Sensor and Simulation Notes Note 242 September 1977 Some Analysis of EC-135 Aircraft Model Data Valdis V. Liepa Thomas B. A. Senior University of Michigan Ann Arbor, Michigan 48109 Abstract Over the last few years the surface currents and charges have been measured on a variety of scale model aircraft using sweep frequency techniques. Four topics bearing on these data are examined in this report. They are: the smoothing of data to remove experimental noise, the assessment of model-lead interactions on charge data, the effect of HF wire antennas on the frequency response of the EC-135, and the manner in which fields are excited on the shadowed side of cylinders.

TABLE OF CONTENTS Section Page No. 1. INTRODUCTION...................... 3 2. DATA SMOOTHING....................... 5 3. MODEL-LEAD INTERACTION IN CHARGE MEASUREMENTS....... 11 4. EFFECT OF HF WIRE ANTENNAS................ 16 5. SURFACE FIELD PHASE AT THE REAR OF CYLINDRICAL-LIKE OBJECTS...................... 21 APPENDIX A. DISCRETE DATA FILTER PROGRAM.............. 31 APPENDIX B. CURRENT DATA MEASURED ON VARIOUS CYLINDERS AS A FUNCTION OF FREQUENCY.................. 34

1. INTRODUCTION In a previous technical report [1] on this contract, data were presented for the surface currents and charges measured on a small scale model of the EC-135 aircraft. The data were obtained using a model 1/216 in scale in combination with the overlapping frequency ranges 0.45 to l.10, 1.00 to 2.20 and 2.00to 4.25 GHz to simulate the full scale range 2.1 to 1l9.7 MHz. As with our study of the F-lll aircraft [2], it was required that the raw data be presented, and because of the need to submit these as soon as they were obtained, it was not possible to include in [1] any analysis or discussion of the data. We here examine four topics relevant not only to the EC-135 model data but to most of our other surface field measurements as well. They are, in the order of presentation: (a) smoothing of the data to remove experimental noise, (b) assessment of the effect of model-lead interaction on charge data, (c) effect of HF wire antennas on the frequency response of the EC-135, 1. Valdis V. Liepa, "Surface Field Measurements on Scale Model EC-135 Aircraft for ACHILLES I and II Data Interpretation," Interaction Application Memo 14, 1977. 2. Valdis V. Liepa, "Surface Field Measurements on Scale Model F-111 Aircraft," Interaction Application Memo 13, 1977. 3

and (d) study of the excitation of fields on the shadowed side of cylinders. A FORTRAN listing of the program used to smooth the data is given in Appendix A, and Appendix B contains some additional data pertinent to topic (d).

2. DATA SMOOTHING No measurement no matter how carefully performed yields data which are 100 percent accurate; and in practice there are always errors caused by the non-ideal nature of the measuring instrument, thermal noise, human fallibility, etc. This is certainly true in the case of surface field measurements; and among the numerous possible sources of error are the reflection of energy from the chamber walls, discontinuities in cables and connectors, interaction between the model and the sensor leads, frequency drift of the signal source, and the instability of the pre-amplifier and network analyzer with temperature and time. In a typical measured frequency response curve such as that shown in Figure 1i, it is clear that most of the small wiggles are not real and are due to one or more of the above sources of error. Nevertheless, there are exceptions: the null at 3.5 MHz is believed real and is even more pronounced for the current measured on the top of the fuselage (see Figure 6 of [1]). The high frequency oscillations can be removed by numerically smoothing the data with a low pass filter algorithm for complex-valued data. The method used is based on the nth order system governed by [3] 3. James A. Cadzow, Discrete-Time Systems, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1973. 5

y(k) = y(1 - a)[u(k) + u(k - 1)] + ay(k - 1) 1 ( 2 2 with ct = - b- b a a = 21/n(1 + cos wlT), and b = a + 2(1 - cos wT), where input and output data sets are u and y, respectively, the order of the system is n, the bandwidth is wm and the sampling time is T. As written, the equations are for processing a time sequence of numbers, but were adapted to process numbers as a function of frequency by changing the time variable to frequency. To avoid the frequency delay which occurs when data are passed through a low pass filter, the program was written to filter the data twice; first in the direction of increasing frequency and then backwards, to give an n = 2 filtering effect for n = 1 input. The other input parameter is f.C This is related to the cut-off frequency of the filter and representative of the number of oscillations passed through the filter for each data set, three of which make up a given figure. A FORTRAN listing of the program is given in Appendix A.

The results of filtering the data of Figure 1 using n = 2 (effective) and fc = 20 and 5 are shown in Figures 2 and 3 respectively. As expected, the filtering does remove the small wiggles and improve the appearance of the data, but it also tends to remove such real features as the null at 3.5 MHz. It is therefore clear that filtering is a technique which should only be used with the utmost discretion; and because of the danger that it may remove valid characteristics, filtering was not applied to the data in [1, 2].

6.0'_EC-195 STRt F F108B PRRF TOP JRtE1153. 1151.1 U9,0K 4.0 2.0 0. 0,19~~~12 SEP 77 U' 0.0 4.0 8.0 12.0 16.0 20.0 2 00. 0 EC-135 STRiF1BO8B PARF TOP JR:E1153.1151, 1.49 1000.0 0.0 -100.0 12 SEP 77 UH -200,.0 - - - 0 _I0 00 0.0 4.0 8.0 12.0 16.0 20.0 FRE0UENC Y (HHI Figure 1: Raw data measured on EC-135 at STA:F1608B. 8

6.0 EC-lS5 STRiF1608B PFRF TOP JRIE153,1151.1 49 E 0 0 40 8.0 12.0 16.0 20.0 0.0 4.0 8.0 12.0 16.0 20.0 200.0 EC-135 STRIF1608B PRRF TOP JRsE1153.1151.1 U9 I 0.0 -100.0 22 SEP 77 UM -200.0. i_ 1. 0.0 4.0 8.0 12.0 18.0 20.0 FREOUENCY (MH[I Figure 2: Data of Figure 1 filtered with fc = 20 and n = 2.

6.0 I EC-135 STRtF16088 PRMF TOP JR:E1153.1151.1 49 2.0 22 SEP 77 UM 0.0 0.0 4,0 8,0 12.0 16.0 20.0 200.0 EC-135 STRtF160BB PRKF TOP JRtEl153, 151.1 49 100.0 0.0 -20 0. 0 —' 22 SEP 77 UM 0.0 4.0 8.0 12.0 16.0 20.0 FRFEUENCY fHH!) Figure 3: Data of Figure 1 filtered with fc = 5 and n = 2. 10

3. MODEL-LEAD INTERACTION IN CHARGE MEASUREMENTS The external shielded loops used to measure the current on small scale model aircraft in a simulated free space environment have been found adequate in most measurement situations [4]. When placed on a model, the loop itself is separated from the surface by the small (approximately 0.5 mm) thickness of the dielectric spacer. There is therefore no direct current path between the loop and the model, and the effect of any capacitative coupling is believed negligible for all practical purposes. Charge probes, on the other hand, are rather different in design and the type that we have used most is a small monopole normal to the surface. The signal lead is passed through a slot cut in the surface and eventually leaves the model at some point on the other side. The coax in this case is electrically connected to the model using conducting tape; and if the point at which the coax leaves the model is improperly chosen, the lead can interact with the model and so distort the fields which are to be measured. Thus, a coax which 4. Valdis V. Liepa, "Sweep Frequency Surface Field Measurements," Sensor and Simulation Note 210, 1977. 11

leaves from the nose of an aircraft model will not distort the charge distribution when the excitation is antisymmetric, but with symmetric excitation (E parallel to the fuselage) where the dominant currents on the fuselage are axial, the conducting lead will provide a continuation of the current path and change completely the frequency response of the aircraft. In most measurement situations it is fairly easy to find a place on the model at which the coax can be taken from the surface with minimal distortion of the field being measured. In some cases the place can be located using a theoretical argument, and in others a combination of intuition and a few trial measurements has proved to be sufficient. From a theoretical point of view a thin conducting lead attached to the model will not perturb the field, provided it is perpendicular to both the incident and scattered electric vectors. For a symmetric model such as an aircraft, the condition is met when the incident electric vector is perpendicular to the plane of symmetry (antisymmetric excitation) and the coaxial lead is in this plane. On the other hand, when the excitation is symmetric there is no universally valid prescription for positioning the lead and selecting the optimum location of the point at which the lead is taken from the surface, but in general it has been found most effective to choose the point on the shadow side close to the middle of the model. With aircraft such as the 12

EC-135, F-ill and E-4 (747) illuminated from the top, the best point is at the center of the bottom of the fuselage in line with the trailing edge of the wings. From a single measurement made with the lead in a particular position, there is almost no way to estimate what effect the lead may have, particularly in the case of symmetric excitation. A procedure that could be used is to repeat the measurement using models of different scales at the corresponding laboratory frequencies, but this is not always feasible, and substantially increases the time and effort required to obtain the needed data. There is, however, an alternative approach in which the original measurement is repeated but with the lead departure point changed while still remaining in the general area where minimal interaction is expected. As an example, consider the measurement of the charge at STA:F1350T for topside incidence with the electric field parallel to the fuselage. In the first case the lead is taken from the bottom of the fuselage at the point in line with the trailing edge of the wing (see Figure 4 of [1] for a photograph of this situation), and the measurement is then repeated with the departure point moved a distance equal to 3/4 of the wingspan towards the nose. The measured data are shown in Figure 4. The two sets of data are almost identical; and though there is about 5 or 10 degrees change in phase around 9 MHz, the amplitudes are very small here so that even a small amount of noise has a noticeable effect. 13

The fact that changing the departure point of the lead produces no significant change in the measured data strongly suggests that any model-lead interaction that may exist has no effect on the field at the point where the measurement is made. If we regard the measured field as consisting of the vector sum of the true (undistorted) field and a model-lead perturbation, changing the lead configuration will modify the amplitude and phase of the undesired interfering signal, and thereby affect the net field in some manner, e.g., amplitude, phase,or change in null positions. The absence of any such effect is evidence that the interference is negligible, and that the measurements are not distorted by the conducting lead. On the other hand, if the measured data do change, it would appear that either or both sets of data have been affected by the lead; and it is then necessary to repeat the measurements with other positionings of the lead until the charges are reduced to an acceptable level. 14

EC-135 TPtFI350T PRRF TOP 1sE1'17.1315.1313 30.0 20.0 10.0 0.0 0.0 4.0 8.0 12.0 16.0 20.0 200.0 _ EC-135 TPtPF150T PRRF TOP gQE1I17., 15.1313 100.0, 4 e 0.0 -100,0 -200.0..., i 29 JUN 77 Un 0.0 4.0 8.0 12.0 16.0 20.0 FREQUENCY nfMH3 Figure 4: Charge measured at STA:F1350T for two signal lead configurations. 15

4. EFFECT OF HF WIRE ANTENNAS The first measurements [5] made on the EC-135 model aircraft showed sharp (resonant) spikes in the current at STA:F1200T when HF wires were present; but since they were considered spurious and caused by probe-lead interactions, they were neglected in the manual reduction and plotting of the data. However, similar measurements made under the present program also showed the same type of behavior. The spikes occur not only in the current data but in the charge data as well,and after numerous tests and trial measurements it has been concluded that they are real and caused by the resonances of the HF wire antennas. The resonances are most pronounced in measurements made under the wires at STA:F1350T for topside incidence with the electric field parallel to the fuselage. To better understand the effect of HF wires, the charge was measured at STA:F1350T in the four cases (a) with no wires, (b) with a single shorted wire only, (c) with a single open wire, and (d) with both wires present. Charge was chosen in preference to the current because the charge probe is smaller and, being brought out from within the model, is less likely to be affected by probe-model interaction. 5. Valdis V. Liepa, "Surface Field Measurements on Scale Model EC-135 Aircraft," Interaction Application Memo 15, 1977. 16

The amplitude data are presented in Figures 5 through 7. Figure 5 shows the charges with and without the two HF wires. The wires have a considerable effect and increase the amplitude from 5 to 50 at 3.5 MHz, as well as producing smaller peaks at other frequencies. The case of a single shorted wire is shown in Figure 6 and here the resonances are fewer and smaller though still clearly evident. The frequencies at which they occur correspond to wire lengths of 0.5, 1.0, and 1.5 wavelengths, as expected on the basis of a transmission line shorted at both ends. With the open wire (see Figure 7), however, the resonant frequencies are shifted and now correspond to wires 0.25 and 0.75 wavelength long. The resonances are those of a transmissionline shorted at one end but open at the other. The peaks are about three times larger than for the shorted wire, and this is again consistent with a transmission line model where the electric field or charge has a maximum near the open end and a minimum at the short. If the charge amplitudes of Figures 6 and 7 are added the resulting curve is similar to that of Figure 5 except in the immediate vicinity of 3.5 MHz, where the charge in Figure 5 is larger than the sum of the charges for the individual wires by about a factor 2. This is not surprising since when two wires are present most of the energy is supported by them, rather than by a wire and the fuselage as in the other cases. The factor 2 is then consistent with the higher Q of a thin scatterer or radiator. 17

60.0 EC-135 STRt Ft350T PRRF TOP 50.0 E K with wires with and without wires 40.0 =_ LEGEND: = I l l x = wavelength o.c. = open circuited HF wire s.c. = short circuited HF wire 20.0 0.75X o.c. 0.25 o.c.,O.. C. 1.0x s.c. without without wires 0.0 0.0 3.49/ 4.0 5.36 8.0 10.46 10.73 12.0 1.0 216.1.0 FRFEQUENCY tMH7) Figure 5: Charge amplitude at STA:F1350T with and without HF wires.

6 0. 0 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ~ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ EC-135 STRtF1350T PRRF TOP WITH SHORTED WI E 50.0 with shorted HF wire riO. 0 2:, tJJ 2 0. 20.0 5-7 f 0.5X s-c. l.Ox S.C. 1.5Xs. 1 0. 0 0. 0__ _ _ _ _9 0.0 U 0 a. 0 16.1 20.0 Fua itue NCYsMHo H Fiqure 6: Charge amplitude at STA:F1350T with shorted HF wire.

6 0. 0 I - EC-135 STS F1350T PARF TOP WITH OPEI WIRE 50.0 E with open HF wire.40 U.' I- 30. 0 LEGEND: PO CD r A = wavelength 20.01 A o.c. = open circuited HF wire O.15X o.c. roo1 I 0. a0.25X o.c. 07Xoc 10. 0 oco 8 — ~~ - — ~ —._~,tP 77 UN 0. 0 8.0 10.46'0" 12.0 16.0 20.0 FREQUENCY (MHZI Figure 1: Charge amplitude at STA:F1350T with open HF wire.

5. SURFACE FIELD PHASE AT THE REAR OF CYLINDRICAL-LIKE OBJECTS To resolve a controversy about the phase behavior of the surface field at the rear of cylinders and cylindrical-like bodies such as an airplane fuselage, the surface fields were measured on a number of metallic cylinders with open and closed ends. The models used were three hollow steel pipes whose diameters and lengths (in inches) were 0.715 and 8.46, 1.735 and 16.88, and 1.165 and 54.88. All three were fitted with copper caps which were soldered in place to produce closed squared-off ends, but the second pipe measurements were first made with the ends of the cylinder open to examine the effect of the termination. As simulators of the fuselage of the EC-135 aircraft whose "average" diameter at station F520 is 155 inches, the three pipes have scale factors 1/216.78, 1/89.34, and 1/133.05 respectively based on their diameters, and the measured data obtained will be shown for full scale pipes at the full scale frequencies derived using these scale factors. Details of the cylinders and their dimensions are given in Table 1. 21

TABLE 1 CYLINDER DESCRIPTION Physical Size Scaled Size* No. Type _ _... Length Diameter Length Diameter Scaling (cm) (cm) L/D (cm) (cm) Factor 1 closed 21.48 1.82 11.827 4656. 393.7 216.78 2a closed 42.94 4.41 9.736 3836. 393.7 89.34 2b open 42.84 4.41 9.724 3827. 393.7 89.34 3 closed 139.38 2.96 47.105 18544. 393.7 133.05 *Values scaled to the average fuselage diameter of EC-135 at STA:F520. The cylinders were mounted horizontally and illuminated with a field incident in a plane perpendicular to the generators with the incident electric field horizontal. Using a small current loop probe the horizontal component of the current was measured at the center front of each cylinder and the corresponding point at the back. In addition, for cylinder numbers 1, 22

2a and 2b, the currents were also measured at the front and back at points 1/4 of the length from an end. Calibration was with respect to the incident field at the front in all cases. The measurements made are listed in Table 2 and the data are presented in Appendix B. Here we present only the data relevant to this section. TABLE 2 MEASUREMENTS PERFORMED (The data are in Appendix B) C ynder.Front Center Back Center Front 1/4* Back 1/4 1 Figure B.1 Figure B.2 Figure B.3 Figure B.4 2a B.5 B.6 B.7 B.8 2b B.9 B.10 B.1| B.12 3 B.13 B.14 *The Front 1/4and Back 1/4 indicates the measurement made at a point 1/4 of the length from an end. 23

From corresponding measurements on the open and closed cylinders it is at once evident that open ends have no significant effect on the currents at the stations considered. Thus, for example, the phase curves in Figures B.6b and B.lOb (Appendix B) are virtually identical. It is therefore sufficient to confine attention to the closed cylinder data. To elucidate the manner in which the current on the rear of a cylinder is excited, consider for example the measurements made at the center of the second cylinder with the ends closed: Figures 8a, b and 9a, b. At the front the phase is almost constant for f > 12 MHz and oscillates about the zero value given by physical optics. At the rear, however, the phase shows a progressive decrease (time convention ei t) with increasing frequency, and the mean rate of decrease of approximately 26.20/MHz implies an effective phase center about 2182 cm behind the cylinder, i.e., an excitation path of this length. The only way that it is possible is if the dominant excitation is around the ends rather than over the (half) circumference. For excitation across the ends and hence along the rear of the cylinder to the center of the back, the path length isD + L/2, and assuming that the phase velocity is that of light the progressive phase in degrees is -360 fMHz(D + L/2)cm c=.....cm + 180 24

where c is the velocity of light in cm/sec and the 180 degree phase change has been added to have the current in the same direction as that in front of the cylinder. For the second cylinder, = -27.760 fMHz + 180 and when this phase is subtracted from the measured phase, the phase at the rear of the cylinder is shown in Figure 10. The progressive phase variation has now been eliminated, and the slight overcorrection or rise in the phase curve with frequency that now exists could be attributed to the approximate nature of the above formula and/or measurement error caused by slight alignment errors in positioning the cylinder parallel to the incident electric vector. A similar analysis can be applied to the phase data at the rear of the other cylinders measured, and leaves no doubt that for cylinders of the electric lengths considered the primary means of excitation of the rear is via the ends. It now follows that computed data for an infinite cylinder have little bearing on the interpretation and understanding of the surface fields on the rear of a finite cylinder. This is in contrast to the situation for points on the front. 25

6 0 - -- ----- - 394 CM DIR CLOSED CYL L=3836 CM FRONT 14. 0'U'-4.4 CZ 2.0 0.0 * o ____________________ RUG 77 U N 0.0 1IQ0 20.0 30.0 40.0 50.0 FREQUENCY (MHZ) Figure 8a: Current amplitude at front center of cylinder No. 2a.

200.0 - --' 394 CM DIR CLOSED CYL L=38S6 CM FRONT 10001 0.0.0 0u -200.0 a AUG' 0.0 10.0 20.0 30.0 40.0 FREQUENCY fMHI) Figure 8b: Current phase at front center of cylinder No. 2a.

4. 0 __ _ _ _ _ __ _ __ _ __ _ _ _ _ __ _ _ _ _ _ 3.0 394 CM DIS CLOSED CYL. Lt3836 CM BSC 2.0 PO 00 1.0 0.0 9 AUG 77 uM 0. 0 10.0 20.0 30. 0 5 0.0 FREQUENCY (MHt) Figure 9a: Current amplitude at back center of cylinder No. 2a.

200.0 _-..... - 394 CM DIR CLOSED CYL. L= 836 CM BRCK 100.0 w'I.* -200. 0 ___,__,__,_9 RUG 77 UMA 0.0 10.0 20.0 30.0 o0.0 50.0 FREQUENCY (MHi) Figure 9b: Current phase at back center of cylinder No. 2a.

20O.0.. - -.. 394 CM D IR CLOSED CYL. L=r386 CM BRCK 100.0 O; [L. Cn 100. 0 1200 * 0,__ _ _1 6 RUG 77 UN E 0.0 10. 0 20.0 30.0 40.0 50.0 FREQUENCT IMHI) Figure 10: Phase in the back of the No. 2a cylinder after path length D + L/2 has been subtracted. (Compare with Figure 9b).

APPENDIX A DISCRETE DATA FILTER PROGRAM (For discussion see Section 2);1. C O L. EX B (, ), (.3 )'): N.I TME'.NOSI0)N F (:13. 3) AMF' (. 3) i 1: 1.33, l: N. I N (4) 3 I 1:::1 NS C (I F IEN4),, 1 CON: I (1 1 ). L'' ) NN I T2( 1.),TI. TL ( 18) 4 L.O:1: C L... I 1CL ( 30) B.1.. N!K 5:I: N' E.::F;EGE:R*2 I...EN 6 DATA BLN,.. / iN/''/ S R E A O'!, NC'~ I: l' T.: 0 C T I~',: 0 [) FI C N A I: F:M:!: t... i' 9 C:1.0:1. 0 1: I T!:1. 1) 1..:1.0:1. FOFL;A1 ( / V NTFLEIR 1 3 1.-I NAME")1: 1' (:, 1 1 C A!s^i12.:I...... S C DS(FI ELEN,0 yL. INNlU M 110) I 3'ILEi... F I,:1. ) -LNI., A i i' 1 ^ t 1 l -J q'1. E.: F:L. I yF E1,1 F -:', I F: 1.'.20)',:.;1 GO T J. i ii... 1 i.:..':.' E (.' 400 ) I7 400 F,:'1;M T'(S * ES... NOT EXI ST' ) 400 GO'T"':1.:I. 0 10: 1 1:) 1:. T'T (1I4). 1,:'".:: F.':.:A) ( I, 1 E'l. F I I........ E" N:. 2'31~:?i GAi: F:' (J2) ) 1-=,JN 1 0I I LT.. -3 I::, t 1 S:~]~TM:. RIE:Z:)A:Ii[~:'1 i:i:'til): )!::"N1: - NN E;'- [i:~,,qi NN2-:I, ( N N2-1) yFN N2) AP(2,PI ( NN2 Z: L200 FF;.A D T' ( N2, 2F o. 8 2:>;,' 1..1 iY i N ^:E... " C 0L, 1 0'.1', (7. A:) 3.j.'i:N':.-.Y ( I!:;',(.0,,)'YlF(NN2' );AMPl( NNNNPI ).F(N( NNXN ) 17 20' NW' 4N:F:, *r N ) I N2 ",:34 A(iL) -', i::l'x. 1:('OiS3 ( P ), SIN (13 ). ) A iMP1: ( I ) i 31

45 C 6C) C F:L.E:F::i T:NG OrINE C z., 1:', 1 - 7'' 1.7 49 1?0 F1!:(!:;i),HAT(/"i(T F:NTf:F ILITE-I:; ORF'IEF:t, CUITOi"::F F:'REQU1EN CY (CYCLES El-F I'lO..)T) Sa} 50t), N FI:: i. iA: 1 CG 1 ) 5:1.02 FJ:iT I,51) 64S -:".B' )=W2 5^ t J 5 T l e1 / s::' 57 =2 l. ~;',,U 2 * (: N. X ) >, 1 * +C. CISW*T ) ) -2 5~ V j:= U.!;'. 2, - C2 ~:CS ( 1: r ) ( / -:j:: * ( iU ( V t,' *'-fL:. 2 | t'; ) Q'.(:ii. j)A(:1. 1 ) i C.>).:.3.:.l - 1:I. -::, 1,-,'.. A'I:,-'..l.,I: 6 4 B:1 )=B(2):.. -...._., 66 2 I0 1.'N 6B )::.: ( I:. A I.:. 7 ]. B.{ ( A. )::.' i A: )) 7"',:~ -! j C 0 N' I N:.; 3'.' 2F 1i:) I...t (.) 7,9 B:. (1i)N: (.. / I) 0:1. ( )::'i:L N N I 87':I 4 Iil C. [NI I NNE [1 3:1:,:1: M U J ( C i 1 )) 91 4 N:::: ( i ) [.36, C.:i:rl,AM A r. I ) I'MlFN1. N 0 1):0 1C, J.96) IF:(: A M F J GE.AHIN)G0 TO( 16 97 A I:':A F1:' ( J ) 98 iO'1 0:1.7 99 1.6'F (- ilIF(J E (A P:: " ~ 4EAMNAX)C) O TO 17:1.0:1. 1 7:1:F ( P: (,).G) N I ) CNC) TC 18 C 32

I 0 1i:':.l..:1: " J 1 04J 18 F: (1:': (.J +E *.'M X)GO TO) 1. 5 10 i> 1.'.~ 5 C: (:) N f':1: Nl.J E:i. 0 C l 1. CI.,)1 t!::::I: 1T _ ( 6 30::. )I.i.''. 40:1.!::'C{)!:;~, "i'l i,:l:'T I I: N A M:: E 1)'T'"1 F: 1:[ L,.:F::1 F: 1:. I- )1:1. Ci C.1:' i!. C: A (!::'- I... 1I' N y 0 y0 y 0 13.:4 C L. I S:. SN (f8 1: I...: N ):i.:1 3 W?:1 D:'1" 1::.:8,I L:..1:: N:.!. 7 J::::1:'T' S:::'.>;:Vv:,:'::):4 00:); []! H i'.:1.:1.? W:;:1:i: 1 i3. S.".. T S! ) T0 T:: I!. E12 0 W I:,:C:1: T' E S( 3. 1. ) F:'H:!: ii, H:1: "i X y 1: N - iF iA X: N N P'\ " / (.1.10 5t,' I r}1 r;01 OjM1:'O:'l ( 41 F:' i:.I, 2 F:' Y )1:' y ):l "' ".. "' i': ('-..; ) 3 21'7 L;:.:.....:1. 2f (:';I....6 15..Y",~',:O Y..........., ) Y 1_3 124 9 61. W:1: l:i (,133 ) F' ( F N',.> -'. Y::' ( NF::1. ) s:: (..... i ) y 1- 2 N.),:.1,() * M 1:' ( IN'::: ( N''.:"'' 1,21 5 03 F:; MA.,,F8.(F 8Y,82 ) ) t.. 3 62 W I -: I T;.::. ( q Y 56' ) 4' ( i': ) 1 F:7 ( N NN2. ) Y A:: ( N"tI.2::'. ) (:t:,4 5 04 t::'C)' M "':T2:: 8. 3 Y F'S,'2^ ) 1:,'3 3'.;i: (5':)'T (:):1.: 10 1.:;^.'=. i: N 33

APPENDIX B CURRENT DATA MEASURED ON VARIOUS CYLINDERS AS A FUNCTION OF FREQUENCY (For discussion see Section 5, particularly Table 2, page 21.) 34

20.0 99U CM DIR CLOSED CYL. L-4656 CM FRONT 16.0 12.0 8.0 4.0 9 RUG 77 UH 0.0 4.0 8.0 16.0 20.0 200.0,O ____ _ - - -- - ___ 394 CM DIP CLOSED CYL. L-4656 CM FRONT,,00,0. 0.0 -100.0 9 RUG 77 UM -200.0.___ __a_._ _ _ _.__.. __ _2.......__ _R 0.0 4.0 8.0 12.0 16.0 20.0 FRE2UENCY [H(ZI Figure B.1: Current at front center of cylinder No. 1. 35

16.0 ------ — i S4 CM DJIR CLOSED CTL. L-4656 CM BRCK 12.0, 8.0, RUG 77 UM 0.0 1, 0.0 4.0 8.0 12.0 16.0 20.0 200.0 _ _ _ _____ 394 CM DIR CLOSED CTL. L-4656 CM BRCK 100. 0. - 0.0 -100.0 9 RUG 77 UM -200.0 ____ __ _..._ ___ _ _ _.. 0.0 4.O 8.0 12.0 16.0 20. FREOUENCT CMHH) Figure B.2: Current at back center of cylinder No. 1. 36

12. O I. _ _ 394 CM DIR CLOSED CYL. L-4656 CM FRONT 0.2! 8.0 IU. 9 RUG 77 UM 0....... 0 _ 0.0 4.0 8.0 12.0 16.0 20.0 200.0 _ S94 CM DiR CLOSED CYL. L=4656 CM FRDOT 0.25 F 0.0 -100,0 -2 00.0 [ ________ ___- ___ ____ 9 RUG 77 UM 0.0 4.0 8.0 12.0 16.0 20.0 FREQUENCY tMH!) Figure B.3: Current at front 1/4 of cylinder No. 1. 37

12.0. -- -.1. —- __ 394 CM DIR CLOSED CYL. L-4656 CH BRCK 0.25 4.0 0.0 ___________ ______ _9 RUG 77 UM _ 0.0 4.0 8.0 12.0 16.0 20.0 2 D 0.0. 384 CI DJIR CLOSED CYL. L-4656 CHM RCK 0.25 0.0 -100.0 -2_00...._ ________ ~ -9 RUG 77 UM 2 0.. _ _ __ _2 _ __ ___ 0.0 4.0 8.0 12.0 16.0 20.0 F REOUEtJCT (HHI Figure B.4: Current at back 1/4 of cylinder No. 1. 38

6. 0 i —- 394 CM DIR CLOSED CYL L-3836 CM FRONT 2.0 8 RUG 77 UM 0.0 10.0 20.0 30.0 40.0 50.0 200.0 _, 394 CM DIR CLOSED CTL L=3836 CM FRONT 100.0 0.0 -10 0. o 8 RUG 77 UH -2 000. _ ___ __ A_ 2 0. _ D. 0 0.0 10.0 20.0 30.0 40.0 50.0 FREQUENCY (HH!) Figure B.5: Current at front center of cylinder No. 2a. 39

3s4 CH DIR CLOSED CYL. L-3836 CM BRCK 3.0 2.0 1.0 2 RUG 77 UH 0. 0; 0 0~. 10.0 20.0 30.0 0.O 50 200.0 - 394 CM DIR CLOSED CYL. L= 836 CH BRCK 0.0 -100.0 9 RUG 77 UM -200. 0 _ __ _ __ __ 0.0 10.0 20.0 30.0 40.0 50.0 FREQUENCY (MHHI Figure B.6: Current at back center of cylinder No. 2a. 40

8.0.i l - 1 - 394 CM DiR CLOSED CYL. L-3836 CM FRONT 0.2 0.0, _______9 BUG 77 UM 0.0 10.0 20.0 30.0 40.0 50.0 200.0- - 394 CM DIR CLOSED CTL. L383S6 CM FRONT 0.25 -100.0 9 RUG 77 UM -200.0 O 2.0_ _ 00_ 0 ____ _ _ _ _ -_ * 0.0 10.0 20.0 30.0 40.0 50.0 F~EOUENC~ tHHit Figure B.7: Current at front 1/4 of cylinder No. 2a. 41

381U CM DIR CLOSED CYL. L-3836 CM BACK 0.25 1.0 v0.09 RUG 77 7U 0.0 10.0 20.0 30.0 40.0 50.0 200.0 I 3U3 CM DIR CLOSED CYL. L=3836 CM BACK 0.25 100.0 0.0 -100.0 ~ 1 00. 0 X W D -2000 ___ 9 RUG 77 UM 0.0 10.0 20.0 30.0 40.0 50.0 FREOUUEtNC (HHE] Figure B.8: Current at back 1/4 of cylinder No. 2a. 42

680._ _________ - ----- - ------- - -----— * S94 CM DiR OPEN tTL. L3wS86 CM FRONT 4. O0 2. 0, 8 RUG 77 UM 0.0 lO.O 2D.0 20.0 40.0 50.0 200.0 _ _ 394 CM DIR OPEN CYL. L=3836 CM FRONT 100.0 0.0 -100.0 -2oo.0 — ________ - — _ _.B RUG 77 UM 0.0 10.0 20.0 30.0 40.0 50.0 F REUENCY (tHH13 Figure B.9: Current at front center of cylinder No. 2b. 43

6.0 O -- - -- --- ---- t --------- - 394 CM DIR OPEN CTL. L-3836 CM BACK 4.0r 2.0 R RUG 77 UM 0. O ______ _ __ _ _ ___ ___ -_ A ___ A 0.0 10.0 20.0 30.0 4O.O 50.0 2 00., 394 CM DIR OPEN CTL. L-3836 CM BACK 0.0 -100.0 - I0. 0 R UG 77 UM 0.0 10.0 20.0 30.0 40.0 50.0 FRECUENCT fMMH) Figure B.10: Current at back center of cylinder No. 2b. 44

394 CM DIR OPEN CYL. L-S836 CM FRONT 0.25 I 9 RUG 77 UM 0.0 10.0 20.0 30.0 1O.O 50.0 200.0.... - 394 CM DIR OPEN CYL. L=3836 CM FRONT 0.25 100.0 i -100.0 -2 00. 0 - -.- -— ___ ___9 AUG 77 UM 0.0 10.0 20.0 30.0 40.O 50.0 FREQUENCY IMH I) Figure B.11: Current at front 1/4 of cylinder No. 2b. 45

394 t.M DJA OPEU tYL. L-3836 CM BRCK 0.25 a 2.0 2. 6 AUG 77 UN 0.0 t.0 2D..D 30.0 40.0 50.0 2DO. D --- -- --- - 394 CM DIR OPEN CTL. L-3S86 CM BACK Q. 5 0.0 -100.0 8 RUG 77 UM -2 DO.D _ _ _. _. __ __ __ _. _ _. __.. _ _._ 0.0 10.0 20.0 30.0 40.0 50.0 FREQUENCT (tHH!) Figure B.12: Current at back 1/4 of cylinder No. 2b. 46

12.0, 394 CM DIl CLOSED CYL.L-18544 CM FRONT 8,0 100.0 0.0 8.0 16.0 24.0 32.0 200.0, - Fiur B.1 CH DIC CLOSED CYLLae85y 4 NH FRONT I_ 0.0.'a0-,.4 0.0 - 00.0 -200.0 ~~~~~~~~~~L_ ~9 RUG 77 UM 0 0 B.0 16.0 24.0 92.O Figure B.]3' Current at front center of

6. o i -- 3S4 CM DIP CLOSED CTL. L-185144 CM BARCK 4.0O 2.0 0.0 —. 0.0 8.0 16.0 24.0 32.0 -100.0 _,___ -2_ __,00. 0 ___ __ __ _9 AUG 77tt FREQUENCY (MH!) Figure B.14: Current at back center of cylinder No. 3 48

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