AIAA CONFERENCE ON PHYSICS OF ENTRY INTO PLANETARY ATMOSPHERES

AUGUST 26.28, 1963. MASSACHUSETlS INST.TUTE OF TEChNOLOGY. KRESGE ALOITORIUM, CAMBRIDGE. MASSACrlUSETTS -

O N T H E S T R U C T U R E O F WAKETURBULENCE

DEDUCED FROM FIELD RADAR MEASUREMENTS

Glen F. Pippert

LINCOLN LABORATORY

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

LEXINGTON 7 3, MASSACHUSETTS

No. 63-446

First publication rights reserved by American Institute of Aeronautlcr and Astronautics. 500 Fifth Aue., New York, N.Y.AbstraCts may be publishedwithout permission it credit is given to author and to AIAA. (Price-AIM Member 5 0 ~ . Nan.Member $l.W).

4

ON THE STRUCTURE O F WAKE TURBULENCE

DEDUCED FROM FIELD RADAR MEASUREMENTS

Glen F. Pipper t

LINCOLN LAB OR AT ORY * MASSACHUSETTS INSTITUTE OF TECHNOLOGY

LEXINGTON 73, MASSACHUSETTS

ABSTRACT

A model is presented for the scattering of electromagnetic radiation

f r o m the turbulent wake of a hypervelocity body travell ing through the a tmos-

phere.

the M.J. T. Lincoln Laboratory Wallops Island experiments a r e used to deduce

the correlat ion function and correlat ion length which charac te r ize the scat ter ing

f r o m the r e -en t ry wakes.

with altitude in the region from 150, 000 ft to 200, 000 ft as

The measurements of r ada r c r o s s section a t s eve ra l frequencies in

The resu l t s show that the correlat ion length va r i e s

where p m is the ambient a tmospheric density and p

cation of these r e su l t s , obtained f r o m sphere measu remen t s , to predict the

cross section for other bodies, using calculated values f o r the electron density

levels , show good agreement with measu red r e su l t s indicating that the r e su l t s

a r e independent of, o r insensit ive to , body shape.

is s e a level density. Appli- 0

,:< Operated with support f r o m the U. So Advanced Resea rch P ro jec t s Agency.

MS-894 PREPRINT W

, I INTRODUCTION

Mcasurements of r ada r c r o s s sections a t a number of frequencies have

been made in the M. I. T. Lincoln Laboratory Wallops Island experimental pro-

g r a m over the past s eve ra l y e a r s on hypervelocity re -en t ry bodies. The re-

entry bodies on which most of the measurements were made were spherical ,

though some measurements have been made on conical shapes a s well.

re -en t ry velocities were generally in the range f r o m 17, 000 i t / s e c to 22, 000

f t /.e.”

The

An examination of the re -en t ry cross section measurements as a func-

tion of altitude generally show the same kind of behavior fo r the var ious body

s i zes and r e -en t ry velocities. The UHF (420 mcps) cross section measu re -

mcnts plotted as a function of altitude for Tra i lb lazer Ik, which was an eight

inch diameter aluminum sphere with a r e -en t ry velocity of about 19, 600 f t / s e c ,

a r e shown in Fig. 1. are shown in Fig. 2.

the data points are shown in the plots with no averaging.

The S-band (2800 mcps) resu l t s fo r the same re- entry

The r ada r repeti t ion r a t e was 320 pu l ses / s ec and all of

A significant feature of the UHF c r o s s section behavior is the r a p i d r i s e

in c ros s section at about 190, 000 I 195, 000 f t altitude. This rapid inc rease is

attr ibuted to the t ransi t ion f r o m laminar to turbulent flow in the wake. The re

a r e seve ra l pieces of evidence which substantiate the assumption of t ransi t ion

to turbulcnce.

pally in the specular lobe, i . c . , where the angle of incidence is equal t o the

angle of rcflcction.

makcs an angle of about 45O with the axis of the wake, relatively l i t t le energy

would be sca t te red back to the r a d a r f r o m the wake unless the wake i s rough,

o r turbulent.

The radiation sca t te red f r o m a laminar wake appears pr inci-

Since the line of sight in the Wallops Is land experiments

An examination of the pulse-to-pulse re turns during this region of l a rge

c r o s s sections shows rapid and violent fluctuation of the signal a s would be ex-

pected f r o m a turbulent, o r c lut ter , region. Also, phase distortion over the

re turned pulse length, and pulse shape distortion and lengthening give fur ther

evidence that the scattering is f r o m a turbulent extended region.

2

, After the UHF c r o s s section reaches i ts peak value i t s t a r t s to decay

quite rapidly while the S-band c r o s s section i s s t i l l r is ing (Fig. 2 ) . Eventually

the two c ross section levels, U H F and S-band, become comparable and both

decay quite rapidly with decreasing altitude. The velocity a t this point i s s t i l l

well over 15, 000 f t / sec.

This general type of behavior i s observed on most of the experiments

where the signal-to-noise ra t io i s l a rge enough. It should be possible to cle-

duce character is t ic pa rame te r s of the wake s t ruc ture f rom the two frequency

measurements by applying a r ada r scattering model to the resu l t s .

purposc of the remainder of this paper to make such deductions about the wake

s t ruc ture f rom the measurements .

I1 RADAR SCATTERING MODEL

It is the

It i s assumed, first of all, that the l a rge r a d a r re turns , above the ba re

The justifications

The argument which

body value, a r e due to scattering f r o m the turbulent wake.

f o r this assumption have been noted in the Introduction.

maintains that mos t of the sca t te red energy from the laminar wake will appear

in the specular lobe holds i r respec t ive of whether the wake i s overdense (the

operating frequency i s below the plasma frequency) or underdense. F o r the

aspect angle of about 45' in the Wallops Island experiments i t doesn't appear

possible to construct any reasonable wake s ize or shape which will predict the

observed signal level for a laminar wake. 1

F o r a turbulent wake the scat ter ing becomes m o r e near ly isotropic a t

the expense of the energy in the specular lobe.

composed of two contributions - a coherent and noncoherent portion.

coherent portion of the sca t te red energy will appear principally in the specu-

lar lobe, thus, the energy in the non-specular direction i s the noncoherent

contribution

The sca t te red energy i s now

The

The scattering process f r o m an overdense turbulent region will dif fer

f rom the underdense scat ter ing process .

ter ing will be principally a sur face phenomenon while f o r the underdense region

the scat ter ing is f r o m a vol.ume.

specular direction i s determined by the random fluctuations in the medium, but

f o r the overdense region only the surface fluctuations contribute ~

For the overdense region the sca t -

In either case the energy sca t te red in a non-

3

The calculation of electron dcnsit ies by the General Applied Science

Laborator ies3 fo r s lender bodies of about the s a m e s ize as the Wallops Island

re -en t ry bodics show that the wake is underdense for S-band a t a l l altitudes

above about 100, 000 ft ,

t ron densit ies a r e calculated to he only sli.ghtly higher, perhaps by a fac tor of

2, for the s a m e s ize bodies.” Thus, thc wake i s predicted to be underdense

at S-band throughout the altitude region a t l eas t f rom 150, 000 - 200, 000 f t .

Fur thermore , for b1un.t bodies the turbul.ent wake elcc-

Fur the rmore , at UHF wiih a 1 p sec p ~ i l s c length the effectivc length of

t r a i l illuminated by the ent i rc pulse when viewed at 45” aspect R J I ~ ~ C i s over

600 f l while thc predicted overdensc region f r o m the GASL ca.lculations i s

always l e s s than 100 it in the 150, 000 - 200, 000 f t region. In addition, s ince

the average surface roughness fluctuations can bc espected t o be less than a liody radius an.d the body diameter for Tra i lb lazer Ik is less than o n e seventh

of a wavelcngth at UHF, the. surfacc will not appear ve ry rough a t UHF.

Finally, soine rough mode1.s o f scat ter ing f rom rough s u r f a c e s 5, S I l ( > \ V

a cross section behavior with frequency which docs not ag ree with the observed

behavior, F o r a rough sur face observed nea r broadside these models predict

that thc c r o s s section should be independent of frequency. For sma l l glancing ..- #

,” -- ...’ angles with a wavelen.gth long with respec t t.o the correlat ion length, o r su,.E-

facc height fluctuations, the cross section should va ry inversely a s the fourth

power of the wavelength.

rricasurements

i Neither of thcsc effects a r e obscrvcd in t h 6 f ie ld

,’

, .J’

A l l of the preceding points indicate that the observec! noncoherent sca t - /’

1:cring is principa1.ly i r o m underdense regions, assumption that the scat ter ing observed in ihe f ie ld ineasurements can be des-

cr ibed by a n underdense scat ter ing model,.

‘Thus w c make the sccond

‘The propagation of waves through randomly fluctuating m e d i a anti t h e

scattering of radiation f r o m random media have been t rea ted extensively i n thc

l i t e ra ture . 7’ 8’

medium can be charac te r ized by the correlat ion function.

form of the correlat ion function then yields the spec t ra l density of the medium.

The mean value of the radar scat ter ing c r o s s section. can be determined directly

f rom the spec t ra l density ( s e e , f o r example, re f . 7 and 8 ) ”

The s ta t is t ical prop’erties of the random fluctuations in a ,/

The Four i e r t r a n s -

t -4

4

J

A genera l correlat ion function fo r a random process is given by 8 Tatarsk i as

-

where r is the correlat ion length, n represents the deviation f r o m the mean

of the refract ive index,

function of the second kind of imaginary argument.

for back scattering is then given by

0 1 q v ) is the Gamma function and Ku(x) i s the Besse l

The r a d a r c r o s s section

- 4 2 3 d r T ( v t 3 / 2 ) k Vnl ro

u = r ( v ) [1 .t 4k2r021u 3'

where k is the wave number and V is the volume.

density N and collision frequency u / 271 and p lasma frequency w / ZT both

small with respec t to the operating frequency w / 271 the square of the devia-

tion f r o m the mean for the index of refract ion i s given by

For a p lasma with electron

C P

where r is the radius of the electron and AN is the deviation f r o m the mean

electron density, The r a d a r c r o s s section p e r e lectron is u = 4vre ~ Thus 2 e

T

AN' 2 - r u T

k4 - (4 )

a n d the back scat ter ing c r o s s section f r o m the p lasma is -

2 3 ro 8 d w T ( v -t 3 / 2 ) V u T AN

0 - (5 1 21" t 3 / 2 qU) [i -t 4k2 ro

For v = I / 3 this express ion corresponds to the c r o s s section derived f r o m the

correlat ion function for the Kolmogorov "two-thirds law" for homogeneous and 8 isotropic turbulence;

exponential correlat ion function of the f o r m

fo r v = 1/ 2 it corresponds t o the c r o s s section for an

F o r a given scat ter ing volume the re a r e th ree pa rame te r s to be de te r -

mined, namely v, ro and AN,

frequencies a r e required to determine the parameters .

a t t h ree frequencies UHF (420 mcps) , S-band (2800 mcps ) and X-band (9000

mcps) , were made in the Wallops Island experiments , the signal-to-noise ra t io

a t X-band was not sufficiently sat isfactory for the purposes of this analysis.

However, by using theoret ical and laboratory resu l t s a s inputs concerning the

behavior of AN it i s possible to use the two frequency measurements at UHF

and S-band to study the correlat ion function and correlat ion length behavior.

TI1 DISCUSSION OF EXPERIMENTAL RESULTS

Thus three independent measurements a t t h ree

While measurements

Given measurements of the c r o s s section at two frequencies we can take

the ra t io of the two equations for the c r o s s section (Eq. 5 ) a t the two frequen-

cies and wr i te

1 + 4 k s 2 2 r o 1, t 312

3 U

u s V ~ ~ ~ 4k:HF roz

o r

- 1 - v + 312 L L

0 J V 1 + 4ks r ) log c UHF s IS

1% ( u s V ~ ~ ~ l t 4k&IF ro

(7)

The volumes do not cancel because the pulse lengths at the two frequencies a r e

not the same and hen.ce do not observe the same volume, and because a portion

of the wake goes overdense for UHF before it does fo r S-band.

l ishes a constraint between v and r

A plot of the equation i s shown in Fig. 3 which shows that when the co r re l a -

tion length associated with the scat ter ing volume i s small, v is difficult to de-

t e r m h e ; o r , al ternatively, very p rec i se measurements of the c r o s s section

a r e requi red to determine v. F o r la rge values of the correlat ion length, io,

the situation is r eve r sed and ro is difficult to determine.

Eq. 8 estab-'

fo r the two frequencies , UHF and S-band. 0

b

J

The behavior of the c ross section expression a s a function of cor re la -

U tion length i s i l lustrated in F ig . 4 where f r o m Eq. 5 i s plotted v (AN)'uT

a s a function of r

functions The correlation functions i l lustrated a r e the exponential, Gaussian,

and "two-thirds lawn functions. The Gaussian correlation function var ies too

rapidly f r o m its peak value a s the correlation length gets l a rge r to obtain any

reasonable agreement for the three measured c ross sections at UHF, S-, and

X-band and i s not considered fur ther .

functions behave generally in a s imi la r fashion a s a function of correlat ion

length and altitude. The difference in magnitude f o r the two functions at smal l

correlation lengths i s sufficiently smal l so that differentiation between the two

on the basis of field amplitude measurements is difficult.

amplitude a t large correlation lengths is somewhat la rger but i s s t i l l not

dramatic ~

f o r U H F and S-band and seve ra l representat ive correlation 0

The exponential and "two-thirds law"

The difference in

Given the constraint between v and r represented by Eq. (8) and i l lus- 0

t ra ted in F ig . 3 we can choose pa i r s of values f o r v and r and plot the function 0

3 U 8drr (v t 3 / 2) ro

(9) - - S

vsuT (AN)' r(,) [i + 4ks2 rozIv + 3f l

a s a function of v and r

Eq. (8) it i s necessary t o evaluate log ( uufFvs ) a t each altitude. To de ter -

mine the volume let I the p d s e a t UHF and S-band respectively.

half the pulse length divided by the cosine of the aspect angle which, f o r the

45 aspect angle and 1 p sec and 2 p, sec pulse lengths a t UHF and S-band r e -

spectively for the Trai lblazer Ik measurements , leads to effective lengths of

210 me te r s and P = 420 me te r s ~

In order to determine v a s a function of ro f rom 0'

s U H F U

and 1 represent the length of wake illuminated by

The length wil l be determined by U H F

0

'UHF =

7

d The laboratory measurements” of turbulent wake width show that the

wake grows approximately a s the third or half power of the distance along the

wake.

grows as x ’ ’ ~ where x is the axial distance along the wake. We will a l so a s -

sume that on the average

than one.

GASL

altitude region f rom 150, 000 to 200, 000 f t .

For the purposes of the volume calculation we will a s sume that the wake

AN = E where E i s some small positive number l e s s

The calculations of the electron density decay along the wake by 3 show that the electron density var ies approximately as 1 / Jx in the

Thus we let

where N

ali ty constant is unity and has dimensions of ml’ 2 m If we let b represent

some init ial turbulent wake radius , we can wri te

is the electron density one me te r behind the body. The proportion- 0

0

J

W

(11) 2 2 2 (AN) dV = n-bo ( € N o ) dx.

W e now integrate f rom x

goes f rom overdense t o underdense at a given frequency, to PA, which is the

length determined by the pulse length and aspect angle.

which is the point along the axis where the wake 1’

Thus

We now can evaluate the logarithm in Eq. ( 8 ) ,

U H F (’s - U UHF vs U

log ( ---) = log ( ) , - x ) us VUHF Us (‘UHF lu

a t various altitudes f r o m the measured values of the c r o s s section and the

known P A ‘

derdense throughout the altitude region f r o m 150, 000 f t t o 2 0 0 , 0 0 0 ft .

an est imate of x can be made f r o m the GASL calculations, and i t should be

pointed out that, fo r the range of values for v and r

values of v and r

However, it i s necessa ry to have some knowledge of the value of

The GASL calculations3 show that f o r S-band the wake i s everywhere un- xl* For U H F

1 la te r determined, the

0 a r e not very sensit ive to the choice of x1 fo r U H F .

0

8

With pa i r s of values f o r v and r determined, Eq. (9) can be evaluated 0

U S for each pair , and plotted a s a function of v and r . Such a

0

plot is shown in Fig. 5 for 150, 000 f t , 160, 000 f t and 170,000 f t .

show that the value of r

v part icular ly at the lower altitudes. The expression was eval-

The curves

for a given v is relatively insensitive t o the choice of 0

U S

VSUT (AN)2

uated f r o m the measured cross section at the th ree altitudes and the calculated

value of Vs(AN) ~

along the edge of the figure.

range between about v = 0.4 and v = 0.6, but the values f o r r0 vary f r o m 0.01m

at the lower altitude to about 0 .045 m at the higher altitude.

v = 0 . 5 and determine r

2 The resu l t s for the th ree altitudes a r e indicated by a r rows

The values of v indicated for the th ree altitudes

We thus choose

as a function of altitude f rom Eq. (8) with v = 0.5, 0

A plot of r as a function of altitude is shown in Fig. 6 . the experimental points and the solid line is a plot of the equation

The c rosses represent 0

)' m e t e r s , (15) P O

I. 5 r = (

0 P m

where p , is the ambient atmospheric density and p

l inc fits the experimental data points very we l l ,

out again that a change i n the choice of v o r the value of the effective volume

does not influence the value of r This fact is more or l e s s obvious

f r o m inspection of the equation f o r the c r o s s section, Eq. (5); since, for s m a l l

values of r

relation length but not to the valucs of v o r the volume.

is s e a level density. The 0

It should,perhaps, be pointed

very much. 0

i n t e r m s of wave length the c r o s s section i s very sensit ive to cor - 0

- 9

By substituting the values for r into the equation for the c r o s s section 0

v

along with the measured values for the c ros s sectton, ( E N ) can be determined.

(Since the c r o s s section i s fa i r ly sensit ive to E N an i terat ive p ro -

cedure was followed, A ch-oice f o r x was made, and E N was then calculated

f r o m Eq. (16j. It w a s then decided whether the choice of x was reasonable,

and, if not, a new choice for x was made, etc. until reasonable agreement

was reached. The determinatior, of r however, was not ve ry dependent on

the choice of x The values of € N O which a r e obtained a r e shown i n Table I.

The value of 2 x l o l o ag rees reasonably well with the level of electron density

of l o lo computed for 150, 000 it by GASL.

scaling the s lender body calculations u,pward by a factor of 2 t o account f o r the

fact that the experimental body was blunt would leave the experimental r e su l t s

in agreement with the calculations to within a factor of 2

0

but not x 0 1'

1 0

1

1

0

) 1'

With a choice o f 0 .5 fo r E and

TABLE I

E N As a Function of Altitude 0

Altitude (ft) t~~ (cmm3) I - 190, 000

180, 000

170, 000 8 x 10

3 .2 x lo9 (determined f r o m U H F )

5 .1 x l o 9 (determined from U H F )

9

10 16a, oao 1.3 x 10

10 150, 000 2 x 10

The calculated. c r o s s sect.ions for Trai:l.blazer 'Ik, using values of ro

determined f r o m Eq. (15) ac.d c N f r o m Table I, a r e compared with averaged

measu red values in F i g a 7 . The good agreement is not surpr i s ing , of course,

s ince the measu red values were used to determine the p a r a m e t e r s required in

the calculations.

turbulence is not yet well estabKshed at that altitude.

0

The deviation at 190, 000 ft is attr:buted t o the f ac t that the

Y

A comparison of theoretical calculations, using r determined f rom 0

Eq. (15) and E N f r o m Table I scaled up by the square root of the rat io of body

diameters , with measurements for a 15 inch spherical rocket motor a r e shown

in Fig. 8 ( a ) and (b) .

0

The target was a r a the r nondescript aerodynamic shape

but the quite good agreement between calculations and measurements lends sup-

port to the observation that the correlation length i s independent of, o r a t least

insensitive to,

pally determines the shape of the c r o s s section curve a s a function of altitude.

It is believed that the body s ta r ted to break up at an altitude of about 150, 0 0 0 -

155, 000 ft.

body s ize or shape. It i s the correlat ion length which princi-

Finally, additional evidence that the correlat ion length i s insensit ive t o

body shape, o r CDA, and that the c r o s s section model i s quite successful in

predicting measured resu l t s is shown in Fig. 9 . Calculations a r e compared

with measured values f o r a 6 diameter. The values f o r t N

by a factor of 2 . 5 bringing them in reasonable agreement with the GASL cal--

culated values for N with E M 0. 5.

rapid change as a function of altitude is very good.

ca r r i ed out above 155, 000 ft because the evidence f r o m other field measure-

ments indicates that transit ion t o turbulence for this body should occur f o r

zero angle of attack between 155,000 and 160 ,000 f t . c r o s s section above 155,000 f t can be attr ibuted to non ze ro angle of at tack

effects with the turbulence not becoming well established much above 155, 000

f t ”

IV SUMMARY AND CONCLUSIONS

0 half angle beryll ium cone with an 8 inch base

were scaled down f r o m the values in Table I 0

Again the agreement in level as well as 0

The calculations were not

The gradual buildup in

Given the assumptions that the la rge r ada r scattering which i s observed

in the field measurements i s due to turbulence in the wake and resu l t s princi-

pally f r o m the underdense region, , the pa rame te r s required to charac te r ize the

r ada r scattering expression were determined f r o m the field measurements

obtained at severa l frequencies in the Wallops Island Trai lblazer Ik re-entry ~

The resu l t s show that the magnitude of the c r o s s section predicted f rom the

s c a t t e r k g expression i s ra ther insensit ive to the choice of correlat ion function

over a f a i r ly wide range of functions.

11

With the exponential c.orre1.ation function chosen to charac te r ize the

s ta t is t ics of the turbulence the correlat ion length was determined a s a func-

tion of altitude.

sely as the square of the ambient a tmospheric density. The satisfactory p re -

diction of the behavior of the average measured c r o s s section f o r other bodies

with different s izes and C

t o body s ize and shape but that the c ros s section behavior a s a function of a l -

titude i s a sensit ive function of the correlat ion length.

that the correlat ion length, r essar i ly the s a m e as the gas density correlat ion length since r

a measu re of the s ize of electron density fluctuations. However, the two co r -

re la t ion lengths are undoubtedly rclated since the electron density fluctuations

resul t f r o m the gas density fluctuations which a r e re la ted to tempera ture

These resu1. t~ show that the cor re la t ion length var ies inver-

A shows that the correlat ion length i s insensitive D

It should he pointed out

which i s determined in this work i s not nec- 0’

is in some way 0

fluctuations

Finally, the determination of cN f r o m the application of the scat ter ing

model t o the measurements yields resu l t s which a r e in reasonable agreement

with theoretical calculations. How good the agreement actually i s c.annot be

determined precisely because the value of E mus t be separately determined;

however, the genera l level of agreement with any reasonable choice of E is

encouraging ~

0

N E - al > 0

0 n

z 0 t- o w (0

-

u) In 0 LT 0

L I 3

~~ __ 328 332 336 340 344 348 352 356 3 60

TIME ( s e c )

I I I 1 I I I I I 600 500 400 300 200 130 I 2 0 115 110

H E I G H T ( k f l )

Fig. 1. UHF Cross Section as Function of Altitude for Trai lblazer Ik

N E W > 0 n 0

m v) 0 LL 0 (D

2 0

10

0

-10

- 20 n a m z

I cn

- 30

-40

TIME ( s e c )

I I I I I I 1 I I 600 500 400 300 200 130 120 115 110

HEIGHT ( k f t )

Fig. 2. S-Band Cross Section a s a Function of Altitude for Trai lblazer Ik

~

t

1

r I..

0. ! 0 0.1 0.2

CORRELATION LENGTH, r (m) 0

0.3

F i g . 3 . Correlation Function Pa rame te r , v , vs Correlat ion Length, r 0

\

I o 2

I O 3

I o4

o 5

o 6

I 6’

I cia

I 6’

’\. UHF

\. I! \

____I S-BAND

\ I ---- 2/3 LAW \ I

EXPON ENTlAL

GAUSS I AN

- I I

--- I \ S-BAND

\ \

UHF \ I I I I I I

0. I 0.2 0.3 0.4 0.5 0. CORRELATION LENGTH, r,(rn)

U for UHF and S-Band vs the Correlation Length, r Fig. 4. V r T ( A W L 0

13-37-79'161

b"

r - _ _ - - - - I

I I I

- I

- I 0

'-150,000 I f t I

- I

0 0.05 0.10 0.15 CORRELATION LENGTH,r (m)

n

150 k f t

160 kf t

170 kf t

0 0.5 1.0 1.5

cr /V o ( A N l 2 vs CORRELATION FUNCTION PARAMETER, v AND CORRELATION LENGTH, r

S S T

0 c37-3%

Fig. 5 (revised)

c N z a Y

b"

1-5050,000 f t - / I

-I I I I

- I

I

/ \ \

I \ I \ M '\ \ I ,000 f t

0 0.05 0.10 CORRELATION LENGTH, r (m)

0

0.15

150 k f t

160 kf t

170 kf t

0 0.5 1.0 1.5 CORRELATION FUNCTION PARAMETER , u

U S

Fig. 5. vs the Correlation Function P a r a m e t e r , v, and the V s n T ( A N ) L

Correlation Length, ro

c

&l 10- z

X

ALTITUDE ( k f t )

F i g . 6 . Correlation Length, ro, a s a Function of Altitude for the Exponential

Correlation Function

17

13 - 37 - 7978 I

0

lu I

t Q)

; Q) c 0 Q) > 0

0 n

16

8

0

-a

-16

z O -24 I- o w 0 d

-

- CROSS SECTION - (40 point average)

~

- 0-CALCULATED POINTS

FPS-6 (S-BAND) CROSS SECTION (40 point average)

2 ALTITUDE ( k f t )

0

-a

-16

Fig . 7 . Comparison of Predicted Values of Cross Section With

Measurements for Trai lblazer Ik

18

i

20

or- & I O

E

2 0

t al

0

aJ > 0

0

a '0

a -10

v -20

z 0 - I- i, w cn

I I I I I I I h I -

UHF CROSS SECTION (40 point average)

-

-

-

-

o - CALCULATED POINTS -

-

-

FPS-6 (S-band) -

- CROSS SECT1 ON (40 point average)

0

250 200 I50 ALTITUDE (kft)

IO0 50

2 0

I O

0

-10

-20

-30

Fig . 8a. Comparison of Predicted Values of Cross Sections With

Measured Values for Trai lblazer IIc

h

(u I Q) t Q)

E

Q) > 0

(3 n

n U

10

0

-10

-20

-30

-4c

-

X-BAND CROSS SECTION (40 point average)

-

- m cn 0 U 0

250 200 I 50 I O 0 ALTITUDE ( k f t )

Fig . 8b. Comparison of Predicted Values of C r o s s Sections With

Measured Values for Tra i lb lazer IIc

13-37-79801

0

-10

-20

-30

2 0

(u L

c Q)

0)

E Q) c 0

z 0 I- o w v)

-

13-37- 7981 I 5

0

- 5

-10

-15 200

UHF CROSS SECTION (40 point average) 0

0 - CALCULATED POINTS I I50

ALTITUDE ( k f t ) I O 0

Fig. 9. Comparison of Predic ted Values of C r o s s Sections With

Measured Values for Tra i lb lazer IIe

21

Y

ACKNOWLEDGEMENTS

I a m indebted to many people who have worked on the collection and

reduction of data obtained in the Wallops Island experimental p rogram. I

am a lso indebted to Miss Nancy Holway who per formed the numer ica l cal-

culations fo r this repor t .

REFERENCES

1.

2.

3.

4.

5.

6.

7 .

8 .

9.

10 0

Pippert , G. F. and Edelberg, S . , The Elec t r ica l P rope r t i e s of the A i r

Around a Re-entering Body, IAS P a p e r No. 61-40, IAS 29th Annual

Meeting, New York, January 1961.

K e r r , D.E. ~ Propagation of Short Radio Waves, M.I.T. Radiation

Laboratory Ser ies , Vol. 13, McGraw-Hill Book Co., Inc., New York

(1951)

Hoffert, Martin, P a r a m e t r i c Analysis of Turbulent Wakes in Slender

Body Re-entry, Technical Memo No. 75, General Applied Science

Laborator ies , Inc. , Westbury, LI . , N. Y., January 1963

Pr iva te Communication f rom GASL

Davies, H. ~ The Reflection of Electromagnetic Waves f r o m a Rough

Surface, P roc . I .E.E. 101-IV, 209, 1954

Hayre, H. S . Radar Scattering Cross Section-Applied to Moon Return,

P r o c . IRE 49, 1433 (1961)

Booker, H. G. and Gordon, W. E . , A Theory of Radio Scattering in the

Troposphere, P roc . Inst. Radio Eng. 38, 401 (1950)

Tatarsk i , V.I., Wake Propagation in a Turbulent Medium, McGraw-

Hill Book Co., New York (1961)

Chernov, Lev A . , Wave Propagation in a Random Medium, McGraw-

Hill Book Co., New York (1960)

Slattery, R , E . and Clay, W. G. , Measurement of Turbulent Transit ion,

Motion Statist ics, and G r o s s Radial Growth Behind Hypervelocity

Objects, Physics of Fluids - 5, No. 7 , 849 (July 1962).

-

-

-