N O T I C E 

THIS DOCUMENT HAS BEEN REPRODUCED FROM 

MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT 

CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED 

IN THE INTEREST OF MAKING AVAILABLE AS MUCH 

INFORMATION AS POSSIBLE 
by

T. F. Trost

M. G. Grothaus

C. T. Wen

DEC 1985

DECEIVED

MASH M fAOMk;

QEPJ. A,

Interpretation of

F-1066 In-Flight Lightning Sign

Report on

N.A.S.A. Grant NAG-1-28

August 1985

(N).SA-CR-176387) INTERPRETATION OF F- 106E N86 -1?320

IN-FLIGHT LIGHTNING SIGNATURES (Texas

Technolo q ica l U:niv.) 51 p HC A04/MF A01

CSCL 01C Unclas

G3/0.5 04914

Department of Electrical Engineering/ Computer Science

Texas Tech University

Lubbock, Texas 79409

^^
INTERPRETATION OF

F-1068 IN-FLIGHT LIGHTNING SIGNATURES

by

T. F. Trost

M. G. Grothaun

C.-T. Mien

Department of Electrical Engineering/Computer Science

Texas Tech University

Lubb=k, Taxes 79409

August, 1985

Prepared for

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia 23665

Under Grant No. NAG-1-28

"Lightning Sensors and Data Interpretation"
ABSTRACT

This report consists of a series of short discussions

covering various characteristic s of the electromagnetic data

obtained on a NASA F-1068 aircraft during direct lightning

strikes. Time scales of interest range from 10 no 'to 400 Ns. The

following topics are discussed:

Lightning current, I, measured directly versus I obtained

from computer integration of measured I-dat.

A method of compensation for the low-frequency cutoff of the

current transformer used to measure I.

Properties of fast pulses observed in the lightning timederivative waveforms.

The characteristic D-dot signature of the F-1068 aircraft.

An RC-discharge interpretation for some lightning waveforms.

' A method for inferring the locations of lightning channel

attachment points on the aircraft by using B-dot data.

Simple, approximate relationships between D-dot and I - dot and

between B and I.

Estimates of energy, charge, voltage, and resistance for a

particular lightning event.

L^ I
t ACKNOWLEDGMENTS

The authors wish to thank M. E. Thomas of NASA Langley

Research Center for supplying the digitized data used in this work

and for providing much supporting information concerning the

instrumentation of the F-1068 aircraft.

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TABLE OF CONTENTS

saglien Ent

I. INTRODUCTION i

II. RESULTS FROM 1982 DATA 2

Comparison of I and I-dot Results 2

I-Sensor Droop 6

Fast Pulses in the Time-Derivative Waveforms 6

F-1068 Signature 12

Aircraft Discharging 15

Changes in Waveform Spectra with Attachment-Point

Location 20

III. RELATIONSHIPS AMONG THE WAVEFORMS IN STRIKE 84-17-01 25

I and I-dot 25

D-dot and I-dot 28

8-dot and I-dot; 8 and I 31

I and E 34

I.V. CONCLUSIONS 40

Data Consistency and Accuracy 40

Characteristics of the Lightning 41

Character,isitcs of the F-1068 42

APPENDIX I. CAPACITANCE OF F-106B 44

APPENDIX II. RELATION BETWEEN D-DOT AND I-DOT 44

REFERENCES 45

iii
I. INTRODUCTION

During the past few years, lightning strikes to the NASA F106B aircraft have yielded such new electromagnetic data on

aircraft - lightning interactions. This report briefly examines

several of the more obvious characteristic s of the data. Roaults

of controlled laboratory tests at Texas Tech University as well as

results from approximate theoretical relationships are used for

data interpretation. Most of the lightning strikes under

discussion are from 1982, with just a single, although important,

strike from 1984.

Related research activities at Texas Tech which are not

explicitly discussed in the present work include an experimental

study of the electromagnetic resonances of , a model of the F-1OSB

attached to resistive wires [ 1] and an experimental study of spark

initiation on an isolated, oonduct4ng object in a strong

electrostatic field (in progress).

1
II. RESULTS FROM 1982 DATA

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Two transient recorders were used in 1982 and were switched

among the four electromagnetic sensors shown in Fig. 1, A fern

lightning strikes were obtained with the recorders connected to

the• I and I-dot sensors, which measure the current and the time

derivative of the current on the noseboom. The results from the

strike which produced the largest current (82-44-04) are shown in

Fig. 2. The lightning waveform depicted in the figure is a

current pulse with a fast rise time and a slow fall time. The

figure compares I to the time integral of I-dot in order to test

the consistency of the two measurements. A small displacement in

time has been introduced so that the two curves are not confused.

Notice that the agreement overall is quite good. However, the

effects of , the coarse quantization of the 6-bit transient

recorders are very evident: in the I waveform, the jumps between

adjacent amplitude levels are quite large, and in the integrated

I-dot waveform the entire trailing edge of the lightninfl pulse is

represented by a constant slope. This constant decline resulted

from a constant negative level in I-dot. The actual I-dot values

were no small on the trailing edge of the pulse that the recorder

* digitized all of them in its first level below zero. This may be

' seen in the I-dot record, which is shown in Fig. 3. Refering to

Fig. 30. notice also that the I-dot signal went off scale briefly

duringg he fastest-rising portion on the leading e g dge of the A h

pulse. Thus some positive area Man missed for the integration.

1 This is consistent with the fact that the integrated I-dot curve

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pulse.

I-62DROE QUOR

For lightning signatures which varied more slowly than the

pulse shown in Fib. 3, the I wensor was found to introduce

distortion in the form of droop . This is to be expected wince

the I sensor was a current transformer with a lower cutoff (- 3

d8 ) frequency fo n 2.8 kHz. Because of the droop, unipolar

lightning currents appeared as bipolar at the sensor output, the

effect being pronounced unless the lightning pules 'wngth n were

muc^z tows than (2n fc) -1 a 60 pr.

In order to estimate the true lightning signatures from the

sensor output waveforms, we have measured the transfer function

of the sensor in our laboratory and have written a computer

program which uses the transfer function to put the low-frequency

content back into the waveforms [2]. The program essentially just

Fourier transforms the sensor output waveforms, divides by the

transfer function, and inverse transforms the results. Two

examples of waveforms processed with this program are shown in

Figs. 4 and S (82-41-19 and 82-41-22). Each example whows the

processed and unprocessed waveforms superimposed. Notice that

most of the undershoot is removed by the processing and no is not R

a true characterintic of the lightning.

Fast Ulm in tht list-ftriyltiyt waYtI ms

A common feature of many of the lightning time-derivative

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waveforms is the appearance of very fast pulses. The pulses occur

F either singly or in groups, and the average number of pulses per

group for 1982 was 2.4. An example of n group of 3 pulses in a Dx 

dot waveform is shown in Fig. 6 (82-,38-02). The 10 no sample

interval of the transient recorders is not short enough to provide

detailed pulse shapes. In fact, the pulses are only two or throve

samples in width, and their true peak values are probably often

missed in the sampling process. In 1982, surprisingly, !1l of the

D-5 dot and B-dot puleew were of positive polarity. This

corresponds to increasing positive charge at the front of the

eircraiZ (where the D-dot sensor is located) and increasing

current fore-to-aft along the fuselage (where the B-dot sensor is

located). The fact that all the pulses had the same polarity

implies a charging mechanism attached to the airplane. That is,

an explanation for the charge accumulation based solely on the

polarization of the airplane by an ambient electric field is not 

satisfactory wince the ambient field would not always be oriented

so as tout the same p polarity of charge on the nose. 

For the pulses that occurred in groups of two or more we have s

measured the time intervals between adjacent pulses. Fig.7 shows

a the distribution of these time intervals; the average value is 300

no. Unfortunately, there is probably some inaccuracy in the

' distribution at short times because of the ringing of the

aircraft. The pulses excite the electromagnetic resonances of the

p

aircraft, which take about 300 no to ring down [33. (The period

^

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pulse following within 300 no of a strong one may be obscured by

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A typical example of aircraft ringing is seen in Fig. 6

following the second, and largest, pulse. An expanded plot of

this portion of the waveform is shorn in Fig. 8, labelled F-106.

Notice that the ringing consists in part of a prominent double

hump shape. This shape has also been observed in laboratory

scale-model tests [4], and one of the waveforms from the

laboratory model is shown in Fig. 8 for comparison with the F-106

data. From the laboratory tests it has been found that the double

hump result s from the reflection from the rear of the aircraft of

a fast current change. That is, the shape is produced by a

current step which is injected at the front of the aircraft,

travels to the rear, and then partially reflects from the trailing

edge of the wings

( first hump) and then from the and of the

fuselage and tail ( second hump). This shape is a characteristic

signature of the F-106 in response to current injection at the

nose. It is clearly observed 58 times in the 1982 D-dot data.

The positive polarity of the pulse preceding the humps means

a positive change in the charge on the nose, so that electrons

must have exited there. See Fig. 9. This is an interesting

result because it means that the nose of the aircraft was acting

as a negative tip, and it is known from laboratory studies [5]

that in a rod - plane gap, if the rod is negative, a higher voltage

must be applied to cause sparkover than if the rod is positive.

12

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D-DOT

20

10 LABORATORY MODEL

F-106

0

70- 140 210 280 350

35 ies 175 245 315

IE-3 TIME (MICROSECONDS)

Fig. 8. Comparison of D-dot double hump signature

of F-106B (82-38-02) and laboratory model.

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The variation of electric field ? C, corresponding to the Ddot wavifcrm in Fig. 6 has been obtained by integrating and

dividing by 0 0. The result is shown in Fig. 10. The fast pulses

in D-dot appear as small, abrupt increases in electric field,

while the main feature of C is an approximately exponential*rise

to 360 kV/m. This indicates that the aircraft experienced an

increase in positive charge or a decrease in negative charge, with

a time constant of about 680 no. The location of the zero

electric-field level is not known and has been arbitrarily located

at the bottom of the plot. Three curves, rather than one, have

been plotted in order to show the effect on g of the uncertainty

in the exact value of D-dot due to the 6-bit quantization of the

transient recorder. The middle curve is the integral of the

Ictual D-dot data, and the upper and lover curves are,

respectively, the integrals of the data after the D-dot zero level

had been shifted up and down by 1/2 of a least-significant-bit

" (LSB).

Values of maximum E and time constant, T, for several

lightning strikes which showed approximately exponential

discharging (or charging) like that in Fig. 10 are given in Table

I. All of these waveforms were similar to Fig. 10 in that they

contained, first, a brief slowly rising portion, then a few rapid

increases, and finally a longer, quasi-exponential rise. The -r

values were measured as the time required for the curves to reach

(1 - a- 1 ) of their final value, not including the slow rise at the

beginning.

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Table I. Aircraft Discharging Parameters

-brit ------- NnxL-i-ikYLv --------P-T J ON1

82-38-02 360 680

82-38-04 120 670

82-40-04 190 300

82-40-07 440 370

82-42-06 160 630

82-42-09 240 600

Fig. li shown the waveform of B-dot that was recorded

simultaneously with the D-dot waveform of Fig. Via. The time

integral of B-dot is shown in Fig. 12, with the effect of a t 1/2

LSB change in B-dot illustrated by the multiple curves:

Unfortunately, these 1/2-bit changes cause a large variation in

the final value of B, indicating the need for finer quantization.

Actually, the B-dot waveform was altered in one respect prior to

integration: the value of the large positive peak, which was at

fujl Bc818 for the recorder, was increased. If this had not been

done, the final values of all three of the curves in Fig. 11 would

have been negative, indicating a large continuing current flowing

on the aircraft instead of a short pulse. While continuing

current is possible, data recorded in 1984 2uggest that the

current in the present case was actually in the form of a short

pulse. A quick look at 1984 data (84-17-01) shows D-dot and Bdot waveforms similar to those here, but in addition, thanks to an

increase in the number of data channels, it also shows I; and the

►°'` 17
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I waveform is essentially a short pulse. Thus, mince 9 and I ar!o

closely related, we assume in the present case that the final

value of a should be zero, and we have multiplied the peak 9-dot

value by the factor, 4.27, which achieves this.

The picture that emerges from Figs. 10 and 12 taken together

is that of a pulse of current which discharges the airplane. The

situation is similar to the discharging of a capacitor through a

resistor. If one assumes that the airplane is the capacitor, with

a capacitance of approximately 500 pF (Appendix I), then, using i

n RC, the 680 no time constant gives a resistance of 1.4 kR for

the circuit. The initial voltage, V, of the airplane can be

estimated also. One way to do this is to estimate I from B and

then make use of tho fact that, at the instant when discharging

begins, V a ImaxR, where Imax is the maximum value of the current.

To relate I and 6 we use the approximate result (6]

9 a po I / (2n r) , (1)

where r is the effective radius of the airplane at the location of

the 9-dot sensor. Substituting 35 E-6 T for maximum 9 (from Fig.

12) and 3.0 m for r (from (6)), gives Imax ' 530 A. Then V n 740

kV.

Gh2a lB t9 MY214£g lReg rs Milb 61112022DI-PQ1nt hge2ti42

An part of the laboratory scale-model tests described in (4]0

a model of the F-106B vas connected to a pair of wires in four

different ways to provide a variety of entry and exit points for

20

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current pulse. Tito current entry and exit points are listed in

Table It.

Table II, Wire Attachments on Model

1 nose engine exhaust

2 nose port vingtip

3 starboard wingtip port wingtip

4 belly tail

For such attachment point configuration, transfer functions

were computed relating the signals measured from small sensors

mounted on the model to the entry- Mire signal applied by a pulsar.

Fig. 13 shows the transfer function s for a n -dot sensor which was

located and oriented like the 6 -dot sensor on the actual airplane

shown in Fig. 1. As indicated on Fig. 13, the transfer functions

are defined as BO O / V IN (w) , where BL(w) in the Fourior

transform of the time - integral of the B-dot sensor output and

V IN (w) in the transform of the pulsar voltage. The frequency axes

have been scaled to corres pond to the actual plane. An inset

along side each transfer function illustrates the model with wires

to show the attachment locations.

The curves in Fig. 13 give information on the various

resonant modem of the model that are excited by the current

pulses. Some of the main characteristics of the curves are,

first, for configurations 1 and 2, a peak at 7 MHz, second, for

configuration 3, a dip at 13 MHz, and, third, for configuration 4,

21
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ORIGINAL PAGE IS
a peak at 20 MHz. Our interpretation of these characteristics is

as follows: The 7 MHz resonance is the lowest one and has current

flowing in the some direction along the whole length of the

fuselage (like a half-wavelength dipole antenna). It in strongly

excited in configurations 1 and 2. In configuration 4 the 7 MHz

resonance is not excited because the midship attachment given

current to the front and back simultaneously; the spectrum peak is

now at 20 MHz. In configuration 3 the 13 MHz resonance is

conspicuously absent. Evidently it is not oucited by the wingtipto-wingtip input.

These results lead one to the conclusion that, if the

attachment point locations were unknown, it would be possible to

infer the locations based on an inspection of the transfer

function. This idea can also be extended to the in-flight data.

Fast components in the lightning signatures can excite many

of the aircraft resonances, and, in fact, in-flight 0-dot

waveforms often have spectra resembling the model transfer

functions in Fig. 13, and it is easy to pick out the three cases, 

peak at 7 MHz, dip at 13 MHz, and peak at 20 MHz. Thus when we

see a particular case in-flight, we infer the corresponding

attachment. However, we cannot say pr2cisgly where the

attachment points wens located. For example, current entry at the

noseboom or at the front of the fuselage would be expected to give

,y

about the same resonances. Also, notice that there is little

difference in the transfer functions for configurations 1 and 2,

It where the exit point was changed. It is probably true in general

that the location of the exit point does not affect the transfer

23'

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functions very much in the resonance region (f 2 7 MHz) because

only a small amount of current in carried off by the wire.

Furthermore, a nearby lightning flash, with no attachments at all,

might produce spectra similar to those discussed here. Thus, at

best, we infer only the likely region for current entry. Table

III categorizes some in-flight results.

Table III. Inferred Attachments

Spectral Attachment In-Flight

Scti! 9912£itUS--_----ife4t£YI_--_-_----93222122-

peak at 7 MHz dose 82-38-02 (see [33),

82-38-04, 82-40-04,

82-40-07, 82-42-060,

82-42-09

dip at 13 MHz wingtip 80-38-04 (see [43)

peak at 20 MHz mid-fuselage 80-38-01 (see [43),

80-38-03A, 81-26-10,

82-37-04, 82-38-078

I

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LIII. RELATIONSHIPS AMONG THE WAVEFORMS IN STRIKE 84-17-OL

The waveforms from the 1984 strike number 84-17-01 are

similar to the 1982 aircraft-discharging waveform n already

discussed, but they represent a more complete set, originating

from eight rather than two external sensors. Several interesting

comparisons can be made among the ea2ht. Basically the event

consisted of a several-hundred-ampere pulse at the noseboom, with

a peak I-dot oi' 26.6 E+9 AJs ( or 26.6 kA/ps) . This is not a

large current for lightning, but it produced a significant

transient on an internal fuselage wire that went off-scale at 52

V. The signature of the current is a common one for strikes to the

F-106B, consisting of a fast rise with some structure and a slow

fall.

Data from 1984 is further improved because of the use of 8-

bit, rather than 6-bit, transient recorders.

I and 1-01

The I sensor measuring noseboom current during 1984 was a

shunt rather than a current transformer as in the past. On

comparing the I waveform from 84-17-01 with the time-integrated Idot waveform we find, in contrast to our similar comparison in

Fig. 2, rather poor agreement. The waveforms are shown in Figs.

14 and 15, and several differences between them may be noted.

The trailing edge of the pulse is almost completely missing in

Fig. 15. This is due to insufficient dynamic range in the I-dot

record. More specifically, the slope on the trailing edge in Fig. 

14 varies from -8.7 E+8 A/s toward zero and thus is always less

25
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than the first digitized level (below zero) in the I-dot record, -

19 E+8 A/s. Other differences between the waveforms are that the

peak value in Fig. 15 is much greater, and the curve descends mcr*

quickly following the peak than in Fig. 14. We expected that the

amplitude of integrated I-dot would be greater than I, because the

arrangement of sensors on the aircraft was such that some of the

current bypassed the shunt but all of it went through the I-dot

sensor= but the two waveforms were expected to have the same

shape. The difference in shape may be due to quantization errors

in I and I-dot or to some problem with the shunt. Further studies

should be,done to determine which of these is the case, because

interpretation of the data is very difficult without knowledge of

the true current, waveform.

8-421 204 1-421

A very simple theoretical treatment (Appendix II) predicts

that

D-dot a 1-dot / (2n rc) (2)

for any fast disturbance, where r is the effective radius of the

airplane at the location of the nose D-dot sensor. In order to

see how closely the actual results follow the simple theory, we

have taken the values 5.07 A/m 2 and 1.14 E*10 A/s from the first

peaks (P1) in D-dot and I-dot for substitution into this equation.

The waveforms are shown in Figs. 16 and 17, respectively. Using r

= 0.8 m, the result is 3.07 is 7.36, which is not too bad.

28

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1-dQ1 and I-det; ! and I

The usefulness of Eq. 1 in Section II of this report may be

checked by using the equation to determine the value of r for a

number of different sets of B and I peak values. B-dot and I-dot

peaks may also be used. For Eq, 1 to be useful, the values of r

obtained should be nearly the same. Table IV shows some results.

The first three entries in the table are taken from data appearing

in [6].

Table IV. F-1068 Effective Radius, r

Source Peaks r

QZ-Ql1l ---------QQM"Rrfd---------- is!-

Langley B-dot, I-dot 4.1

gnd. test

INDCAL B-dot, I-dot 3.6

code

Texas Tech nor 3.0

lab. model

84-17-01 8-dot, I-dot 2.7

(first peaks)

84-17-01 B-dot, I-dot 3.8

(largest peaks)

84-17-01 8, I ( from shunt) 3.2

84-17 -01 B, I ( from I-dot ) 5.7

a

The 8- dot waveform and its time integral, 8, used for the last

four entries in Table IV are plotted in Figs. 10 and 19. All

values of r ;,n the table cluster together, lying between 2.7 and

4.1, except for the last one, at 5.7. There does not seem to be

any obvious explanation for this large value. Possibilities

appear to be, first, inaccurate data due to inadequate sampling

31
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w

T4

Ul T-I Lo Ul T-4

1

rxj

O

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 O

44

ro

4J

0

• 0;

32
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i

I^ o

e-I r,

i

00

+r^i

r1 •t;

w

0

r^

w

o

b

w

4)

4J

H

C^J

t^

t M '1 U7

w

Tt C7 nJ

j

W

33
speed and, second, inaccuracies due to excessive spacing between

amplitude quantization levels.

I and 9

The integral of the nose D-dot signal in Fig. 16 leads to the

9 waveform of Fig. 20. This reveals aircraft discharging like

that discussed above for the 1982 data. However, for 84-17-01

more complete data is available. In addition to the four sensors

already described (Fig. 1), other sensors were used as follows: I

on the tail, D-dot on the tail, D-dot under the port wing, and n -

dot under the port wing for transverse currents. The tail I

record consists of fluctuations between 0 and 71 A during the

entire length of the transient recorder memory, 690 go. 71 A is

the first level above zero, and no the average current was, very

roughly, 35 A. The polarity was such that electrons were flowing

onto the airplane. We interpret this as a weak, continuing

lightning-channel current which was 4h!£HID9 Of 21£21202 . A

large amount of corona would be expected an the airplane

extremitiew during this charging phase. When the required

conditions were met, a new channel formed from the noseboom, and

the airplane was discharged. The development of the noseboom

channel probably took place in atop-vise fashion. This is

suggested by the structure on the leading edge of the current

pulse in Fig. 14. Two consecutive sharp rises in current are

seen; they are labeled P1 and P2 in the figure. These sharp

increases correspond to pulses in the I-dot waveform, and the 

pulses have been labeled with the same notation in Fig. 17. In

34
41i

^ 0

1,o *H

14

41

^,.0yy

'V

• M.1

44

0

b

r-1 N

0

1J

J

4J H

0

0

Oh

K! W 1^I,

co

• w r1

b

• WW

^`^J N

b^

W

rx (SO Tt [^J

V

E

35

r

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4

.

a

' fact, the two events are also revealed in D-dot and 9. See Figs.

{ 16 and 20. The situation here is an example of a group of fast P D P

pulses like those analyzed earlier in this report in Fig. 7. We

thus come to interpret these pulses as corresponding to the

development, or connection, of a discharge channel. Once the peak

current im reached in Fig. 14, there is a brief semi-flat spot,

and then an exponential decay b4gins as the charge stored on the

aircraftcurs into the new channel. The exponential discharge is P P g

i also soon in the C waveform of Fig. 20. Remember that, with this

interpretation, the true zero of E would be at the top of the

curve, not at the bottom.

A simplified equivalent circuit for this scenario is shown in

Fig. 21. The airplane is represented by the capacitors C.

Charging current at the tail is supplied by the source Ic, and the

channel at the noseboom is represented by the variable resistor.

One imagines that the resistance of the resistor drop s from a high

value in step- wise fashion, producing the pulses P1 and P2r and

reaches a value, R, for the discharge phase.

We have taken the beginning of the discharger phase to be at

point X in Fig. 14. The time constant, T, for the discharge (the

time to fall to e- 1 ) is found from Fig. 14 to be 320 no. With

reference to tho circuit in ,Fig. 21, a number of electrical

parameters can now be computed. Using T a RCs the resistance, R.

is found to be 1040 n. The voltage across the zapacitor, C, and

thus the airplane, after the channel has connected and the

discharge begins is given simply by V = - IR. Taking I as the

current at point X in Fig.13 0. 665 As gives V = - 692 kV. Hers it

36 

E
JT9

Equivalent circuit for aircraft

charging and discharging scenario

applied to strike 84-17-01.

IC

37
Ir.

` is better to use Fig. 1S than Fig. 14 because as mentioned above • g p , m ,

some traction of the total current bypassed the sensor which was

used to obtain Fig. 14. Next, the total energy, W, stored in the

capacitor in given by W = 1/2 CV2 n 120 J. The peak power

delivered to the channel can also be founds P - IV = 4.60 E+8

W, or 460 MW.

An alternative method for calculating the voltage and energy

uses the charge, q, transferred from the capacitor. From Fig. 21

one sees that the capacitor current is the difference between the

, tail current (Ic) and the noseboom current (current through R).

Integrating this difference gives q = - 298 E-6 C. To determine

the charge, 0, on the capacitor at time X, q must be added to the

charge remaining at the end of the pulse, which is given by - CIcR

n - 18.2 E-6 C. Thus 0 = - 316 E-6 C, and V = 0/C = - 632 kV.

Then W n 1/2 CV2 = 99.9 J.

The two methods in the preceding paragraphs for calculating

the energy give nearly the same results, and we conclude that W

100 J. Hot& that our calculations apply to the discharge phase of

the event; a quantitative analysis for the channel development

phase, when the resistor in Fig. 21 is varying, has not yet been

carried out.

A small but interesting effect, which we neglected, is the

very slight drop in E after 1.3 ps in Fig. 20. This may be due to

a late-time.increase in the channel resistance, R. Another result

from Fig. 20 is that the time constant for discharge of E is less

than that for I in Fig. 14. This indicates the approximate nature

of our understanding of this type of lightning event; future data

38
should help to provide a better understanding.

To put the values calculated above into perspective, we have

compared the electrical discharge from the airplane to the

discharge of a typical power-supply capacitor in an electronics

package. The results are shown in Table V. The peak power, P.

was calculated in both cases assuming a resistance of 1040 A.

Table V. Comparison of Discharges, Airplane and Capacitor

------------ Q_ MEL---v--cv_->---Q_VQ --- w-M ----E_M_

Airplane .0005 632,000 316 100 4.20 F.+S

Capacitor 100 100 100000 0.5 96.2

One can see from the values that C and 0 are small for the

airplane, but V is large. Thus the energy stored and the peak

power.delivered are large for the airplane.

39
r.

r

{

IV. CONCLUSIONS

This report is concerned with the extraction of information

from the in-flight data, and several basic types of information

k"

have been discussed. These are 1) the consistency and accuracy of

the data recordings, 2) the electromagnetic characteristics of the

lightning, and 3) the electromagnetic characteristics of the F106B.

Rats &Qbliattagy and h2gura2z

Comparisons between Land the time-integral of I-dot showed

good agreement in Fig. 2 (from 1982) but poor agreement in Figs.

14 and 13 ( from 1984). Finding the reason for the lack of

agreement in Figs. 14 and 15 will require the study of data from

additional strikes.

The old I sensor distorted the lightning pulses because of

its low - frequency cutoff behavior, making the pulses bipolar. See

Figs. 4 and 5. We showed that we could correct for this

distortion. Actually, there are only a few old waveforms that

need to be processed in this way, but they are significant ones

because they tie together the F-106B data with ground-based

studies of other workers. 'These waveforms ( Figs. 4 and 5) are

similar, for example, to the lightning current waveforms that have

been inferred by Weidman and Krider [ 7] from remote measurements

of lightning fields.

Computer integration of the time derivative data, as in Figs.

10 and 12, can leave considerable uncertainty in the final value

of the integrated waveform, due to the errors introduced by

40

r , p ^., "t=om. ^.
t

' quantizing the data. The new 8-bit transient recorders will help

i to alleviate this problem, but the gains of the recorders must

always be carefully adjusted to make maximum use of the available

dynamic range.

QW221trialign s1 the Lightning

Fast pulses, like those marked with arrows in Fig. 6, are

very prominent in the time-derivative data. They come in bunches

of two to three and are among the fastest components 2M observed

in lightning fields. They may be associated with the development

of leader channels on the noseboom, as illustrated in Fig. 9,

` where negative charge is carried off of the airplane. The time

required for three pulses is typically in the range 100 to 700 no. 

By integrating D-dot waveforms like the one in Fig. 6, one

discovers that there is an approximately exponential variation in

D, and E, following the occurrence of the fast pulses. This in

similar to the decay of the voltage of a capacitor as it

discharges into a resistor. A possible interpretation of the

overall event is that a channel is produced during the time of the

pulses, and the charge on the aircraft dumps into this channel

.. during the time of the exponential variation. In Figs. 14 and 20 

the waveforms for E and simultaneous current, I, are given for one 

such event, strike 84-17-01. Values of various quantities for the

F

exponential discharge phase are given in Tables I and V, where all

{ values seem reasonable. In particular, in 84-17-01 it appears ve 

have an event with an energy of 100 J, which is fairly potent. 

If the RC-discharge idea for strike 84-17-01 is correct, the

41
necessary apparatus for an approximate simulation of this event on

the ground is suggested by Fig. 211 A high- voltage power supply

is connected to the tail of the aircraft through a large resistor

to simulate the source, Ic. The aircraft is charged to - 650 kV

and then allowed to spark over at the noseboom to a 1000 R

resistor connected to ground.

Although Section III contains numerous comparisons between

measured quantities, one ratio of quantities has thus far not

been mentioned-- E / H. From Figs. 19 and 20 and using B = po H

we find ( max. E )/( max. H) = 3710 0. This value is ten times that

of a free - space electromagnetic wave, indicating the importance of

the electric field vis - a-vis the magnetic as earlier suggested by

Baum E83.

^r

Finally, the simple relationships between D-dot and I-dot in

Eq. 2 and between B and I in Eq. 1 are only roughly correct for

the lightning fields.

Charegterlstice of the E-1961

The double-hump signature shown in Fig. 8 is a characteristic

of a nose-mounted D-dot sensor on the F-106B or other similar

delta-wing aircraft subjected to a fast transient input at the

nose. It is an example of the influence of aircraft shape on

lightning waveforms.

s.' Because of aircraft resonances, the spectral content of

lightning signals from the B-dot sensor can be used to infer the

locations of the lightning attachment points on the aircraft, as

illustrated in Table III. This result is one benefit of 

42

s..
laboratory ncale-model measurements (Fig. 13).

As a final comment, it is interesting that the timederivative data reveals important short-time-scale information —

fast lightning pulses and aircraft resonances and reflections

(double hump)-- while by merely integrating, one gets data which

emphasize a longer-time-scale picture, giving the overall

discharge time and energy and suggesting the RC circuit

interpretation.

43
e

^r.

APPENDIX It CAPACITANCE OF F-1068

The capacitance between a circular disk of radius r and a

sphere at infinity is given by Cd n 8Ee r. For a sphere rather

than a disk, Cs n 4nEo r. We approximate the capacitance of the

F-106B to lie between that of a disk of radius 5.8 m and that of a

sphere of the same radius. We obtain Cd n 410 pF and Cs - 645 pF,

and thus for the airplane we take C n 500 pF.

APPENDIX Its RELATION BETWEEN D-DOT AND I-DOT

The simplest case for the propagation of an electromagnetic

disturbance is one where the disturbance maintains the same shape

as it travels and thus is given by f(z-vt). This would be the

situation for a wave inside a uniform, lossless coaxial

transmission line, for example. We will assume this is

approximately correct for propagation of lightning disturbances

along the noseboom and forward fuselage of the F-106B. For the

propagation speed, v, we use c - 3.00 E+8 m/s.

We will let the z axis run through the nosebcom and forward

fuselage and take the fore - to-aft lightning current and surface

charge to be approximately symmetrically distributed about this

axis. The equation of conservation of charge can now be written

in the form

6i/6z + 6q/6t a 0 ,

where i is current and q is surface charge per unit length in the

axial direction. If i is a function of z-ct, then

44

c

i
f

6i/6z n - 1/c 6i/6t .

Charge conservation now becomes

6q/6t a 1/c 6i/6t .

I,f the fuselage is approximately circular with radius r, then the

charge per unit area is q / (2n r), and this is the same as the

electric displacement, D. Thus, dividing the equation above by

2nr, we find

D-dot a I-dot/ (2n rc) ,

using the "-dot" notation employed in the body of this report.

REFERENCES

1. Wood, 0. W. and T. F. Trost, "Electromagnetic Resonances

of Cylinders and Aircraft Model with Resistive Wires," Air Force

μ Weapons Laboratory Report AFWL - TR-84 - 90, Kirtland AFB, Now Mexico,

1985.

t 6 2. Wen, C.-T. "Analysis of Lightning Transients on an

i Aircraft, * M. S. Thesim, Texas Tech University, May, 1985.

3. Trost, T. F. Rt !l. "Some Results and Limitations of

Prony Analysis of In-Flight Lightning Data," Proc. Intl. Conf. on

Lightning, Ft. Worth, Texas, 1983.

r 4. Turner, C. D. and T. F. Trost, "Laboratory Modeling and

45

i^
a 

Analysis of Aircraft-Lightning Interactions," N. A. S. A,. CR 169435,

1982.

5. Hutzler, B. 2& 8j. "Nigh Voltage Laboratory Tests and

Lightning Phenomena ,* Proc. Intl. Conf. on Lightning, Paris,

trance, 1985.

6. Trost, T. F. and F. L. Pitts, "Analysis of Electromagnetic

Fields on an F-1068 Aircraft During Lightning Strikes," Proc.

Intl. Conf. on Lightning, Oxford, England, 1982.

7. Weidman, C. D. and E. P. Krider "The Radiation Field

Waveforms Produced by Intracloud Lightning Discharge Processes,"

r.

I

J. 6eophys. Research, vol. 84, pp. 3139-3164, 1979.

rS. Baum, C. E. "Simulation of Electromagnetic Aspects of

Lightning," Lightning 12ghngl9gy, NASA Conf. Pub. 2128, 1980.