Engineering feasibility study on structural dynamics, antenna electrical properties, and systems of kilometer wave orbiting telescop

Haddock, F. T.

English

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PHASE I1 FINAL RePORT 
ENGINEERING F E A S I B I L I T Y  STUDY I 
OF A KILOMETER WAVE ORBITING TELESCOPE 
Submitted by 
FRED T. HADDOCK 
NATIONAL AERONAUTICS AND SPACE 
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PHASE I1 FINAL REPORT 
ENGINEERING F E A S I B I L I T Y  STUDY 
OF A KILOMETER WAVE ORBITING TELESCOPE 
' .  
8 .  
Submitted by 
FRED T. HADDOCK 
NATIONAL AERONAUTICS AND SPACE 
ADMINISTRATION GRANT NGR-a -00 5- 13 1 
UNIVERSITY OF MICHIGAN 
RADIO ASTRONOMY OBSERVATORY 
Ann Arbor, Michigan 
July 1968 
I . Introduct ion 
The Ue&vetrity e€ M&ohi@jen Redie Aetrenemy Observetory (UM/RAQ) 
has completed the  second phase of i t s  inves t iga t ion  of t he  engineering 
f e a s i b i l i t y  of a Kilometer Wave Orbiting Telescope (KWOT). 
one of the KWOT study was i n i t i a t e d  i n  Nuvember, 1965, and completed 
in October, 1966. The p r inc ipa l  conclusion of t h e  f i r s t  phase 
study was t h a t  mission f e a s i b i l i t y  appeared favorable enough t h a t  the  
study should continue. 
Phase 
The present  phase two etudy began February 1, 1967, and ended 
January -31, 1968. 
been g r e a t l y  extended and mission f e a s i b i l i t y  appears very favorable.  
The inves t iga t ion  of t h e  s t r u c t u r a l  .dynamics has 
11. KWOT Concept 
An antenna with high d i r ec t iona l  gain (small beam area)  is 
required t o  map the  sky and measure the  f lux  dens i ty  of r ad io  sources 
a t  frequencies below 5 MHz. 
sources ,  a beam a rea  of not  more than about 80 square degrees is 
required.  
l a r g e  physical  s t r u c t u r e  i n  o r b i t  i s  required.  
beam antenna is proposed f o r  flux dens i ty  measurements of d i s c r e t e  
sources  and contour mapping of the  cosmic background noise.  
compound interferometer  w i l l  then be used t o  prcwide an estimate 
of source s ize  f o r  t h e  l a rge r  and s t ronger  sources and b e t t e r  da t a  
on t he  s t a t i s t i c a l  cha rac t e r  of t he  cosmic background due t o  many 
In order  t o  measure severa l  dozen 
To achieve t h i s  reso lu t ion  a t  frequencies near 1 MHz, a 
A moderately broad- 
A 
- 2- 
i .  
weaker sources. The KWOT structure that was studied (See Figure 1) 
has the required antenna directional gain and stays within reasonable 
system weight limits. The proposed KWOT structure consists of a 
central observatory surrounded by four sub-satellites, with all 
five bodies connected by a set of conducting and non-conducting fila- 
ments. The conducting portions of the connecting elements form a 
# 
rhombic antenna and an interferometer array of dipoles. As seen in 
Figure 1 this structure is essentially planar since the maximum dimen- 
sion out of the paper is only 4meters. The overall diameter of the 
structure is 10 kilometers so that the rhombic leg length is 17 wave- 
lengths long at 1 MHz. The radio astronomy signals from the rhombic 
and interferometer are combined in such a way that an antenna pattern 
is generated which combines the resolution of the interferometer with 
the unidirectional properties of the rhombic. / 
The entire MOT structure spins about an axis perpendicular to 
its plane with a period of approximately one hour. 
serves to scan the antenna array over the sky and, with the precession 
of the spin axis which is brought about by an active thruster control 
system, will provide complete sky coverage. 
generated by the spinning motion also aids in maintaining the shape of 
the structure for this mode of operation. 
grams MY use the active control system to stop the antenna array from 
spinning and control the pointing of the antenna beam. 
This spinning motion 
The centrifugal force 
Some types of observing pro- 
111. Phase Two Program 
In view of the encouraging results of the phase one study (l), it 
4, 
-3 - 
was proposed that additional work be done in the structural dynamics 
area, the antenna electrical properties study area and the systein 
study area. 
were started during the phase one study in that the phase two study 
was funded at a level of approximately 20% of that recommended in 
the proposal. 
First priority was given to continuing those tasks which 
( 2) 
IV. Summary and Conclusions of Phase Two Engineering Feasibility Study 
A. Structural dynamics studies. 
1. 
-* 
Motion of a lumped-mass model representing a kilometer 
wave orbiting telescope. This study is completely described 
in the special report listed as reference 3 which is being 
submitted as part of this final report. 
The study consisted of a numerical analysis Qf- the 
- ----.-____ - 
planar motion of a lumped-mass model representing the 
KWOT structure. 
ticles with interconnecting non-linear springs and 
an in-plane tangential thrust capability. 
the effects of small perturbations from a free-space con- 
dition of uniform rotation due to the gravitational gra- 
dient and t o  control thruster activation were investigated. 
Orbital constraints were assumed, with the reference 
satellite describing a circular orbit at synchronous 
altitude. In addition, a coordinated spin-up deployment 
was studied. 
structural damping and orbital eccentricity were not 
studied. 
The model consisted of a system of par- 
Specifically, 
The effects of three-dimensional motion, 
- 4- 
a 
With t h e  a id  of a S c i e n t i f i c  Data Systems (SDS)-930 
computer, perforrdng double p rec i s ion  ar i thmetic ,  and 
a CALCOMP-565 automatic p l o t t e r ,  s tud ie s  of t he  motion 
of t he  model were made. S ix  types of graphical  dis- 
plays were produced. 
a. 
b. 
Radial dis tance devia t ion  t i m e  h i s tory .  
Spin rate devia t ion  t i m e  h i s to ry .  
1 C. Angular pos i t ion  t i m e  h i s tory .  
d. 
e. Control switching func t ion  t i m e  h i s tory .  
f .  Expanded sca l e  c o n t r o l  switching funct ion t i m e  
Angular pos i t ion  devia t ion  phase plane diagram. 
h is tory .  
Over 150 of the most i n t e r e s t i n g  and informative 
d i sp lays  have been reproduced i n  re ferehce  3. 
The inves t iga t ions  performed using the  computer 
may be c l a s s i f i e d  i n  categories:  
equilibrium, small per turba t ions  from equilibrium, 
l a r g e  per turba t ions  from equi l ibr ium and deployment. 
v e r i f i c a t i o n  of 
Resul ts  ind ica te  t h a t  t h e  amplitude of t he  s t r u c t u r a l  
o s c i l l a t i o n s  exci ted by t h e  deployment method a r e  wi th in  
the l i m i t s  def ining allowable s t r u c t u r a l  d i s t o r t i o n ,  
and t h a t  a simple conf igura t ion  con t ro l  system can 
counteract  small  per turbat ions from a freespace 
equi l ibr ium ro ta t ing  coiibiticin for  8 l i f e t i m e  i n  e---- CIb-ZPU 
of one year.  
i 
-5 -  
2. s t m v  of a winn ing  cable-connected system 
This study is completely described i n  the  in. 
s p e c i a l  r epor t  l i s t e d  as re ference  4 which i s  being sub- 
mit ted as a p a r t  of t h i s  final repor t .  
The problem of a cable  connected system spinning 
in o r b i t  raises two bas i c  s t a b i l i t y  questions:  w i l l  
the  system continue to move at a fa ir ly  coiistant spin 
ra te  i n  t h e  predicted o r b i t  and w i l l  t h e  i n t e r n a l  
motion of t h e  system, i n  t h i s  case  the  connecting cable,  
remain bounded near some des i red  motion? Several  
papers on these two problems appear i n  the  l i t e r a t u r e .  
A l l  dea l  only with motion i n  t h e  plane of t h e  o r b i t .  
The purpose of t h i s  study was t o  present  a more 
genera l  approach. The methods of ana lys i s  described 
can be appl ied t o  general  cab le  connected s t ruc tu res .  
The method presented i s  s p e c i f i c i a l l y  appl ied t o  the  
problem of a point mass spinning about a much hezvier  
body t o  which it is connected by a l i n e a r  e l a s t i c ,  
constant  dens i ty ,  constant  c ros s  s e c t i o n a l  a r ea  
cable.  The system, i n  turn,  i s  i n  o r b i t  about $he 
earth. 
-._ _ _  - .-.-_ - ---_ -- 
The Lagrange equations of motion f o r  t h e  lumped 
system were shown t o  be  a system of nonl inear ,  ordinary 
d i f f e r e n t i a l  equations. Daxping was included in t he  
equat ions and i t s  e f f e c t s  on s t a b i l i t y  inves t iga ted .  
The simplest  lumped mass model, t h e  dumbbell, 
-6- 
x 
was used t o  examine i n  more d e t a i l  t h e  bounds on t h e  
types of motion which can occur wi th in  the  energy l e v e l s  
of t h e  conservative s y s t m .  The o r b i t s  i n  which t h e  
dumbbell may move were shown t o  be  e s s e n t i a l l y  those 
i n  which a po in t  mass may move ;  
i n  o r b i t  of t h e  dumbbell means a s i z a b l e  change i n  
s p i n  r a t e .  
however, a small change 
The bounds a re  found by examining t h e  f i c t i t i o u s  
p o t e n t i a l  functions f o r  t he  dumbbell system. Results 
from a numerical i n t eg ra t ion  of t h e  exact equations for 
t h e  dumbbell i nd ica t e  t h a t ,  f o r  most cases, i t  i s  
reasonable t o  assume t h a t  t h e  cen te r  of mass of t h e  
system moves in a Keplerian o r b i t .  This a f fo rds  one 
t h e  luxury of being a b l e  t o  c a l c u l a t e  t h e  p o s i t i o n  of 
t h e  c e n t e r  of mass independent of t h e  r e l a t i v e  motion 
of t h e  system. It was shown t h a t  the motion of a dumb- 
b e l l  whose c e n t e r  of mass moves i n  an  undisturbed 
Keplerian o r b i t ,  and t h a t  of a l i g h t  mass spinning about 
a very heavy mass which a l s o  moves i n  an undisturbed 
Keplerian o r b i t  are almost i d e n t i c a l .  The l a t t e r  model 
is henceforth r e fe r r ed  t o  8 s  t h e  s i n g l e  mass model 
s ince  only the  l i g h t e r  mass moves r e l a t i v e  t o  the  o r b i t a l  
point.  The above r e s u l t  was used t o  j u s t i f y  t h e  o r i g i n a l  
model and o r b i t a l  assumptions. i 
B. Resis t ive  lo s ses  on th in  wire antennas. 
This study i s  compiecely described i n  the  s p e c i a l  
-7- 
r epor t  l i s t e d  as reference 5 which i s  being submitted as 
a p a r t  of t h i s  f i n a l  repor t .  
The purpose of t h i s  study was t o  determine t h e  e f f e c t  
of resistive los ses  on the cu r rez t  d i s t r i b u t i o n  of long, 
t h i n  c y l i n d r i c a l  antennas. Tne f i r s t  s e c t i o n  of t h i s  r epor t  
descr ibes  a computational technique f o r  ob ts in ing  the curren t  
on a t h i n  a=tenna. 
obtained f o r  a 1 1/2 and a 3 wavelength antenna. 
c a l c u l a t i o n s  were performed f o r  a v a r i e t y  of source pos i t i ons  
and f o r  p e r f e c t l y  conducting and uniform lossy wires.  The 
r e s i s t a n c e  pe r  u n i t  length of these  imperfectly conducting 
w i r e s  w a s  taken as 0.08565 ohms/meter. 
made i n  order  t o  accentuate t h e  e f f e c t s  of antenna lo s ses  
and i s  l a r g e r  than  t h e  va lue  which w i l l  be encountered i n  
t h e  KWOT s t r u c t u r e .  
The szc~ar !  s e c t i m  presezts cke r e s u l t s  
These 
This choice x...s 
The f i n a l  s e c t i o n  descr ibes  an approximation t o  t h e  
cu r ren t  d i s t r i b u t i o n  which allows t h e  r e s i s t i v e  lo s ses  t o  
be estimated and then extended t o  antennas longer than  
those considered i n  t h i s  work. This  was done i n  the  case  
of a 12wavelength antenna and t h e  behavior noted. 
cu r ren t  peaks were decreased by a f a c t o r  of 8 
and t h e  p o s i t i o n  of t h e  peaks and n u l l s ,  and magnitude of t h e  
n u l l s  were unaffected by t h e  add i t ion  of losses.  
The 
= 0.81 -a 
Since t h e  r e s i s t ance  of 0.08565 ohmslmeter i s  much 
i 
l a r g e r  than  t h e  va lue  which w i l l  be encountered i n  t h e  KNOT 
antenna, i t  appears t ha t  t h i s  problem of r e s i s t i v e  l o s s e s  
-8- 
w i l l  not se r ious ly  a f f ec t  t h e  antenna operation. 
C. KWOT system s tudies .  
Resul ts  of t h e  systems inves t iga t ion  a r e  described 
in t h e  spec ia l  repor t  l i s t e d  as re ference  6 which i s  being 
submitted as a p a r t  of t h i s  f i n a l  r e p x t .  This spec ia l  
repor t  was p r in t ed  by E e l i  Aerosystems w h o  par t i c ipaEed  i n  
t he  systems inves t iga t ion  bu t  ai: no cos t  t o  the  p r o j e c t  .-----...--- -.- _. - 
The bas i c  KWOT system i s  a t t r a c t i v e  f o r  t h e  following 
reasons : 
1. 
2. 
3.  
4. 
It l i e s  e n t i r e l y  i n  a p i a m .  Tkc  c e n t r i f u g a l  
force  r e su l t i ng  from the  spinning motion can be 
used t o  keep the s t r u c t u r e  extended. No conpres- 
s i o n  members are requi red  i n  the  s t ruc tu re ,  but  
r a t h e r  t h i n  fi laments which ex2erience only tension. 
The rhombic antenna kas a unidLrectiona1 beam which 
l i es  i n  the  plane of the  s t ruc tu re .  Therefore, 
t h e  same spinning motion w i l l  sweep the  bean about 
t h e  c e l e s t i a l  sphere. A broad-side array,  on t h e  
o the r  hand 
t o  be  un id i  r ec t i  ona I. 
The rhombic antenna has d i r e c t i v i t y  i n  both the  
E and H plane, i s  r e l a t i v e l y  broadband, and r equ i r e s  
r i q u i r e s  a three-dimensional s t r u c t u r e  
EO i n t e rcomec t ing  t ransmission l i nes .  
When t h e  rhombic s i g n a l s  a r e  properly combined 
with those from t h e  d ipo le  a r ray ,  a pattern r e s u l t s  
-9- 
L 
which combines the E plane directivity of the 
dipole array with the unidirectional character 
of the rhombic. 
5 .  The KWOT structure is compact when stowed, but is 
easy to deploy and adjust. 
Being composed of flexible filaments, the FJOT 
structure is not szbject te serious deformation 
from temperature gradients as are long rigid 
booms. 
6. 
7. There are no metallic structural members to distort 
-.__ -.- _ _  - - - _  - the antenna field. ----_.__ 
8. The KWOT antenna generates a real beam, which is 
physically scanned Over the celestial sphere in 
a controlled manner. Thus, the reduction of the 
data is simple and straightforward, with none of 
the uncertainties that arise in aperture synthesis 
due to changes in the strength of emitting objects, 
or in the parameters of the receiving system. 
REFERENCES 
(1) Haddock, F.T., Phase I Final Report, Engineering Feasibility Study 
of a Kilometer Wave Orbiting Telescope, HGR 23-005-131, University 
of Michigan Radio Astronomy Observatory, Ann Arbor, Michigan, Octo- 
ber, 1966. 
Haddock, F.T., Proposal to NASA, "Phase Two Engineering Feasibility 
Study of a Kilometer Wave Orbiting Telescope",ORA-67-555-P31 
November, 1966. 
Hegg, Daniel R., "Motion of a Lumped-Mass Model Representing A 
Kilometer Wave Orbiting Telescope'', 
Astronomy Observatory Report No. 68-6, March, 1968. -.-- 
Crist, S.A., "Motion and Stability of a Spinning Cable-Connected 
System in Orbit", University of Michigan Radio Astronomy Observa- 
tory Report No. 67-7 Revised December, 1967. --- 
(2) 
(3 )  
University of Michigan Radio 
(4) 
(5) Schoendorf, W,H., "Resistive Losses on Thin Wire Antennas", Univer- 
sity of Michigan Radio Astronomy Observatory Report No 68-9, 
February, 1968. - __ 
(6) Bell Aesosystems/University of Michigan, "Kilometer Wave Orbiting 
Radio Telescope", 17 page brochure, 1968. _-  
I 
. 
- 
1 
a . 


Engineering feasibility study of a kilometer wave orbiting telescope, phase 2 Final report

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