INSULATIVE PERFORMANCE OF SELECTED ABLATIVE MATERIALS IN A LOW ENTHALPY HYPERSONIC AIRSTREAM. May 1966

Size: px

Start display at page:

Download "INSULATIVE PERFORMANCE OF SELECTED ABLATIVE MATERIALS IN A LOW ENTHALPY HYPERSONIC AIRSTREAM. May 1966"

Diana Hopkins
5 years ago
Views:

AEDCTR-66-26 "w MAY 30 1966 JUN 111968 INSULATIVE PERFORMANCE OF SELECTED ABLATIVE MATERIALS IN A

May 1966 Distribution of this document is unlimited. PROPERTY OF U.

1 AEDCTR "w MAY JUN INSULATIVE PERFORMANCE OF SELECTED ABLATIVE MATERIALS IN A LOW ENTHALPY HYPERSONIC AIRSTREAM J. B. Carman, Jr. ARO, Inc. May 1966 Distribution of this document is unlimited. PROPERTY OF U. S AIR FORCE ^" LIBRARY AF 40[600jl200 VON KARMÄN GAS DYNAMICS FACILITY ARNOLD ENGINEERING DEVELOPMENT CENTER AIR FORCE SYSTEMS COMMAND ARNOLD AIR FORCE STATION, TENNESSEE

obligation whatsoever, and the fact that the Government may have formulated, furnished, or in any way supplied the said drawings, specifications-, or other data, is not to be regarded by implication

2 NOTICES When U. S. Government drawings specifications, or other data are used for any purpose other than a definitely related Government procurement operation, the Government thereby incurs no responsibility nor any obligation whatsoever, and the fact that the Government may have formulated, furnished, or in any way supplied the said drawings, specifications-, or other data, is not to be regarded by implication or otherwise, or in any manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use, or sell any patented invention that may in any way he related thereto. Qualified u^ers may obtain copies of this report from the Defense Documentation Center. References to named commercial products in this report are not to be considered in any sense as an endorsement of the product by the United States Air Force or the Government.

3 INSULATIVE PERFORMANCE OF SELECTED ABLATIVE MATERIALS IN A LOW ENTHALPY HYPERSONIC AIRSTREAM J. B. Carman, Jr. ARO, Inc. Distribution of this document is unlimited.

FOREWORD The work herein was conducted for the General Electric Company at the request of the Ballistic Systems Division (BSD), Air Force Systems Command (AFSC), under Program Element

), contract operator of the Arnold Engineering Development Center (AEDC), AFSC, Arnold Air Force Station, Tennessee, under Contract AF40(600}-1200.

4 FOREWORD The work herein was conducted for the General Electric Company at the request of the Ballistic Systems Division (BSD), Air Force Systems Command (AFSC), under Program Element , System 133B. The results of the tests were obtained by ARO, Inc. (a subsidiary of Sverdrup and Parcel, Inc. ), contract operator of the Arnold Engineering Development Center (AEDC), AFSC, Arnold Air Force Station, Tennessee, under Contract AF40(600} The tests were conducted on November 22, 1965 under ARO Project No. VC0647, and the manuscript was submitted for publication on January 11, This technical report has been reviewed and is approved. John W. Hitchcock Jean A. Jack Major, USAF Colonel, USAF AF Representative, VKF DCS/Test DCS/Test li

ABSTRACT Tests were conducted to investigate the insuiative performance of selected ablative materials when exposed to a relatively low enthalpy hypersonic airstream.

into a Mach 10 airstream at 15- and 25-deg angles of attack. The model was tested at a high free-stream Reynolds number, 2.

5 ABSTRACT Tests were conducted to investigate the insuiative performance of selected ablative materials when exposed to a relatively low enthalpy hypersonic airstream. Samples of cork, an elastomeric shield material, phenolic glass containing a buton resin, and phenolic glass, mounted on the surface of a sharp flat plate, were injected into a Mach 10 airstream at 15- and 25-deg angles of attack. The model was tested at a high free-stream Reynolds number, 2. 2 x 10^ per foot, to produce turbulent flow over the samples. The test results, which consisted of back surface temperature histories on the in. -thick samples, showed that cork provided the greatest heat protection. 1X1

CONTENTS Page ABSTRACT iii NOMENCLATURE vi I. INTRODUCTION 1 II. APPARATUS 2. 1 Wind Tunnel 1 2. 2 Model 1 2. 3 Instrumentation. 2 III.

Installation Photograph 6 3. Model Detail a. Flat Plate 7 b. Ablation Sample Insert 8 4. Typical Schlieren Photographs a. a - 15 deg 9 b.

6 CONTENTS Page ABSTRACT iii NOMENCLATURE vi I. INTRODUCTION 1 II. APPARATUS 2. 1 Wind Tunnel Model Instrumentation. 2 III. PROCEDURE 3. 1 Test Conditions Data Reduction 3 IV. RESULTS AND DISCUSSION 3 REFERENCES 4 ILLUSTRATIONS Figure 1. Tunnel C 5 2. Installation Photograph 6 3. Model Detail a. Flat Plate 7 b. Ablation Sample Insert 8 4. Typical Schlieren Photographs a. a - 15 deg 9 b. a = 25 deg 9 5. Flat Plate Centerline Flow Characteristics a. a = 15 deg 10 b. a ~ 25 deg Material Insulative Performance a. a - 15 deg 12 b. a = 25 deg 13

AEDCTR-66-26 NOMENCLATURE b Model skin thickness, ft c Model skin specific heat, Btu/lb- R h Local heat-transfer coefficient, Btu/ft2-sec- R L Model length, in.

heat-transfer rate, Btu/ft 2 -sec T aw Adiabatic wall temperature, R ATgp Material sample backface temperature change, R T w Model wall temperature, R T B Wind tunnel free-stream static temperature,

7 AEDCTR NOMENCLATURE b Model skin thickness, ft c Model skin specific heat, Btu/lb- R h Local heat-transfer coefficient, Btu/ft2-sec- R L Model length, in. ML Theoretical local Mach number at edge of model boundary layer M m Wind tunnel free-stream Mach number p Model wall static pressure, psi p^ Wind tunnel free-stream static pressure, psi q Local heat-transfer rate, Btu/ft 2 -sec T aw Adiabatic wall temperature, R ATgp Material sample backface temperature change, R T w Model wall temperature, R T B Wind tunnel free-stream static temperature, R t Time of model exposure to tunnel free stream, sec w Model skin specific weight, lb/ft3 x Distance along model from leading edge in flow direction, in. o Angle of attack of model test surface (positive angle = test surface windward), deg vi

SECTION I INTRODUCTION Pressure and heat-transfer measurements on a sharp flat plate and backface temperature measurements on selected ablation samples were made at a nominal free-stream Mach number

2 x 10 6 per foot. The objective of this test was to investigate the insulative capabilities of four ablation materials in a relatively low enthalpy hypersonic airstream.

8 SECTION I INTRODUCTION Pressure and heat-transfer measurements on a sharp flat plate and backface temperature measurements on selected ablation samples were made at a nominal free-stream Mach number of 10 and at angles of attack of 15 and 25 deg. The test was performed in the 50-in. hypersonic tunnel (Gas Dynamic Wind Tunnel, Hypersonic (C)) at a free-stream unit Reynolds number of 2. 2 x 10 6 per foot. The objective of this test was to investigate the insulative capabilities of four ablation materials in a relatively low enthalpy hypersonic airstream. No ablation data for the particular materials were available in this flow regime. As material response to heating at low enthalpj^ might differ from the response at high enthalpy conditions, these data were necessary to complete an effective study of material performance. SECTION 11 APPARATUS 2.1 WIND TUNNEL Tunnel C is an axisymmetric, continuous flow, variable density wind tunnel with a 50-in. -diam test section. The tunnel operates at a nominal Mach number of 10 at stagnation pressures from 200 to 1800 psia. Stagnation temperatures up to 1900 R are utilized to prevent liquefaction of the air in the test section. A sketch of Tunnel C and associated equipment is shown in Fig MODEL The investigation was conducted on the stainless steel flat plate shown in Figs. 2 and 3. The model was provided with interchangeable heat-transfer and pressure panels for flat plate surface flow calibration. The panels were designed to fair smoothly with the model surface except near the nose of the model where a in. -wide and in. -deep gap was located to allow for thermal expansion {Fig. 2). Surface instrumentation was arranged as shown in Fig. 3a.

Material samples were designed as inserts to replace one of the calibration panels. As shown in Fig. 3b, the 0. 150-in. -thick sample was bonded to a 0.005-in.

Ablation materials tested included samples of cork, an elastomeric shield material {ESM}, phenolic glass, and phenolic glass containing a buton resin (Buton A500). 2.

9 Material samples were designed as inserts to replace one of the calibration panels. As shown in Fig. 3b, the in. -thick sample was bonded to a in. -thick stainless steel panel which was, in turn, bonded to a piece of Textolite. Sample backface temperatures were monitored by thermocouples attached to the underside of the stainless steel panel. Ablation materials tested included samples of cork, an elastomeric shield material {ESM}, phenolic glass, and phenolic glass containing a buton resin (Buton A500). 2.3 INSTRUMENTATION Each channel of the Tunnel C pressure measuring system, consists of a 1- and a 15-psid frequency modulated transducer. These are switched in and out of the system automatically to allow measuring to the best available precision. The Chromel-Alumel thermocouple outputs were recorded on magnetic tape at a rate of 20 times per second. The reference junction of each thermocouple was maintained at 132 F. Model flow field photographs were obtained with a single-pass, collimated beam schlieren system. Typical photographs are shown in Fig. 4. SECTION III PROCEDURE 3.1 TEST CONDITIONS Transient heat-transfer data were obtained by injecting the model into the airstream for a specified period of time while model thermocouple histories were recorded. The model was then retracted into the installation chamber below the tunnel and cooled with air until the model reached a uniform temperature. This procedure was repeated at the test conditions summarized below: Nominal Free-Stream Conditions Total pressure, p 0 = 1800 psia Total temperature, T 0 = 1896 R Mach number, M B = Unit Reynolds number, Re^ = 2. 2 x 10^ per foot Static pressure, p^ psia Static temperature, T w =91. 7 R

t, sec a, deg 5 15, 25 30 15, 25 60 15, 25 120 15 15, 25 Ablation Sample Material 0.05-in.

temperature Backface temperature Pressure 3.2 DATA REDUCTION Free-stream conditions were computed assuming an isentropic expansion of a variable specific heat gas following the method of Ref. 1.

10 t, sec a, deg 5 15, , , , 25 Ablation Sample Material 0.05-in. -thick stainless steel Cork, ESM, Phenolic Glass, and Buton A500 Cork, ESM, Phenolic Glass, and Buton A500 Cork, ESM, Phenolic Glass, and Buton A500 Data Heat transfer Backface temperature Backface temperature Backface temperature Pressure 3.2 DATA REDUCTION Free-stream conditions were computed assuming an isentropic expansion of a variable specific heat gas following the method of Ref. 1. Values of aerodynamic heating rate were calculated using temperaturetime data in the relation q = wbc dt v dl Heat-transfer coefficients were calculated using the equation where h = q/(t avk - Tw) T aw = T M [ (0.2 MJ) 1 SECTION IV RESULTS AND DISCUSSION In order to obtain the desired heat-flux levels, it was necessary to provide turbulent flow in the area of the ablation samples. As shown in Fig. 5 by the sudden increase in h, transition started at approximately 30 percent of the model length for both angles of attack, and the flow was fully turbulent over the ablation material. Measured heat-transfer coefficient values for laminar and turbulent flow closely agreed with those predicted by the methods of Ref. 2. Surface pressure measurements, however, differed somewhat from those given by wedge theory, because of disturbances in the flow caused by a shock emanating from the thermal expansion gap (see Fig. 4). The sudden drop in pressure aft of the

AEDOTR-66-26 x/l - 0. 55 in Fig. 5b may be attributed to leading-edge corner effects as illustrated by the estimated location of the intersection of the Mach lines with the model centerline.

Cork had the best insulative properties of the materials tested, whereas ESM and Buton A500 showed similar but somewhat less insulative capabilities.

11 AEDOTR x/l in Fig. 5b may be attributed to leading-edge corner effects as illustrated by the estimated location of the intersection of the Mach lines with the model centerline. Insulative performance of the materials is illustrated in Fig, 6. Cork had the best insulative properties of the materials tested, whereas ESM and Buton A500 showed similar but somewhat less insulative capabilities. Phenolic glass offered the least insulation capacity. REFERENCES 1. Randall, R. E. "Thermodynamic Properties of Air: Tables and Graphs Derived from the Beattie-Bridgeman Equation of State Assuming Variable Specific Heats. " AEDC-TR-57-8 (AD ), August Harms, R. J., Schmidt, C. M., Hanawalt, A. J., and Schmitt, D. A. "A Manual for Determining Aerodynamic Heating of High-Speed Aircraft. " Bell Aircraft Corporation, Report No (AD229434), June 1959.

$SCREEN ^ ^-INSTRUMENTATION RING SECTION \ \ \ \ THROAT 7 MACH 10-1 ' QUARTZ WINOOWS$ TRACTION SYSTEM DIFFUSER SECTION Tunnel Assembly WINDOWS FOff MQD L INSPECTION Off

TRACTION SYSTEM DIFFUSER SECTION Tunnel Assembly WINDOWS FOff MQD L INSPECTION Off

TRANSFER TESTS OR QUICK MODEL CHANGE PRESSURE TRANSDUCERS TANK ENTRANCE DOOR FOR

12 SCREEN ^ ^-INSTRUMENTATION RING SECTION \ \ \ \ THROAT 7 MACH 10-1 ' QUARTZ WINOOWS SAFETY OOOR FAIRING \ -HklHI \0OOR TEST SECTION MOOEL SUPPORT INJEC T ION/RE TRACTION SYSTEM DIFFUSER SECTION Tunnel Assembly WINDOWS FOff MQD L INSPECTION Off PHOTOGRAPHY WINDOWS FOR SCHLIEREN PHOTOGRAPHY AIR DUCTS TO COOL MODEL FOP HEAT- TRANSFER TESTS OR QUICK MODEL CHANGE PRESSURE TRANSDUCERS TANK ENTRANCE DOOR FOR MODEL INSTALLATION OR INSPECTION MODEL INJECTION AND PITCH MECHANISM Test Section Fig. 1 Tunnel C

13 Fig. 2 Installation Photograph

-6.00-4 31 a o -H H a CO 9 H*- 9-2.00 -lo50-1.00 cd u 01 +J O» 2.985 3 O O 1.

001 Leading- Edge Thickness I 1 1 1 1 1 o O 00 00 <N «rh in 00 00 * * * CO 00 CO m t> o T-i Body Station Top View

14 a o -H H a CO 9 H* lo cd u 01 +J O» O O I o in t> * in O Pressure Port Thermocouple < Pressure Port and Thermocouple in Leading- Edge Thickness I o O <N «rh in * * * CO 00 CO m t> o T-i Body Station Top View Side View a. Flat Plate Fig. 3 Model Detai N IN (N M o m Pressure or Thermocouple Panel Location of Two Ablation Samples, Pressure or Thermocouple Panel All Dimensions in Inches T 3.30 > m c n

oo > n 2.985 Flow Thermocouple Top View 0.

15 oo > n Flow Thermocouple Top View Stainless Steel 0,150 Sample Bond Textolite Side View All Dimensions in Inches b. Ablation Sample Insert Fig. 3 Concluded Thermocouples Located on Underside of Stainless Steel

16 Nondimensional Distance from Leading Edge, x/l a. a 15 deg Nondimensional Distance from Leading Edge, x/l b. a = 25 deg Fig. 4 Typical Schlieren Photographs

G <D r-i u H <H «H CD «00 U I o 0.012 0.008 I 1 1 1 Heat-Transfer Theory Using: Measured Pressure.

17 G <D r-i u H <H «H CD «00 U I o I Heat-Transfer Theory Using: Measured Pressure. Theoretical Pressure (Wedge) 0> IG <H I «CM a -p CO =H U N. EH 3 I 4-> +j pa cd d) Nondimensional Distance from Leading Edge, x/l CD Ü O s a C O H CO - G CD O fn g 3 H CO TJ en fl CD I O 15-deg Wedge Theory O O f Intersection Expansion Gap of Mach Lines (M L = 5.28) Nondimensional Distance from Leading Edge, x/l 1.0 a. a deg Fig. 5 Flat Plate Centerline Flow Characteristics 10

$-p Ö <L> H 0 r-t =>H =H 0) a oc u i ü f-l 0) 0) (A «H I I/ICM Ö +J rt <M r-( \ H 3 1 4-> +J CO cs 0) > X 0.016 0.012 0.008 0.$ 8 Nondimensional Distance from Leading Edge, x/l 1.0 o H CD d o vs.

18 -p Ö <L> H 0 r-t =>H =H 0) a oc u i ü f-l 0) 0) (A «H I I/ICM Ö +J rt <M r-( \ H > +J CO cs 0) > X I I I I Heat-Transfer Theory Using: Measured Pressure. Theoretical Pressure (Wedge) Ablation Sample Location L Nondimensional Distance from Leading Edge, x/l 1.0 o H CD d o vs. a o a H w c CD s -a '^ a a) O M 55 ft o o t XT 25-deg Wedge Theory Expansion Gap V Intersection. of Mach Lines (M L = 3.38) : Nondimensional Distance from Leading Edge, x L 1.0 b. a - 25 deg Fig. 5 Concluded 11

800 «700 < 0) be s a o 600 500 p s 0) H <D Ü <H X Ü

60 80 100 Time of Exposure to Airstream, t, sec a.

19 800 «700 < 0) be s a o p s 0) H <D Ü <H X Ü a I a i CO rh «S H 0 p as SB Time of Exposure to Airstream, t, sec a. a = 15 deg Fig. 6 Material Insularive Performance

cd 5 h n < 600 0 bb 500 C 3 XI / Symbol Ablation Sample Material O Ö o 0.05-in.

Surface Temperature) 0 Phenolic Glass a Buton A500 O V ESM Cork 0) rh 200 a I IM rh

20 cd 5 h n < bb 500 C 3 XI / Symbol Ablation Sample Material O Ö o 0.05-in.-thick Stainless Steel 0) -*-> 400 S H cd ü (Ref. Surface Temperature) 0 Phenolic Glass a Buton A500 O V ESM Cork 0) rh 200 a I IM rh d r) oj IOO +J d s Time of Exposure to Airstream, t, sec 120 b. a m 25 deg Fig. 6 Concluded 13

$I UNCLASSIFIED Security Classification DOCUMENT CONTROL DATA R&D (Security cles8\ticbtion ct title, body of abstract and indexing annotation must bo entered when the- overall report is classtued)$ , Operating Contractor, Arnold Air Force Station, Tennessee 3 REPORT TITLE 2» RCPOfit SECURITY C L A3SI FIC A T I OK UNCLASSIFIED 2b SROUP N/A INSULATIVE PERFORMANCE OF SELECTED ABLATIVE MATERIALS IN

, Operating Contractor, Arnold Air Force Station, Tennessee 3 REPORT TITLE 2» RCPOfit SECURITY C L A3SI FIC A T I OK UNCLASSIFIED 2b SROUP N/A INSULATIVE PERFORMANCE OF SELECTED ABLATIVE MATERIALS IN

21 I UNCLASSIFIED Security Classification DOCUMENT CONTROL DATA R&D (Security cles8\ticbtion ct title, body of abstract and indexing annotation must bo entered when the- overall report is classtued) ORIOINATIN G ACTIVITY (Corporate author) Arnold Engineering Development Center, ARO, Inc., Operating Contractor, Arnold Air Force Station, Tennessee 3 REPORT TITLE 2» RCPOfit SECURITY C L A3SI FIC A T I OK UNCLASSIFIED 2b SROUP N/A INSULATIVE PERFORMANCE OF SELECTED ABLATIVE MATERIALS IN A LOW ENTHALPY HYPERSONIC AIRSTREAM 4 DESCRIPTIVE NO'*'ES (Tvpa of report and inclusive dales) N/A S AUTHORfSJ (Last name, lint name, initial) Carman, J. B., Jr., ARO, Inc. 6 REPORT DATE May 19G6 8a CONTRACT OR GRANT NO A F 40 ( 60 0 } I b System 133B c Program Element B TOTAL NO OF PASES 19 0r,ISIN ' T0R ' S BEPOBT NUMBERfS) AEDC-TR b NO OF REFS 3b OTHER REPORT N o(s) {A ny other number» that may be teal gned thia report) 10 AVAILABILITY/LIMITATION NOTICES Qualified users may obtain copies of this report from DDC Distribution of this document is unlimited. II N/A SUPPLEMENTARY NOTES 13 ABSTRACT N/A ] 12 SPONSORING MILITARY ACTIVITY [Ballistic Systems Division, Air Force Systems Command, Norton Air Force Base, California Tests were conducted to investigate the insulative performance of selected ablative materials when exposed to a relatively low enthalpy hypersonic airstream. Samples of cork, an elastomeric shield material, phenolic glass containing a buton resin, and phenolic glass, mounted on the surface of a sharp flat plate, were injected into a Mach 10 airstream at 15- and 25-deg angles of attack. g The model was tested at a high free-stream Reynolds number, 2.2 x 10 per foot, to produce turbulent flow over the samples. The test results, which consisted of back surface temperature histories on the 0.15-in.-thick samples, showed that cork provided the greatest heat protection. DD FORM 1 JAN & UNCLASSIFIED Security Classification

UNCLASSIFIED Security Classification KEY WORDS LINK A ROI.E WT LINK 8 LINK C ablative materials low enthalpy performance hypersonic flow turbulent flow I.

REPORT SECURITY CLASSIFICATION: Enter the overall security classification of the report. Indicate whether "Restricted Data" is included.

22 UNCLASSIFIED Security Classification KEY WORDS LINK A ROI.E WT LINK 8 LINK C ablative materials low enthalpy performance hypersonic flow turbulent flow I. 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 tn accordance with appropriate security regulations. 2b. GROUP: Automatic downgrading is specified in DoD Directive 5200, 10 and Armed Forces Industrial Manual. Enter the p.ronp 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 capitals in parenthesis immediately following the title. A. 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 authors) as shown on or in the report. Entei last name, first name, middle initial, If T.ilitary, 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 month, 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, Le., enter the number of pages containing information. 7b. NUMBER OF REFERENCES: Enter the total number of references cited in the report. 8». CONTRACT OR GRANT NUMBER: If appropriate, enter the applicable number of the contract or grant under which the report was written. 86, 8c, os Bd. PROJECT NUMBER: Entei the appropriate military department identification, such as project number, subproject number, system numbers, task number, etc. 9«. 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 NUMbERfS): If the report has been ass.-gned 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 INSTRUCTIONS 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 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 offi-e 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.nay also appear elsewhere in the body of the technical report. If additional space is required, s 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 securily'classification of the information in the paragraph, represented as (TS), (S). (C), or (U) There is no limitation on the length of the abstract. ever, the suggested length is from 150 to 225 words. r i How- 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 wll be followed by an indication of technical cantext. The assignment of links, rules, and weights is optional UNCLASSIFIED Security Classification

S 3 j ESD-TR W OS VL, t-i 1 TRADE-OFFS BETWEEN PARTS OF THE OBJECTIVE FUNCTION OF A LINEAR PROGRAM

S 3 j ESD-TR W OS VL, t-i 1 TRADE-OFFS BETWEEN PARTS OF THE OBJECTIVE FUNCTION OF A LINEAR PROGRAM I >> I 00 OH I vo Q CO O I I I S 3 j ESD-TR-65-363 W-07454 OS VL, t-i 1 P H I CO CO I LU U4 I TRADE-OFFS BETWEEN PARTS OF THE OBECTIVE FUNCTION OF A LINEAR PROGRAM ESD RECORD COPY ESD ACCESSION LIST ESTI