'1 -- w.-** '' TI` Hi E me,~,,>, S i, airs. w- *,'^ cur "y ^T <>:''^., ~~ iililaf: ltJ N I V E 1R S I, 34 7 1 1 i) ii M I c; I:! i(A Nr J; li' xxxix THE RADAR CROSS SECTION OF THE B-70 AIRCRAFTcls R. E. Hiatt and T. B. A. Senior February 1960 3477-1-F = RL-2101 Report No. 3477-1-F on "'NATONAL S3tlt INFORMATION" "Unafthr- IDMc'%osu' Subjedt to Criminal Sanctions '; EXCLU OM GDS (DD 5 254 GP- -) Purchase Order No. LOXO-XZ-250631, s ) ) y~ ~~^.yjX~' is *-i nl Prepared for NORTH AMERICAN AVIATION, INC. LOS ANGELES DIVISION INTERNATIONAL AIRPORT LOS ANGELES 45, CALIFORNIA (Prime Contract AF 33(600)-38669),.~. - S

>t-CRE I I l i: Ut. N I V tv1 R 1' Y 0 f;)4 7 7- I - F M I Ct t 1 GA N This document contains information affecting the national defense of the United States within the meaning of the Espionage Laws, Title 18, U.S. C., Section 793 and 794, the transmission or revelation of which in any manner to an unauthorized person is prohibited by law. ii SECRET

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1. 2. 3. 4. SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F TABLE OF CONTENTS Introduction Beam Analysis 2. 1. Preliminaries 2, 2. The Idealized Surfaces 2, 3. The Cross Sectional Plots 2. 4. Further Remarks 2. 5. Summary Conclusions Radar Absorbing Material for the B-70 Experimental Procedures and Results 4. 1 Introduction 4. 2. Experimental Facilities and Procedures 4. 3. Results 4. 3.1. Series A: 4. 3. 2. Series B: 4.3.3. Series C: 4. 3. 4. Series D: 4. 3. 5. Series E: 4. 3. 6. Series F: 4. 3. 7. Series G: 4. 3. 8. Series H: 4. 3. 9. Series I: Vertical Polarization, Dielectric RAM, 388 Me Horizontal Polarization, Dielectric RAM, 388 Me Vertical Polarization, Magnetic RAM, 388 Me Horizontal Polarization, Magnetic RAM, 388 Me Dielectric RAM, 918 Me Vertical Polarization, Magnetic RAM, 918 Me Horizontal Polarization, Magnetic RAM, 918 Me Effect of Increased Climb Angle, 459 Mc Effect of Inclined Duct Walls, 388 Me 1 4 4 6 12 14 18 56 66 66 68 73 73 83 92 101 106 115 126 134 139 143 145 148 149 150 4. 4. Summary of Experimental Results 5. Recommendations 6. Acknowledgements 7. References Appendix ix CCriDCT

SECRET TB F UNIVER SITY OF M I CH IG A N 34'77_1 -F I. INTRODUCTION The purpose of this report is to describe the theoretical and experimental work carried out by the Radiation Laboratory on the radar reflection characteristics of the B —70 aircraft. In addition to finding the radar (backscattering or monostatic) cross section on the basis of the specifications and models made available to us, a considerable amount of effort has been expended in locating the sources of the dominant returns, and hence in finding ways in which the cross section can be reduced to a more desirable level either by structural modification to the aircraft or by the use of radar absorbing materials. The theoretical work was confined almost exclusively to a consideration of the return at aspects near to broadside, and this analysis is described in detail in Section 2. The major sources of the return here are the sides of the ducts acting either by themselves or in combination with the undersurfaces of the wings to form corner reflectors. Further contributions are provided by the fuselage itself and by the tail fins. The corner reflector effects canbe diminished by changing the dihedral angle, and the formulae relating the change in cross section to the dihedral angle were derived by Dr. F. B. Sleator andMr. D. M. Raybin of this laboratory (see Appendix). As a result of this and other analyses, certain slight structural modifications to the aircraft are suggested which are sufficient to provide a substantial reduction in the beam cross section at those aspects having operational significance. These modifications are summarized SECR SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1.-F at the end of Section 2, and amount to a tilting of the duct sides and tail fins with respect to the vertical, coupled with a tilting of the wings above the horizontal. One of the major aims of the experimental program was to study the cross section at aspects near to forward (out to, say, 500 from nose-on) and to determine ways in which this could be reduced to 40 square meters or less. It was immediately recognized that at these aspects the cross section is almost entirely provided by returns from the air intake ducts. The depth of penetration of the field into the ducts is a function of both the frequency and the aspect, and it is clear that the corresponding return couldbe reduced to a negligible amount by merely blocking up the ducts. Practically, of course, this is not possible, but the equivalent electromagnetic effect canbe achieved with the use of suitably shaped screens and meshes over the apertures. Unfortunately, to function satisfactorily at the higher frequencies the grid spacing must be small and this in turn entails a loss in aerodynamic performance which may not be acceptable. Since it was understood that the NAA is investigating the possible use of widely spaced meshes for the lower frequencies, it was decided to concentrate upon the use of radar absorbing materials suitably placed within the ducts in order to achieve the desired reduction in radar cross section. Section 3 is devoted to a description of the radar absorbing materials which are available at this moment and which are capable of functioning atthe temperatures 2 SECRET

THE UNIVERSITY OF MICHIGAN 3477 -— F experienced within the ducts. One of the more promising materials is Ferroxcube 105, a preliminary investigation of which has been made by Professor D. M. Grimes of the Electrical Engineering Department, The University of Michigan. The experimental work as such is described in Section 4. This work was carried out at K and X band frequencies using mainly an 8 ft (1: 25 scale) model, but also on occasions a 4 ft (1: 50 scale) model. Cross section patterns were obtained at a variety of elevations for azimuthal angles out to 1000 off nose-on. Those for the model without absorbing materials are reproduced here, as are a sequence of patterns indicating the reduction in cross section consequent upon the introduction of RAM at different locations within the ducts. It is shown that by the selective use of such materials the stipulated figure of 40 square meters out to 50~ off nose-on can be achieved. The conclusions reached as a result of the experimental investigations are summarized at the end of Section 4, and the overall recommendations given in Section 5. The contract agreement with the NAA also provided that The University of Michigan would act as consultant on problems associated with the reduction in the scattering cross section of the B-70 antennas. This consulting service was provided in the form of a lecture given by Professor K. M. Siegel to NAA personnel in Los Angeles on 20 January 1960, and the problem is not therefore treated in this report. 3 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 2. BEAM ANALYSIS The purpose of this section is to describe the calculations which have been carried out to determine the backscattering cross section of the B-70 aircraft for angles at and near to broadside. Calculations have also been made to show the effect of tilting the wings by as much as 20~ above the horizontal or tilting the tail fins inwards by this amount, and all the relevant formulae, numerical results and cross sectional plots are given herein. It will be seen that a major reduction in the return at most broadside angles can be achieved in this manner, and ways are suggested by which the cross section can be still further reduced by structural modifications of this type. Other ways of reducing the effect of the broadside return are also proposed. 2. 1. Preliminaries From a study of the aircraft using diagrams and a model it is apparent that the major sources of the return for angles at and near to broadside are (a) the tail fins (b) the fuselage (c) the vertical surface of the ducts. This surface can combine with the under surface of the wings to form one or more corner reflectors whose cross sections can then be appreciable (and, indeed, dominant) over a large range of angles. The cross sections of (a), (b) and (c) have been computed at frequencies of 10, 000, 3, 000, 1, 000 and 400 Mc, corresponding to wavelengths of 0. 03, 0.10, 0. 30 and 0. 75 m respectively. At these frequencies the dimensions of 4 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F the contributing surfaces are all large compared with the wavelength and this allows the methods of physical and geometrical optics to be used in the calculations. At lower frequencies, however, these methods are no longer applicable (one or more of the dimensions being comparable with the wavelength), but the cross sections can be estimated at least in order of magnitude by other means and turn out to be much smaller than at the higher frequencies. In addition, the returns are not then dependent on the detailed structure of the aircraft, and for this reason the numerical work has been confined almost exclusively to the higher frequencies. The coordinate system which has been used is shown in the following two diagrams. The angle 0 measures the tilt of the wings above the horizontal and is allowed to range from 0 to 20 (see Fig. 1); S is the angle in the broadside plane between the direction of observation and the horizontal (the aircraft being assumed to be in level flight), and a is the angle out of the broadside plane, taken as positive when towards the nose of the aircraft (see Fig. 2). The calculations have been made for 0 a, 3 45~. FIGURE 1 5 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F / 1 / I FIGURE 2 2.2. The Idealized Surfaces In order to determine the cross sections of the tail fins, the fuselage, the duct side and the duct-wing combination, each of these structures is replaced by an equivalent surface or structure to which a mathematical analysis can be applied. Taking first the vertical side of the duct, it is felt that a good approximation to the original shape (as regards the radar return) can be obtained by taking 5 flat surfaces whose aspects are as shown below. 9.50 4/ -) --- 100 70 2.'5~ 2.5~ FIGURE 3 6 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -- F If these surfaces are numbered 1 through 5 starting from the left (duct-inlet end), the dimensions are as follows: Surface Slant Length Depth 1 5.21 m. (205 in.) 1.65 m. (65 in.) 2 4.83 m. (190 in.) 1.65 m. (65 in.) 3 10.2 m. (400 in.) 1.45 m. (57 in.) 4 7.62 m. (300 in.) 1.27 m. (50 in.) 5 4.47 m. (176 in.) 0.76 m. (30 in.). When 3 = 0, the cross section of any one of these plates is 4rA2 Csin(ke sina)) 2 A2 | ksin a' where A is the area, Yt is the slant length (i. e., actual length rather than projected length) and a' is the angle between the direction of observation and the direction of the peak return from the plate. The peak direction is, of course, normal to the plate surface, and the peak return is 47r A2 o- = --- 2 as follows by putting a' = 0 in the above. Because of the large values of k e for each of the plates, klt sin a' is large compared with unity for every value of a' (apart from a' =0) which has to be considered. Accordingly, sin(k-eCsina') has been replaced by unity in all calculations for non-zero a', so that the pattern factor employed is merely (k esin a'). This Approximation is equivalent to following the peaks of the side lobes, and the resulting cross section for given a' is the largest that would be observed at angles in the immediate vicinity of a'. 7 SECRET

'ECRE1 I 1 t L N l \ h R. I [ Y L I M I H I G A, N \Vhen3 i 0, each of the plates will combine with a portion of the adjacent \xin surlface to form a corner reflector. The selection of the portion to be associated with each plate is largely a matter of judgement, and from a study of the aircraft diagrams it was decided that the appropriate portions could be approximated by the following rectangular areas. In each case the length was chosen equal to that of the corresponding duct plate. Wing Portion Length Breadth 1 5.21 m. (205 in.) 1.80m. (71 in.) 2 4.83 m. (190 in.) 1.85 m. (73 in.) 3 10.2 m. (400 in.) 4.06 m. (160 in.) 4 7.62 m. (300 in.) 5.33 m. (210 in.) 5 4.47 m. (176 in.) 5.33 m. (210 in.) The calculation of the cross section for each of these corners involves the consideration of a corner reflector whose arms are not equal and, in addition, whose angle may differ from 90~ (as will be the case if 0 / 0). The appropriate formulae have been derived and are given in the Appendix as functions of 3 and 0 for a' = 0. The numerical values obtained for the 5 corners and the associated duct plates (3 = 0) are given in Tables 1 through 5. In each table a' is taken to be zero, and consequently, in order to determine the total contribution of these corners at some chosen azimuth, the tabulated values must be multiplied by the appropriate pattern factors (k e sin ca). The half and tenth power points of the corner reflector patterns in the azimuthal direction are given in the following table. From these values it is apparent that only with corner reflectors 1, 2 and 8 SECRET

:ECRE"I T H I L N I V ER NiI V L p'a t) F RM 1 (' AI!:,, " 4 - - 1 (at larger wavelengths) 3, is it possible to get two or more significiios-;'l.t! hl tions to the total scattering cross section at any given azimuth angl. 0.03m 0.10m 0. 30m 0. 75 CORNER 1/2 1/10 1/2 1/10 1/2 1/10 1/2 1/10 1 0.07~ 0.16~ 0.24~. 550 0 73 1. 1.640 1. 83~ 4.10~ 2 0.08~ 0.18~ 0o26~ 0.59~ 0.790 1.770 1.990 4.440 3 0.04~ 0.08~ 0.13~ 0.28~ 0.38~ 0.84~ 0.940 2.10~ 4 0.05~ 0.11~ 0.18~ 0.37~ 0.50~ 1.12~ 1.25~ 2.80~ 5 0.080 0.19~ 0.28~ 0.64~ 0.850 1.910 2.14~ 4.78~ 1...........I I Turning now to the fuselage of the aircraft, the scattering cross section is estimated by considering an equivalent cylinder whose radius a and length o are both large compared with the wavelength. The cross section of such a cylinder is a = 2 a sin (k sin) a k-esin a J which is, of course, independent of 3- On the other hand, the presence of the wings to the aircraft produces a shielding effect which is a function of 3. The amount of shielding was estimated by eye and was taken into account by choosing- differently for different /3. For /3 = 0, the dimensions of the chosen cylinder were a = 1. 5m., =30.5m. + The shielding is also a function of a, but this effect can be ignored because of the restricted beamwidth in the azimuthal direction. 9 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F and the corresponding cross sections for a =3 = 0 are A a 0.03 m 2.22 x 105 m2 0.10 m 6.67 x 104 m2 0.30m 2.22 x 104m2 0.75 m 8.89 x103 m2 In consequence, the fuselage only produces a significant contribution to the total cross section for azimuthal angles very near to zero (broadside). For variations in the elevation angle 3 it is necessary to modify the length of the equivalent cylinder. The required length for each / is obtained by gauging the illuminated portion of the fuselage, and the resulting cross sections are as follows: 10~ 200 30~ 400 450 0.03 2.1 x105 1.2x105 9.8x104 8.0x104 7.5x104 0.10 6.2x104 3.5x104 2. 104 2.4x104 2.2x104 0.30 2.1 x104 1.2x104 9.8x103 8.0x103 7.5x103 0.75 8.4x103 4.7x103 3.9x103 3.2x103 3.0x103 The only surfaces remaining to be considered are the tail fins, and for purposes of analysis these are replaced by equivalent rectangles. Let us first treat the case in which the fins are vertical. In the broadside plane (a = 0) only one fin is seen (the other being completely in shadow) and, in addition, some shadowing may be produced by the wing. In consequence, the dimensions of the chosen rectangle are dependent 10 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F on the value of 3. When = 0, the dimensions were chosen as 4. 6m and 4. 6m, and the cross sections for a = 3 = 0 are then x C 0.03m 6.10x106 m2 0.1Om 5.49 x105 m2 0.30m 6.10 x104 m2 0.75m 9.75 x103m2 As / increases the lower portion of the fin is obscured, leading to a reduction in the height of the equivalent rectangle, and by analyzing the degree of shadowing the following cross sections were obtained. 3 ao 10~ 1.7 x 102 m2 20~ 2.9 x 101 m2 30~ 8.0 m2 For /> 30~, a negligible portion of the fin remains unobscured. The fact that the above results are independent of wavelength is a consequence of the cancellation of the wavelength dependence of the flat plate cross section and the pattern factor. For variations of a with 3 = 0, a shadowing of the nearer fin occurs, but now a portion of the second fin can become visible. Taking one fin alone, however, the half and tenth power points are x 1/2 1/10 0.03m 0.08~ 0.19~ 0.10m 0.28~ 0.62~ 0. 30m 0. 83~ 1. 87~ 0.75m 2.10~ 4.64~ 11 SECRET

SECRET T HE UNIVERSITY OF MICHIGAN:3477 - F a:,i, in particular, for all but the largest wavelength the contribution from one fin has dropped to an insignificant level by the time a reaches 2. 50 (the angle at which the return from corner reflector 4 comes in). Since the contribution from the second fin will only produce a small percentage change in the above results, a calculation of the return from the unobscured portion of this fin is a tivt'leh academic and will be ignored. If the tail fins are not vertical, but instead are tilted inwards at an angle 0', the peak return is tilted up by twice this amount. The largest return from 0 a fin in the elevation range 0 < /3 45 then occurs at3 = 0, and the cross sections for such a fin with a - 3 = 0 are as follows. 0' u 5~ 8.60x 102 m2 10~ 2.17 x 102 m2 15~ 9.88 x 101 m2 20~ 5.59 m2 These results are again wavelength independent and it will be observed that a tilt of as little as 5~ is sufficient to reduce the cross section to less than a tenth that of the fuselage at all frequencies. This will be true for all values of 3. 2. 3. The Cross Sectional Plots In Figures 4 through 7 the cross sections are plotted as a function of 13 for a = 0. Each figure is for one wavelength and the various curves are for 12 SFCRFT

SEC RET THE UNIVERSITY OF MICHIGAN different inclinations 0 of the wings to the horizontal, the fins being vertical.. The cross sections are dominated by the returns from the fuselage and fins. and it is only at the lower frequencies that the returns from the duct-wing combinations become significant. In consequence, the tilting of the wings has little effect upon the patterns. The small oscillations present in the curves are produced by the shadowing effect of the wings on the fuselage and fins. Table 6 gives the numerical data on which Figures 4 - 7 are based. Figures 8 through 11 differ from Figures 4 - 7 only in that the contribution of the fins has been removed, and apply, therefore, to the case in which the inclination of the fins to the vertical exceeds (about) 50. In Figures 12 through 15 the cross sections are plotted as a function of i3 for a = 2. 50, the azimuth at which corner reflector 4 produces its peak return. No other corner reflector nor the fuselage contributes, and the return from the tail fins (here assumed vertical) is only apparent at the longer wavelengths. The numerical data is given in Table 7. Figures 16 through 19 similarly show the cross section for a = 7. 00, and at this azimuth the corner reflector 3 is the sole contributor, (except for a small contribution from the corner reflectors 1 and 2 at: = 0 for the longest wavelength). The bulk of the data can therefore be taken directly from Table 3. Analogous plots for a = 9. 50 and 100 are given in Figures 20 - 23 and 24 - 27 respectively. For the first of these sets the corner reflector 1 is mainly responsible, though some contribution 13 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F does come from the adjacent reflector. The data is given in Table 8. In the second set the situations are reversed, and the relevant data is shown in Table 9. In all of Figures 12 through 27 it is apparent that a major reduction in the return for all angles 3> 0 can be achieved by tilting the wings. A more detailed discussion of this will be given in the next section. The final set of curves (Figs. 28 through 31) show the cross section as functions of a for 3 = 0. The tilting of the wings here has no effect and the four figures are for the different wavelengths. The half beam width to one-tenth power is seen to vary from 10. 5~ to 120, depending on the wavelength, and these are values which are entirely specified by the angular spread of the vertical surface of the duct. It is to be expected that this width will be much the same for all values of 0, notwithstanding the fact that the structure of the beam is a function of elevation. 2.4. Further Remarks All the results in this section have been obtained by physical and geometrical optics, and since these methods require that the wavelength be smaller (and preferably much smaller) that the dimensions of the contributing structures, the lowest frequency for which the methods can be rigorously justified (as regards the B-70 near broadside) is 400 Mc. At lower frequencies, however, it is expected that the cross section will be appreciably less than the cross sections which we have derived for 400 Me. Moreover, as the frequency 14 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F decreases the cross section depends less and less on the detailed structure of the aircraft, and ultimately, when the wavelength becomes much greater than the overall dimensions of the aircraft, it is the volume of the aircraft which specifies the magnitude of the return. At frequencies greater than 400 Mc, however, the wavelength is small compared with all the important dimensions, and because of the formulae used the cross sections are polarization independent. Let us now consider the effect of tilting various portions of the aircraft's surface. The portions which can be adjusted in this manner are the fins and duct sides (which can be tilted inwards or outwards) and the wings (which can be tilted up or down). Taking first the fins, if these are both tilted outwards by an amount 0 I', the peak return will occur at 13 I' and will therefore appear in the lower quadrant. Away from the peak (specular) direction, the return falls off rapidly with increasing angle, and it is therefore clear that tilting outwards offers no advantages: indeed, such tilting produces a greater return in the lower quadrant. Tilting inwards, on the other hand, deflects the peak return into the upper quadrant where it is of no consequence, and we have seen that a tilt of as little as 50 is sufficient to reduce the fin return to an insignificant level throughout the entire lower quadrant. Considering now the wings, if these are tilted 0~ downwards, the angle of the corner reflectors will be reduced by this amount and it is then possible for a triple-bounce return to occur at some angle 13 in the lower quadrant. The 15 RFCRFT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F magnitude of this return will be comparable to that from a right angled corner, and will appear in the lower quadrant for any downward tilt of the wings. For this reason, a downward tilt is not recommended (a more complete discussion is given in the Appendix). Tilting the wings upwards, however, will reduce the return from every corner reflector for all /3> 0, and this is clearly shown in the various cross sectional plots. When 3= 0 the tilting of the wings has of course no effect, but apart from this elevation the reduction in the cross section is greater the more the wings are tilted. Nevertheless, the amount of reduco tion decreases with increasing 0 and this suggests that a tilt of 5 may be sufficient. Throughout the above paragraph it has been assumed that the sides of the duct are vertical, but a major improvement will result from tilting these + sides inwards. If the tilt is Po and if the wings are also tilted upwards by 0~ + Po, the magnitude of the return in the lower quadrant can be determined from Figures 12 through 27 if the?3t on these graphs is replaced by '1-p' Excluding for the moment the plane a = 0 (at broadside the fuselage return dominates), it can be seen that a-tilt of, for example, 5 in combination with a wing tilt of 100 (0 = 50 on the graphs) reduces the return to less than 2 x 10 m2 for all a - 0 and all 3; in combination with a wing tilt of 15~ (0 = 10~ on the graphs), the corresponding level is 5 x 103 m2. An outward tilt is detrimental for the reason given in the discussion of the fins. An outward tilt is detrimental for the reason given in the discussion of the fins. 16 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F It will be appreciated that such returns are less than the broadside returns (a = 0) at the higher frequencies even when the fins are tilted. On the other hand, broadside returns are essentially due to the fuselage alone and it is not impossible that the use of an equivalent cylinder has given an unduly large return. Any fore -and-aft curvature which is present in the actual fuselage will reduce the return at a = 0, whilst increasing the cross section at other values of a, and may bring down the broadside return to 104 m2. In practice, therefore, it is felt that the overall cross section throughout the entire broadside beam in the lower quadrant can be reduced to 10 m2 by tilting both the duct sides and the fin through 50, and by tilting the wing by (about) 10. 0~. In passing, we note that with the unmodified aircraft the experimental 4 2 results in Section 4. 3. 1 show a peak broadside cross section of 10 m at a simulated frequency of 388 Me (pattern A-i). For comparison with this we see from Figure 7 that the calculated peak return at 400 Mc is 1. 9 x104 m2 Bearing in mind that the experimental value is a near-field measurement and is for a somewhat lower frequency (both of these would tend to reduce the cross section), the agreement between theory and experiment is extremely good. Finally, it should be pointed out that the analysis has been based upon the aircraft shown in the diagrams supplied to us and in consequence no account has been taken of any radomes or antennas which may be subsequently added to the plane. 17 crFDIT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 2.5. Summary Conclusions To reduce the peak cross section of the broadside beam as observed in the elevation range 0 13 450, the fins should be tilted upwards, the duct sides should be tilted inwards and the wings should be tilted upwards. A 5 tilt for the fins should be sufficient. With the same tilt for the ducts and a 10~ tilt 4 2 for the wings, the peak cross section will be reduced to approximately 10 mI2. The azimuthal beam width is essentially determined by the curvature (fore-andaft) of the ducts, and will not be affected to any marked extent by the above changes. Alternatively, if the aim is to reduce the width of the broadside lobe at the expense of some increase in the peak return, this can be achieved by leaving the wings horizontal and the duct sides vertical, but straightening (fore-and-aft) the sides of the duct. If it is assumed that the tail fins are tilted as described above, the effect of this new modification will be to raise the peak return (at a = 3 = 0) to approximately 8 x 10 m2 for X = 0. 03 m (4 x 10 m for X = 0. 75 m), but to reduce the half beam width (to one hundredth power point) to approximately 0.1 for X= 0. 03 m (2. 4~ for X = 0. 75 m). Although this appears to be an attractive proposition it may not be practically possible to straighten all the duct including, for example, portions 1 and 2 shown in Figure 3. Any curvature which is left in the duct will obviously increase the above (minimum) beamwidths. 18 SECRET

Cross Section of Corner Reflector 1 (a = 9. 5~) 00 0 i =0 =5~ I 10~ =15~ 0 =20~ 0.03 1.03 x 106 0~ 0.10 9.29x 104 independent of 0.30 1.03x 104 0.75 1.65 x 103 0.03 1.49 x 105 1. 15 x103 2.95x102 T1.38 x102 8.36 x101 0.10 1.34 x 104 1.12 x 103 2.95x 102 1.38 x 102 8.35 x 10 0.30 1.48 x 103 3. 32 x102 2.39x102 1.37x 102 6.18 x 01 0.75 2.37 x 102 5.85 x101 5.54 x01 5.12x101 4.66 x10 0. 03 5. 77 x 105 4.58 x103 2.95 x 102 1.38 x102 8.35 x01 2 0.10 5.18 x 104 4.54 x 103 2.95x102 1.38 x102 8.35 x10o 0.30 5. 5 x 103 2.37 x103 1.91 102 1.38 x 102 8.36 x 01 0.75 9.20 x 102 4.97 x102 1.76 x 102 1.28 x 102 8.29 x 101 0.03 1.23 x 106 4.58 x103 1.18 x10 1.38 x102 8.36 x 10 3 - 0.10 1.11 x 105 4.5.8 x 0 1.18 x 103 1.38 x102 8.35 x01 0.30 1.23 x 104 4.13 x103 1.07 x103 1.38x102 8.36 x101 0.75 1.97 x 103 1.24 x103 5.74 x102 1.25 x102 3.60 x01 0.03 2.04 x 106 4.58 x 103 1.18 x103 5.52 x102 8. 36 x 01 o 0.10 1.83 x 105 4.58 x103 1.18 x103 5.52 x102 8.35 x 01 40.30 2.03 x 104 3.95 x 103 9.60 xl02 5.51 x102 8.36 xl01 0.75 3.25 x 103 2.10 x103 9.26 x102 3.21 x102 5. 29 x 01 0.03 2.07 x 106 4.58 x103 1.18 x103 5.52 x 102 3.34 x102 0 0.10 1.86 x 105 4.58 x 103 1.18 x 103 5.52 x102 3.34x102 0.30 2. 06 x 104 4. 09 x103 5. 80 x02 3.73 x 102 2.92 x 102 0.75 3.30 x 103 2.18 x 03 1.03 x103 4.56 x02 1.55 x02 H zT z Cl) p1 I m -I 0 0 -z TABLE 1

Cross Section of Corner Reflector 2 (a = 10~) X3 =0o~ = =5~0 ==10~ 0e 15~ 0 =20~ 0.03 8.90x 105 00 0.10 7.94 x 104 independent of 0 0.30 8.84 x103 0.75 1.41 xx103. 03 1.35 x 105 9.83 x 102 2.54 x 102 1.19x102 7.18 x10 0.10 1.21 x104 9.50 x 102 2.54x102 1.19 x 102 7.18 x 10 100 0.30 1.35 x 103 3.00 x102 2.12 x102 1.17 x 102 4.92 x101 _0.75 2.15 x 102 5.29 x 101 5. 02 x 101 4.62 x 101 4.16 x 10 0.03 5.24 x105 3.93 x103 2.54 x 102 1.19 x 102 7.18 x 101 0.10 4.70 x 104 3.87x 103 2.54 x 102 1.19 x 102 7.18 x 101 20~ 0.30 5.22 x103 2.11 x 103 1.48 x102 1.19 x102 7.18 x 101 0.75 8.36 x102 4.50 x 102 1. 58x 102 1.12 x102 7. 05 x 101 0.03 1.12 x 106 3.93 x 10 03 1 x 1.19xl02 7.18 x 10 0.10 1. 00 x105 3.93 x 103 1.01 x 103 1.19 x 102 7.18 x101 300 0.30 1.t2x104 3.58 x103 9.28x102 1.19x102 7.18 x01 0.75 1.79 x103 1.12 x 103 5.08 x102 1.03 x102 2.61 x 01 0.03 1.85 x 106 3.93 x 103 1.01 x103 4.74 x 102 7.18 x 10 O 0.10 1.66 x105 3.93 x 103 1.01 x103 4. 74 x102 7.18 x 10 400.30 1.85 x104 3.35 x 103 7.90 x 102 4. 71 x 102 7.18 x 10 0.75 2.95 x103 1.86 x103 8.09 x 102 2.82 x 102 4.55 x101 0.03 1.78 x106 3.93 x 103 1.01 x 103 4. 74 x 102 2.87 x 10 0.10 1.59 x 105 3.93 x 103 1.01 x 103 4. 74 x 102 2.87 x 102 450 0.30 1.77 x104 3.45 x103 4.49 x102 3. 00 x102 2.55 x 102 0.75 2. 83 x 103 1.91 x 103 8.94 x 102 3. 98 x 102 1.36 x102 -cI I I 43 z m (a )-4 F < 0 ~ 0 z TABLE 2

Cross Section of Corner Reflector 3 (a = 7. 00) B = 00 =5~ =10~ =15~ =020 0.03 3.03 x 106 0 0.10 2.71 x 05 independent of 0 0.30 3. 02x104 0.75 4.38 x103 0. 03 2.88 x10 4.36x103 1.12x103 5.26x102 3.18 x102 P0 0.10 2.58x105 4.36x1 03 1.12x103 5.26 x102 3.18 x102 0.30 2.87 x 104 4. 01 x 103 3.76 x 102 5.26 x 102 3.18 x 102 0. 75 4.59 x 103 1.05 x 103 8. 06 x 102 5.21x z102 2. 85 x102 0.03 1.07 x 107 1.74 x 104 1.12 x 103 5.26 x 102 3.18 x 102 200 0.10 9.59 x 105 1.74 x 104 1.12x103 5.26 x 102 3.18 x102 0.30 1. 07 x05 1. 18 x 04 1.12 x103 5.26 x102 3.18 x102 0.75 1.71 x104 7.44 x103 1.07 x 103 1.97 x 102 7.83 x 10 0. 03 9.08 x 106 1. 74 x 104 4.49 x103 5.26 x 102 3.18 x 102 30~ 0.10 8.15 x 105 1.74 x 104 4.49 x 103 5.26 x 102 3.18 x 102 0.30 9. 05 x 104 1. 01 x 104 2.80 x 103 5. 26x 102 3.18 x 102 0. 75 1.45 x 104 1.08 x 104 3.83 x 103 3.72 x 102 1.13 x102 0.03 7.11 x 106 1.74 x 104 4.49 x 103 2.10 x 103 3.18 x 102 0.10 6. 37 x105 1. 74 x 104 4.50 x 103 2. 10 x 103 3.18 x 102 0.30 7.08 x 104 1.40 x 104 4.49 x 103 2.10 x 103 3.18 x 102 0.75 1.13 x104 8.99 x 103 4. 26 x103 2. 06 x 103 2.75 x102 0.03 6.05 x106 1.74 x 104 4.49 x103 2.10 x 103 1.27 x 103 0 0.10 5.43 x105 1.74x104 4.50x 103 2.10 x 103 1.27 x103 0.30 6.03 x104 1.57 x104 1. 54 x03 2.10 x 103 9.07 x102 0.75 9.65 x 103 7.91 x 103 4.14 x 103 1.72 x 103 1. 05 x103 COy? c-j -. I trT 2 z -4 C) -4 0 z iOr m —, MI TABLE 3

Cross Section of Corner Reflector 4 (a = 2. 5~) $ 9 9=0~ 9 =5 0 3,10~ | =15~ 9 =20~ 0. 03 1. 31 x 106 o 0.10 1.18 x 105 independent of 0 0.30 1.31 x 104 0.75 2.09x103 0.03 2. 79x106 2.45x103 6.32x102 2.96x102 1.79x102 0.10 2.50 x 105 2.45 x 103 6. 32x 102 2.96 x 102 1.79 x 102 10 0. 30 2.78 x 104 2.42 x 103 6.32x102 2.96x1 102 1.79x102 0. 75 4.45 x 103 9.52 x102 5.95 x102 2.58 x102 6.55 x101 0.03 4.63 x 106 9.81 x103 6.32x1 102 2.96 x 102 1.79 x 02 2 O 0.10 4.15 x 105 9.81 x 103 6.32x 102 2.96 x 102 1. 79 x 102 0.30 4.61 x104 8.49 x103 6.32x102 2.96 x 102 1.79x102 0.75 7. 38 x 103 4.57 x 103 6.32 x 102 2. 00 x 102 4.47 x 10 0.03 3.93 x 106 9.81 x 103 2.53 x 103 2.96 x 102 1.79 x 102 o 0.10 3.53 x 105 9.81 x 103 2.53 x 103 2.96 x 102 1.79 x 102 0.30 3.92 x 104 8.09 x 103 2.53 x103 2.96 x 102 3.92 x 10Z 0. 75 6. 27 x 103 5. 00 x 103 2. 41 x 103 2.68 x 102 1.18 x 102 0.03 3.08 x106 9.81 x103 2.53 x 103 1.18x103 1.79x102 O 0.10 2.76 x 105 9.81 x 103 2.53 x 103 1.18 x 103 1.79 x 102 0 30 3.07 x104 9.30 x103 9. 37 x102 1.18 x103 1.79x102 0.75 4. 90 x103 4.10 x103 2.33 x 103 1.10 x103 1, 76 x103 0 03 2.62 x 106 9. 81 x 103 2.53 x 103 1.18 x 103 7.16 x 102 45 0| 10 2.35 x105 9.81 x103 2.53 x 103 1.18 x 103 7.16 x 102 0.30 2.61 x 104 9.58 x 103 1.44 x 103 1.18 x 103 1.84 x 102 4.18 4. 18 x 103 3.58 x 103 2.19 x 103 8. 70 x102 6.74 x 102 H ffq tt C2 r-J 0 ^,... m -H -4 i-4 z 0 - TABLE 4

Croes Section of Corner Reflector 5 (a = - 2. 5~) 0~ =50 [ e =10~ = 15~ 0 -20~ 0.03 1.62 x105 t0o 0.10 1.46 x104 0.10 1.46 10 independent of 0 0.30 1.62x103 0.75 2.59 x102 0. 03 6.30 x 105 8.44 x 102 2.18 x1 10 2 1.02 x02 6.16 x 101 0.10 5.65 x 104 8.44 x 102 2218 x 102 1.02 x 102 6.16 x 101 0.30 6.28x103 7.99x102 6.51 x101 1.02x102 6.16x101 0.75 1. 00 x 103 2.19 x 102 1.59 x 102 1.O0 x 102 5.90 x 10. 03 5.73 x 105 3.38 x 103 2.18 x102 1 02 x102 6.16 x 101 20~ 0.10 5.14x 104 3.3 x 103 2.18x102 1.02 x 102 6.16 x 101 0.30 5.71 x103 3.12 x 103 1.08 x102 1.02 x 102 6.16 x 101 0. 75 9.14x 102 8.29 x 102 1.43 x 102 9.48 x 101 6.16 x 01 0.03 4.87 x 105 3.38 x 103 8.70 x 102 1.02 x 102 6.16 x 101 0.10 4.37 x 104 3.38 x 103 8.70 x 102 1.02 x 102 6.16 x 10 30 0.30 4.85x 103 2.91x103 5.21x102 1.02x101 6.16 x 01 0.75 7.77 x 02 7.14 x102 5.55x 102 8.31 x 10 5.77 x 101 0.03 3.81 x 105 3.38 x 103 8.70x 102 4.07 x 102 6.16x101 400 0.10 3.42x 104 1.22 x103 8.70 x 102 4. 07 x 102 6.16 x 01 0.30 3.80 x 103 2.54 x 103 6.18 x102 3.13 x 102 1.84 x 101 0.75 6.08 x 102 5.68 x 102 4,61 x102 3.24 x 102 4.50 x 101 0.03 3.25x 105 3.38x 103 8. 70x 102 4. 07x 102 2.46 x 102 0.10 2.91 x 104 1.79 x 103 8. 70 x 102 4. 07 x 102 2.46 x 102 0.30 3.24x103 2.30x103 6.95x102 1 3.72x102 4.37 xl01 0.75 5.18 x102 4.87 x 102 4.06 x 102 2.93x 102 1.80x102 H MT z -4 C c0 < O i oK <y" m 7H -4 "4 z Z TABLE 5

Total Cross Section at a~ = 0 (fins vertical) 4-c -ci z 0 -rJ) 0 z (n MI

Total Cross Section at a - 2. 5~ e =5~ o = 100 0 15~ =20~ 0. 03 1.31 x 1 0.10 1.21x105 0. 30 1.66 x 104 Independent of 0 0.75 5.55 x 103 0.03 2.79 x 106 2.45 x 103 6.32 x 102 2.96 x 102 1.79 x 102 100 0.10 2.50 x105 2.45 x 103 6.33 x102 2.97x102 1.80 x 102 0.30 2.78 x 104 2.43 x 103 6.42 x102 3.06 x 102 1.89 x102 0.75 4.51 x103 1.01 103 6.55 x 102 3.18 x 102 1.26 x 102 0.0 4.63 x 106 9.81 x 103 6.32 x 1 102 2.9 0 1.79 x 102 200 0.10 4.15 x 10 9.81 x103 6.32x102 2.96 102 1.79x102 0.30 4.61 x104 8.49 x103 6.34 x102 2.9 x102 1.81 x10 0.75 7.39 x 103 4.58 x 103 6.42 x 02 2.10 x 102 5.50 x 10 0.03 3.93 x16 9.81 x103 2.53 x 103 2.96 x 102 1.79 x 102 0.10 3.53 x 10 9.81 x 103 2.53 x 103 2.96x 102 1.79 x 102 0.30 3.92 x 104 8.09 x 103 2.53 x 103 2.96 x 10 3.92 x104 0.75 6.27 x103 5. 00 x103 2.41 x 13 2.71 x 102 1.21 x 102 0.03 3. 08 x 106 9.81 x 103 2.53 x 103 1.18 x 103 1.79 x 102 400 0.10 2.76 x 105 9.81 x 103 2.53 x 103 1.18 x 103 1.79 x 102 0.30 3.07 x 104 9.30 x 103 9.37 x 102 1.18 x103 1 79 x 102 0.75 4.90 x103 4.10 x103 2.33 x103 1.10x103 1.76 x103 0. 03 2.62 x 106 9.81 x 103 2.53 x103 1.18 x 103 7.16 x 102 0.10 2.36 x 105 9.81 x 103 2.53 x103 1. 18 x 103 7.16 x 102 0.30 2.61 xl10 9.58 x103 1.44 x103 1.18x 103 1.84 x 102 0.75 4.18 x103 3.58 x103 2.19 x 103 8.70 x102 6.74 x 102 )rrJ z rr 0-< 0 O I ^2 lu, m -I tC3 Cl C) 0 -z TABLE 7

Total Cros Section at = 9. 5~ e ~ e =5~ 0 =1 e =15~ 0 =200 0.03 1.04x106 0 0.10 1.04x105 0o 0.0 1.04x10 independent of O l0.30 2.16x104 _ 0.75 1.30x104 0.03 1.50x105 1.16 x 03 2.98 x102 1.40x 102 8.45xl 10o 0 0.10. 51xl04 1.26 x 103 3.31x10 1.55x102 9.38xl 0.30 3.21 x 103 718x 102 5.11 x102 2.88 x 102 1.25x 102 0.75 1.97x103 4.84 x102 4. 59 x102 4.23 x 102 3.81 x102 0.03 5.84 x105 4.63 x 103 2.98 x102 1.40x102 8.45xlO0 20~ 0.10 5.85 x104 5.09 x 103 3.31 x102 1.55 x 102 9.38xl 10l 0.30 1.25 x104 5.09 x 103 3.82 x102 2.91 x102 1.76 x102 0.75 7.64x103 4.12x103 1.44x103 1. 03x103 6.49x102 0.03 1.25xl106 4.63x103 1.19x103 1.40x 102 8.45x101 ' O 0.10 1.25x105 5.14 x 103 1.33 x103 1 55 x 102 9.38x 101 0.30 2.67 x104 8.73 x103 2.26 x 103 2. 91 x102 1.76 x102 0.75 1.63x104 1.03 x104 4.66 x 103 9. 54 x102 2.46 x02 0.03 2.06 x106 4.63x 1:3 1.19 x103 5.58 x102 8.45 x 101 400 0.10 2 07 x105 5.14x103 1. 33x103 6 20 x 102 9.38xl01 0.30 4.41 x104 8.26x1 03 1. 98x103 1 16x103 1.76 x 102 0.75 2.70x 104 1.70x 104 7.43 x 103 259x103 4.18 x 102 (0.03 2.09 x106 4.63 x 103 1.19 x 103 5.58 x102 3.38 x 102 450 0.10 2.08 x105 5014x103 1.33x103 6.20 x 102 3.75 x 102 0.30 4.34 x104 8.52 x 103 1.16x103 7. 59 x 102 6.20 x 102 0.75 2.61 x104 1.76 x104 8.21 x103 3.65 x103 125 x 103 H za < Cu 1-4 0 ~ ~ Tll -4 Z 0-4 C) 0 z -- m TABLE 8

Tota Cross Section at a =1IO0 x 0300 050 e- ItP 0 =150 1e= 20" 0. 03 9, 01 x1&o oo 01 90x( independent of & 0. 30 2. 02 x104 0. 75 1. 28 x104__ _ _ _ _ ___ _ _ _ _ _ _ _ _ _ _ _ 0. 03 1. 37 x105 9. 96 x102 2.57 x102 1.2 0 x 102 T 2 7 x1IC 10 0.10 1.38 x104 1. 09 x1&3 2. 90 x102 1. 36 x102 3,20 x10 I 10 0. 30 2. 98 x103 6. 67 x102 4J176 x102 2. 69 x102 1. 18 xI&( 0. 75 L.85 x1&3 4.57 x102 4.33 x102 4.O00xlG (2 3. 63 x102 0. 03 5. 30 x 1& 3. 98 x103 2T 57Tx 0 1. 20 x102 7. 27 x101 20 0.10 5.34 x104 4.42 x1&3 2. 90 x102 1. 36 x102 S. 20 x101 0. 30 1. 16 x104 4. 73 x103 3. 59 x102 2. 71 x102 1. 64 x1&2 0. 75 7. 19 x103 3. 89 x103 1. 37 x1&3 9. 92 x102 6. 43 x102 0. 03.1.13 x106 3. 98 x1&3 1. 03 x1I03 L2OxI&0 7. 27 x 1 0 300 0.10 1. 14 x1 4.50 x103 1.16 x 1 1. 36 x102 8. 20 x1&c 0.30 2.47 x104~ 8.13 x 103 2. 10 x103 2. 71 x1&2 1. 64 x1&2 ___ 0. 75 1.54 x 104 9.71 x10e 4. 47 x103 4.82 x103 2. 74 x 102 0. 03 1. 87 x106 3. 98 x103 1. 03 x1&3 4. 81 x102 7. 27 x101 400 0.10 1. 88 x1&5 4.50 x103 1 16 x10 3 5.42 x 102 B.20 x10 1 0.30 4. 10 x104 7.72 x 1& 1.5 x 1&3 1. 08 x103 1. 64 x1&2 0.75 2.54 x104 1. 64 x104 7. 20 x13 2. 50 x103 4. 11 x102 0. 03 1. 80 x106 3. 98,x103 1. 03 x103 4.81 x102 2. 91 x I& 450 0.10 1. 82 x105 4.50 x10 3 1. 16 x103 5.42 x1(9 3. 28 x102 0.30 4. 05x 104 7.96 x10 3 1. 09 x 103 7.12 x102 5. 78 x 102 0.75 2.56 x 104 1.7TOx 104 7,98 x103 3.54 x103 1-. 21x1I03 H z4 0-4 Cf mI MI -4 0-4 z TAB LE 9

SECRET THE UNIVERSITY OF MICHIGAN 3477 -1 -F cq Cc, a) a) 0 -.b 3 in degrees FIGURE 4 28 SECRET

SECRET THE UNIVERS ITY OF MICHIGAN 3477-1 -F 107 I7 i I I I I I:'I cq CQ as 0) - b 3 in degrees FIGURE 5 29 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 10' 106 C) *-> c) E 0 b 105 - i - 0. 30 Am (Fins Vertical):- I N6,__ _ = 0 0 0 10 20 30 An 104 103 v / in degrees FIGURE 6 7v 30 C l:D ICT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 107 10 CV 2 0 Q) -4-4 b b 3 in degrees FIGURE 7 31

SECRET THE UNIVERSITY OF 3477-1 -F MICHIGAN 106 105 C) c) -.s b X -0.03 ma= 00 (Fins Tilted Invza:rs) all 9 at 50 or More) I, r _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ i i _ 104 103 0 10 20 30 40 B in degrees FIGURE 8 32 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 106 105 CI Q) -.b b - -X=0. 10m a - 0. -. (Fins Tilted Inwards at 5~ or More) e.. = r = - l-.,= -- ---- it} - He ftX3' _ j<<.. i,' L 'mlnA 104 103 0 10 20 3U 4U 3 in degrees FIGURE 9 33 SFCRFT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 106 CM so.El Ca b 3 in degrees FIGURE 10 34 SECRET

SECRET THE UNIVERSITY OF 3477-1-F MICHIGAN 10G 105 CCl k C) b 104 103 3 in degrees FIGURE 11 35 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 108 - 4-) b 3 in degrees FIGURE 12 36 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 108 cq (1) Q) 5 b P in degrees FIGURE 13 37 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 108 7 10 106 C) 4C) b 105 104 103 102 10 (3 in degrees FIGURE 14 38 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 108 107 106 CD Qa C) b 105 104 103 102 10 0 10 20 30 40 3 in degrees FIGURE 15 39 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 108 CQ;-> C1.b b 0 10 20 30 40 f in degrees FIGURE 16 40 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 108 0 10 20 30 40 3 in degrees FIGURE 17 41 SECRET

SECRET THE UNIVERSITY 3477-1 -F OF MICHIGAN 108 107 106 cq (M a) 0 - -1 b 105 104 103 102 10 3 in degrees FIGURE 18 42 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 108 10l 106 C)Q C) 0 C.) b 105 104 103 102 10 0 10 20 30 40 3 in degrees FIGURE 19 43 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 107 106 105 104 C) 103 102 10 1 f in degrees FIGURE 20 44 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 107 106 105 104 103 102 10 1 0 10 20 30 40 3 in degrees FIGURE 21 45 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 107 106 105 105 cl v-l 0 b 103 102 10 1 0 10 20 30 40 P in degrees FIGURE 22 46 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 7 L0 10C I0c 105 104 C) C)C).b vf 103 102 10 1 0 10 20 30 40 3 in degrees FIGURE 23 47 Crfrn -r

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 7 10 - = X=0.03 m|-a =10~ 106 __, IU1 _ _ 105. 1 0 104,... 103 i I C i I = 102 1 - 0 i-! -- -— '" —.. -- - ---.. - 0 10 20 30 40 3 in degrees FIGURE 24 48 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 10 106 105 cq 0 (i) +j a) 5.5 10 104 103 102 10 1 0 10 20 30 40 3 in degrees FIGURE 25 49 qFCRFT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 107 C.) C.) b 0 10 20 30 40 0 in degrees FIGURE 26 50 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 107 10 106 105 cs a) ~r4 c) Q 0 ^b 104 103 102 10 1 10 20 30 40 f in degrees FIGURE 27 51 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 107 106 105 U2 m k aQ b 104 103 102 0 2 4 6 8 10 12 14 a in degrees FIGURE 28 52 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 7 -t I. -: l -T i. i -+ - t I i f, p t i t. i l 106 105 C,, b — a, i I Il_ II! T r t -L --- —--......ins.Vel ),Fn Vertical II II IEE! EE EEEIEETiE,,, n!, /_ _^~~ -- -^ 19 d I I I 4 10 73L 103 102 0 2 4 6 8 10 12 14 ain degrees FIGURE 29 53 SECRET

SECRET THE UNIVERSITY OF 3477-1-F MICHIGAN 1 7 i....... I I 106 5 10 cI2 ril C.) Q -I.m.. ( = 0. 30 m (Fins Vertical)......7-l tX 1\t t t.T.....X t....) l l l l Ll! '~,/ ' b, \.' -,, \ i=<<<,. 104 3 10 102 0 2 4 6 8 10 12 14 a in degrees FIGURE 30 54 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 10 106 105 CIA C)l 4 -C) zc.. b 104 3 10 102 14 a in degrees FIGURE 31 SERET SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 3. RADAR ABSORBING MATERIAL FOR THE B-70 The results of studies reported in Reference 1 as well as the work at NAA in Columbus have shown that the high cross section of the B-70 in the forward area is due to reflection from the air-intake ducts. An examination of photographs of the models (Fig. 32) would also lead one to this conclusion. One of the requirements in the present study was to determine the optimum method of minimizing this cross section by the addition of RAM along the duct walls. This work is described in Section 4. Another requirement called for a survey of RAM which might be suitable for lining the duct walls of the B-70 and the results of the survey are given in this section. For a RAM to be satisfactory for use in the B-70 it must operate at temperatures up to 6500 F. Ideally its physical properties should also include toughness, resistence to shattering and the ability to be machined or moulded to fit the duct walls, or to be painted or sprayed on the duct walls. It should be able to absorb 90 0/0 or more of the incident energy from 100 Mc to 10, 000 Mc. The required thickness should be well under an inch and the weight per unit area of the layer should be a minimum. Of the above requirements, the one which has received least attention among workers in the radar absorbing field is that concerning temperature. This requirement immediately rules out dielectric foams of plastic materials, hair flex and rubber absorbers. To the best of our knowledge, there are only 56 SECRET

0 -t71l VIEWS OF THE B-70 MOE MODEL

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F two organizations in this country that have been actively at work to develop a high-temperature RAM. The first, Rutgers University, has just started a program to produce a high-temperature RAM using ceramics (see Ref. 2), but it is much too early to capitalize on this effort. The second organization, Emerson and Cuming, Inc., has developed a high-temperature RAM, designated BNA-100 (Ref. 3), which consists of conductively-loaded foam materials. BNA-100 is a low-density material made of carbon-coated hollow microspheres, with the microspheres self-bonded in a hot press. A 2" thick layer of BNA-100 has a reflection coefficient of 3 to 5 70 for frequencies higher than 1000 Mc. Such a layer weighs about 2. 6 pounds per square foot. At the present stage in the development BNA-100, it may be slightly marginal in respect to its ability to stand the 650~ F temperature. It is believed, however, that this limitation will be overcome as the work continues. Further work on this material is needed to improve the particle-to-particle bonding, but it may be possible to solve the problem by enclosing the material within a silicon laminate. If the 2" thickness is maintained, the reflection coefficient will increase as the frequency decreases. It is doubtful, however, if the reflection coefficient would increase above 50 ~/o at frequencies higher than 100 Mc. The only other type of radar absorbing materials which would appear to come close to the physical and, in particular, the temperature requirements 58 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F for the B-70 application are the ferrite absorbers. These have been under development for a number of years (see, for example, reports on the work at the Naval Research Laboratories (Ref. 4), Battelle Memorial Institute (Ref. 5) and The University of Michigan (Ref. 6) ), and it has been demonstrated that broad-band performance can be achieved. NRL reported on a material (Ref. 4) with a power reflection coefficient of 5 %/ or less from 100 to 10, 000 Mc. This material is pyramidal in form with a total thickness of 1" and uses a Ni-Mn-Zn ferrite. A flat piece 0. 217" thick has a power reflection coefficient of less than 5 % from 100 to about 1400 Mc. Based on the NRL results with pyramidal absorbers, it would seem that one should be able to develop an absorber 0. 5" thick with a power reflection coefficient of 10 ~/ or less from 200 Me to 10, 000 Me. The maximum temperature for this material is about 150~ C. It should be understood that the referenced NRL data represents their best results after a rather thorough study of low-temperature ferrites. The University of Michigan (Ref. 6) has materials with a reflection coefficient of less than 5 ~/ from 100 to 1000 Mc. To achieve this with a ZnY + 1 % sodium silicate, an estimated thickness of 2" to 3" would be required at 100 Mc. The required thickness decreases rapidly with wavelength and should be well under an inch for frequencies above 400 Mc. These estimates are based on curves appearing in Reference 6 which give depth of penetration for 59 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F an infinite sheet rather than the usual minimum thickness required for an absorber backed by a conductor. The Curie temperature of the lossy ferrite materials being developed at The University of Michigan extends to 300 C or better, but until now no particular effort had been made to work with the higher Curie temperature ferrites. The military has been slow to use ferrite absorbers for airborne applications because of their weight. The weight per square foot of a 1" thick piece of the usual ferrite absorber is about 20 pounds. In the B-70 application, however, the advantages to be gained by the use of a relatively small amount of RAM suggests that more serious consideration should be given to the use of materials which might normally be regarded as too heavy or too thick. In this connection, the authors would like to press for the design of aircraft in which the requirement for low cross section is borne in mind at the initial design stage. Absorbing material would not then have to be added in order that an aircraft, whose design was already complete, might satisfy the requirement. Moreover, the presence of absorbing material on the aircraft may not increase the overall weight since the lower cross section enables the weight of the countermeasure package to be reduced. In surveying the possible sources for a ferrite RAM it immediately becomes apparent that there has been little or no emphasis on the selection of ferrites with high Curie temperatures. At temperatures higher than the Curie temperature the permeability of ferrites decreases rapidly. To our knowledge, no ferrite RAM with Curie temperatures near 6000 F has been 60 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F developed in this country, but the authors are aware of the successful work of the British on high-temperature lossy ferrites. The Royal Aircraft Establishment at Farnborough, Hants. has used an 0. 060(' layer of a Plessey P-type absorber as a cover on the forward half of a "bullet" in the jet exhaust of a Canberra bomber. It is believed that the use of such coatings is now standard on these aircraft. One of the materials used was reported to be a combination of aluminum oxide (95 %/ ) and ferrite (5 /o ). The material acts as a lossy layer of so many ohms and not as a matched absorber. It was designed to be effective at S and X bands (10 cm and 3 cm) and for temperatures in excess of those used in the B-70 ducts. A reduction in cross section of the order of 10 db has been reported. The material is made by the Plessey Company of nlford, Essex. The energy that enters the B-70 ducts must propagate down the ducts as if it were a waveguide. The modes propagated will, of course, dependupon the frequency involved and the polarization of the incident wave, and it is of interest to consider methods of attenuating energy in a waveguide. Maximum attenuation occurs when a dielectric absorber is in a strong E field, which is in the center of the guide for the fundamental mode. On the other hand, absorbers having high magnetic loss will perform most efficiently whenplaced in strong H fields, that is, near the guide walls for most waveguide modes. The similarity of the B-70 duct problem and the waveguide load problem became apparent in a discussion with R. W. Wright of NRL. Wright's group has recently developed a high-temperature waveguide load (Ref. 7) using a 61 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F ferrite as the lossy material. This load was made by lining the walls of standard L-band (1300 Mc) waveguide with Ferroxcube 105. The load was about 40" long, the large length being necessary to distribute the heat over awide area. The thickness of the material varied from a few mills at the input end to about 0. 2" at the far end. The extra thickness at the end was for the purpose of increasing the loss there to help distribute the heat over the entire load. The load proved to operate quite satisfactorily at L band, and also performed well at 3000 Me and in the 10, 000 Me range. The ferrite material used in this load has a Curie temperature of 4650 C (869~ F). The load has been operated up to 720~ F apparently with good performance. It has successfully passed some shake-table tests and a humidity test cycle. Detailed information has been given on this load because it is a good example of the use of a large slab of ferrite material as a lossy material at temperatures in excess of those expected in the B-70 ducts. In addition, the loss mechanism is not unlike that expected in the B-70 ducts. Workers at Battelle, NRL and in the Solid State Group at The University of Michigan involved in the development of ferrite RAM, believed it was feasible to develop broad-band absorbers which would perform at temperatures well in excess of 630~ F. There are, for example, the following commercial materials with high Curie temperatures: Type Curie Temp. Ferroxcube 4C 600~ F Ferroxcube 4D 750~ F Ferroxcube 4E 930~ F 62 CFRCFT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F These materials are cited only to show that ferrites with high Curie temperatures have been developed. Information on their loss characteristics in the frequency range of interest is not available. To learn more about the properties of Ferroxcube 105, information on this and similar ferrites was requested from the Ferroxcube Corporation of America. Although two requests were made, including a request for quotation on a sample, very little information was obtained. A request was then made to NRL for a sample of Ferroxcube 105. The only sample they were able to provide was a small one which had alreadybeen mixed with a silicone resin binder. The binder was Dow Corning number 993, and the Ferroxcube 105 made up 85 %/ by weight of the mixture. The material provided by NRL was given to Professor Grimes of the Electrical Engineering Department of The University of Michigan in order that it might be tested and analyzed in his Solid-State Laboratory. Part of the Ferroxcube 105 mixture was shaped to form a sample 0. 2 " thick for their coaxial sample holder and measurements were made of reflection coefficient versus frequency. The results obtained for power reflection coefficient are given in Table 10. Following a procedure described in Reference 6 and using a sample 0. 04" thick, the Solid-State Laboratory also made measurements to determine the permeability of Ferroxcube 105 versus frequency. The results are included in Table 10. 63 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F TABLE 10 Frequency (Me) 500 600 700 800 900 1000 1100 1200 2600 3000 3500 4000 Per Cent Power Reflection (Thickness = 0.2 ") 52.6 51. 6 48.1 43.5 39.2 35.8 30.2 29.3 4.9 0.5 1.2 0.8 Permeability 4.10 3.77 3.58 3.23 3.15 2.80 2.75 2.48 1.78 1.66 1.41 1.41 -j -j -j -j -j -j - j -j -j -j -j -j 2.64 2.40 2.43 2.43 2.27 2.28 2.15 2.10 1.56 1.65 1.48 1.42 The remaining part of the sample provided by NRL was subjected to spectrographic and chemical analysis by the Detroit Testing Laboratory, Inc. Their report showed that iron, nickel, zinc and cobalt were the predominant metals contained in the sample. A copy of the complete analysis has been forwarded to NAA. Since there was some uncertainty in this analysis due to the small sample provided and due to the presence of the resin binder, another contact was made with Ferroxcube Corporation of America. As a result of this contact made near the end of the present study a sufficiently large sample 64 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F of Ferroxcube 105 powder will be obtained. Professor Grimes will continue his study of the material as part of his Air Force contract on ferrite absorbers. The results of the search for an absorbing material which would be satisfactory for application in the B-70 ducts were somewhat disappointing in that so little information on high-temperature RAM was available. For this reason, undue attention may have been focussed on Ferroxcube 105. Based on the performance of this material as a waveguide load one would predict fairly good performance in the B-70 ducts. The limited information resulting from The University of Michigan tests on the NRL sample do not indicate outstanding characteristics. It is hoped that an effort will be made to develop an optimum hightemperature RAM for the B-70, although Ferroxcube 105 may prove to be a satisfactory absorber in the interim. 65 CFrPFT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 4. EXPERIMENTAL PROCEDURES AND RESULTS 4. 1. Introduction Experimental measurements were made to determine the optimum method of reducing the cross section of the B-70 in the forward area to 40 m2 or less. Most of the effort was restricted to cross section reduction by the addition of RAM to the interior of the ducts. By covering up the duct apertures with metal foil (see Patterns A-2 and B-2) it was shownthat a significant reduction is achieved when the electromagnetic energy is prevented from entering the ducts. It seems feasible to use large mesh screens to lower the cross section in the 100 to 300 Me range, but no work was done on this since the technique was being investigated at NAA, Columbus. One other effort not concerned with the use of RAM was investigated, and will be discussed later. This study involved the effect of tilting the vertical duct walls to produce a non-rectangular duct cross section. The investigation divides into two parts, with a RAM having dielectric loss being used in the first part, and a RAM having magnetic loss in the second. Measurements were first carried out to determine the optimum locations for the RAM. Later measurements were made to determine the effectiveness of locating RAM at positions prescribed by NAA. In many instances the reduction achieved by using RAM at the prescribed locations was insufficient, in which case an effort was made to determine the minimum additional RAM necessary to achieve the 40 m2 level. + The magnetic RAM used has dielectric loss also, but the dielectric loss will be small since the E field is near zero in a thin absorber backed by a conductor. 66 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F In general, it can be said that the optimum locations appeared to be about the same regardless of the type of RAM used. Dielectric RAM from commercial suppliers was used in the first tests since it was readily available. As a result of the investigation to find a RAM suitable for the B-70, it appeared that a material with magnetic loss would more nearly meet the thickness and temperature specifications (see discussion in Section 3). Thereafter most of the measurements were made with a thin magnetic RAM made in ourlaboratory. In the patterns which follow, the RAM used is denotedby a type number which can be identified from the following table. TABLE 11 Type Number Identification of RAM 1 McMillan Laboratory X-band resonant absorber Type T-XT-2 with a measured reflectivity+ of -19 db. 2 Emerson and Cuming X-band dielectric absorber Type Eccosorb AN-73; measured reflectivity about -20 db. 3 McMillan Laboratory K-band resonant absorber Type T-KQ-2; measured reflectivity about -20 db. 4 Emerson and Cuming K-band dielectric absorber Type Eccosorb AN-72; measured reflectivity better than -20 db. 5 Magnetic absorber, home-made according to formula supplied by R. W. Wright and W. H. Emerson of the Naval Research Laboratory. The absorber consists of 73 0~/ J carbonyl iron powder in an epoxy resin. The epoxy resin is coil seal No. 11 made by the National Engineering Products Company of Washington D. C. The thickness is approximately 0. 040". NRL recommends a thickness of about 0. 72" for a resonant X-band absorber. The reflectivity of this material was measured to be -4 db at 9700 Me and -9 db at 22. 9 KMc. 6 Emerson and Cuming unmatched lossy dielectric Eccosorb Type LS-26; measured reflectivity at X band -6 db. 7 Magnetic material; similar to type 5 except that it is about 0. 070" thick. The measured reflectivity at 23 KMc is -4 db. +A reflectivity of -n db means that for normal incidence the reflected power is ndb less from a flat piece of RAM than from a flat metal plate of the same size. 67 CEi DET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 4. 2. Experimental Facilities and Procedures The measurements were made on an indoor scattering range using conventional cw equipment and techniques. The maximum range available was about 40 feet, which is considerably less than that required to be in the far field. The range limitations and the residual reflections in the room limited the accuracy and the repeatability of the measurements. Scattering patterns were taken at slightly different rangesto evaluate the contributions due to the room reflections. The changes caused in the larger reflected signals were slight - usually less than one db. Changes in the level of the signal when the return is the order of the nose-on cross section ranged from one to four db for individual lobes. Any changes in the level averaged over several degrees were small. The small asymmetries in the scattering pattern were found to be due to asymmetry in the model and in the measurement room. Since the objective in these measurements was to determine the amount of cross section reduction that could be achieved, and since this involved the comparison of the scattering pattern of the same aircraft with and without RAM inserts, it is believed that inaccuracies due to range limitation, etc will generally cancel out. As a result, the value determined for the cross section reduction should be quite reliable. 68 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F A block diagram showing the equipment is given in Figure 33, and a photograph of the equipment and measurement room is shown in Figure 34. At X band, frequency stabilization was achieved by the use of a reference cavity. At K band the oscillator frequency was phase-locked to an S-band crystal exciter. Background reflections and direct coupling between the transmitter and receiver through the hybrid tee were minimized by the proper adjustment of the RF tuners. The Scientific Atlanta receiver and recorder were used. Spheres and corner reflectors were employed as standard scatterers to calibrate the level of the return from the aircraft being studied. Three aircraft models which were provided by NAA were available for this study. All were made of wood which had been metalized by The University of Michigan and the scales of the models were 0. 01, 0. 02 and 0. 04. The corresponding lengths of the models were two feet, four feet and eight feet respectively. The scattering characteristics of all three were studied at X and K bands and the results are given in Reference 1. In the present study most of the work was carried out with the 0. 04 scale model at simulated frequencies of 388 Mc and 918 Mc. An explanation of the designations showing the amount and location of RAM used in the subsequent patterns is given in Figure 35. All positions along the duct walls are referred to in inches measured from the beginning of the outer duct wall, with points forward from the beginning of the duct taken 69 SECRET

z m 0 -z FIGURE 33

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SECRET THE UNIVERSITY OF 3477-1 -F MICHIGAN -4" -33" -2" Corresponds to Station 1211. 7 on NAA Drawing 259-900070 (2-26-59) -1" 0" -- Reference Line Inner Duct Walls Outer Duct Walls - 1" 2" 3" 4" 5" etc. Length of RAM strips used on models would - be increased by scale factor to obtain corresponding full scale length View of Duct System Showing Numbering Scheme for Location of RAM FIGURE 35 72 CFrPFT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F to be negative. A 1" strip on the 0. 04 model is equivalent to a 25" strip on the full-scale aircraft. 4.3. Results 4.3.1. Series A: Vertical Polarization, Dielectric RAM, 388 Me Fifteen patterns are presented in this group simulating results at 388 Me with vertical polarization. Patterns taken in the horizontal plane of the model are denoted by a climb angle of 0~. Other patterns are taken with the model at a climb angle of 10~ where the model is rotated about a vertical axis. Note that the plane of the observing radar intersects the plane of the model at an elevation angle of 10~, but that the observing radar is at exactly -10~ in elevation for the nose-on aspect only. Since the objective is to lower the nose-on cross section to 40 m2 or below, this level is shown on all patterns. A comparison between the Standard Pattern A-1 and Pattern A-2 indicates the level of achievement one could expect if all the energy that entered the ducts were absorbed or reflected in another direction. Here the peaks have dropped by 14 db with a reduction in average level of about 8 db within + 60~ from nose-on. The lobes at 65~ are due to the specular return from the sides of the foil "wedges" used to cover the duct apertures. Patterns A-3, A-4 and A-5 show that most,of the incident energy does not penetrate far into the ducts, and this agrees with ray tracing results reported by NAA. 73 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F From Patterns A-6 and A-7 it is seen that RAM is more effective when placed on the inner walls than it is on the outer. This was found to be true in other tests, and could have been predicted since the inner walls are favorably curved and are also more nearly in the direct view of an observing radar at angles 00 to 500 or so fromnose-on. Patterns A-10, A-11 andA-12 show that little is to be achieved by adding RAM to the top and bottom of the ducts, and this too was found in other measurements, both with horizontal polarization and at the 10~ climb angle. Pattern A-12, the standard pattern for 10 climb angle, shows little change as a result of the change in elevation angle. Patterns A-13 and A-14 show more favorable results at 10~ than for the corresponding condition at 0~ climb angle. This was consistently found throughout the tests. 74 SECRET

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THE UNIVERSITY OF MICHIGAN 3477-1 -F, I,, I 777, 1 1! I I i Ill I i I i i I I, F 7r 2 I I 7? I i - I.,, I. -r I, T II 1 I I i. I- -I -d I I I 1 i I I T I i I I: I LL i I 'll, -, i I ll' I I I I i'! i I 1 , li 4Pattern No. A-4 Model Rc -Model 8-70 (.04) Vertica -,Polarization V -Model Freq. 9700 Mc Y *Simu.lated Freq. 388 Mc Aspect Climb An~ le 0 Roll Angle 0 Type of Ram Used I Location of Ram 'Anj 4-RAM ACROSS D UCrS-. AT 2? INSIDE DUCTS Radar Cross Section a- Given at J- Simulated Frequency I I I HI I I i! i I i I I I Dtates About 31 Axis,, &berving IL7 __Radar gle of Climb 1 f I 1 1 iI I 4, -, -1 ''I i fill! I H H kil :111 MiI i . I-, I i I I -!J I -1 -, i v I'ml 2L) ' [I T-r-r" I I -I. I7 f I I I 1 I I I! Hi Ill-III 11, IK.~ iI I 1 1, i i i- 11 114 Ttl - L, -1 - I, -r 4,- - -,I -1 1 1 11 II 1 114t4i P q I lH11TW 11 I job I II!I ose Aspec;;.1 fAl N I I h I Al I Ill 1-w Li I i i L I I-'- I I laid j I 40 Ml Level!T-r ITT Tt I I l l I 1 1 1 1 1 J I l l 1 Ili k 1 ij 1 i I I 36 1,-7 -U[ j T- -JT72 7 fit c*p-r 1 21 u I 76

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SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F T7. Pattern No A -9 Model Rotates About. + 2__. b. - Model B-70 (.04) Vertical Axis _ —___ __ Polarization V 4 --- -4 — - - - Model Freq. 9700 Mc - Simulated Freq. 388 Mc - | Aspect -8- - - Climb Angle 0 - Observing - --- i — 8 -- -.8 Roll Angle 0~ Type of Ram Used 1 -.adar - - -t aI Location of Ram i Angle of Climb 10 - ___ Inside Duct Walls 0" To 6" - Outside Duct Walls 0" to 6.ll2. - ___Radar Cross Section a- Given at _Simulated Frequency -~0 B 40 M Leve3l + TT lu1 - i4tt.li.U-i-: '- Pattern No. A- 10 Model Rotates About -1n'- -L 1 - J - -IT I li | 1'21 | -- -- |Model B-70 (.04) Vertical Axis.Hj-' --- -— I - 4 — 4 --- ---- Mode'l Freq. 9700 Mc s |T" --- — | ^p4I -- Thit rt t t ~t;t Simulated Freq. 388 Mc; t-ITTtl I ti^t__ -^ -_.. Ape TT'^r Loct iot of Ram 'Angle of Climb T; 1 M O u iide D uct W4lls o ". ^ T o l o ^. 4. - [ - __ _ I-T Model B-71 0 (.04) Vertical Ax i -it 4 1 1 I' M Lod el Freq. 9700 S Mc - ' ' T -7 1 'Simulated Fflreq. 388 McClimb Angle Osr in ' Type of Rom Used i " 1 / -'- i i,; { I I nside Du ct Wall OP ll''i ToP t '1 I4 -1 t6, K 7 1. ~ I i 1 i r I I I ~ AN2GL 79 SECRET

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THE UNIVERSITY OF MICHIGAN 3477-1 -F I ~ I, I I -.. I Itesi AboutT Pattern No. A-/3 Model Rot, 2- Model 8-70 (.04) Vertical Polarization V 4- Model Freq. 9700 Mc ~ Simulated Freq. 388 Mc -6 Aspect Climb Angle 1QO 8Roll Angle 00 - Type of Ram Used 2. Locat ion of RamAnl Nose Aspect 40M' Level IAxis2 Observ ing ___Radar Feo Cimb I 16) 6 - - I 1 Al ii I - 1 1 ' L J l 81 RFCPFT

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SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 4. 3. 2. Series B: Horizontal Polarization, Dielectric RAM, 388 Mc This group of patterns differs from the A series in that the plane of the E vector is parallel to the plane of the model. Generally the radar cross section is smaller with this polarization due to the smaller contribution from the several vertical edges that are seen at the forward aspects. In Patterns B-1 and B-2 a considerable reduction in cross section is again evident when the ducts are covered with foil. Patterns B-3 and B-4 show that a reduction over a wide range of forward angles cannot be achieved by working well within the ducts; this is consistent with results for vertical polarization. Patterns B-6 through B-9 show that RAM along the inner duct wall is effective for this polarization and frequency, and that little improvement is to be gained by adding RAM to the other side wall or to the top and bottom, but that RAM on the top and bottom alone is not effective. The increased effectiveness of RAM on the vertical walls, as distinguished from RAM on the top and bottomis believed to be due to (1) the curvature of the vertical walls and (2) the ratio of height to width. This ratio is more than 3 to 1 at the narrowest point, so that the area of RAM necessary to cover the side walls is much greater than that required to cover top and bottom. In addition, the field will be stronger in the narrower direction than in the wider direction. 83 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F In Patterns B-10 through B-12, the effect of moving a 6" strip of absorber progressively farther back on the inner wall is seen. The reduction in cross section is good when the strip starts 1" or 2" inside, but Pattern B-12 shows that little reduction is achieved with RAM 3" inside the ducts. In fact, other measurements (the patterns are not included here) showed that the decreased effectiveness was quite evident when the RAM started 2.5" inside the duct. For Patterns B-13 and B-14, RAM with poor reflectivity was used. Type 4 was used in B-13. This is a good absorber for K band but at the X band frequency used, the reflectivity was measured as about -3 db. The type 6 material used in Pattern B-14 has a reflectivity of -6 db (see Table 11 for more information on the materials). These patterns show very effective cross section reduction, but it should not be concluded that a poor RAM will be sufficient for all conditions. This question is discussed further at the end of Section 4. 84 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F Pattern No. B-I M Model B-70 (.04) Polarization H Model Freq. 9700 Mc Simulated Freq. 388 Mc Aspect Climb Angle 0~ Roll Angle 0~ No Ram T 1 ^-4 7 i i I - 1 1 1 741. I" I w; llw ~.!^ HII 1 7^ T " '' Pottern No. B-2 Model Rotates About Model 6-70 (.04) Vertical Axis 1 — Polarization N 1 Model Freq. 9700 Mc - * Simulated Freq. 388 Mc I - Aspect - j Climb Angle 0 Roll Angle 0e _@erving t No Rom R d r T-R I Angle of Climb DUCT APERTURES COVERED I/TH METAL FOIL Radar Cross Section a, Given at Simulated Frequency i Ti' I i jtrr ~t7 — - I- I -! i~ ii 4 I- - I iI iI I I I] 77 I. -1 -1 H4 I . -1 -1- - L-41L I; -Iii mI t, -I; I, - I : -1- : I;1 - I i- 1 II i I —,,I I I fl -,L, I. I r — - -r.........O Fl H 4 5 -7 4 W I i i ir i I.... I I I I. - - 1 - - I li L 1.I 1t I K t — i rT iI1 I 11 41T! 1.! 11111 1'' 1! 1..i......i I[ 'I 1 il I l il llll iil I 1 I 1! on i; r 1T7 — t I 'i i i I mli tt tff t -- TT 1 i i 4- 4 m Level ~C t j Nose A 11J 1 41 IfflTT-~ 7TT ninr n 'iii~ t~~~ 1Lc9 —1WA1LL6Um m L -------- MUM.&'~ ifR~H I: I i i 85 SECRET

THE UNIVERSITY OF MICHIGAN 3477-1 -F n ... I! I I 1, I I I I 1 I I I I U I I I, r: I I I i I -p-4 V pf~ tiV J1 -i 1111-1 -1 - 4 -1 1 12'-,'I4r I I I -— t- L,j I r I. 8 j it- - - ii I i. -1 I j z iI71 1 I I I I j,i-, I j. I I f - i... I i I --- 4-,' 11 -- - i. i i f, I - I K I!.-I i I I 1 t I I if.. I - I Patten No.Model Rotates About ModelI 8-70 (.04) Vertical Axis PolarizationH Model Freq. 9700 Mc Simulated Freq. 388 McV ~Aspect - Climb Angle 00 bevn Roll Angle 0 RdrType of Ram Used I Location of Ram Ageo lm RAMU A C R05S DVUC TL - A Ti WIN~DE DU1C TJ I i I I - 1 J, I I i.: - 1 1 LI I- 1 I;I 1 I T, I [I t - 11111 - I I I i i I I -1 - 11 I I I I I I I i i I -'T -1. J I I I! i I I -1 -Ll I i I I, - — t II! - I 1 -F 1 ! III III I i. I 11 I I Ti -rQ777rr Radar Cross Section a- Given at Simulated Frequency It I I II i F, 1 I I I I I I I 1, I Ii i i I I I, i, I I- I II I I I I I I; 1 I 1 'I I I ti-j I -, P.- 114 41 Fril i~lk 7171 i I I I I i I I I I I I I I I I .j T! H t t1-1 TIT I I I T Nose Aspect Ld 1 L i Mt 40 Level I I"I 1-1 t It fall Th 4, 1 fall illi 11 -4 -1.1 J.' I o I + i6 72 66 40. AN 86

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F Pattern No B-5 Model Rotates Model B-70 (.04) Vertical Axis Polarization H Model Freq 9700 Mc 'Simulated Freq. 388 Mc Aspect Climb Angle 0~ 0 Roll Angle 00~ Type of Ram Used _ Location of Ram Angle of "RAM ACROSS DUCT APERTURES3 Radar Cross Section a Given at Simulated Frequency 87 SECRET

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SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 4.3.3. Series C: Vertical Polarization, Magnetic RAM, 388 Me This group is comparable to the A group in that the frequency (X band) and the polarization (vertical) are the same. In group A, however, the RAM was a well-matched commercial absorber with dielectric loss, but in the Series C patterns an absorber of type 5 with magnetic loss was employed and, in addition, no effort was made to achieve a good match. The intent was to have a magnetic absorber with nominal loss that might more nearly match the properties of a ferrite RAM on the full-scale aircraft. The measured reflectivity at the X-band frequency was -4 db. In this series, a particular effort was made to check the effectiveness of the three locations for RAM inserts which were most acceptable to NAA on the basis of aerodynamic considerations. The station numbers for these locations in order of preference are given below, with the approximate dimensions in inches appropriate to the 0.04 model (see Figure 35 for an explanation of the notation). For the outer wall a 4", rather than a 3.75", piece was used for the second and third NAA locations. Location Station Numbers Position on.04 Model Inner Wall Outer Wall Inner Wall Outer Wall 1 none 1275 to 1325 none 2.5" to4.5" 2 none 1230 to 1325 none.75" to 4.5" 3 1276 to 1321 1230 to 1325 2.5" to 4.5".75" to 4.5" 92 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F Patterns C-l, C-2 and C-3 show results for the three NAA locations described above. It is seen that little benefit is obtained from the 2. 5" to 4.5" location on the outer wall; that.75" to 4. 75'" is better, and that the addition of a strip on the inner wall 2.5" back was not very effective. Pattern C-4 shows the importance of having RAM on the first 2" of the inner duct wall. This fact was demonstrated many times. In Patterns C-5 through C-10 RAM is used from.75" to 4. 75" on the outer wall, and the effectiveness of adding RAM on the inner duct wall, forward to the duct aperture as well as inside the duct, is shown. As may be seen, there are several combinations that lower the cross section to 40 m2. A 2" strip is sufficient if properly located as shown in Pattern C-7. In Patterns C-ll to C-13 the 10~ climb angle is studied. It is again demonstrated that it is easier to achieve the desired 40 m2 level at a 100 climb angle than at the 0~ elevation aspect. The RAM locations used in these three patterns are the three NAA preferred locations. 93 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F Pattern No. C-/ Model Rotc Model 8-70 (.04) Vertical Polarization V - Model Freq. 9700 Mc - Simulated Freq. 388 Mc Aspect Climb Angle 00 Roll Angle 00 Type of Ram Used 5 Location of Ram Angle Inside Duct Walls None Outside Duct Walls Z4 to 4f Radar Cross Section a Given at Simulated Frequency eference Pattern With — -- Additions See No A-l. Pattern No. C-2 Model Rotates About Model B-70 (.04) Vertical Axis Polarization V Model Freq. 9700 Mc ' Simulated Freq. 388 Mc 1 Aspect Climb Angle 00 Observing Roll Angle O0 Type of Ram Used 5 Radar Location of Ram 'Angle of Climb Inside Duct Walls None Outside Duct Walls to 4t Radar Cross Section a Given at Simulated Frequency -- I l - I $l i l l I i!l l I 94 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 95 CC: DIT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F Pattern No. C-5 Model Rotates About Model B-70 (.04) Vertical Axis Polarization V Model Freq. 9700 Mc +. Simulated Freq. 388 Mc Aspect Climb Angle 0~ -O Roll Anglp 0~ Observing Type of Ram Used 5 Radar Location of Ram Angle of Climb Inside Duct Walls -i"to I" o,^ tL" ta q'i" Outside Duct Walls 3/4" 't 0' Radar Cross Section a- Given at Simulated Frequency.' Pattern No. C-6 Model Rotates About -2- Model B-70 (.04) Vertical Axis - Polarization V -- - -4- Model Freq. 9700 Mc — 4... Simulated Freq. 388 Mc i - - Aspect -6 - Climb Angle Observing Roll Angle 0~ Radar Type of Ram Used 5 - Location of Ram ' 'Angle of Climb "km '__, -. - Inside Duct Walls -3 a r- o/',, az or,.... 11 111 - Outside Duct Walls - to 4 n "l -; / _ ____]1- - Radar Cross Section or Given at - 0p4 -'. 1 1 - A.0 ~ Simulated Frequency | - - "^ r-n - - - - Nose Aspect — -- - -- T - -:40 M Level 96 SECRET

THE UNIVERSITY OF MICHIGAN 3477-1 -F I - I i... -I L (I rl il -02 -2 -4 8 - 1 j I., -I l I.11. A Pattern No. C-7 Model Rot( -ModelI B -7 0 (.04) Verti cal Polarization V Model Freq. 9700 Mc Y Simulated Freq. 388 Mc -Aspect - Climb Angle Q Roll Angle 00 Type of Ram Used 5 Location of Ram Ag Inside Duct Walls 0' to, 2"f Outside Duct Walls 31 to 4 As 4 4 Radar Cross Section a1 Giveni at Simulated Frequency I — I I I1 ~ rates About - 5:~&Obervingle of Climb - 2 -6-4 - 8 1 -10 — 2 -4 -8 -- I I 2 i m i i i i i i i i i i i i Il. t a - ~. ] I..1 - II ti U I I I I I I I I 11 — tlLu i i I t i i i i i i K i i 1 1 l 44 - -11 'I iI-t -~ 1 II Tir TIT It. __Nose Aspect - - 40 M' L evel - _ I IV - 2 — -4 - -- - 4 - 8 8 Pattern No. C-8B Model Rotates About - -- - -2 - Model B-7& (.04) Vertical Axis____ vvv I'Polarization V 4- - Model Freq. 9700 Mc 9- - - 4 — Simulated Freq. 388 Mc Cloaiob ngolae'nl o lm Routsid ge Dc al.t Simulatedo Frequenc _ _ d0.-'.L4-b1_ O -tsidt 4uct Walls IIto 4__ -iT7 A -ANose Aspect 4 M2 Level - oil I__ _6 ~, 11 1~ 3 1A 97 fCPrPIT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 98 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F...... Pattern No C-ll Model Rotates About - -2-~ -- - -- Model B-70 (.04) Vertical Axis _ Polorization V ----- - -- - t Model Freq. 9700 Mc -- 6 _ Simulated Freq. 388 Mc Aspect -- 8;, Climb Angle 100 — Roll Angle 00 Observing --- Roll Angle 0o I1 -; Type of Ram Used 5 dr Location of Ram 'Angle of Climb -_ - - ____ Inside Duct Walls None Outside Duct Walls Z t"'f" - -- t - J l ' Radar Cross Section a Given at r j Simulated Frequency For Reference Pattern With I __ _- A No Additions See No A- IZ....i. I Nose Aspect i 99 SECRET

SEC RET THE UNIVERSITY OF 3477-1 -F MICHIGAN t t 100 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 4.3.4. Series D: Horizontal Polarization, Magnetic RAM, 388 Me Most of the discussion that proceeds the C series applies here except that horizontal polarization is now used. The polarization and the frequency are the same as in series B. The RAM is of type 5 (magnetic loss) and has a reflectivity of -4 db. This series shows that it is much easier to achieve the 40 m objective with horizontal polarization than with vertical polarization. In Patterns D-1 to D-3 and D-5 to D-7 results are shown for the three NAA preferred locations with 0~ and 10~ climb. The 40 m2 objective is obtained for both the second and third location at both climb angles. Pattern D-4 is shown as a standard pattern with no RAM for the 10~ climb angle. 101 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F Pattern No D -/ Model Rotates About Model B-70 (.04) Vertical Axis Polarization H Model Freq 9700 Mc:Simulated Freq. 388 Mc Aspect Climb Angle 00 O bserving Roll Angle 0~0 Type of Ram Used 5 Radar Location of Ram iAngle of Climb Inside Duct Walls None Outside Duct Walls 2Yz" t, 4YAY _Radar Cross Section a Given at Simulated Frequency -For Reference Pattern With — No Additions See No B-i Nose Aspect 102 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F EL 103 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F Pattern No C - 5 Model Rotates About *Model B-70 (.04) Vertical Axis Polarization H - Model Freq. 9700 Mc; Simulated Freq. 388 Mc Aspect Climb Angle 10~ - Roll Angle 0~ - bservin Type of Rom Used S j Radar Location of Ram Angle of Climb Inside Duct Walls None Outside Duct Walls 2Ya" to 4 " Radar Cross Section ao Given at Simulated Frequency -72I' A 104 SECRET

SECRET THE UNIVERSITY 3477-1-F OF MICHIGAN 105 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 4. 3. 5 Series E: Dielectric RAM, 918 Me In the next three groups (E, F and G), results for the K band model measurements are shown. The model frequency was 22. 96 KMc corresponding to a simulated frequency of 918 Me. The Series E measurements were made with both vertical and horizontal polarization using the Emerson and Cuming dielectric absorber. Patterns E-1 through E-6 show results for verticalpolarization at 0~ climb. Pattern E-2 shows that the 40 m2 level is not obtained with good RAM at the third preferred NAA location, but succeeding patterns show that this level can be reached by adding more RAM on the inner wall. Pattern E-6 is presented to show the significant contribution which comes from the vertical edges that form the beginning of the outer duct wall and from the wedge that forms the beginning of the inner duct walls. A comparison with E-5 shows that an average reduction of about 2 db is obtained when the vertical edges are broken by the addition of a metallic, serrated edge. The serrations are of the order of a wavelength in depth. Patterns E-7 through E-9 are for the 10~ climb angle with vertical polarization. These patterns show that the cross section level is 2 or 3 db lower than for similar conditions at 0~ and indicate that any acceptable choice of RAM for the 00 climb angle will be quite satisfactory for the 100 climb angle. 106 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F Patterns E-10 through E-13 are for horizontal polarization. Patterns E-10 and E-12 show that this RAM at the third preferred NAA location is hardly sufficient at 0~, but is quite adequate for 10 climb. Patterns E-11 and E-13 show that a 4" strip of RAM on the inner wall centered at the point where the duct starts, plus the usual strip on the outer wall, is more than adequate for both climb angles. 107 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 1 l I-77.. 'If i,II, 108 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F Pattern No E-3 Model Model B-70 (.04) Ver Polarization V Model Freq 22.96 KMc Simulated Freq. 918 Mc Aspect Climb Angle 0~ Roll Angle 0~ Type of Ram Used Location of Ram Inside Duct Walls NONE Outside Duct Walls 0"ir-6 Radar Cross Section a Given Simulated Frequency 1 [ t t t 109 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F Pattern No E-5 Model Rotates About Model B-70 (.04) Vertical Axis Polarization V Model Freq 22.96 KMc 'y Simulated Freq. 918 Mc Aspect Climb Angle 00 Observng Roll Angle 0~ Observing Type of Ram Used Radr Location of Ram Angle of Climb Inside Duct Walls -2 *2" Outside Duct Walls 3/" t3 4 4" Radar Cross Section ro Given at Simulated Frequency I l TV k- I -1- 1 110 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F I Pattern No E-7 M --- Model B-70 (.04) Polarization V -- Model Freq 22.96 KMc I Simulated Freq. 918 Mc - Aspect - Climb Angle 10~ 'Roll Angle 0~ I 111 SFCRFT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F Pattern No E-? Model Rotates About Model B-70 (.04) Vertical Axis Polarization V Model Freq. 22.96 KMc 9 i Simulated Freq. 918 Mc Aspect Climb Angle 10~ Oe Roll Angle 0~ erving Type of Rom Used Rad Location of Ram Angle of Climb Inside Duct Walls -2"+t-2" Outside Duct Walls %4tr^% i Radar Cross Section a Given at Simulated Frequency Pattern No. E-/o Model Rotates About Model B-70 (.04) Vertical Axis Polarization H Model Freq. 22.96 KMc 9 Simulated Freq. 918 Mc Aspect ollimb Angle 0~ d Observing Roll Angle 00 Type of Ram Used ~ '" Radar Location of Ram Angle of Climb Inside Duct Walls Z'1b1'3 Outside Duct WalIs"~tr 'Is Radar Cross Section a Given at Simulated Frequency I I: li f! I I! I II1 H IM I I i i Ii l ~ l t t 112 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 113 qFCPFT

SECRET THE UNIVERSITY OF 3477-1 -F MICHIGAN 1 liii 1<. I i I I I r I-i! I KiI 11, i 1 i l' i I ', I I i-l-Liti i I - , - 4,; I,t- - 4 i ii I — 111-4 -+-T -l I -I- L il l if It HIH I i I I i F4 14 H I V It..................... -A -F Pattern No. E-/3 Model Model 8-70 (.04) e Polarization H Model Freq. 22.96 KMc Simulated Freq. 918 Mc Aspect Type of Ram Used Location of Ram Inside Duct Walls -4*r.Z Outside Duct Wallsjq%6' *f Radar Cross Section a- Given Simulated Frequency I F I IF I I I IRotates* About -- wtical Axis I ofClmb l II II ILIIiIiI I11 F 1 i 1,, I! I I , - I. - J-,; I I I 1! i I I I I - I I i I — ] 1, I] Ti I-1 i I -d -H.LI 2 I F i I i I I i I i I i -- - I — -, i I I Britoil I i 4-1 i i I I at I4 I I i I I L I I i I — Th a-8 - HFF F HF F F; i F F F F 1F F ~ i F1! Fk Fi 4 I i i I 4 —l -- 14, I -: 1 rl, 4 -1 irl I 1. -, 1`14,4 11-'U'V witli I I i I i I I lvlffl F 11FF 11. F1 I i FF! I F I1~ II 1 F f~ FI 114 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 4.3.6. Series F: Vertical Polarization, Magnetic RAM, 918 Me This is a continuation of the E series with the chief difference that a magnetic RAM was used in all patterns except F-17. For Patterns F-1 through F-14, the reflectivity of the RAM was -9 db. In Patterns F-15 and F-16 a magnetic RAM with a reflectivity of -4 db was used, while in Pattern F-17 a dielectric RAM with a reflectivity of -20 db was employed. All patterns are for vertical polarization. Patterns F-l, F-2 and F-3 are for the three NAA locations, and it is obvious that more RAM (or a better RAM) is required. With RAM from 0" to 4" on the outer wall the general level is well down except for a large return near nose-on. In the interest of locating the source of this return, RAM was placed across the ducts (but well inside), and the resulting Pattern F-5 shows that the original return near nose-on return was due to energy entering and being reradiated from the ducts. In Patterns F-6 through F-ll, additional RAM was added as shown on the patterns in order to find the most effective method for reducing the cross section to 40 m2. With RAM as shown in F-10, the results obtained are almost acceptable. It is doubtful if more can be achieved by additional RAM, although better RAM would, of course, give some improvement. As shown in Pattern F-9 and F-ll, the return can be decreased considerably by minimizing the effect of the contribution from the vertical edges. 115 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F In Patterns F-12, F-13 and F-14 results are given for the three preferred NAA locations with the 100 climb angle. The average return in F-14 is below 40 m2. With the use of RAM similar to that required for the 0~ climb angle (as in Pattern F-10), the return at the 10~ climb angle would be well below 40 m2. In order to relate the radar scattering pattern to the quality of the RAM, three more patterns are presented. Pattern F-15 used a magnetic RAM (made in the laboratory) with a measured reflectivity of -4 db. It was presumed that the amount of cross section reduction achieved would be inferior to that obtained with a -9 db material. A comparison of F-15 with F-3 shows that there is, in fact, very little difference. The RAM locations for these two patterns are the same as in Pattern E-2, where the -20 db dielectric absorber was used. E-2 is seen to be better than both F-3 and F-15. In Patterns F-16 and F-17 this study is continued. In these two patterns the RAM locations are the same as in F-6. The RAM used is as follows: Pattern Type Reflectivity F-6 5 -9 db F-16 7 -4 db F-17 4 -20 db There is little difference between Patterns F-6 and F-16, but Pattern F-17 shows definite improvement over the other two patterns. The amount of the improvement averages about 2 or 3 db. 116 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F Pattern No. -2 Model Rotates About Model B-70 (.04) Vertical Axis Polarization V Model Freq. 22.96 KMc 9 Simulated Freq. 918 Mc s Aspect Climb Angle 0. i Obsrvin Roll Angle 0* Type of Ram Used or Location of Ram Anglo of Climb Inside Duct Walls NOME Outside Duct Walls *r' 44" Radar Cross Section ar Given at 117 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F Pattern No F-3 Model Rotates About Model B-70 (.04) Vertical Axis Polarization V Model Freq 22.96 KMc A Simulated Freq. 918 Mc Aspect Climb Angle 0~ Roll Angle 0~0 r Type of Ram Used 5 Location of Ram 'Angle of Climb Inside Duct Walls 2 "tr4" Outside Duct Walls 34"*IY 4" Radar Cross Section cr Given at Simulated Frequency 118 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 119 SECRET

THE UNIVERSITY OF MICHIGAN 3477-1 -F <TV 4 6 Ii 8 ii JF I 2 ILi -6 I-8 i I I I I r-" T - I I i — i I - I-'! -L i i i I i i II 1 1 I ilk T I iI iii -iII Patitern o.F-7 Model Roe Model 83-70 (.04) Vertica Pqlarization V Model Freq. 22.96 KMc Simulated Freq. 918 Mc LIAspect ~ Climb Angle QO1 Roll Angle 0~ Type of Ram Used 5 ~~ Location of Ram An Inside Duct Walls 0Or '5" Outside Duct WallIs 0IV#X" Radar Cross Section a, Given at Simulated Frequency IIlW l~ l 1 1 l 'I I 4 1 1 1 )tates About 7 _ -77 il AxisI I ~#~~rviI i__ _ _Radar gle of Climb - 1 1 I! I I; I-, I I I f 1-14,1 I -r - I 11 I - i I. - L i 1 II 71, -I, ` II- I I I- iI I II I- i -i 14 I21 4HI a I I I I - I -I 'i i 1-1 4 iltI TI 41' T-1 I I I I I HHHHHHHHHHHHP i +++ H+H HHHHHH, i i l I I I I I I IMITH I i I I 1 1ii ii I "- 1 1 1 1 1 1 1 1 1 i 1 1 1 1 4-4 44-4 i 1 i 1 1 i U -4-4 -T T77111771 F. TT i - I I L I II1 —.L-. -1 I I., I. -. I I. I i i i i i i i i i i i i i i i i i i I i i i i i i i i i:! i i i ! i! i 0 i! i i i i i , i -T H H — FH-I+H++1_ -,4k. + I IK+ I-ll I <6'nj I '44M Lve 2IL'I IT72 F ii 120

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F Pattern No F- 9 Model Rototes About Model B-70 (.04) Vertical Axis Polarization V Model Freq. 22.96 KMc - Simulated Freq. 918 Mc I Aspect Climb Angle 00 Roll Angle 0~0 Observing Type of Ram Used 5 Radar Location of Ram Angle of Climb Inside Duct Walls -2" -,2" Outside Duct Walls 0or 6 Radar Cross Section a Given at Simulated Frequency Metal Foil With 4 Notches About One Wavelength Deep Are Attached To The Three Vertical T Leading Edges That Form The Ducts. l -— IT. 121 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 122 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F Pattern No. F-/3 Model Rotates About Model B-70 (.04) Vertical Axis Polarization V Model Freq. 22.96 KMc - Simulated Freq. 918 Mc Aspect Climb Angle /0~ Roll Angle 00 bserving Type of Ram Used 5 d Rdar Location of Ram IAngle of Climb Inside Duct Walls NONE Outside Duct Wolls 4("to 4 Radar Cross Section Xa Given at Simulated Frequency IiJllilil jjilI- il t 123 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F. 124 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 125 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 4. 3. 7. Series G: Horizontal Polarization, Magnetic RAM, 918 Me This series is a continuation of the 918 Me study started in the E group. The polarization is horizontal and the RAM is the magnetic material with a reflectivity of -9 db. Patterns G-2 through G-7 show results for 0~ climb; first, for the three NAA preferred locations, and then for additional RAM on the inner duct wall. The last two patterns show the average level to be well below 40 m. Patterns G-8 through G-14 show the results for the same conditions as above, but at 10~ climb angle. The average level of the cross section for the RAM locations in the last three patterns is well below 40 m2. 126 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F t 127 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477 1 —F 1 128 SECRET

SECRET THE UNIVERSITY 3477-1-F OF MICHIGAN - r -I 129 qFCRFT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F I 130 SECRET

THE UNIVERSITY OF MICHIGAN 3477-1 -F — F - I., I III Io -.1-I.I.., KI'K1-Pattern No.Gf Model Rotates About II 2Model B-70 (.04) Vertical Axis 1j~I1 T~, H Polarization I 'H ~Model Freq. 22.96 KMc ' 'H ~ Simulated Freq. 918 Mc I Aspect I rIt Climb Angle 100 I6inag Roll Angle 00 1~Type of Rom Used I TI I d Location of Rom Anl fCib i lI Inside Duct Walls None, IJI I I I ~~Outside Dct Wal.4s i~i Radar Cross Section a, Given at' Simulated Frequency 41 Ht I I IIII! It~ V FL I I fif 11111,11t, 11 -H 1 R - L I I -1- I -[I -ji L [1- I - [ 4, -1-11 t I -, I 1 till II I IT I, 1 1 I 1 1!TI it I'll. I...........,- WIllilllijll 4 - Tl-J __4 i ljj I, I li Iraqi M-f il II. I - 11 '-Hi' 1... I.. = A i i a i i i I,,, I I I, - I -. I. - I I kiti 1111MI-Hr fl-l- -1 H' fl`ff 11141, 'tll i-d-Ifi lhb itHil [ I I I I I I I; I 1 1 II, 1 11=1, 0 1 A 1-1 I 1 1 1 1;; 1 1! i 1! i i 1 1 1 1 i 1 1 i 1 1 1 1 1 1 R 1 1 1 1 r 1 1 1 1 1 i 1 1 1 i 1 1 j 1 1 i 1 . I - -1. - --.. -. - -- . I i I i I I I l 1, 1-WfiA.-I1.-. I I i — H 1-1-fit, I I - -11-' fi-H-l lifflil-d- -A4111111 -1 it- I 1414 H, I I I i I 11- it 14, tit lfillii Ir i I I 1 1, , 717T17]~i~fTUt'tfi~hh~if~ththft ose Aspect - !I 1 1 1 1! 1 1 I'M I Ig I, I MI ml ml! lammms-ig i I i; i i i; i I i i i i i i i 6 it i;.m HI i i i i i V i mi Hi in i 40 M"Leve ioK1TLITI . i..., I. M,, rp, i Fvff=3w lp I I I TM -vrqr ----- 131

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F - - - - Pattern No G-/l Model Rotates About Model B-70 (.04) Vertical Axis Polarization H - - Model Freq 22.96 KMc '<Simulated Freq. 918 Mc Aspect Climb Angle 100 o - Observing Roll Angle 00~ *-O earv Type of Ram Used Location of Ram Angle of Climb Inside Duct Walls Z" 1o 4Ya" Outside Duct Walls " +t' 4'^4 Radar Cross Section a Given at Simulated Freauencv T- |l - Nose Aspect;! 1; t —40 M2 Le"el 4I ii ' rlin ' ~ I IlT ~ ii i - tiii iI- 0 -Wii i WNOR 132 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F ~ —i — L,-2 --- I j!I I;.,.,t-4,-- ---- — r6 -I Ii i I 1st_ _ i T ~ T- - I [ I 4- 1-, 4 + Pattern No C -/3 Model Rotates About Model B-70 (.04) Vertical Axis t! Polarization H Model Freq. 22.96 KMc 9 -I Simulated Freq. 918 Mc J Aspect I +- Climb Angle 10~ s - Roll Angle 0~ 0bservin I Type of Ram Used S. Radar T Location of Ram Angle of Climb, Inside Duct Walls o" to 2. Outside Duct Walls 4/4" to 4/4 ' Radar Cross Section a Given at I Simulated Frequency I l[- l t l! Jl ]! l l! il l I I II! l i jW 1 1 1 l! l l' I! I. i 4 -6 - i I I I I I 4 - it -i +f I I I I I I I I I I I i i I I I I i I I i I i I i I ! I i I I I I I I I i I, I i I i i - - - — ] I + 4H __r. -. I,, I-r-, i I 1 i I - - 01 i i 1 1 i I I I I i - I I I I, I - f i I 1 1 i i i [ l i i i I I I i i, I T - l l i - I - 1 1 i l - i l i - Jr- 4I-4 I ii H 7I I I I I' _i I I 1 i —1 r 40Mt LeIt if., T Pattern No G -4 Model Rotates About;I IJ-+ 4-V4 Model B-70 (.04) Vertical Axis -2 TI - - 4H Polarization H - 4T Model Freq 22.96 KMc 9 - - Simulated Freq. 918 Mc 1 6o eAspect II Climb Angle 0~ 4 IrType of Ram Used S - _ Radar T 1lt Location of Ram Atngle of Climb Inside Duct Wa I lls t- "T Hti+,, T Duct Walls 4 IMod1 l -No es A A e Radar Cross Section H - Given at Simulated Freqe 918 Mc _4 Asec 'o 4~~~~0 MtL v l. ------- 133 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 4. 3. 8. Series H: Effect of Increased Climb Angle, 459 Me This group of patterns is presented for the sole purpose of showing the behavior at climb angles of 100, 200 and 30. When using the 8 foot model (0. 04 scale) it was not feasible to work at climb angles of more than 10~, and consequently, for this series, the 4 foot model (0. 02 scale) was used. The measurements were made with vertical polarization at a simulated frequency of 459 Mc. Four standard patterns with no RAM are shown for climb angles of 00, 10, 20~ and 30~. The asymmetry in the lobes at +- 16~ (see Pattern H-1) was attributed to asymmetry in the ducts of the 2 foot model, and was verified by measurements made with the model inverted and by measuring the ducts only, both upright and inverted. An inspection of the model revealed a slight difference in the duct widths near the narrowest point. Patterns H-2, H-4, H-6 and H-8 show results with RAM on both the duct walls from 0" to 2" (corresponding, of course, to 100" strips on the fullscale aircraft). The RAM used was the resonant dielectric absorber manufactured by McMillan Laboratories (type 3). Judging from this series of patterns and the several patterns on the 0. 04 model at 10~, a cross section reduction to 40 m2 for level flight will result in a similar or better reduction at climb angles up to 30 at least. 134 SECRET

THE UNIVERSITY OF 3477-1 -F MICHIGAN 135

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F Pattern No. H- 3 N Model B-70 (.02) Polarization V Model Freq. 22.96 KMc Simulated Freq. 459 Mc Aspect Climb Angle 100 Roll Angle 00 I 136 SECRET

THE UNIVERSITY OF MICHIGAN 3477-1 -F II 4' 22.2 I I 1 -.1.' 2222 4 4' iv Pattern No. H- 5 Model B-70 (.02) Polarization V Model Freq. 22.96 KMV~ Simulated Freq. 459 M( Aspect Climb Angle P-00 Roll Angle QO Model Rotates About Vertical Axis I ---Oibserving Radar Anl fClimb i. I; I I I.; I - 1 I I i; i i I 1 1 i b .. i: i I! i i 1 " 1 1 I I i I I I I i 12 4 No Ram Radar Cross Section o Given at Simulated Frequency. I I j I I I;, I I 1 1 i I I I 1 1 1 I j I I 1 1 I I ! 1 1 I 1 1 I 1 1 I 1 1! 1 1 I 1 1 1 1 1! 1 1 1! 1 I 1 I ! 1 1 1 !,! m 1 1 1! 1 m I 1! 1 1 1 1 1 1 1 i I I I i I I! - I " I I 1 L I 1 4 --it I 1 i i 1- i!l ] J-U 11 I i TT 'IT V! 1117 T1 -F Ii 4 -4 IF '4 Nose Aspect T [4 t I M I I I i1 1 1. IiA lli I I I vF ITJ 2 [ L k -.- +," I I I I I I i 1111 M " Level - - 6 i t L i I 11 i 11 - -1 i I ' 4: j I rt L I.4!I,, II. 11 I i I i. I i I' .! I -I -, 4 olit t. I 1, I, 410 I -1(.1 kI + I -e I! i -IT li, -f - LL Ij I I'mmill Lti II III FM III, I III III III III I Hill I E III I III I ~ 4,,,i 1 E iI 5 L 4 U t I.....1 - d I-I.. 137 SqFCRFT

SECRET THE UNIVERSITY 3477-1-F OF MICHIGAN.1 IT * I I i I I I J! T Pattern No. H- 8 Model B-70 (.02) iPolorization V i Model Freq. 22.96 KMc _ Simulated Freq. 459 M, Aspect Climb Angle 30~ 7I Roll Angle 0~ Model Rototes About i Vertical Axis Ic:I, Observing i p, Radar r -i T: i iiL I I i. 1 I 1 I ' rr<, t IiAn t Type of Ram Used 3 Location of Ram t Inside Duct Walls 0' to 2" + Outside Duct Walls 0" to 2" Radar Cross Section a Given at Simulated Frequency li!liit l lll ll! ll llllI I1lllII II gle of Climb * -T I i: I r4.. II I I 1:! l I I i I I!i I I I i I I I i fi ' I i I I i i *1 i m l If4 I{+fK i +1-H Cth 1 H-+ HT, +W 4Ft ~~~~~~~~~~~i- r; j 3X H+:1 1 1 I I I: il eH- I i.ItfW0-llf~~~f r rrT T~~rrT~ T I '1T-' t T:TT1 T 1 ti Ii r ~, F |i I i! '.~: f:IE 40 M' Level +L I-i-1 I1III II R MI II I j i2 I 138 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 4. 3. 9. Series I: Effect of Inclined Duct Walls, 388 Me The four patterns in this series were made to check the effect of tilting the inside surfaces of the duct walls. Mr. D. Levine of NAA reported that ray tracing studies in their group indicated that a significant (10 to 15 db) reduction in cross section could be achieved if the inside duct walls were inclined at an angle of 2~ or 3~ to the vertical, resulting in a duct whose cross section is not rectangular. It was suggested that this reduction in the radar cross section is due to the scattering of much of the energy in directions other than backscattering. No absorbing material is, of course, involved. A brief analysis of this idea was made at the Radiation Laboratory and indicated that for certain aspects a small reduction might occur, but that it would be much less than 10 db and that the range of aspects over which the reduction occurred could be relatively small. An experimental investigation of this question was made. To simulate the tilting of the ducts, wood wedges which had been metalized were inserted along the two vertical walls of each duct. These simulated a 2 tilt in the duct walls. The wedges on the outer walls extended 8 inches into the ducts, while those on the inner walls extended 3. 5 inches into the ducts (the curved inner walls made it more difficult to use a long wedge there). The effect of the 2~ wall tilt is shown in Patterns I-1 through 1-4. In each of the 4 patterns, the wall condition remains the same. The first two 139 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F patterns are for climb angles of 0~ and 10~ with vertical polarization. The second two are for 0 and 10 with horizontal polarization. An examination of the results shows a modest reduction of 2 or 3 db in some of the lobes (see I-1 for example). In other cases, the lobes are more narrow with little change in level. Pattern I-3 shows a 3 or 4 db increase in the first two lobes near 0~. From theoretical considerations and from these measurements, it is concluded that this approach will not provide the desired reduction in cross section. 140 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F t I 141 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 142 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 4.4 Summary of Experimental Results Over 100 patterns have been included to show the results of the experimental study. For the simulated frequencies covered (patterns not included give data at 230 Me) measurements show that the radar cross section of the models can be reduced to what would correspond to an average of 40 m2 or less by the use of RAM, at least in the laboratory. It is believed that reduction to this level is also possible and feasible on the full-scale plane. The amount of RAM required to achieve the desired results varied considerably with the test conditions. For example, more RAM is required for vertical than for horizontal position; more RAM is required for 900 Me than for 400 Me; and more RAM is required for 0~ climb angle than for the 10~. There is little or no question about the most effective locations for the RAM, assuming, of course, that the duct apertures are to be left open. These locations proved to be on the inner and outer duct walls at or near the beginning of the duct. To reduce the radar cross section to 40 m2 for the more difficult condition, RAM was used as follows: on the outer duct walls 0 to 5", and on the inner walls from -2" to 4". (0 to 6" was actually used on the outer wall, but a 5" strip would probably be equally effective.) These locations are explained in Figure 35, and correspond on the full-scale aircraft to 125" linings on the outer walls starting at the beginning of the duct and 150(' linings on the inner duct walls starting 50" before the beginning of the duct aperture. The resulting surface area of RAM is approximately 128 square feet per duct, making a total of 256 square feet for the 143 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F whole aircraft. The above tests were made with the -9 db RAM, and it is doubtful if one can be sure of having a RAM better than this at all the radar frequencies of interest. Since this amount of RAM is required for the most difficult condition tested, these locations are recommended for any future tests. The tests also showed that the cross section reduction was greater with better RAM. Tests repeated with RAM having a reflectivity of -4 db, -9 db and -20 db showed a worthwhile reduction with the -4 db material, about the same with the -9 db RAM and better results with the -20 db RAM. (See Patterns F-6, F-16 and F-17.) For a less difficult condition, tests were made with a RAM having a reflectivity of -3 db and other tests were carried out with a -6 db RAM. As shown in Patterns B-13 and B-14, the results were quite satisfactory in each case. 144 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 5. RECOMMENDATIONS To reduce the peak cross section of the broadside beam as observed at elevations up to 450 below the horizontal, the fins should be tilted upwards, the duct sides should be tilted inwards and the wings should be tilted upwards. A 50 tilt for the fins should be sufficient. With the same tilt for the ducts and a 10 tilt for the wings, the peak cross section will be reduced to approximately 164 square meters. The azimuthal beam width is essentially determined by the curvature (fore-and-aft) of the ducts, and will not be affected to any marked extent by the above changes. As regards the forward aspects, work should be continued to find or develop the most suitable RAM for the B-70 application. Ferroxcube 105 is suggested as one material which is known to be satisfactory from a temperature point of view. It is believed to have a reflectivity which is nearly adequate, but it is doubtful if it is superior to many other high temperature ferrite absorbers which have not been investigated. Judging from the results already achieved with low temperature RAM (Ref. 4), it should be possible to develop a ferrite RAM whose power reflection coefficient is 10 %0 or less from 200 Mc to 10, 000 Mc and whose thickness is no greater than 0. 5 inches. In an application where weight is more critical than thickness, materials of the silicone foam type, such as described in Reference 3, should be considered. 145 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F The experimental studies have shown that the radar cross section of the B-70 can be significantly reduced in the nose-on area. For all the conditions of polarization, aspect and frequency studied in the laboratory, it was possible to reduce the cross section to 40 square meters or less over a range of azimuth angle of ~ 50~ from nose-on. Caution should be exercised, however, in extrapolating these results to prove that the same reduction can be achieved on the full scale model for all frequencies of interest. Since the tests described in this study have covered frequencies near 390, 460 and 920 Me, there are still important regions in the frequency band of interest that have not been investigated. The methods used in this study will probably be satisfactory for all frequencies within the above limits of 400 to 1000 Mc. Above 1000 Me, where the amount of reduction required tends to be greater, further experimental studies should be made.+ These tests should simulate frequencies as near to the upper frequency limit as possible, and should be performed on a range long enough to eliminate any question concerningthe far field requirement. Since the RAM to be used on the full scale aircraft will probably be most effective at these higher frequencies, one can be optimistic about the expected reduction in the cross section. Nevertheless, these tests should be made. In addition, the materials employed in future tests should approximate as closely as possible the RAM to be used on the sefull scale aircraft. + The authors are aware that NAA, Columbus is investigating the cross section reduction problem at 3000 Mc. 146 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F At higher frequencies and with vertical polarization, difficulty may be experienced in obtaining a sufficient reduction of the echoes within 100 or so of the nose. The use of an absorber, or perhaps a metal diffuser, placed in the center of the duct and far enough back to be in the non-critical flow region should prove to be effective in solving this problem. Some attention should also be given to the frequencies below 400 Me. Here the required amount of reduction is small but the performance of the RAM will itself be poor. Depending on the reflectivity of the RAM selected for the full scale aircraft it may or may not be necessary to use a wide mesh screen as an aid in the solution of the low frequency cross section reduction problem. + It is of interest to note that the cut-off frequencies at the beginning of the ducts are 122 Me and 89 Me for vertical and horizontal polarization, respectively. 147 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F 6. ACKNOWLEDGEMENTS The authors are indebted to Professor K. M. Siegel for his advice and guidance during the performance of the work described in this report; and to Mr. William Bahret of WADC and to workers at NRL, Battelle and Emerson and Cuming, Inc. for valuable information on radar absorbing materials. Their thanks are also due to Professor D. M. Grimes for helpful discussions on ferrite absorbers in general, and for his measurements on specific ferrite materials; to Dr. F. B. Sleator and Mr. D. M. Raybin for their analysis of the dihedral reflector presented in the appendix; to Mr. R. L. Wolford who was responsible for most of the cross section measurements, and to other members of the Radiation Laboratory for assistance with both the theoretical and experimental programs. 148 SEC RET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1-F 7. REFERENCES 1. "Radar Reflection Characteristics of the B-70 Bomber", K. M. Siegel, September 1959. Prepared for the Scientific Advisory Board, U. S. A. F. 2. Rutgers University - RADC Contract AF 30(602)-2058, Ltr. report, October 1959. 3. Emerson and Cuming, Inc. Engineering Reports 1, 2, 3 and 4 on Contract AF 33(616)-6114, "Microwave Absorber Materials", December 1958, March 1959, June 1959 and September 1959. 4. NRL Report No. 4745, "Absorbent Materials for Electromagnetic Waves", R. W. Wright, May 1956, AD-99303. 5. Battelle Memorial Institute, "Research on Methods of Reducing Radar Cross Sections of Aircraft", Falkenbach and Harrison, Final Report on Contract AF 19(602)-1414, August 1957 and Battelle Memorial Institute, "Research Scientific Report No. 1, Contract AF 19(604)-3046, October 1958. ASTIA No. AD 304734. 6. University of Michigan Report No. 2799-4-T, "Hexagonal Ferromagnetic Absorbers", D. M. Grimes, W. W. Raymond and R. G. Wells, Contract AF 30(602)-1922. 7. NRL Report 5304, "Waveguide Dummy Loads and Attenuators Utilizing HighLoss Ferromagnetic Materials", W. H. Emerson, R. W. Wright, A. G. Sands and M. V. McDowell, June 1959. 149 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F APPENDIX OPTICAL ANALYSIS OF THE DIHEDRAL REFLECTORS by D. M. Raybin and F. B. Sleator We assume a dihedral reflector with rectangular sides of dimensions L1 and L2 normal to the intersection and interior angle -- + 0, struck by 2 a plane wave with propagation vector normal to the intersection of the sides and making angle 3 with the side 2. If 3 is within the range 20 <3 <- -0, 2 then part of this beam will be doubly reflected, the width of this part being determined by 3 and either L1 or L2, depending on certain relations between these three quantities noted below. The doubly reflected beam will be split into two beams separated by an angle 40, the part striking side 2 first leaving at an angle 3 + 20 and that striking side 1 first leaving at an angle 3 - 20, as shown in Figure A-1. It can be shown by the geometry of the figure that each doubly reflected beam has the same width as it had before the first reflection, and that at every point in a plane normal to the final direction of propagation its phase is the same. Let Bi be the width of that part of the incident beam which suffers a double reflection, B'i, B2i be the widths of the parts striking sides 1 and 2 first, respectively. Then by the geometry of the setup, Bli is the lesser of the two quantities 150 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F -+e -~ 2 B FIGURE A-1 151 SFCRFT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F i 1 sin (-+ -) = L cos ( 3- ) L2 sin (3 -20) and B21 is the lesser of the quantities L1 sin (-2 -3-0) =L1 cos (+ 0) L2 sin3. (In the case illustrated, the second quantity is less in each bracket. It can be shown that both parts of B1 are necessarily limited by the same side, i. e. L1 cos(/3-e) < L2 sin(f3-20) <=:L1 cos((3+0) <L2 sin..) Also, let L'i, L"' be the effective width of side i with respect to the first 1 and second reflections respectively, i. e. L1 be that part of side 1 struck by the part Bl of the incident beam and L1 be the part struck by the first reflection i of B2, with corresponding definitions of L and L2. Then if side i is limiting (i =1, 2) we have L' = L = L. (In the figure shown, i =2). The above considerations then yield B =Blr = L1 cos(f-0) = L2 sin(8-2e) B = B = L2 sin = L1 cos (3+ 0). Each part of the reflected beam is assumed to give the same diffraction pattern as an aperture of dimensions equal to those of the beam oriented normal to the direction of propagation of the reflected beam. Thus we write for the 152 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F amplitude of the field at a point on the axis of the incident beam due to B r A1 =L3. Bi sin L- sin201 kB-r sin 20 2 r -k + 2L3sin -L cos (3-0)sin20 k sin 20 where L3 is the dimension of the dihedral parallel to the intersection of the sides, and for that due to B2 rkL2 2L3 sin k2 sin Ssin20 k sin 20 A2 = In the case where L1 is the limiting dimension, these can be written r kL, - 2L3 sin 2- cos ( -0) sin20 Al =s k sin 20 2L3sinL 2 cos (3+ 0) sin 20 k sin 20 A2 = and similarly if L2 limits, 2L3sin [-2 L sin (-20) sin 20 k sin 20 A2 = 2L3sin [ k2 L isinsin2 k sin 20 Note: This expression is reconciled with the usual form of the diffraction pattern for a flat plate, in which the factor of 2 is absent, by the observation that the angle used here is not that between incident beam and normal but between incident and specular beams. 153 gFCRFT

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F The amplitudes A1 and A2 can be added directly only if the relative phases are considered. This could be done, but for present purposes we are interested in the maximum possible returns from the dihedral at the given angles of incidence, and these are given by the sums of the moduli of the two contributions. Thus the maximum total amplitude should in general be taken as AT =A1I +| A2 and the cross section proportional to the square of this quantity. The above analysis holds for the dihedral with obtuse angle. If, instead of increasing the right angle, we diminish it by an angle 0, a similar situation prevails, with the incident beam being split into two parts separated by an angle 40 as before, for a large part of the angular incidence range. The amplitude of the total backscattering return will thus be approximately as before, with differences occurring in certain ranges due to a switch in the limiting side of the dihedral. These differences however may be insignificant in comparison to another effect which has not been mentioned, namely, that at certain angles of incidence, e. g. 13 = 0 in the diagram above, there is a singly reflected beam (or if 0 is negative, a triply reflected one) whose peak is exactly in the direction of the transmitter-receiver, and whose effective amplitude is thus in general much 154 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F larger than that of the doubly reflected beam in either case. The ultimate decision in the design of the dihedral may then be governed by the desirability of excluding this angle from the range of interest. We are led to a more specific analysis of the situation at hand, which can be outlined as follows. With the dihedral oriented as shown in Figure A2, we assume first that the range of interest for 03 is from horizontal to 45~ below horizontal, and that we may change the orientation of either of the sides L1, L2 with respect to the horizontal and vertical. As shown in Case I, L2 is maintained horizontal and L1 inclined at angle + 0 from the vertical. Here there is a specular return at the angle /3 = 0 which is in general within the range of interest, and which in Case Ia) is singly reflected and limited only by Lq, and in lb) is triply reflected and may be limited either by L1 or L2 Thus for given L1, the specular return in Ia) is equal to or greater than that in lb). In Case II, L1 is maintained vertical and L2 is rotated through an angle ~ 0 from the horizontal. Here the specular return in HIIa) occurs only at one extreme of the 0 range, i. e. 0, = 0, and is limited as before by L1. In Case lib) the specular return occurs at3 = 20, which is in general still within the range of interest, and is limited by either L1 or L2. The choice here then depends on which side limits and which position of the specular beam is less objectionable. If it is deemed essential to remove the specular beam entirely from the range of interest, a configuration such as that shown in Case III should be considered, 155 SECRET

SECRET THE UNIVER SITY OF 3477-1 -F MICHIGAN L2 L1/ b) Case I L2 a) L1\ Case II Case II Case III FIGURE A-2 156 SECRET

SECRET THE UNIVERSITY OF MICHIGAN 3477-1 -F in which both sides of the dihedral are rotated slightly through positive angles, with > 6, and the specular beam occurs at / = - S. With the permissible range of 0 limited by other considerations, this configuration offers less reduction in the doubly-reflected backscattered return than either of the other two cases; however there may still be enough reduction available to make it preferable on the whole. 157 SECRET