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AFFDL-TM-73-120-FXG Tyffl'fr AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF LABORATORIES AIR FORCE SYSTEMS COMMAND WRIGHT PATTERSON AIR FORCE BASE OHIO LOW MACH NUMBER TEMPERATURE MEASUREMENTS USING ENCAPSULATED LIQUID CRYSTALS Max E. Hillsamer August 1973 Project Nr. 1366 Approved for public release; distribution unlimited High Speed Aero Performance Branch Flight Mechanics Division Air Force Flight Dynamics Laboratory Reproduced From Best Available Copy
62

AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

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Page 1: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

AFFDL-TM-73-120-FXG Tyffl'fr

AIR FORCE FLIGHT DYNAMICS LABORATORY

DIRECTOR OF LABORATORIES

AIR FORCE SYSTEMS COMMAND

WRIGHT PATTERSON AIR FORCE BASE OHIO

LOW MACH NUMBER TEMPERATURE MEASUREMENTS USING ENCAPSULATED LIQUID CRYSTALS

Max E. Hillsamer

August 1973

Project Nr. 1366

Approved for public release; distribution unlimited

High Speed Aero Performance Branch Flight Mechanics Division

Air Force Flight Dynamics Laboratory

Reproduced From Best Available Copy

Page 2: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

AFFDL-TM-73-120-FXG

LOW MACH NUMBER TEMPERATURE MEASUREMENTS USING ENCAPSULATED LIQUID CRYSTALS

Max E. Hillaamer

August 1973

Project Nr. 1366

Approved for public release; distribution unlimited

High Speed Aero Performance Branch Flight Mechanics Division

Air Force Flight Dynamics Laboratory

Page 3: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

FOREWORD

Thia report was prepared by M.E. Hillsamer of the High Speed

Aero Performance Branch, Air Force Flight Dynamics Laboratory,

Wright-Patterson Air Force Base, Ohio. The work was performed as

part of the AFFDL ln-house research under Task Hr. 136603 "Aerodynamic

Heating to Military Vehicles", Project Mr. 1366 "Aeroperfonance and

Aeroheatlng Technology", and covers work conducted between December

1972 and March 1973.

Models for the tests were designed and fabricated under the

direction of Mr. John E. Fehl, Aerospace Vehicle Branch (FXS), and

tests vere conducted by personnel from Aeromechanics Branch (FXM)

and Experimental Engineering Branch (FXN) of the Air Force Flight

Dynamics Laboratory. The author gratefully acknowledges their

cooperative assistance.

This report has been reviewed and is approved.

IlLlP P. ANTONATOS Chiei, Flight Mechanics Division Air Force Flight Dynamics Laboratory

11

",. .... 1.

Page 4: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

ABSTRACT

An experimental program was conducted to evaluate the use of

encapsulated liquid crystals as a Beans of determining temperature

profiles in regions of interfering flows on wind tunnel models at

supersonic speeds. The tests were conducted on both plane surfaces

and on an ogive cylinder model equipped with 3 dimensional shock

generators at Mach numbers of 1.89 and 3.00 in the Trisonic Gasdynamic

Facility of the Air Force Flight Dynamics Laboratory. Freestream

Reynolds number were 1.0 and 3.0 million per foot.

Results show that models coated with encapsulated liquid slurry

and overcoated with a protective plastic film provided better

temperature profiles than models equipped with paper substrated

liquid crystals. Temperature profiles were easily discernible over :.# ' .V.'.."--

the entire surface of the ogive cylinder model within viewing range

of the camera, and specular reflections on the non-planar surfaces

did not invalidate any data*

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Page 5: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

CONTENTS

ABSTRACT PAGE

I. INTRODUCTION 7 1

II. APPARATUS

A. Models 3 B. Liquid Crystal Coatings 4 C. Wind Tunnel 6 D. Instrumentation 6

III» TEST DESCRIPTION

A. Test Conditions B. Test Procedure C. Data Reduction

IV» RESULTS

A» General B. Mach 1.89 Data C. Mach 3.00 Data

V. CONCLUSIONS

REFERENCES

LIST OF TABLES

TABLE

I. Test Conditions

II. Model Configurations Tested

iv

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10 H 16

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Page 6: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

ILLUSTRATIONS

FIGURE

1« Sketches of Flat Plate MOdels

a. Model C with Fin A

b. Model A or B with Fin B

2. Ogive Cylinder Model D

3. Color-Temperature Variation of NCR Type W-15 Encapsulated Liquid Crystals

4. Facility Layout

5. Comparison of Paper and Slurry Mounting Methods for Encapsulated Liquid Crystals

a. Paper Mounting, No Fin

b. Slurry Mounting, No Fin

c. Paper Mounting, Fin A, Xy - 8 in., «p ■ 10 deg.

d. Slurry Mounting, Fin A, Xy - 8 in., 6p - 10 deg.

e. Paper Mounting, Fin A, Xy ■ * in., 6p - 10 deg.

f. Slurry Mounting, Fin A, Xy - 4 in., «p - 10 deg.

g. Paper Mounting, Fin A, Xj, - 0 in., «p - 10 deg»

h. Slurry Mounting, Fin A, Xj, - Oiin., 6p - 10 deg.

6. Comparison of Temperature Profiles for Paper and Slurry Coated Models

a. Paper Mounting, Fin A, Xy - 0 in., «p - 10 deg.

b. Slurry Mounting, Fin A, Xy • 0 in., «p - 10 deg.

7 Through \2» Temperature Distributions in the Interference Regions on Model C.

7. Fin A, Re. - 3.0xl06/ft ]f

«. X- 8 in., 8 - 15 deg« >

PAGE

20

20

21

,:23>:

24

2*

25

25

26

26

2?

27

29

28

f.

..»".

b. Xy • 4 in., «p • 15 deg. "tf - 30

• ■■* ■ • •>" I '■ .

Page 7: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

FIGURE

8. Pin A, Re„ - 1.0xl06/£t

a. Xy - 8 in., «F - 15 deg.

6p - 15 deg. b. X- ■ 4 in.

e. Xy ■ 0 in.,

9. Pin B, Re, - 3.

a. Xy - 8 in.

b. Xy - 4 in.

10. Pin B, Re„ - 1.

a. Xp - 8 in.,

b. Xp - 4 in.,

c. Xp - 0 in.,

11. Pin A, Re„ - 1.

a. Xp " 4 in.,

V. Xp - 0 in.

12. Pin B, Re„ - 1.

a. Xp - 4 in.,

b. Xp - 0 in.

13. Temperature Profiles on Model D, Re. - 3.0x10 /ft, o • 0 deg. |

a. Pin A, 6 • 0 deg. *

b. Pin A, «p - 5 deg.

c. Pin A, «p ■ 10 deg.

d. Pin A, «| - 15 deg.

14. Temperature Profiles on Model D, Re. - 3.0x10 /ft, a *.12 deg.

6p - 15 deg.

Oxl66/ft

6p - 15 deg.

6p - 15 deg.

0xl06/ft

6p - 15 deg.

«P f3 15 deg.

«p - 15 deg.

0xl06/ft

6p fr 5 deg.

6 • 5 deg.

0xl06/ft

6-5 deg.

6p - 5 deg.

PACE

31

32

33

34

35

36

37

38

39

40

41

42"

«. Pin A, «p - 0 deg.

43

43

44

44 V

45

vi

Page 8: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

FIGURE PAGE

46

46

b. Pin A, 6p ■ 5 deg. 45

c. Pin A, *p - 10 deg.

d* Pin A, *p • 15 deg.

15. Temperature Profiles on Model D, Ke„ 3.0x10 /ft, o ■ 0 deg.

a. Pin B, 6p - 0 deg. 47

b. Pin B, *F - 5 deg. 47

c. Pin B, «p - 10 deg. 48.

d. Fin B, 6p f 15 deg. 4«

16. Temperature Profile« on Model D, Re. -3.0x10 /ft, o ■ 12 deg.

a. Pin B, «p - 0 deg. - 49

b. Pin B, «p - 5 deg. 49

c. Pin B, 6p - 10 deg. 50

d*. Pin B, «p - 15 deg. ; 59

17. Temperature Profiles on Model C, M. • 3.0, Fin A, 51 Re. - 3.0xl0ö/ft., Xy - 0 in., «p - 15 deg.

18. Temperature Profiles on Model D, M. • 3.0, Re. ■ 3.0x10 /ft, ■ o • 0 deg. ' ' 'f-f.-. I . •/

a. Fin A, «- f 0 deg. ' , 52

b. Fin A, «p - 10 deg. v 52

19. Temperature Profiles on Model D, M. - 3.0x10 /ft.,'.,'- o • 15 deg.

a. Fin A, 6p - 0 deg.

b. Fin A, «p - 10 deg.

- ■.-->

viii

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Page 9: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

Symbol

M

r

T

X

ac

6

y

LIST OP SYMBOLS

Description*

Mach mmber, dimensionless

Reynolds number, 1/ft

Recovery factor

Temperature, deg F or deg R

Axial distance measured from model leading edge» in.

Angle of attack, deg.

Fin or canard deflection angle, deg.

Ratio of specific heats

Wavelength of light, nm.

Subscripts

AW

F

0

V

00

Adiabatic Wall Conditions

Fin or canard

Total or stagnation conditions

Model wall conditions

FreeBtream conditions

-*'

> .»'.v.

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: ■■. ^ '>' -.•'.

viii -.AV .v-

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Page 10: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

I. INTRODUCTION

Aerodynamic heating of aircraft and missile configurations in

the supersonic flight regime, while not so severe as to cause

catastrophic failure, can'result in degradation of the structure.

Of special interest are regions around wing-body or fin-body

junctions where localised "hot spots'* develop because of intersec-

ting flow fields*

The purpose of the present study was to investigate and evaluate

Methods of obtaining aodel surface teaperatures and heat transfer

rates in regions of.interfering flow fields at low Mach numbers*

Several methods have been used in wind tunnels to measure temperatures

and heating rates in regions of interfering flow fields at Mach numbers

of 6 and above. Neumann and Burke (Reference 1) compare results

obtained by them and others in interfering flow fields of 2 and 3-

dimensional shock generator models. Models used were thin skin flat

plates equipped with standard thermocouple instrumentation* Incomplete

mapping of high heating regions resulted because of lack'of adequate

Instrumentation in areas of interest. Thin skin thermocouple instru-

mented models are also quite costly to build.

Various investigators such as Jones and Hunt (Reference 2) and

Patterson (Reference 3) have used a method of obtaining quantitative

heat transfer measurements with temperature sensitive phase change

coatings applied to models made of low conductivity materials, such as

Teflon or Stycast. Schulte (Reference 4) used this phase change ,

•'".■"■'■ -.-■."...;■• .. ■• ■'.".-- , ". ■* ■ -'-\ '*'- . ■', / :. *'■ ' ';.;

■ ■ ■■. .:■••■••;, it:: ': ■ ■* ■ *: ..■,:■:/,:■.■: ;.;• ■ . - ,. .-■■■.-•• . . ■■ ■ •{:;■ «■-.•»*■ T..: - .•';..-• .-

■■ ; ■..•■.:.•••.-.. ■■..."■ . • . ; ■ (f-.■ -i---*-. ■♦ • • . ■' •„., . /: ... ■■ ■ '■■■■ ; ■ •' •; ':\ W^v?.; • ; .

": ' • ''. i» '..'.•.. ■.'•. •' ' '■ .'■ ■'' *i'- ■'*■ '■' '• •. ■ i ■

Page 11: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

coating method to quantitatively obtain heat transfer rates in inter-

ferfering flow regions on a flat plate model in the AFFDL High Temperature

Facility at Mach 10.

An obvious disadvantage in the use of the phase change coating

technique is that the phase change is not reversible. Model surfaces

must be cleaned and coated before each test run. Also, the Stycast

castable model material used for the model fabrication is not completely

homogeneous, and thermal properties of the material vary from batch

to batch.

McElderry (References 5 and 6) conducted boundary layer transition

studies at supersonic speeds using cholesteric liquid crystals attached

to plexiglass models. The start of transition was determined by the

color change of the liquid crystals due to increases in model surface

temperatures. Klein (References 7 and 8) was probably the first

investigator to report on the use of liquid crystals for aerodynamic

testing.

While the investigations of McElderry and Klein were mainly concerned

with locating boundary layer transition and turbulent regions, the liquid

crystals technique appeared applicable to complete thermal mapping of

models, with special emphasis on regions of interfering flow fields.

Advantages of this method are that model fabrication costs can be low,

complete temperature profiles can be obtained, color changes of the

liquid crystals are reversible, and the liquid crystals are obtainable

over a wide range of lower temperatures suitable for supersonic wind

tunnel facilities.

The present studies evaluated methods of attaching liquid crystals to

Page 12: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

the models, placement of light sources and cameras, mechanical stresses

on the coatings and thermal mapping of the models* No means was

available for obtaining temperature-time variations on the models, so

transient heat transfer values were not obtained.

II. APPARATUS

a. Models

Four plexiglass models were constructed for use in this study.

Plexiglass was chosen for its low thermal conductivity, uniformity of

material, and ease of machining.

Two models, identical in size and shape, were used to evaluate methods

of attaching liquid crystals. The models were flat plates 8 in. wide,

16 in. long and 3/4 in. thick with sharp leading edges of 15 deg bevel.

The top surface of the first model was recessed approximately 0.014 In.

from 0.250 in. back of the leading edge to the rear of the model. This

recess was provided for mounting plastic covered, paper backed sheets of

liquid crystals with two-aided masking tape. A smooth model surface was

thereby achieved. The top surface of the second model was not recessed

and was painted flat black to provide a dark base for the liquid crystals

slurry an alternative to the paper backed sheets previously used.

The third model tested was a flat plate identical to the second

model except that the width was 14 in. Use of the wider mod^l assured

that flow disturbances from the front corners of the model would npf

affect the flow in the region of shock generation.

Two shock generators were used with the flat plate models. Each

generator was 7 3/4 in. long, 2 in. high and 1 3/8 in. wide with flb^rp

leading edges of 20 deg bevel. The leading edge sweep angle of the first

•v ..,-■..'

' 1-~X~y •i '>

■:.'.•*••-•■'

Page 13: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

was 0 deg and 30 deg on the second. Holes drilled through the flat

plates permitted the shock generators to be bolted on at any desired

position. The shock generators were aluminum painted flat black to •

reduce glare* from Camera lights.

To evaluate the use of liquid crystals on non-planar surfaces,

an ogive cylinder model, 12 in. long and 3 1/4 in. base diameter was

fabricated from plexiglass and painted flat black. Two different size

canards were supplied for shock generation on the body of the model. ;

Both canards had a leading edge radius of 0.016 in. and a leading edge

sweep angle of 57 deg with'a trailing edge sweep angle of 10 deg.

The larger canard (A) had a base chord of 3.73 in. and a span of 2.62

in., and the smaller canard (B) had a base chord of 1.90 in. and a

span of 1.36 in. The canards were equipped with roll pins which were

inserted into a hole in the side of the model 2.57 in. forward of the

base and held in place with a set screw. Canard angle with respect

to the model could thereby be adjusted.

Figure 1 is a sketch of the flat plate models with shock generators.

Figure 2 presents the ogive cylinder model with control canards attached*

B. Liquid Crystal Coatings .

Cholesteric liquid crystals are chemically cholesterol esters

mostly of fatty acids. These nonflammable substances are liquid in

mobility but crystalline in optical properties. When illuminated with

unpolarized white light, incident at a given angle, only one light

wavelength is reflected at each viewing angle. Small temperature changes

Page 14: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

cause a shift in the molecular structure of the liquid crystals, and

light of a different wavelength is then reflected. Fergason (Reference

9) presents more complete documentation on the properties and character-

istics of the liquid crystals.

By selectively mixing liquid crystal substances color changes

through the entire visible spectrum can be obtained with increase in

temperature. The temperature span of color changes can be as small as

1.8°F or as large as 90*F. Temperatures can be measured with better than

0.18'F accuracy, and reaction time of the liquid crystals to temperature

change is less than 0.2 sec. Temperatures at which known liquid crystals

operate range from -4°F to 480°F. The color changes of the liquid crystals

are reversible, and the substances can be cycled through their temperature

ranges, any number of times.

Liquid crystals in their raw form are responsive to mechanical stress,

electromagnetic radiation and chemical vapors in addition to temperature.

The National Cash Register Company (NCR) has an encapsulation process ;

whereby microscopic amounts of liquid crystal compounds are encased, :fn

hard spherical shells id to 30 microns in diameter. ;; f

The encapsulated liquid crystals are more stable and less responsive

to mechanical stress or chemical vapors.

Encapsulated liquid crystals are available from NCR in either

sheet or slurry form. The sheets are made by sandwiching a thin layer

of encapsulated liquid crystals between a top sheet of clear plastic

and a back of black paper. The sheets are fastened to the model surface; - .'' "' . . "-■"•- '''■ ">■ '? ,

with two-sided masking tape. This method was used on the first model

tested in the present study» %1-Y £;^<:

'■'. 't:'" >' ;- ''"''■■1A . *•"-,

.'■■-; 3"*V ;'c 't ■-*:*-■ ' -■'

Page 15: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

Encapsulated liquid crystals in the slurry form were sprayed

on the surface of the model with an artist's air brush. After the

slurry dried a protective coating of Krylon plastic was applied to

the model surface. A hard, smooth model surface was obtained with a

total coating thickness, including flat black paint, liquid crystals

and Krylon coating, of 1.1 mil. This method of application was used

on one 8 in. wide flat plate and 14 in. wide flat plate and the

ogive cylinder model. All models were coated with NCR type W-15 encapsu-

lated liquid crystals, which has a temperature span of 10.8 deg F from

start of red to start of blue color change* Figure 3 shows the range

and color change temperatures of this particular compound.

C. Wind Tunnel '

In-house testing was conducted in the AFFDL Two^Foot Trisonic

Gasdynamics Facility (TGF). This facility is a closed circuit, variable ;

density, continuous flow wind tunnel using air as the working fluid.

A variation in Mach number from subsonic to Mach 3.0 is provided through

the use of fixed two-dimensional planar nozzle blocks. :,:

Stagnation pressure and temperature can be set by the operator jrad

are automatically controlled to within +1 psf and +1°F respectively. [

Figure 4 is a sketch of the general layout of the wind tunnel. j^

Reference 10 describes the facility and associated equipment in full '

detail. ''[■:■''J^-.'S

D. Instrumentation , ■ * i:

Color photographs of the model at each attitude constituted th«

entire model data acquisition. A 4 x 5 graphic view caaera was pl*c*d,.\' >?• ■- v ■-• •-,

directly normal to the model surface approximately 6 feet fro» the -

V

Page 16: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

subject. The light sources were two 500 watt, 3200 kelvin lamps about

30 degrees on each side of, and slightly higher than the camera. Four

second exposures at F22 were made on type L Ektacolor film.

III. TEST DESCRIPTION

A. Test Conditions

Tests to compare paper mounted encapsulated liquid crystals (ELC)

with slurry coated models were conducted at Mach 1.89 and a freestrearn

Reynolds number about 3 million per foot. Stagnation pressure was

1600 psfa, and stagnation temperature was varied from 100 to 115°F in

5* increments. The two 8 inch wide by 16 inch long flat plates were

used during this phase of the test.

The 14 in. wide by 16 in. long flat plate and the ogive cylinder i •

were tested at Mach numbers of 1.89 and 3.00 and freestrearn Reynolds

numbers about one and three million per foot. Table I lists test

conditions for each model.

B. Test Procedure \

All models were provided; with ELC coatings several days before start

v ■ of the tests and stored so;that testing would not be delayed by model

preparation. No deterioration in coatings was evident because of

storage. \

Prior to starting the wipd tunnel for each test run, each flat plate /

model was rolled so the coated surface was in the horizontal plane. i

After starting the tunnel, 'the model was rolled 90 deg with the coated

V surface toward the camera. ) This starting procedure reduced the danger of

the model damaging the windows in case high starting loads would cause

!

y ' . '.- " : ■■'■.-

Page 17: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

the model to break loose.

First test point pictures were taken at the maximum required stagna-

tion pressure and minimum stagnation temperature. The temperature was then

increased with photographs obtained every 5 deg. Stagnation pressure and

temperature were then reduced to minimum required conditions and the

procedure was repeated.

Shock generator fins were tested at the most rearward locations first

so that the shock generators would cover the mounting holes in the surface

of the model on succeeding runs. During Mach 3 testing the mounting holes

toward the front of the flat plate were filled with modelling clay to

assure a smooth surface ahead of the shock generator.

The ogive cylinder model, D, was installed with the fin mounting

hole toward the camera. Initial test point for each run were at maximum

stagnation pressure and minimum stagnation temperature. The model was

pitched from 0 deg to 12 deg with test photos being obtained every 4 deg.

Stagnation temperature was then increased and the angle-of-attack sequence

was repeated.

Table II is a summary of model configurations used during testing

\ ■ •

in the 2 Ft TGF.

C. Data Reduction

There was no method available for removing the model from the tunnel

airflow' and providing a time base to obtain transient heat transfer rates.

Therefore, all data presented in this report are in the form of temperature

distance lines or isothermal line patterns in the region of the shock

8

Page 18: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

generators. These Isothermal lines were obtained fron 8 x 10 in. color

prints of the test photographs taken at each test point.

The standard 2 Ft TCP data reduction was used to provide stagnation

and freestream operating conditions in the wind tunnel.

IV. RESULTS

A. General

Data presented in this report are from two separate test periods in

the 2 Ft TGF. The majority of test time was concentrated in the Mach

1.89 studies, with only sufficient runs at Mach 3.00 to determine the

suitability of the method. Results presented in this report are at a

stagnation temperature of 100*F for Mach 1.89 and 115*F at Mach 3.00.

The higher temperature was necessary to produce color change profiles

at Mach ?.0.

A total of 392 color photographs of model temperature profiles were

obtained during this test. Because of the time Involved in reducing

data from all the photographs, only representative temperature profiles

are presented. Reproduction of color photographs is quite costly, so

only representative color prints are presented in this report. Sufficient

fine detail was not obtainable from black-and-white prints of the color

negatives. Temperature profiles presented were obtained by plotting distances

measured from color photographs. None of the data were reduced to heat

transfer coefficients because no adequate time base was available to

determine heating rates.

Page 19: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

B. Mach 1.89 Data

The first phase of this study consisted of determining the most

suitable method of attaching liquid crystals to the flat plate models.

Comparisons of the paper and slurry type mounting methods are presented

in figure 5 (a-h). For identical fin locations, high temperature areas

are the same on both models. However, much clearer detail is evident on

the slurry coated model because of the smoother test surface. The

paper backed ELC appeared to bubble and wrinkle when exposed to the

tunnel airflow causing tripping of the model boundary layer. Streaks of

color on the paper coated model are evidences of this boundary layer

tripping. With the fin at its most forward location (fig. 5 g)

the entire rear section of paper mounted ELC came off during testing.

Klein (Reference 7) utilized raw (not encapsulated) liquid crystals

in the slurry state which were free-flowing during wind tunnel operation.

The coating tended to leave regions of high shear, and necessitated

recoating the model after a period of testing. His recommendation was to

cover the liquid crystals with a thin transparent plastic coating which

would shield the crystals from mechanical stresses. The slurry coated models

used in the present study were coated with Krylon plastic spray over the ELC.

This method provided a hard model surface which showed no airflow shear

effects. Although reflections from the light sources are evident, color

changes due to temperature were visible in color photographs over the

entire model surface.

10

Page 20: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

The rough appearance of the model surface in figure 5 (b,d,f and h) was

caused by the method of Krylon spraying used, and the model boundary layer

was not affected in any way.

A representative comparison of the temperature profiles obtained from

the two types of model coatings is shown in figure 6. While the patterns

are generally the same on both models, the line of constant temperature are

much clearer on the slurry coated model (fig. 6 b). Broken and nonuniform

color patterns on figure 6a were caused by the paper mounting separating

from the model as mentioned-previously. Clearly defined regions on the

slurry coated model (figure 6 b) show the bow shock from the fin and a

high temperature, region between the bow shock and the fin.

Figures 7 through 10 present temperature profiles on the 1A x 16 in.

flat plate (model C ) with the shock generator fins at a deflection angle of

15 deg. Color photographs from which the temperature profiles were derived

show boundary layer tripping occuring at the higher Reynolds number. This

tripping was the result of leading edge surface irregularities caused by

slight mismatches between the stainless steel leading edge and the plexi-

glass test surface.

Bow shock angles from the shock generator fin are shown in the tem-

perature profiles of figures 8 through 10 and are greater than the 48 deg.

Shock angle predicted for a 15 deg wedge in Reference 11. The higher shock

angles shown on the profiles were caused by the shock generator fin being

behind the bow shock from the basic model. Two different flow fields, one

from the flat plate and the other from the shock generator fin, intersect

to form the flow field producing the temperature profiles« These figures

Page 21: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

show that as the fin is moved forward, the initial shock angle decreases

until at X - 0 in., the shock angle is about 50 deg. The initial shock F

angle from the fin is also greater for the lower Reynolds number case.

A comparison of figures 7 and 9 showed that the shock angle was approxi-

mately 3 deg. less for the 20 deg. swept fin (B) than for the 0 deg.

swept fin (A).

Secondary areas of high temperature are shown close to the fin/plate

junction. While no oil flow or surface pressure data are available for

these flow conditions on the model, the flow field appears to compare with

that discussed in Reference A, Section IV. A conical corner flow region

starts at the plate/fin junction, and vortices emanating from the corner

vertex produces regions of separation and reattachment with higher tempera-

tures evident in the reattached regions.

Temperature profiles in the interference region of the model with

the fins at 5 deg. deflection are presented in figures 11 and 12 for a

Reynolds number of 1.0 million per foot. Predictions from Reference 11

for a 5 deg. wedge show an undisturbed shock angle of about 36.5 deg.

Profiles of figures 11 and 12 indicate a minimum shock angle of about

28 deg. for the 20 deg. swept fin (figure 12b) to 37 deg, for the 0

deg. swept fin (figure 11a). As in the profiles for fin deflection angles

of 15 deg., the profiles in figures 11 and 12 show secondary areas of

high temperature between the fin and bow shock»

Results of using encapsulated liquid crystals on a non-planar sur-

face are demonstrated in the temperature profiles of figures 13 through 16.

Reference 7 indicated difficulties in obtaining acceptable results with

12 . " ^i.%':i: &:?\

11

M i :

r • i ' ! i I. 1

Page 22: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

liquid crystals because of specular reflections and adverse angles of *

illumination and viewing. On planar models these problems can be resolved

by using a single light source and camera placed normal to the model sur-

face. However, on curved surfaces light source and camera placement must

be compromised by trial and error. Profiles on the ogive cylinder model

presented in figure 13 through 16 indicate very good resolution of fin in-

duced separation and high shear regions can be obtained on bodies of rev-

/ olution equipped with control'canards.

/ • . ■

Generally, the temperature patterns are quite similar for all canard

deflection angles and model/angles of attack. A high temperature region

i is seen in the location of the canard bow shock. A second high temperature

region extends along the canard in a region of high shear. Between the two

high temperature areas is a low temperature secondary separation region.

Although no oil flow data Ware obtained, temperature profiles indicate flow

characteristics similar to /those formed on the flat plate models and results

at higher Mach numbers suclWas presented in References 4 and 12.

The base geometry of jcanards A and B was contoured to match the surface

of the ogive cylinder wi^h a canard deflection angle of 0 deg. As the

;/ ■■■■• :-':

canards were deflected* to 15 deg., a gap appeared between the front'-point

of the canard and the Model body. This gap was unavoidable and is espe-

cially apparent in figures 13 and 14. At a canard deflection of 0 deg.,

the color change star\ is 0.10 to 0.20 in. behind the front of canard A.

Small disturbances in temperature profile occvring about the 9.25 in.

station were caused by thexroll pin used to fasten the canard to tue node!. ■ ■ ■ \ '-":•-•.:•'■

■ ,: ■*: >.-::■ ■ .■■:';- r&Hi -■' '

k 13

Page 23: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

C. Mach 3.00 Data

A very abbreviated test program was conducted in the 2 ft TGF at

Mach 3.00 to determine the sutiability of the models and test procedures

at higher Mach number. Maximum stagnation temperature in the TGF was

limited to 115-F by mechanical constraints. The adiabatic wall temperature

was calculated by the equation

TAW"

'l+(^)rM 2

K^K _ To

where r - 0.85 for laminar flow and 0.89 for turbulent flow. For Mach 3

flow at a stagnation temperature of 115*F the adiabatic wall temperatures

were calculated as 59.8'F for laminar flow and 74.4#F for turbulent flow.

While the color change range of the ELC was suitable for Mach 1.89 testing,

model surface temperatures at Mach 3 were suspected of being too low to

produce color change profiles of an acceptable quality. Representative

results of Mach 3 testing, presented in figures 17 through 19, show that

good temperature profiles were obtained in the interference regions of

the models. \

Figure 17 shows temperature profiles on the flat plate model C with

fin A at the most forward position and deflected 15 degrees. At Mach 3

there were no evidences of leading edge imperfections causing tripping of

the model boundary layer as was observed at Mach 1.89. The fin bow shock

angle shown in this figure is approximately 43 deg. Reference 11 predicts

14

Page 24: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

a shock angle of 32.2 dcg for a 15 deg wedge at Mach 3.0. The greater

measured than predicted shock angle was caused by the flow fields from the

model and fin intersecting to form a flow field similar to the one discussed

in Reference 4, Section IV and earlier in this report. Also shown in this

figure are a low temperature separated region and a high temperature, high

shear region close to the fin.

Figures 18 and 19 present temperature profiles on model D with canard

A. Profiles produced on the non-planar model at Mach 3.0 are quite similar

to the Mach 1.89 data. The most notable difference is the Mach 3.0 inter-

ference regions are narrower than those on Mach 1.89 data. This is due to

the lesser canard shock angle at the higher Mach number. The high tempera-

ture, high shear region and the low temperature separation area are evident

in figures 18 and 19...

I

15

Page 25: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

I

i

V. CONCLUSIONS

The use of encapsulated liquid crystals was shown in Reference 5 to

produce better results than raw liquid crystal for temperature measure-

ments on planar models. While Reference>5 presented results of using

paper mounted ELC, the present study shows the ELC in slurry form, s

sprayed on and oversprayed with a protective plastic coating was the

most suitable method of using liquid crystals for aerodynamic testing.

No adverse effects from mechanical stresses were noted, and color patterns

were not obscurred by specular reflections.

Use of encapsulated liquid crystals on non-planar surfaces was demon-

strated in this study. Temperature profiles were easily discernible over

the whole viewing range of the camera, and high temperature regions were

obtained on the surface of the ogive cylinder model greater than 75 deg j

■•» , .■■■'.■'('

from normal camera viewing line. j

f The addition of a technique for cooling and shüding the model from j

the alrstream plus a fast model injection system with time base would pro- \ " ■ ■ • I

vide a means of obtaining transient heating rates using liquid crystal !

coatings. High speed movie photography would be necessary to observe the

formation of color patterns on the model.

Results of the present study have shown that encapsulated liquid j j

crystals provide a useful tool in determining flow patterns and regions i

of high temperatures on models in supersonic flows. This method will be f

used in future tests to determine high heating areas on weapons systems

externally stored on the underside of an aircraft wing at supersonic speed«.

More complete mapping of the high heating regions can be accomplished by

this technique than with thermocouples on thin skin models. U% f

16

i

i. ■E

n ',;-:%± :"?U ■ ' *" **■■&-

-r-: .-!_■ '■'j-■>■'■'-' ;.- P

''■£&■■ ' ■' '- ''' .'(

-* '?*?>■ ■■,, v ■ *.

}

* '■. r>... '•??-' --- ■; *. ' ,- '; ■

;,, £• - *.-

.': -<B.<» .-. /■/

Page 26: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

REFERENCES

1. Neumann, R.D. and Burke, G.L. "The influence of Shock Wave-Boundary Layer Effects on the Design of Hypersonic Aircraft?, AFFDL TR 68-152, Mar 1969

2. Jones, R.A. and Hunt, J.L. "Use of Fusible Temperature Indicators for Obtaining Quantitative Aerodynamic Heat-Transfer Data", NASA TR R-230, Feb 1966

3. Patterson, Jerold L. "Heat Transfer Testing in the AFFDL High Temperature Facility Using the Phase Change Coating Technique", FXG TM 70-12, Aug 1970

4. Schultz, H.D. "Experimental and Analytical Investigation of Temperature Sensitive Paints", AFFDL-TR-72-52, June 1972

5. McElderry, E.D. "Boundary Layer Transition at Supersonic Speeds Measured by Liquid Crystals", FDMG TM 70-3, June 1970

6. McElderry, E.D. "Boundary Layer Transition Mapping at Supersonic Speeds Measured by Liquid Crystals", AFFDL-TM-73-5-FXG, January 1973

7. Klein, E.J. " Application of Liquid Crystals to Boundary Layer Flow Visualization", AIAA 3rd Aerodyanmic Testing Conference, AIAA Paper 68-376, April 1968

8. Klein, E.J. "Liquid Crystals in Aerodynamic Testing", Astronautics & Astronautics, Vol. 6 Nr. 7 July 1968, pp 70-73

9. Fergason, J.L , "Liquid Crystals", Scientific American, 211 (2), August 1964

10. Allen, N.H., "The Two-Foot Supersonic Gasdynamics Facility", AFFDL/FXM, 1 August 1968

11. Ames Research Staff, "Equations, Tables, and Charts for Compressible Flow", NACA Report 1135, 1953

12. Bramlette, T. Taz, "Flow Field, Pressure and Heat Transfer Associated with Small Fins in Laminar Hypersonic Flow", SCL-RR-720339, )r November 1972 V: ";« &'-:1;

I t. f ■•;

17 <.%r. ■ r ".'

r :'. '' ■ -y.".:' :

■ ..; v ,-• '" .. "•

•j.--..'r>::-'- ;;}. ?:■ ■ '■ ■* .

<<;v

Page 27: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

Table I, Test Conditions

Model Mach Nx • Re. X106/£t Po, PSFA To, °F

A, 8" x 16" Paper Coated

1.89

i

3.0 1600 100— 115

B, 8" x 16" Slurry Coated

1.89 \ \

t \ i /

3.0 1600 100 — 115

C, 14" x 16" 1.89. /

\

3.0 1.0

1600 560

100— 115 100 —115

D, Ogive Cylinder 1.89 (

3.0 1.0

1600 560

100—115 100 —115

C, 14" x 16" 3.00

/

' 3.0 1.0

2900 1000

110, 115 110, 115

D, Ogive Cylinder 3.0 / 3.0 1.0

2900 1000

115 115

;

\

? v,

l

18

^^■^■^^^i^^^

Page 28: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

Table II, Model Configurations Tested

Mach Mr. X106/ft

Model Fin X, in. 6 deg a deg

1.89 3.0 A (8 x 16) A 0,4,8, off 10 0

1.89 3.0 B (8 x 16) A 0,4,8, off 10 0

1.89 1.0 & 3.0 C (14 x 16.) A & B 0 4 8 off

5,15 0.5.15 0.5,10,15

0

1.89 1.0 & 3.0 D (ogive-cyl) A & B 0,5,10,15 0,4,8,12

3.00 1.0 & 3.0 C (14 x 16) A off, 0,4,8 5,15

3.00 1.0 & 3.0 D (ogive-cyl) A & B 0,10 0,5,10,15

19

Page 29: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

a. Model C with Fin A

b. Model A or B with Fin B Figure I. Sketches of Flat Plate Modele

j2fL

Page 30: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

o

I

cO

21

Page 31: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

110 r

100

90

J H* 80

70 -

60 400

From Edmund Scientific Co. Bulletin Nr. 7II3I7-I

■B R 500 600

X.nm 700

Figure .3. Cobr-Temperature Variation for NCR type W-15 Encapsulated Liquid Crystals .>• .1.:

22 r&.i-

Page 32: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

u

«0 c

o O

(J

O (9 'C t-

Q U. U. <

0) L. D

Ü

23

■..yj'i'nyri!. FT »vm-aS-WÜ «Al'BWU^.- - J,.1..- ,>l""Jg/ r^T.T ^.T'^iFA'f/

Page 33: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

Paper Mounting, No Fin

Slurry Mounting, No Fii

arison of Paper and Slurry Mo UP. oes for Encapsulated Lieuid Crv

Page 34: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

d. Siurrv Mountir.a, Fir. A, X =8in., : =10 dec F F

:ure 3 (Continued)

Page 35: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

v =ii -i

Page 36: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

g. Paper Mounting, Fin A, X =0in., 6 =10 deg, F F

Figure 5. (Concluded)

27

Page 37: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

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Page 39: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 40: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 41: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 42: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 43: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

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Page 44: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 45: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

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Page 46: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 47: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 48: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 49: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

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Page 50: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 51: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 52: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

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Page 54: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

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Page 55: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 56: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
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Page 58: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 59: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 60: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

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Page 61: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,
Page 62: AIR FORCE FLIGHT DYNAMICS LABORATORY DIRECTOR OF ...FOREWORD Thia report was prepared by M.E. Hillsamer of the High Speed Aero Performance Branch, Air Force Flight Dynamics Laboratory,

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