' damage Figure 21. - Distribution of' damage in 275 lightning discharges to aircraf't.

NACA TN 4326 Figure 22. - Two-million-vol t discharge entering model aircraft vertical fin and leaving antenna mast below fuselage.

Figure 23. - Two-million-volt discharge entering model aircraft vertical fin and leaving pro- peller. A streamer may be noted off wingtip.

NACA TN 4326 Figure 24. - Laboratory discharges to scale model of jet aircraft showing str okes to nose and wingtip tank.

56 NACA TN 4326 Figure 25. - Plot of equipotentials about jet aircraft in cross field before and after lightning stroke contacts tail of aircraft.

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