I THE UNIVERSITY 7030-2-T OF MICHIGAN 7030-2-T = RL-2147 A MODIFIED FOCK FUNCTION by S. Hong and V. H. Weston November 1965 Contract AF 04(694)-683 Prepared for BALLISTIC SYSTEMS DIVISION AIR FORCE SYSTEMS COMMAND UNITED STATES AIR FORCE NORTON AIR FORCE BASE, CALIFORNIA

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THE UNIVERSITY OF MICHIGAN 7030-2-T TABLE OF CONTENTS Page ABSTRACT iv I. INTRODUCTION II. INTEGRAL EQUATION GOVERNING THE SURFACE FIELDS 2 III. ANALYTIC SOLUTION 6 IV. NUMERICAL SOLUTION 10 V. APPLICATION: ESTIMATION OF THE BACKSCATTERING CROSS 14 SECTION OF A CONE-SPHERE VI. ACKNOWLEDGEMENT 18 VII. APPENDIX A: EVALUATION OF N(p) 19 VIII. REFERENCES 22 iii

THE UNIVERSITY OF MICHIGAN 7030-2-T ABSTRACT A modified Fock function is obtained to describe the current distribution on a smooth convex boundary, composed of a flat plane smoothly joined to a parabolic cylinder with the join in the penumbra region. Both analytical and numerical method are used to obtain the modified Fock function which now depends on the distance between the shadow boundary and the flat plane-parabolic cylinder join. The modified Fock function is applied to estimate the backscattering cross section of a cone-sphere. iv

/ THE UNIVERSITY OF MICHIGAN 7030-2-T I INTRODUCTION When a high frequency plane electromagnetic wave is tangentially incident upon a locally parabolic convex surface, the distribution of the induced current near the shadow boundary is described by the Fock function (Fock, 1946). However, if a portion of the scattering surface near the shadow boundary is no longer parabolic but flat (e. g. wedge-cylinder or cone-sphere), the effect of the surface discontinuity at the join of the flat plane and parabolic cylinder must be taken into account. Weston (1965) has, in a previous paper, discussed an extension of the Fock theory when the position of the surface discontinuity coincides exactly with the shadow boundary. It is the purpose of this paper to present a modified Fock function which provides the current distribution in the penumbra and shadow regions when the surface discontinuity is in the penumbra region. This new modified Fock function describes the current distribution as a function of two variables: one is the distance between the shadow boundary and the observation point, and the other the distance between the shadow boundary and the flat plane-parabolic cylinder join. The method to be used is as follows: an exact integral equation governing the total magnetic field on the boundary is formulated by Maue's method (Maue, 1949). The high frequency asymptotic expression of the exact integral equation is a Volterra type, and both analytic and numerical solutions of the Volterra equation are obtained. These solutions may be called the modified Fock functions. In section 5, this modified Fock function is applied to estimate the backscattering cross section of a cone-sphere. 1

THE UNIVERSITY OF MICHIGAN 7030-2-T II INTEGRAL EQUATION GOVERNING THE SURFACE FIELDS Consider a plane electromagnetic wave A iky -iWt in=ze (1) incident upon a perfectly conducting convex cylinder whose boundary is composed of a smoothly joined flat plane and a parabolic cylinder (Fig. 1). I X din y Fig.1 GEOMETRY OF SCATTERING SURFACE In terms of a Cartesian coordinate system whose origin is taken at the shadow boundary, the surface of the scattering body is represented by the following equations: 2 X = y 2R x = tana (y+ - tana) T for y - R tana for y < - R tan a (2) (3) R is the radius of curvature of the parabolic section near the origin and is assumed - -- - r I, i

THE UNIVERSITY OF MICHIGAN 7030-2-T large in comparison with wavelength. The total magnetic field on the boundary is defined as _ A -iwt Htotal = zue. (4) Then the scalar function u is the solution of the following Maue's equations (Maue, 1949): - u(P) 2 eiky i f ds H() (kr)u(Q). (5) an 2 r 1 r is the distance between two points P and Q, and n is a unit vector normal to the boundary. It was shown by Weston (1965) that on the flat section the field reflected from 1 the surface discontinuity is of the order kR. Therefore, for the high frequency region, the reflected field contributes to higher order corrections, and u on the iky flat section becomes equal to the geometrical optics term 2 e. On the parabolic section, let us define u(y) - I(y) eks for y > - R tan a, (6) where s is the distance along the surface between the shadow boundary and the observation point: y s = +(y)dy. (7) Using the relationships (5), (6), and (7), we obtain an integral equation governing I(y): 3

THE UNIVERSITY OF MICHIGAN 7030-2-T -R tana A iky- -Rtan dt '1 H1)(kr ) I(y) = 2eik iks ()ik cosa 1 -00. [exp ikt - ks (Y) +( ) i 00 / t2 ^ ^^'^, (1) ik dt (t) t2 2 H()(kr 2 lt r2 1 2 -Rtana 2 * exp iks(t)- iks(y)} (8) with 2 2 R ()2 r = (y-t)+y2 +tana (t+ - tana) (9) 1 2R 2 and r2 = (y-t)2 + (y2-t2) (10) 2 4R In order to obtain an appropriate high frequency asymptotic form of I(y) near the shadow boundary, we shall set (kR)1/3 = m ky = m2 1) kt = m2, and I(y) = J(g) When the surface discontinuity lies in the penumbra region, m tan a is of the order of unity or less, and can be replaced by ma for large m. The asymptotic expression of (9) becomes 4

THE UNIVERSITY OF MICHIGAN 7030-2-T 3 -i -mma J(Q) = 2e +ma) 2 3/2 + 4 2 92 3 (~+mar) m a2 exp 8(-) +im (_) -_i m-2(+ma) -i 2 2 2 6 7r 4.- (e - 0) -e 24 4dJ(( J - )12 24 +O(m2). (12) 4 r -ma When ma goes to infinity, the second term in (12) disappears, and the solution becomes the so-called Fock function (Cullen, 1958). This means that when the position of the flat plane-parabolic cylinder join is far away from the shadow boundary, the current distribution is given by the Fock function. Otherwise, the Fock function has to be modified. The solution J(Q) of (12) will be called the modified Fock function. When a is identically zero, the solution of (12) was obtained by Weston (1965). In the following two sections, the solution of (12) is obtained when ma is finite but is not identically zero. 5 -~ -~-~~ ~

THE UNIVERSITY OF MICHIGAN 7030-2-T III ANALYTIC SOLUTION In this section the solution of (12) is derived when the distance between the shadow boundary and the position of the surface discontinuity is small, so that m3a3 is negligible. In order to solve (12) by the Laplace transform method, it is convenient to modify (12) by setting g = 0-ma, = ~0-ma, and J(9-ma) = j(O). (13) Substituting these new variables into (12) and taking the Laplace transform of both sides of the integral equation, we obtain j(p) = 2N(p) -- 1+ 4.. M(p) (14) where J(p) = dep j(0), -0 (15) aO M(p) = dO e - 0 e3 -p - e and (16) 00 N(p) = d e J- o (0 - ma)3 -i 0 -pe - i 6 e 4 do 1. -. -2 L J - OD 6

THE UNIVERSITY OF MICHIGAN 7030-2-T 4 22 exp i(0 800) im a ( -02 ] (17) 8 m -^r '1T_-^ 1 - J (17) M(p) has been evaluated by Weston (1965) as M(p) = 47r [ Ai (q) - Ai (q)-iBi(q) + - (18) 1/3 with q = -ip2, where Ai and Bi are Airy functions of the first and second kind, respectively, and the prime denotes differentiation with respect to the argument. The denominator of (14) becomes 2 7riAi(q)d Ai(q) - i( iBi(q)]. (19) 3 N(p) is evaluated in the Appendix under the assumption that (ma) is negligible. We obtain 2i F3 1 1 j(p) = - [ 2 3 + 1 [Ai(x) -iBi(x)] dx [Ai(q)- iBi'q(q)] 2 L 0 (20) 1 - q a 2 2%+ 2~3 m2 [Ai(q) - iBi (q)]+ q [i(q) - iBi (q)]t The desired solution J(Q) is obtained by taking the inverse transform of (20) and using the relationships e = 0 - ma and j(0) = J(0-mma): /3L - ic - exp i2 (~+m j(-) = 2 dq w( )j 1-q m a 2i l 23 -i2 3 lC - 2 3 JT - i23 w(x)dx -i2 m w(q) + qw(q) (21) - m a wl^q)+qw1 7

THE UNIVERSITY OF MICHIGAN 7030-2-T with w1 (q) = i ~r [Ai'(q) - iBi'(q)] When ~ is sufficiently large and positive, the contour integral may be evaluated in terms of the residues at the zeros of w1(q). For numerical calculation of the residue series, it is convenient to substitute the following relationship:. 7T. 2 T w,(q) = e 24 Aiqe I, q = e 3. (22) The high frequency asymptotic expression of the total field in the shadow region for a small ma is u(y) = eiks exp im a23 e 3 f3~Ai (-/3B) +2 e 2 i23 3 +20 Ai(-x)dx 1- m 2 e m.x 2 l 2 + e r3 r 2- Ai(-I) (23) with d = 7 ). When a goes to zero, Eq. 23 becomes equal to the solution given by Weston (1965), except for a factor two. The reason for this is that when a is identically zero the amplitude of the total field on the flat portion is taken to be unity, while it is taken to be two in this paper. Numerical values of /E1, Ai(-j3,) and f Ai(-x)dx are given by Weston (1965). There e, when kR3 is negligible, each mode of the creeping waves given Therefore, when kRa is negligible, each mode of the creeping waves given 8

THE UNIVERSITY OF MICHIGAN 7030-2-T by (23) is different from the Fock solution by the factor (Goodrich, 1959) e1 i 2 i exp i1312 2T mae 3 +2 Ai(-x)dx I \ + x)d { 1L Jo 1 ( 5 27r 1 -2m2a2 3 e 3 21-I3ma2 e r 2 -i 1 - +e 13 22 3 Ai(-1) ' +e 3m a 2 Ai(). (24) 9

THE UNIVERSITY OF MICHIGAN 7030-2-T IV NUMERICAL SOLUTION In this section, a numerical method is described to obtain the solution of (12) 33 without the assumption that m a is negligible. The high frequency asumptotic expansion expansion reduces Maue's integral equation from that of the Fredholm class to that of the Volterra type which is much easier to handle numerically. Several methods are available for the solution of the Volterra integral equatio When a high speed digital computer is available, the simplest approach is to expand the unknown in a set of algebraic functions J1'..., Jn' and to require the integral equation be satisfied at n different points. The solution of (12) may be approximated by setting J = J( =nA-ma). (25) n A is the distance between two adjacent points on the contour of integration. Insertion of this expression in (12) gives J =H +-K j +4K J +2K J +. +2k J +4K J n n 3 noo n n1 n n n-2 n-,n-l n-1 (26) with (nA- ma)3 -i 7r mx -= 6 e e4 (nA)2 H =2e d -- n 4 (nA- MO - 0 2 -00 (27) n 4 22 + (nA),.m a,. ma 2U - exp i (n ---- + i m - (nA-mca-) -i -- (nA) 8 (nA-mc -) 2 2 ) and i7 K e (n-m) exp -i - (28) n, m 4 i7 24 10

THE UNIVERSITY OF MICHIGAN 7030-2-T As shown in (26), the current at the nth point (: =nA- ma) can be obtained by simply substituting the previously known currents between the Oth to the (n - 1)th points. This is the reason why, for high frequency scattering, the asymptotic expression of the integral equation governing the surface is simpler to solve numerically than the exact (Maue's) equation. In Figs. 2 and 3, numerical solutions of the modified Fock function are compared with the regular Fock function. 1__.L

THE UNIVERSITY THEUNIERSTYOF MICHIGAN 7030-2-T 2.0 -7 I — - - - Fock Function (mca=o)) Modified Fock Function, ma=0.4 1.8 - 1.6 - 1. 4 - 1.2 - 44 4% 4% ma0. 6 i li J 1. 0 0.8 -0.6 N - I I IU 1 -0.8 - 0' 4 6 0.4 0.8 1.2 4 3 FIG. 2. Amplitude of J in the Penumbra Region. 12 12 I

THE UNIVERSITY OF MICHIGAN 7030-2-T 40- - - Fock Function (mac= - Modified Fock Funct 35 30 25 -20 I bhi - \ / 4 15 10 / / ma=0.-6 6 -5 \ / -5 -0.8 -0.4 0 0.4 F2iY3 FIG. 3. Phase of J in the Penumbra Region. a) tion I I I I / r / / / / 2 13

THE UNIVERSITY OF MICHIGAN 7030-2-T V APPLICATION: ESTIMATION OF THE BACKSCATTERING CROSS SECTION OF A CONE-SPHERE It is known that a good approximation to the nose-on backscattering cross section of a cone-sphere can be had by adding the contribution of a sphere creeping wave to the physical optics estimate of the scattering from the cone-sphere join (Senior, 1965). Nevertheless, Senior reported that there is evidence of a small but systematic discrepancy between the amplitudes of the creeping wave contributions from a cone-sphere and a sphere alone. This phenomenon may be explained by results obtained in the previous sections. When a plane wave is incident upon a cone-sphere at nose-on direction, the cone-sphere join lies near the shadow boundary We have to take into account that the geometry of the scattering surface near the shadow boundary is no longer entirely spherical but a portion of it is conical. Fock has shown that when a high frequency plane electromagnetic wave is incident upon a three-dimensional conducting body, the dominant mode of the creeping waves may be described by the two-dimensional solution (Goodrich, 1959). Therefore, we may apply the results of the previous sections in analyzing the diffraction problems of a cone-sphere. At nose-on incidence, the distance between the cone-sphere join and the shadow boundary is very small in many practical cases, and the result given by (23) may be applied. For example, when the cone angle (2ca) is 25 degrees, Senior (1965) gives the formula for the backscattering cross section of a cone-sphere at nose-on incidence as a/X = 0.02190 A(1. 916- 0. 05593 kR) + exp tir (1.45410 - 1. 16335 kR)1' (29) A is the ratio between the amplitudes of the two dominant creeping waves; one is supported on a spherical portion of a cone sphere, and the other on a sphere alone. Senior (1965) has obtained an approximate expression of A on the basis of physical reasoning. We may obtain A from (24) as 14

THE UNIVERSITY OF MICHIGAN 7030-2-T A + 2 Ai( dxI) d 132 kR 2/3 e (30 + e ( )23 a Ai (-1) exp {i ( 2 a et - (30) 2 Insertion of this expression in (29) gives the backscattering cross section of a cone-sphere with the cone angle 2a = 25. The result is shown in Fig. 4. In order to assist the computation of the backscattering cross section of either a conesphere or a wedge-cylinder at nose-on incidence, the numerical value of A as a function of both kR and a is shown in Fig. 5. This figure provides a reasonably accurate means in estimating the creeping wave contribution when kR is of order 5. For a smaller kR, a more refined evaluation of A is necessary, which may be achieved by including higher order terms in the asymptotic representation of Maue's equation (5). When a plane wave is not incident along the nose-on direction, the distance between the shadow boundary and the cone-sphere join is not necessarily small. In this case we may use the numerical method described in the previous section to obtain the creeping wave contribution. 15

0.20 (Y2 p.A a) t r 0. 15 / \ 010- / / 7 \\1 \ 0. 10 / / \ /\ 2 I / I \' t \\/ I 0. 05 G b 0 / - C) 7.5 8.5 kR 9.5 10.5 FIG. 4. Nose-On Backscattering Cross Section of a 250 Cone-Sphere. Z Experimental Results.With A = 1 - With A Given by Eq. 30

I 1.5 =7.5~ 1.3 3 =- 12.50 Al 150 c 1.1 z -4J - 3 4 5 6 7 8 9 10 o kR s vo degree 6 0 c 7.5~ __ am 1. 4 - C) 0 2 -1 > 22: 3 4 5 6 kR 7 8 9 10 I kI IJ A FIG. 5. Absolute Value and Phase of A Given by Eq. 30: 2a= The Cone Angle.

THE UNIVERSITY OF MICHIGAN 7030-2-T VI ACKNOWLEDGMENT The authors wish to thank Dr. T. B. A. Senior for assistance with the manuscript and Messrs. J. Ducmanis and H. Hunter for assistance with computation. 18

- THE UNIVERSITY OF MICHIGAN 7030-2-T VII APPENDIX A EVALUATION OF N(p) In this appendix the integral oo (O - (0mc)3 -im) 0 _P~) i 6 e T2d N(p) = dOe 6- - e2J d 4 - 4( " 0) (0J-OD ~t r 4 22 ). 9 ma 2+m * exp m 1 02 +; m c~ (0-~ ) ~ exp i 8(0-) --- 26 2 31 (A. 1) 3ma3 is evaluated when ma is small so that (ma) and higher order terms are negligible. The integrand of (A. 1) may be further simplified by making the change of variable 0 - 0 = x and using the relationship 00 02 x2dxf 2 exp Jo x 4 22 i i ma 2.0 +im a e- 2 + 22=x( = 2J~r e (A. 2) We obtain e -i7 0 4 d (0 exp i -i -- 02+i 2 (0- 0) C 4 2 4 (00-0 ^28(^"0) 2 2 - co0 3 3.m a. 7 e 6 4 4 - 0 922 2 eir r n x 2 m (A. 3) 19

I THE UNIVERSITY OF MICHIGAN 7030-2-T Neglecting terms involving (mra) and higher order in (A. 3), N(p) may be written as a sum of the two functions: - 7 4 e 22 N(p) = N 1 (p)+m a 2f27 1 7r e 33 4- N2(p)+ O(m a ) 4 2; (A. 4) with 0. 02 dx 8x J -e Jo (A. 5) and Go-p 2 ( x - 8 N (p)= dee dx (x-e) 04 03 8x e (A. 6) N1(p) was evaluated by Weston (1965) [N1(p) is equal to 4 TF(p) where F(p) was evaluated in the appendix] as 1 F[ 3 2 N1(p)- e 82 1/3 with q = - ip2 N2(p) can be evaluated by integration by parts: 2t (A. 7) N2(P) = dN(p) d2 -,N1(p) +2-2 M(p) dp dp (A. 8) M(p) is givenby (18). U 20 20

THE UNIVERSITY C 7030-2 -T )F MICHIGAN Using (A. 7) and (A. 8) we obtain N(p) = 7 1/3 lrs 1 ) i22. 4 2 Aiq ix iiWd - -, 0.5/3 I q2] (A. 9) -1/3 2 2 + 7r 2 m a Ai(q) [{Ai(q) - iBi(q)~ + q {Ai I(q) - iBi?(q)} I 21

THE UNIVERSITY OF MICHIGAN 7030-2-T VIII REFERENCES Cullen, J. A., (1958) "Surface Currents Induced by Short-Wavelength Radiation," Phys. Rev., 109 1863-1867. Fock, V., (1946) "The Distribution of Currents Induced by a Plane Wave on the Surface of a Conductor, " J. Phys., 10, 130-136. Goodrich, R. F., (1959), "Fock Theory - An Appraisal and Exposition, " IRE Trans. Ant. Prop., AP-7, 28-36. Maue, A. W., (1949), "On the formulation of a general diffraction problem through an integral equation," Z. Phys., 126, 601-618. Senior, T. B. A., (1965), "The Backscattering Cross-Section of a Cone Sphere, " IEEE Trans. Ant. Prop., AP-13, 271-277. Weston, V. H., (1965), "Extension of Fock Theory for Currents in the Penumbra Region," NBS, J. Res., 69D, 1257-1270. - 22 - --

Unclassified Security Classification DOCUMENT CONTROL DATA - R&D (S$curity classification of title, body of abstract and indexing annotation must be entered when the overall report is classified) 1. ORIGINATING ACTIVITY (Corporete author) 2a. REPORT SECURITY C LASSIFICATION The University of Michigan Unclassified College of Engineering, Department of Electrical En g GROUP Radiation Laboratory, Ann Arbor, Michigan 3. REPORT TITLE A Modified Fock Function 4. DESCRIPTIVE NOTES (Type of report and inclusive daete) Technicl Report 5. AUTHOR(S) (Last name, first name, initial) S. Hong and V. H. Weston 6. REPO RT D1ATE 7a. TOTAL NO. OP PAGES 7b. NO. OF REFS November 1965 22 6 8a. CONTRACT OR GRANT NO. AF 04(694)-683 4. ORIGINATOR'S REPORT NUMBER(S) 7030-2-T b. PROJECT NO. c. Sb. OTH R REPORT NO($) (Any other numbers that may be assigned this report) d. 10. AVA IL ABILITY/LIMITATION NOTICES Qualified Requestors May Obtain Copies of This Repcr t From DDC 11. SUPPL EMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY Ballistic Systems Division Air ForetSvstem_ Commandt United States Air Force, lNorton Air Fore B 13. ABSTRACT A modified Fock function is obtained to describe the current distribution on a smooth convex boundary, composed of a flat plane smoothly joined to a parabolic cylinder with the join in the penumbra region. Both analytical and numerical methods are used to obtain the modified Fock Function which now depends on the distance between the shadow boundary and the flat plane-parabolic cylinder join. The modified Fock function is applied to estimate the backscattering cross section of a cone-sphere. I mmft - —.. - - .M. - - - - tsea ornla 0 DP 1?AN 641473 Unclassified Security Classification

I. Unclassified Security Classification 14KEYWORDS LINK A LINK B LINK C KEY WORDS ROLE WT ROLE WT ROLE WT Diffraction and Scattering Fock Function, Modified Cone-Sphere Il -. v i I. INSTRUCTIONS 1. ORIGINATING ACTIVITY: Enter the name and address of the contractor, subcontractor, grantee, Department of Defense activity or other organization (corporate author) issuing the report, 2a. REPORT SECURITY CLASSIFICATION: Enter the overall security classification of the report. Indicate whether "Restricted Data" is included. Marking is to be in accordance with appropriate security regulations. 2b. GROUP: Automatic downgrading is specified in DoD Directive 5200. 10 and Armed Forces Industrial Manual. Enter the group number. Also, when applicable, show that optional markings have been used for Group 3 and Group 4 as authorized. 3. REPORT TITLE: Enter the complete report title in all capital letters, Titles in all cases should be unclassified. If a meaningful title cannot be selected without classification, show title classification in all capitas -in parenthesis immediately following the title. 4. DESCRIPTIVE NOTES: If appropriate, enter the type of report, e.g., interim, progress, summary, annual, or final. Give the inclusive dates when a specific reporting period is covered. 5. AUTHOR(S): Enter the name(s) of author(s) as shown on or in the report. Enter last name, first name, middle initial. If military, show rank and branch of service. The name of the principal author is an absolute minimum requirement. 6. REPORT DATE: Enter the date of the report as day, month, year; or monthr year, If more than one date-appears on the report, use date of publication. 7a. TOTAL NUMBER OF PAGES: The total page count should follow normal pagination procedures, i.e., enter the number of pages containing information. 7b. NUMBER OF REFERENCES; Enter the total number of references cited in the report. 8a. CONTRACT OR GRANT NUMBER: If appropriate, enter the applicable number of the contract or grant under which the report was written. 8b, 8c, & 8d. PROJECT NUMBER: Enter the appropriate military department identification, such as project number, subproject number, system numbers, task number, etc. 9a. ORIGINATOR'S REPORT NUMBER(S): Enter the official report number by which the document will be identified and controlled by the originating activity. This number must be unique to this report. 9b. OTHER REPORT NUIMBER(S): If the report has been assigned any other report numbers (either by the originator or by the sponsor), also enter this number(s). 10. AVAILABILITY/LIMITATION NOTICES: Enter any limitations on further dissemination of the report, other than those imposed by security classification, using standard statements such as: (1) "Qualified requesters may obtain copies of this report from DDC." (2) "Foreign announcement and dissemination of this report by DDC is not authorized." (3) "U. S. Government agencies may obtain copies of this report directly from DDC. Other qualified DDC users shall request through (4) "U. S. military agencies may obtain copies of this report directly from DDC Other qualified users shall request through., (5) "All distribution of this report is controlled. Qualified DDC users shall request through 'I If the report has been furnished to the Office of Technical Services, Department of Commerce, for sale to the public, indicate this fact and enter the price, if known. 11. SUPPLEMENTARY NOTES: Use for additional explanatory notes. 12. SPONSORING MILITARY ACTIVITY: Enter the name of the departmental project office or laboratory sponsoring (paying for) the research and development. Include address. 13. ABSTRACT: Enter an abstract giving a brief and factual summary of the document indicative.of the report, even though it may also appear elsewhere in the body of the technical report. If additional space is required, a continuation sheet shall be attached. It is highly desirable that the abstract of classified reports be unclassified. Each paragraph of the abstract shall end with an indication of the military security classification of the information in the paragraph, represented as (TS). (S), (C), or (U). There is no limitation on the length of the abstract. However, the suggested length is from 150 to 225 words. 14. KEY WORDS: Key words are technically meaningful terms or short phrases that characterize a report and may be used as index entries for cataloging the report. Key words must be selected so that no security classification is required. Identifiers, such as equipment model designation, trade name, military project code name, geographic location, may be used as key words but will be followed by an indication of technical context. The assignment of links, rules, and weights is optional. I I Unclassified Security Classification I