AIR FORCE MISSILE DEVELOPMENT CENTER TECHNICAL REPORT

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP81-01043R002500200002-6
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 116
• Document Creation Date: December 27, 2016
• Document Release Date: October 23, 2013
• Sequence Number: 2
• Publication Date: January 1, 1958
• Content Type: REPORT

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ylrot;h?,.1,1641,.f., 4 I
,IIMIJI;V;titopt;,`..4,!Arlyq'tiomait'A.t3fWittre,terelt?, V,1
Scientific Consultants to the
Operations Research Office
IR FORCE MISSILE DEVELOPMENT CENTER
AIR RESEARCH AND DEVELOPMENT COMMAND
'UNITED STATES A.IR FORCE
Holloincin Air, Force Bose, New Mexico
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"Sun stand thou still at Gibeon. and the sun stood still "
1
Joshua 10?
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SUMMARY
This Technical Report is a consolidation of ten papers pre-
pared by scientific consultants to the Operational Research
Office at the Air Force Missile Development Center during the
summer of 1957.
Each paper is the report submitted, upon the completion o
his studies, by a consultant or consultant team. Pyrheliometer
measurements showing the solar energy which can be expected
to be available to a solar furnace located at Cloudcroft
Mexico, are reported in the first paper.
New
This is followed by
an appraisal of the potential performance of such a solar furn-
ace. The next paper, written by two of the nation's
astronomers, explains certain basic
out standing
optical considerations
governing the design of solar furnaces. This is followed by
three penetrating papers on the theory of absorption and re-
flection in solar furnace components and of the concentration
of radiation through, and outside of, focal spots. Next is an
examination of the rigid-body torsional oscillation which would
restilt fiom aerodynamic excitation. Another study in which
theories of transient temperature di:strfbution in a solar target
are discussed is followed by a., presentation of an alternate
e sign method
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W('
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FOREWORD
The order of arrangement of the individual papers was
selected to secure as logical a presentation as possible for
the reader who would choose to read the report from cover
to cover. The sequence starts with measurement of solar
energy, then to performance of the proposed Department of
Defense furnace, then to considerations governing design, fol-
lowed by theoretical studies which would ,pertain to any solar
furnace, and lastly, to topics of least interest from the point
of view of optical considerations and of least immediate prac-
tical application. The reader can stop at any point after the
second paper and still have a fair concept of the proposed so-
lar furnace.
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STAT
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v
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1\
1. PRELIMINARY MEASUREMENTS OF THE SOLAR
RADIATION AT CLOUDCROFT', NEW MEXICO
Introduction
II. Instrumentation
III. Measurements and Results
Discussion
NOTES ON THE POTENTIAL PERFORMANCE OF TF
CLOUDCROFT SOLAR FURNACE
I.?Til.t.....,o4q0.ti.ot ?
III. Off-axis Images from Spherical Mirrors. ...
SUGGESTED METHOD'S OF ALIGNING THE PL
THE SO LAR FURNACE HELIO$TAT MIRRORS,]
I. An Optical Method
II. A Second Optical Method
III. A Mechanical Method. UI'
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_
v
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1\
1. PRELIMINARY MEASUREMENTS OF THE SOLAR
RADIATION AT CLOUDCROFT', NEW MEXICO
Introduction
II. Instrumentation
III. Measurements and Results
Discussion
NOTES ON THE POTENTIAL PERFORMANCE OF TF
CLOUDCROFT SOLAR FURNACE
I.?Til.t.....,o4q0.ti.ot ?
III. Off-axis Images from Spherical Mirrors. ...
SUGGESTED METHOD'S OF ALIGNING THE PL
THE SO LAR FURNACE HELIO$TAT MIRRORS,]
I. An Optical Method
II. A Second Optical Method
III. A Mechanical Method. UI'
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PRELIMINARY MEASUREMENTS' OF
?SOLAR RADIATION AT
CLOtJDCROFT, NEW MEXICO
Measurements of the solar radiation at Cloudcro
exico, havebeen made with a normal incidence pyrheliomete:
?he readings ,an aNrer-age transmittance has beende
mine,d that canb.eusedto calculate t4:0 available flux al
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I. Introduction
Preliminary design has bten.? made for ?the, constr4cti,on?..,Of.;,.. a 1,farrge???? ?
? oplar-ittrnaCe?,...hear.?CloUdc?roft w Mexico, to be operated by the Air
Force Missile De?Ve..1..0p4neilt ? C..enter???fOr. the Department ,?of...ir?Defense??????
?:proper
is necessary. SP'ectrara,diometric ?'neasurements(1) at nearby Sunspot,
? New Mexico, have furnished ,data for ,successfully deterthining the solar
constant. Ficiwever, accurate atmospheric transrnissAO: ata, a e no,
available in the infrared portion of the spectrum and the amount of solar
radiation r eceived at Sunspot cannot be conveniently calculated. If thest
data were available, precise calculations of the received solar energy
flux would be most difficult since intense water
1135, 1379,72 and 2650, are located in a spectral
ion
contributing about 40 of the total energ To atetransmission coef-
rared region. 0??;.r.,0??[generally obtained from curves
moothly over t os o e water-vapor an
in at e
order t amount o Solar radiation be ki.own.
measurement of the solar ra4iation.
? rr
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I. Introduction
Preliminary design has bten.? made for ?the, constr4cti,on?..,Of.;,.. a 1,farrge???? ?
? oplar-ittrnaCe?,...hear.?CloUdc?roft w Mexico, to be operated by the Air
Force Missile De?Ve..1..0p4neilt ? C..enter???fOr. the Department ,?of...ir?Defense??????
?:proper
is necessary. SP'ectrara,diometric ?'neasurements(1) at nearby Sunspot,
? New Mexico, have furnished ,data for ,successfully deterthining the solar
constant. Ficiwever, accurate atmospheric transrnissAO: ata, a e no,
available in the infrared portion of the spectrum and the amount of solar
radiation r eceived at Sunspot cannot be conveniently calculated. If thest
data were available, precise calculations of the received solar energy
flux would be most difficult since intense water
1135, 1379,72 and 2650, are located in a spectral
ion
contributing about 40 of the total energ To atetransmission coef-
rared region. 0??;.r.,0??[generally obtained from curves
moothly over t os o e water-vapor an
in at e
order t amount o Solar radiation be ki.own.
measurement of the solar ra4iation.
? rr
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I. Introduction
Preliminary design has bten.? made for ?the, constr4cti,on?..,Of.;,.. a 1,farrge???? ?
? oplar-ittrnaCe?,...hear.?CloUdc?roft w Mexico, to be operated by the Air
Force Missile De?Ve..1..0p4neilt ? C..enter???fOr. the Department ,?of...ir?Defense??????
?:proper
is necessary. SP'ectrara,diometric ?'neasurements(1) at nearby Sunspot,
? New Mexico, have furnished ,data for ,successfully deterthining the solar
constant. Ficiwever, accurate atmospheric transrnissAO: ata, a e no,
available in the infrared portion of the spectrum and the amount of solar
radiation r eceived at Sunspot cannot be conveniently calculated. If thest
data were available, precise calculations of the received solar energy
flux would be most difficult since intense water
1135, 1379,72 and 2650, are located in a spectral
ion
contributing about 40 of the total energ To atetransmission coef-
rared region. 0??;.r.,0??[generally obtained from curves
moothly over t os o e water-vapor an
in at e
order t amount o Solar radiation be ki.own.
measurement of the solar ra4iation.
? rr
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evident that curves given in Figures 3, 4, and 5 are greatly
resented in Figure 2 indicate that a differexit slope might be drawn for
morning and afternoon measurements. This same morning-afternoon
arac eristi.c exists fordata taken at Tucson onAugust 2 with an Eppley
rheliometer. These data corrected similarly to that in Figure 2,
so included are average data from Miam
The data presented in Figure 2 are essentially an average of flux
measurements taken in.August. These measurements show a consider-
able spread but readings taken during a single day indicated good agree-
ment The data taken on ?August 26 are shown in Figure 7. Since
seasonal and daily variations in (I) are well known(2) measurements
should be taken over the year before extrapolation of these data to other
months. This limitation. is ,recognized, but the methods employed in ca
culatirig data for Figures 3 4, and 5 do not depend on the values of C
and the calibration curve. When more accurate measurements of
are made in sufficient quantity, the calculation o
day and year will be correspondingly more dependable.
t4ritOon recordedvariations of having the Same absorption pa
same air-,mas.s appear., real.:he differences could.be-:cauSed by
. .?,,
ambient correction to the'pyrheliometers although other wor
find suchan e ect significant., difference might also
s.,..catter.14.g or abaor
ce the readings might also correctly indicat the
-? 4,04 ?,.4
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evident that curves given in Figures 3, 4, and 5 are greatly
resented in Figure 2 indicate that a differexit slope might be drawn for
morning and afternoon measurements. This same morning-afternoon
arac eristi.c exists fordata taken at Tucson onAugust 2 with an Eppley
rheliometer. These data corrected similarly to that in Figure 2,
so included are average data from Miam
The data presented in Figure 2 are essentially an average of flux
measurements taken in.August. These measurements show a consider-
able spread but readings taken during a single day indicated good agree-
ment The data taken on ?August 26 are shown in Figure 7. Since
seasonal and daily variations in (I) are well known(2) measurements
should be taken over the year before extrapolation of these data to other
months. This limitation. is ,recognized, but the methods employed in ca
culatirig data for Figures 3 4, and 5 do not depend on the values of C
and the calibration curve. When more accurate measurements of
are made in sufficient quantity, the calculation o
day and year will be correspondingly more dependable.
t4ritOon recordedvariations of having the Same absorption pa
same air-,mas.s appear., real.:he differences could.be-:cauSed by
. .?,,
ambient correction to the'pyrheliometers although other wor
find suchan e ect significant., difference might also
s.,..catter.14.g or abaor
ce the readings might also correctly indicat the
-? 4,04 ?,.4
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evident that curves given in Figures 3, 4, and 5 are greatly
resented in Figure 2 indicate that a differexit slope might be drawn for
morning and afternoon measurements. This same morning-afternoon
arac eristi.c exists fordata taken at Tucson onAugust 2 with an Eppley
rheliometer. These data corrected similarly to that in Figure 2,
so included are average data from Miam
The data presented in Figure 2 are essentially an average of flux
measurements taken in.August. These measurements show a consider-
able spread but readings taken during a single day indicated good agree-
ment The data taken on ?August 26 are shown in Figure 7. Since
seasonal and daily variations in (I) are well known(2) measurements
should be taken over the year before extrapolation of these data to other
months. This limitation. is ,recognized, but the methods employed in ca
culatirig data for Figures 3 4, and 5 do not depend on the values of C
and the calibration curve. When more accurate measurements of
are made in sufficient quantity, the calculation o
day and year will be correspondingly more dependable.
t4ritOon recordedvariations of having the Same absorption pa
same air-,mas.s appear., real.:he differences could.be-:cauSed by
. .?,,
ambient correction to the'pyrheliometers although other wor
find suchan e ect significant., difference might also
s.,..catter.14.g or abaor
ce the readings might also correctly indicat the
-? 4,04 ?,.4
Declassified in Part - Sanitized Copy A proved for Release
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Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
evident that curves given in Figures 3, 4, and 5 are greatly
resented in Figure 2 indicate that a differexit slope might be drawn for
morning and afternoon measurements. This same morning-afternoon
arac eristi.c exists fordata taken at Tucson onAugust 2 with an Eppley
rheliometer. These data corrected similarly to that in Figure 2,
so included are average data from Miam
The data presented in Figure 2 are essentially an average of flux
measurements taken in.August. These measurements show a consider-
able spread but readings taken during a single day indicated good agree-
ment The data taken on ?August 26 are shown in Figure 7. Since
seasonal and daily variations in (I) are well known(2) measurements
should be taken over the year before extrapolation of these data to other
months. This limitation. is ,recognized, but the methods employed in ca
culatirig data for Figures 3 4, and 5 do not depend on the values of C
and the calibration curve. When more accurate measurements of
are made in sufficient quantity, the calculation o
day and year will be correspondingly more dependable.
t4ritOon recordedvariations of having the Same absorption pa
same air-,mas.s appear., real.:he differences could.be-:cauSed by
. .?,,
ambient correction to the'pyrheliometers although other wor
find suchan e ect significant., difference might also
s.,..catter.14.g or abaor
ce the readings might also correctly indicat the
-? 4,04 ?,.4
Declassified in Part - Sanitized Copy A proved for Release
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evident that curves given in Figures 3, 4, and 5 are greatly
resented in Figure 2 indicate that a differexit slope might be drawn for
morning and afternoon measurements. This same morning-afternoon
arac eristi.c exists fordata taken at Tucson onAugust 2 with an Eppley
rheliometer. These data corrected similarly to that in Figure 2,
so included are average data from Miam
The data presented in Figure 2 are essentially an average of flux
measurements taken in.August. These measurements show a consider-
able spread but readings taken during a single day indicated good agree-
ment The data taken on ?August 26 are shown in Figure 7. Since
seasonal and daily variations in (I) are well known(2) measurements
should be taken over the year before extrapolation of these data to other
months. This limitation. is ,recognized, but the methods employed in ca
culatirig data for Figures 3 4, and 5 do not depend on the values of C
and the calibration curve. When more accurate measurements of
are made in sufficient quantity, the calculation o
day and year will be correspondingly more dependable.
t4ritOon recordedvariations of having the Same absorption pa
same air-,mas.s appear., real.:he differences could.be-:cauSed by
. .?,,
ambient correction to the'pyrheliometers although other wor
find suchan e ect significant., difference might also
s.,..catter.14.g or abaor
ce the readings might also correctly indicat the
-? 4,04 ?,.4
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1q11717 - WA% 10,4A,A ,,10.04(A
VaKTN4'i,
Time
(MST)
11:25:10
11:27
11:29
11:31
11:32
11:33
11:34
11:35
11:37
11:37:10
11:39
11:40
11:43
11:44
11:45
11:46
11:47
11:48
11:49
Dial Reading
Pyrheliometer covered.
6.5
3.0
? 0.8
-0.2
? -1.0
-1.0
-2.0
-2.0
Pyrheliometer uncovered.
73.5
84.5
90.6
91.5
91.6
92.0
91.8
92.0
92.0
18
'
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Eppley Reading
(langleysimin)
1.21
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Date
Measurements of (1:0 at Cloudcroft
VIIIM?11????
Summer 1957
Time Air Mass .m I) in Langleys /min
(Local sun time corrected to mean radius)
July 27 8:00 1.73
29 12:00 1.03
2:49 1.31
3:09 1.40
'3:27 1.50
August 8 9:30 1. 26
9 9:14 1.33
10 9:48 1.21
11:55 1.05
12 9:00 1.39
9:26 1.29
16 8:57 1.43
9:58 1.20
10:51 1.10
20 7:54 1.96
9:59 1.21
21 7:33 2.27
8:13 1.76
22 7:09 2.79
23 9:07 1.41
26 11:09 1,,11.
2:23
3:13 1.54
3:57 1 91
4:37 2.54
4:54 2.98
-01043R0025002nonm_R
19
1.31
1.55
1.47
1.46
1.44
1.42
1.41
1.47
1.54
1.41
1.44
1.46
1.51
1.51
1.26
1.47
1.26
1.36
1.15
1.45
1.56?
1.51
1.47
1.42
1.32
1.28
,????
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Calculation of in and Correction of Measurement
Time:
Latitude 9:
Longitude:
:Hour angle t:
Apparent declination of sun
Measured
9:17 MST, 9.14 loca sun tirne
32?57'
105?44'
2 hr 46 rnin
16?10'
1,37 iangleys minute
Latitude 0:
Longitude:
Hour angle t:
Apparent declination of sun
hs = sin 43 sin cos 9 cos S cos
-0.2145 + 0.7473 0.5328
elevation of sun 32?12'
44,14 Lit, 1.4 ?.u.
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Calculation of in and Correction of Measurement
Time:
Latitude 9:
Longitude:
:Hour angle t:
Apparent declination of sun
Measured
9:17 MST, 9.14 loca sun tirne
32?57'
105?44'
2 hr 46 rnin
16?10'
1,37 iangleys minute
Latitude 0:
Longitude:
Hour angle t:
Apparent declination of sun
hs = sin 43 sin cos 9 cos S cos
-0.2145 + 0.7473 0.5328
elevation of sun 32?12'
44,14 Lit, 1.4 ?.u.
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2 0020 -
?
414
4S,
. ,vq,3t,or,O.o3 ?,?11:04'47.9.1ri.t`c'?-"k;WP,
f
tvi
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,
ID Introduction
The individual spherical mirrors making up the mosaic of mirrors
of the condenser of the Cloudcroft Solar Furnace may be specified in a
variety of focal lengths. Inasmuch as the choice of focal length may be
one of the critical factors in determining the net flux concentration b
the furnace, it is desirable to determine from the optics of off-axis
image formation the optimum focal length of the mirrors in each annu-
lar ring of the mosaic
II. Mirror Locations
These calculations are based on an aperture of the paraboloid of
105 ft. and a focal length of 44.76 ft. The mirrors forming the mosaic
are for these considerations 2 ft. x 2 ft. squares as specified in the
proposal of 18 May 1956, prepared by the Pittsburgh Des Moines Steel
Company, except for certain modifications suggested below. It is as
that the mirrors are to he arranged in zones
around the vertex of the paraboloid.
of concentric arra
. Relationship between arc lengths,. ? f the
corresponding ordinates
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410.0????
parabola and "t
?Itft,;
tt
However, from the equation of the parabola:
2
2 .px, hence:
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and: cb'c
The integral in Eq. 1 is readily evaluated:
4fi
V,
,4t
Jir
;?,c9;;,,,
3.,kr;,17
cty
Successive integral values of y at 2 ft intervals, are substi-
tuted in Eq. 2) and the corresponding values of s are computed as
recorded in Columns i and 2 of Table I. In 'Column 4 of Table I are
'recorded values of y obtained by interpolation corresponding to the
integral, values 'of s 'in Column 3. Since there ?to be an. aperture
12 ft. n ? diameter at...th.e.,,center of the paraboloid, the computed values.
?.......?????????-?? ? ?????, .
in Figure
record o all data computed in the evaluation of Eq.
contained in Table VI in the Appendix.
?
`kl rtA4:0
\IWO ,ukf
_
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(2)
Table I
7 ft. 7.00513 ft. 7 ft. 6.995 ft.
9 .9,01605 9. 8.984
11 11 02764 11 10.972
13 13.04516 13 12,995
15 15.0698 15 14.931.
17 17.1021 17 '16.900
19 19..1419 ' 19 18.861
21 21.1903 21, 20.814
23 23.2496 23 22.757
25 25.3212 25 24.690
27 27.4041' 27, 26.612
29 29.4986 29 28.524
31 31.6100 31 30.422
33 33.7323 33 32.310
35 35.8728 35 34.184
37 38.0282 37 36.046
39 40.1999 39 37.895
41 42.3917 41 39.730
43 44.5994 43 41.551
45 46.8282 45 43.360
47 49.0789 47 45.1.53
49 '51.3471 49 46.930
51 53.6378, 51 48.694
53 55.9518 53 50.443
55 58.2868 52.177
b. A meridian sectipn 'of the parabdioid is-shown in Figure
A spherical mirror M is tangent to the'paraboloid at point
on the center of which impinges, a ray parallel to the principal axis.?
the paraboloid. From the geometry of Figure 9, the values of the desi
nated angles
and length L are caleti.lated and tabulated nTa e
_
14
en.
to,
0
3
II
t,
ir
Table II
Zone
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Aism
7 ft 6 995 ft. 85032t 4?2.8' 81?04' 45.045 ft.
9 8.984 '849/6' .5?44' 78?32' 45.191
11 10.972 83001' 6?59' 76?02.' 45.459
.13 12,.995. 8,1?46' '8?14' 73?32' 45.703
15 14.931. 80032' 9?28' 71004! 46.01.7
17 .16.900 79?19' 120?41' -68?38' 46.421,
19 18.861 78?06' 11?54' 66012' .46:738
8 21 20.814 76?55' 13?05' .63?50' 47.199
9 23 22,-757 75044' 14?16 61?28' 47.642.
10 25 24.690 74?35' 1.5?25' 59?10' 48.172
11 27 26.62i - 73?27' 16?33' 56?54' 48.731
12 21 28.524 72020' 17?40' 54?0' 49.321
13 31 30.422 71?14' 18046' .52?'28' 49.936
14 33 32.310 70009' 19?51' 50?18' 50.582
15 3534184 69?06' 20054' 48?12' 51.287
16 . 37 36.046 68?04' 21?56' 46?08' 52.016
17 39 37.895 67003' 22057' 44?06' 52.769
18 41 39.730 66?04' 23?56' 42?08' 53.574
19 43 41.551 65?06' 24?54' 40?12' 54.406
20 45 43.360 64009' 25?51' 38?18' 55.251
21 47 45.153 63?14' 26?46' 36028' 56.146
2 49 46.930 62?20' 27?40' 34?40' 57.059
3 51 48.694 61?27' 28?33' 32?54' 57.995
24 53 50.443, 60?36' 29?24'. 31?12' 58.973
5 ?55' 52.177 9?46' 30?14' 29?32' 59.969
he variation of L with arc -length is shoWn graphically in
igure 10.
It is to be noted that the value,s o
and y given in Tables
and II refer to the midpoints of the respective mirrors while in Table
-III they refer to the, inner edges of the mirrors.
417,4 ny,,,m 4,.,romor
ty,
Al2.7.12.111?1,v 1,,..v.:21,amksta.la:,
ti??1 ? ? ,144,...ta
Declassified in Part - Sanitized Copy Approved for Release
?
Table III
Zone S y Zone
5 9980 ft. 13 30 29 475 ft.
8 7.9895 14 32 31.366
3 10 ? , 9.970 .15 34 33.247
1.2 11.9635 16 36 35.115
14 13.943 17 ,38 36.970
16 15.916 18 40 38.812
18 . 17.880 19 , 42. 40.640
20. 19.838 ' 20 44 42.455
22 21.786 21 46 44.256
10 24 23.732 22 .48 46.041
11 26 25.651. 23 50 47.812
12 28 27.568 24 . 52 49.568
25 54 51.310
III. Off axis Images from Spherical Mirrors
a.. The astigmatic image distances1 and s of Figure 11, as
measured along the chief ray, are known to be related to the angle of
incidence and reflection i, the object distance s and the radius of
curvature r of the reflecting surface by (1).
IMMO
2
r cos
or the primary or tangential focus s2, an
for the secondary or sagittal focus
50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
9tf,
?
Declassified in Part - Sanitized Copy Approved for Release
50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
Taking the object distance s as infinity, become
and F the principal astigmatic ,focal points by definition, and the
equations reduce to Onlywhen an infinitely narrow bundle of rays forms the images
? above are these images line images. The conical bundle of ray 'from
the sun of angle ? in diameter 'forms an image composed of a s'eries
of overlapping circles whose centers lie on or w as the case may
The distance between the'two principal focal points measured along the
\
A concave spherical mirror of square section EFGH, as in
Figure 12, forms two 1in images JK. and LM centered on the Chief ray
BC when the incident light strikes the mirror off-axis as along the line
AB at angle i to the normal BD. The secondary or sagittalimage lie,s
in a plane. containing the chief rays White. the primary or tangential
. Since the diameter of these circles is the product of the distance
rorn the point in the image to the point on the mirror from which the
light comes and the angular diameter of the sum, it is apparent that
image JK will have the dimensions of Figure 13a and image LM, those
of 13b where L is taken as BC, JK as w, and LM as A in Figure 5.
The slight distortion of Figure 1:31D?comes from the fact that in
Figure 12, rays HL and GL are, shorter than,rays and FM. The
image distortion effect' in this instance is negligible since the,mirror
aperture and image lengths are small comparedto the, ocal length and
image stands normal to sudh a plane The image di.stancesr-in E ua- ? 'will, erefore, be neglected in t e isCussionbelo
ions and 6) abov,e are measured along BC
fect in image ?TIC .j.s Pi
make the a
edge poorly 'defined.
constructing a plane tlit inclides BC, the ifnage.
. ? . ,. ? ? J.A.A 40. yr a. O.; , lho .44.0,
0;11 11
1.14 ? J. . J. A
and, with a plane at right angles to this that includes line image LM, ? tively.
Declassified in Part - S;nitized Copy Approved for Release @ 50-Yr 2013/10/23 : CIA-RDP81-01043R002500200002-6
014,0,.1,,,tr,r;;F,61p:ra:r,p, Re1',
vq,INY-ah
(cl'''t100
411
471514 ""'''^m62450.501,,,viZtrsovokiti",v,
Declassified in Part-Sanitized Copy Approved for Release 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
lux Concentration
On the assumption that the intensity across the three images.
above is, cOnstant, the one of smallest dimensions should' have the high-
est flux density and should, therefore; be used as the focal point :for
the seprate Spherical mirrors of the solar furnace array. Since
, a sin s always smaller than a ta,n2 I, and the third case ? above is
intermediate the primary or w focus appear's most favorable.
b. The efficiency of a single spherical mirror in sending light
flux to a target s seen as the ratio of the area of the target when pro-
jected onto a plane normal to the chief ray from the spherical mirror,
o the area of the image of the sun on this plane as produced by the
sphericalmirror. It is therefore
Effici enc
sin
Le flux produced at. the target may be obtained fromthe pro-
ected,area of the circular ring or zone of mirrors of which the mirror
valuate
in
e flux' in ca
lux
q ?
was a part, the solar constant and the efficienc
sec contributed by the zone is
1
))4142.40thoausitatr.:fniqgja
x 0.0264 cal c sec x efficiency. 10
Considering the solar constant as 0.0264 cal/cm2/sec, the
focal length of the parabolic mirror array as 44.76
e mean dia-
meter of the sun as 32 and the mirrors each 2 ft x 2 ft, the Values o
and y from Tables I and II permit the efficiencies of spheri-
cal mirrors as they might actually be employed. Column 2 of Table IV
lists these calculated values.
a...b].e IV
Zone Spherical Mirrors .Parabolic Mirrors
No. Efficiency Flux (cal/ sec) Efficiency Flux (cal/ s ec) Cumulative
Flux Total
0.941
',906,.
3. 0.864
08l7
0771
0.720
7 :0 6.7.2
'8' 0.622
0.575
.10, '0 529'
1.1 0.485
.0.445
13 0.406
14 0.371
15, 0.337
16, 0.308
.17 0.280.
18 0.254
19 43,1
21' '0.190
.,
22 172'.
.23 0.156,
:24 0.141
25 0.127

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1874
2496
2900
3228
3500
3681
3822
3887
3903
3879
815.
726
3602
34.
332.1
3171
3010.
2846
268
2519
35
2203
2050
1906
1782
0.975 1943
0.961 2647
0.941 315
0.919 363
0.895 4062
0.866 4429
0.839 4775
0.807 5042
0.775 5267
0.714 5437
0.707 55
0.672 563
?637 5648
0.603 564
0.568 5587
0.534'5500
0.501 5384
0.468 23
0.437
0.4
89
350 448
2
84
7,748
1,378
5,441
9,868
4,643
9,685
4,952
:0,389'
15
22
8
fl.
4
Declassified in Part-Sanitized Copy Approved for Release @50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
'e flUX....c"Ontil;:ctiti011,,Of.,e.ah...i7xiirOi. ring zone is presented in
Column 3 of Table IV. It is to be ,noted that the values of s are odd
numbered for the efficiency calculation since values for mirror centers
are required; however, I or, flux calculations, s and
are for even
numbered, positions 'since edge measurernents.are required.
Unfortunately, the total flux from this calculation reaches
value p1 only 75,634 calories/sec while 88,690 calories/sec. are re-
quired for a flux density of 700 cal/cm2 s c.
is a fact that the fluX density across the mirror image is not
constant as was assumed above but is constant along the length or
or
only when these lengths are greater than o/.. L. When the lengths
are less than osZ, L, as in Figure 14, the extreme images pro-
duced by the edges of the mirror, overlap and in the overiappe4...sec..7.
all areas of the mirror. This fact peri7.4t....s:
recalculation of the eWciency' of the spheical mirror in that in the
.overlapped section, the spherical rnirror is equal in light cohcentr,
?
? For the sagittal focu?'f,a spherical.rnirror, the 'overlap see-
tion, 'if One occurs, approximates the. shape 'of the tar get proj5ectiii as,
referred to' above.
oreover, ft x 2 ft Amirrors are used 3.nstea
the 2 ft x 2 ft one's as presently plarth d for-the solar furnace e
imensions and area of the overlap section approximately equal those
lIt22g12a1.41.14144.11avenAug,,,.
odtk:WeavklEhilialataaw.A.14,,e4L..0
of the projected target, These comparisons are shown in Table V. e-
\
low'.
Zone Overlap Section o
'
No. 1 x 2 ft Mirrors
Table V
Target Projection.
Major Minor
rea Axis is
rea
4887ft 0 4126ft.. 0 1315ft. 0.4159ft. 0 4110ft. 0.1342ft.
0.4200 0.4100 0.1344 Same 0.4078 0.1.333
0.4223 0.4076 0.1339 value 0.4038 0.1319,
4 0.4243 0.4039 0.1329 for 0.3986 0.1303'
0.4268 0.4000 0.1318 all 0.3936 0.1286
0.4301 0.3957 0.1309 zones 0.3875 0.1266
7 0.4322 0.3901 0.1290 0.3807 0.1244
8 0.4354 '0.3847 0.1275 0.3734 0.1220
9 0e4381 0.3782 0.1255 0.3655 0.1195
10 0.4413 0.3718 0.1236 0.3573 0.1167
11 0.4443 0.3647 0.1214 0.3486 0.1139
,
12 0.4462 0.3571' 0.1172 0.3394 0.1109
13 0.4492 0.3488 0.1162 0.3299 0.1078
14 0.4518, 0.3399 0.1132 0.3201 0.1046
15 0.4548 0'.3309 0.1100 0.3102.101
16 0.4560. 3214 0.1069 0.3000 0.9803
17 0.4566 0.3112 0.1030 5 0.2896 0.9463
18 0.4575 0.3010 .09,93 '0.2791 0.9122
9 0.4575 0.2903 0.0952 S S , ' 0.2686 0. 8777
0 4568 0.2789 0.09092579 0.8427
.4557 267. 0.0850 g082
4
22
4536 0.2556 0.0820 5 5 0.2367 .773
.4506 5 0.2431.771'.' . S ' '0,2260 5 0.7386
24 0.4469 0.2307 0.0723 0.2151 0.7044
25 4420 ' '0.2178 0.0672.205 ,
ese data make it. appear that the projectedarea of the.
may . 'an lie within, the overlapped sections of the' mirror images.
-
Declassified in Part - Sanitized Copy Approved for Release C50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
pk,
ft,
.011
Declassified in Part - Sanitized Copy Approved for Release
I \
Under these circumstances the flux produced by each pair of 1 ft x 2 It
mirrors may be computed as though they were parabolic sections mak-
ing images e)4, L in diameter. The efficiencies of such parabolic mir-
rors rnay be calculated a
Efficiency
n
11
and are shown in Column 4 of Table IV and the flux cOiatribufion as cal-
culated from Eq. (10) for each zone is shown in Column 5 of that Table.
A minor error in the results tabulated should be noted here.
The substitution of 1 ft x 2 ft mirrors naturally doubles the number o
values of L, i, etc,, and. the number of mirror zones. This effect was
not considered in the computation since the smaller mirrors were con-
sidered as located centrally in the space required for the larger ones.
recalculation of the flux concentration based on a more exact formu-
ation
would tend to raise the flux values given above.
? _?
o umri 6.ofTable IV is the curn-ulative total of the,,flux contri-
utions of the several zones starting with the innermost zonei'
On the
basis of 100 efficiency withnolosses,due . o absorption, reflection an
s a owin mirror of 19 zones would suffice to achieve a flux density
700of cal/cm2/sec. If the entire 25 zones are used, this same flux
10M,V
4tailLIM111)4,1,?2114.:,11!.37,1/,',-,AgLI
tr
t=1,1S,41,tfllap etaa
50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
)0
density may be ahieved with an overall loss due to above effects o
23 5%.
..The:Ei.CalCU14,tiOns .,Of :the Aux ? c.ont.ri.i.itiOns.
rors to the target have not consid.er,ed the effect of the limb darkenin
of the sun as described by Jose
proposed here
(2)
It is to be nbte that in the cheme;
the target projection does not lie in the center of a cir-
?cul,ar focal spot for a single mirror, and, fherefore, the percentage
increase in flux due to limb darkening may not be in the amount Jose
proposes.
Declassified in Part -Sanitized Copy Approved for Release 50-Yr 2013/10/23 ? CIA RDP81 01043R0025002000 -6
pk,
ft,
.011
Declassified in Part - Sanitized Copy Approved for Release
I \
Under these circumstances the flux produced by each pair of 1 ft x 2 It
mirrors may be computed as though they were parabolic sections mak-
ing images e)4, L in diameter. The efficiencies of such parabolic mir-
rors rnay be calculated a
Efficiency
n
11
and are shown in Column 4 of Table IV and the flux cOiatribufion as cal-
culated from Eq. (10) for each zone is shown in Column 5 of that Table.
A minor error in the results tabulated should be noted here.
The substitution of 1 ft x 2 ft mirrors naturally doubles the number o
values of L, i, etc,, and. the number of mirror zones. This effect was
not considered in the computation since the smaller mirrors were con-
sidered as located centrally in the space required for the larger ones.
recalculation of the flux concentration based on a more exact formu-
ation
would tend to raise the flux values given above.
? _?
o umri 6.ofTable IV is the curn-ulative total of the,,flux contri-
utions of the several zones starting with the innermost zonei'
On the
basis of 100 efficiency withnolosses,due . o absorption, reflection an
s a owin mirror of 19 zones would suffice to achieve a flux density
700of cal/cm2/sec. If the entire 25 zones are used, this same flux
10M,V
4tailLIM111)4,1,?2114.:,11!.37,1/,',-,AgLI
tr
t=1,1S,41,tfllap etaa
50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
)0
density may be ahieved with an overall loss due to above effects o
23 5%.
..The:Ei.CalCU14,tiOns .,Of :the Aux ? c.ont.ri.i.itiOns.
rors to the target have not consid.er,ed the effect of the limb darkenin
of the sun as described by Jose
proposed here
(2)
It is to be nbte that in the cheme;
the target projection does not lie in the center of a cir-
?cul,ar focal spot for a single mirror, and, fherefore, the percentage
increase in flux due to limb darkening may not be in the amount Jose
proposes.
Declassified in Part -Sanitized Copy Approved for Release 50-Yr 2013/10/23 ? CIA RDP81 01043R0025002000 -6
pk,
ft,
.011
Declassified in Part - Sanitized Copy Approved for Release
I \
Under these circumstances the flux produced by each pair of 1 ft x 2 It
mirrors may be computed as though they were parabolic sections mak-
ing images e)4, L in diameter. The efficiencies of such parabolic mir-
rors rnay be calculated a
Efficiency
n
11
and are shown in Column 4 of Table IV and the flux cOiatribufion as cal-
culated from Eq. (10) for each zone is shown in Column 5 of that Table.
A minor error in the results tabulated should be noted here.
The substitution of 1 ft x 2 ft mirrors naturally doubles the number o
values of L, i, etc,, and. the number of mirror zones. This effect was
not considered in the computation since the smaller mirrors were con-
sidered as located centrally in the space required for the larger ones.
recalculation of the flux concentration based on a more exact formu-
ation
would tend to raise the flux values given above.
? _?
o umri 6.ofTable IV is the curn-ulative total of the,,flux contri-
utions of the several zones starting with the innermost zonei'
On the
basis of 100 efficiency withnolosses,due . o absorption, reflection an
s a owin mirror of 19 zones would suffice to achieve a flux density
700of cal/cm2/sec. If the entire 25 zones are used, this same flux
10M,V
4tailLIM111)4,1,?2114.:,11!.37,1/,',-,AgLI
tr
t=1,1S,41,tfllap etaa
50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
)0
density may be ahieved with an overall loss due to above effects o
23 5%.
..The:Ei.CalCU14,tiOns .,Of :the Aux ? c.ont.ri.i.itiOns.
rors to the target have not consid.er,ed the effect of the limb darkenin
of the sun as described by Jose
proposed here
(2)
It is to be nbte that in the cheme;
the target projection does not lie in the center of a cir-
?cul,ar focal spot for a single mirror, and, fherefore, the percentage
increase in flux due to limb darkening may not be in the amount Jose
proposes.
Declassified in Part -Sanitized Copy Approved for Release 50-Yr 2013/10/23 ? CIA RDP81 01043R0025002000 -6
Declassified in Part- Sanitized Copy Approved for Release @50-Yr 2013/10/23: CIA-RDP81:01043R002500200002-6
FIGURE 12
LI"' 'to tde, ?iz ejaiLagg ,
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
.7932 7931:
971- ,989713
-1933 101.1933_
.4590. ,-1-03.4590-.
_ .
7-6.80 105-. 7680-
1-1193 108.1199.
.110 5141-
.9501 950-1
.4274_ 115.4274--
.453 117-9453
120.5031
.1001 1001.7356 125.7356
.4088 128.4088
.
1.08125 3.51068
1.10558 4.52269
1.13040 5.54136
1.15571 6.56817
1.18150 7.60455
1.20777 8.65191
1.234519 9.71161
1.261731 10.78502
1.289404 1L87348
317530 12.97828
1.346103 14.10067
1.375112 15.24185.
1.404553 16.40304
1.434415 58539
O.078071
O.100388
.-122571
? 144705
? 1667-84
. 188789
? 210686
. 232468-
? 254159
275757-
297217
? 1851
3397.46
360745 .
Table VI Continued
5. 0 1954869
. ,
.2066576
9 .2178283
2289989
? 3 2401696
.2513403
4 .2625110
4 2736817
1 .2848523
53 .2960230
55 .3071937
1225
13.69.
.521
1681
1849
2025
2209
2401
26.01-
2809
_3025
9438
938.2.83.
9534.83
9694.8
9862.83
10038
10222 83
10414
10614.83:
10822.83
11038 83
6 im3 8
6-8650
6465
.4623
99:.31:18
100.19.40
101.1080
102 0531
1 0283
1.04 0328
105 0658
131 1188
133 8650
13-6.6465
139.4623
142 3118
145 1940
148.1080
151.0531
154 0283
157.0.328
160.0658
1.464687
1.495364
1 526435
1.557-889
1 589721
? .621917
1.654469
1.687-367
1.720601
1.754164
1 788045
2P
P
18.78997
20.01-789
21
27017
22
54776
23
85167
25
18379
26
54196
27
93007
29.34784
30.79610
32.27555
v-4-11y-2-4-11-
P -? )
.381653
.402376'
.422915
.443339
.46353Z-
.483588
.503505
? 523169
.542672
.56Z014
581125
f_ 94-
131
17.0828
18.0103
18.9297
19.8439
20-7477
21.6454
.2.5369? -
23.4170
24.2900
25.1557
26.012
/
P V
-27P 2-!-1 r
35.8728
38.0282 -
40 1999
42.3917
44..5994
- 46.8282
49.0789
51.3471
53: 6378
55.9518
58.2868
44 7.6 ft.
89.52 ft:-
8013 83.ft-
CD'
In
0
0
CIQ ?
17c.1
CD
CD
CD
0
CD CD
0
CD
113
-c)
CD
0
0 .
?
IF
0-`
CD
0
0
i?-??
-CD
0
0
jDvaISgV
-
IlaiLdVHD
4(,
.,3
Otk
4;}
t,
7047, :..12,12.0.ditratikat al& ,1
MAO' ItEitLAS, ' adfatiatt1
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/23 : CIA-RDP81-01043R002500200002-6
4.110-
An Optical Method' (By Dr. Fred Allison)
This method is based on adjustments made possible by means of
the Gaussian eyepiece.
The frame holding the heliostat mirrors is brought as nearly as
possible into the East-West vertical plane and clamped. With the helio-
stat so positioned the mirrors, one by one, are to be aligned with their
planes parallel by means of the adjustment screws.
A theodolite of high precision and large aperture sec:isirelymount-
ed on a "cat walk' as close proximity as possible to the heliostat
mirror, is adjusted so that the azimuth circle and the axis of the tele- \
scope lie in horizontal planes
In order to expedite the work of a.lignment, it is suggested that the
mirrors in groups of four may be aligned without resetting the theo-
dolite in the following manner.
The theodolite telescope, its axis set in the N-S plane and the
,d
cross hairs.of the Gaussian eyepice properly illuminate directed
at tfie contiguous corners of fOur mirrors, as See
.1?1.014/0?111?0????????
Figs
*Note: The foregoing paper was written early in the summer, when it
was understood, according to temporary plans then .ava.ila.bld, that the
heliostat mirror could be set in the vertical plane0 Revised plans do not
permit vertical setting of the heliostat mirror. For positions of the
heliostat mirror other than vertical, the method above suggested, with
certain obvious modification's in the adjustment of the theodolite and the
should have practically the same applicability.
onstant-deviation prism
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
? n
6.;
a;
,o?-?
Declassified in Part - Sanitized Copy Approved for Release
15 and 16) One of these mirrors, say A, is adjusted by the screws until
it is autocollima.ted with the telescope 'i.e., until the light reflected
from A forms an image of the cross-hairs in coincidence with the direct
image of the cross-hairs as seen in the eyepiece.
In a precisely similar manner, one proceeds with the adjustment
? Of B to obtain ,coincidence of the cross hair image with the two already
in coincidence. In the same way the cross-hair image due to light re-
flected from C is brought into coincidence with the other three; and
finally, the image due to D. Five cross hair images would thus be in
coincidence when the planes of the fourrnirrors are parallel. If the mul-
tiplicity of cross-hair images in the field of view should cause confu-
sion one could first adjust mirror A, with the corners of B, C and D
covered then proceed to align each of these three in turn keeping the
corners of the others covered.
The operation described above would be repeated for other groups
of four mirrors An the same double row until all mirrors of the helio-
stat were included.
Some variations in the procedure may be suggested.
0
a. Set the telescope on the four contiguous corners of mirrors B,
, E, and G. (See Fig. 15j Instead of readjusting the theod.olite by the
levels adjust it until the cross-hair image due to B (and D) falls on the
cross-hairs of the eyepiece. Then adjust E and G as above described.
'Wyk, ?ALL, Ago ta '1,ar
'00MA at.lorar
fni
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'
The next setting would be in the corners of EF G and so on. This
process, would align only two mirrors at a setting and the errors would
be accumulative".
b. Instead of working with the groups of four mirrors groups of
two, as M N, etc., using the same method may be aligned across each
horizontal row.
Once the mirrors are adjusted for parallelism the test for accu-
rnu.la.ted errors in their overall alignment throughout the heliostat mosaic
is suggested as indicated below.
The telescope is autocollimated on a selected mirror and is then
accurately turned in azimuth through 90 looking into a constant-deviation
prism which is on an adjustable mounting in front of a second selected
mirror in the same horizontal row. (See Fig 17) If the planes of the
two selected mirrors have been correctly aligned, the light incident on
the second selected mirror will retrace its path through the constant-
deviation prism and the cross hair images due to the returned light
will be in coincidence with the cross hair image of the eyepiece. By
Proper adjustment of the telescope in altitudes the second Mirror ma
be selected in any horizontal row as well as in any vertical column o
mirrors.
Whether the methods above suggested would yield satisfactory re-
? ..,SUlts could be determined by preliminary experimentation.
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1i
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jii02.1.51:22tiLmLMe.....1.1.04 (By Dr. Gordon Hughes
The method to be proposed assumes that an observer and adevice
'may be held in a relatively fixed position within some 10 ft of the helio-
stat mirrors.
N)
Suppose a relatively rigid metal tube, say some 8 to 9 ft long, is
rovicleclwith side ports as indicated in Figure 18. Mirror
a half
silvered surface placed at 450 with the axis of the tube. Mirror "b", is
full silvered and placed as shown. An electric lamp with its filament
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instrument is designed with appreciable length, it iiiio0,1d be possible to
align alternate mirrors and then Check between the alternate pairs
A pentapriarn may be employed to replace mirror b" if the defora
.mation of the tube under Its own weight throws the device out of ,a4n-
,ment.
,Advantages: of this method of alignment:
There ' no loading' of the. glass surface using this technique.
b. The mirrors may be 'aligned when the heliostat is in any
posi-
in the shape of an x is placed at the focal point of lens and obser- tion.
4
ved through lens L2 with an eye lens c. The reference signal is from the heliostat itself with this de-
Two dishes of mercury, M1 and Mz, are observed. Since these
two surfaces are parallel two images of the light source indicate that
mirror ib" Should be adjusted until the single image of the lamp fila-
ment is seen. A color filter at point F in the system might be employ-
e to distinguish the light returned from the two floating Mirrors.
Now' if the device is placed before two of the heliostat"mirrors in-
stead of the two floating rnirrdrs they may be aligned with an accuracy
determined` by, the sharpness of the lamp filaments and their magnifida-
tion.
If the alignment procedure starts at one side of the heliostat an
progresses across the entire face an error may accumulate of suffi-
cient
-
'T thk/U ?
o? ? render the alignment as unsatisfactory.. Since the
idLi1
vice so that random motions of the heliostat from wind gusts will not
negate the method.
d. The device will work even though it may be turned through
small angles with reference to the normal to the mirrors.
e. Cumulative errors in the alignment may be detected and cor.
III. AMechanical.Method (By Dr.
?
This method is"basedon the possibilities 0f' achieving' horizontal.
adjustments s
of the cross warm type. it is asstithed that in, the revised design of the
heliostatmountingthe mosaic mirror maybe set in thehorizontal plane.
With the mirror so positioned and with a movable walk-way imrnediaely
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5
11
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above the mirror, the procedure of bringing in turn by the adjustment Heliostat Mirrors
screws, each of he component mirrors into the horizontal plane as de-
termined by the spirit level could be accomplished with comparative
ease and speed. The work could be facilitated by using a number o
workers each provided with a properly designed spirit level.
This method appears to have the following advantages:
a. Precision comparable and probably superior to that of optical
c. Highly trained personnel not required
d. Ease and speed of operation.
A disadvantage as compared with optical methods: The spirit level
would make contact with each mirror, a.ddings its weight thereto.
4"4'. 42Mt;1,
Y., avALIAi '
k.aedik ni5ag 711.4 4 44d.a. ble,4M1 P. .4 a 4
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Declassified in Part -Sanitized Copy Approved for Release @50-Yr 2013/10/23 : CIA-RDP81-01043R002500200002-6
CHAPTER, 4
BASIC OPTICAL CONSIDERATIONS
IN THE CHOICE OF A
DESIGN FOR A SOLAR FURNACE
ABSTRACT
Simple relationships exist between the aperture of a solar
furnace the target size the angle of convergence, the maximum
,..attainable concentration ratio, the overall efficiency, and the
amount of spill light 'surrounding the target. For optical system
having continuous unobstructed surfaces and'nosphebry the
angle aber-
ration, the concentration ratio is determined solely
of convergence. Various systems differ considerably., however,
in the amount by Which their apertures exceed that of an ideal
system of, equal performance; In the resulting *efficiency at which
YeL101412 ?
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ty,t
A
'1.
tt
?
,
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they operate; in the associated amount, of waste light spilled
outside the target; in the distribution of this spill light and in
the relative convenience with which they can be fabricated and
adjusted. A paralpoloidal mirror with heliostat does not seem
to be an optimum choice. The optical possibilities afforded by
other two mirror systems are discussed and illustrated by 9x-
ample. We also present a structural design for a two mirror
system which appears to possess some practical advantages
over the heliostat-paraboloid combination.
'17,14 dna,
? "12:1 t'a.,$,LithWAa'??dal?Z Tig ;41;1L114e,'
.11.5tat(tttit'a(tt(t '41/:?4(.( Y? ..;?.44:1t toh./,..ALLf: t?iti?
4
Introduction
The purpose of a solar furnace is to concentrate as much flux as
possible onto a specified target area. There are many different opti-
cal systems which might be used 'for this purpose, and they differ con-
siderably both in performance and practicability. The use of a parabo-
loid, which has been given first consideration for the Cloudcroft fur-
nace does not appear to be an ,optimum choice, The purpose of this
report is to call attention to the range of possible alternatives and to
show by example what might be achieved. It would be regrettable in-
deed if design and construction were to proceed without recognition o
these alternatives.
For a specified target size and a specified solid angle from which
flux converges toward the target, there is (as shown below) a fundamen-
tal upper limit on the amount of flux which can be concentrated onto the
target. No optical system, however ideal it may be can exceed this
upper. limit. If an optical System receives more than this amount o
flux, it canriof'd,eliver all of the received flux onto the specified target
.area?, and it accordingly has two faults: Is bigger than theoreti-
cally necessary. (b It spills the excess flux into a halo around the
target where it is not wanted., In theseterms, a
....Of the proportions now under consideration .O...r t.
104 foot aperture and 120
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araboloidaLmirrorn
loudci.oft furnace
s more than
cone o convergence
It
1;
k,t
'0'4P
?
T "
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1.7 times larger than ideally necessary, and it spreads the excess light
(44% of the total received) over an area 7 times as large as that of the
target. While we know of no practical furnace system exactly meeting
the conditions required for ideal performance, we do know of practical
systems which excel a paraboloid.
The criteria of an ideal system would be that it have no spherical
?
aberration and no coma in short, that it meet the Abbe sine condi-
tion. This situation is represented by Figure 19, where the sine condi-
tion requires, for any particular ray, that
sin 8.
If the angular radius of the sun is taken to be 16 minutes of arc and if
the target radius is r, we have
215r.
The aperture under these conditions is
I 2h0 430 r si?n 00
If the target diameter is 5 inches 2.5.),as contemplated for the
-
Cloud.croft furnace, and if the peripheral angle e0 is 6 the aper-
ture turns out to be about 78 feet. This is the maximum apeiture of an
ideal system for which all of the light can be delivered to a 5 inch tar-
et. If there were no reflection or absorption losses, the maximum
ossible concentration rati.o for = 60 would be
;
(P.
2
'
,
215 sin.2 (60 34600
0
Any optical system with continuous unobstructed surfaces and free of
spherical aberration Can produce the same concentration ratio for the
same value of 90 but the associated aperture will automatically be
greater than 2h0 if the sine condition is not also met. One can also
arrive at the foregoing conclusions from purely geometrical arguments
without invoking the sine condition 2.92: se.
The geometrical efficiency of an optical system having continuous
unobstructed surfaces and free of spherical aberration will be simply
2
=NM
NOS
where Y is the radius of the aperture. For a paraboloid with 0
and with a 5P-inch paraxial solar image we find 2Y is about 104 feet,
yielding:
( 78
104
6%.
This result can be laboriously verified by dividing the paraboloid o
any other system having the same Y, f, ) into annular zones, compu-
ting the image profile for each zone, finding what fraction of this'image
actually hits the target weighting these zonal efficiences in proportion
o the relative areas of the zones and'finally'summing the zonal co
tri.butions. This procedure.was actually carried out for two very di.
ferent systems and the results (with suitable allowance, for o structe
areas) have checked the conclusions above.
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kk?
'VJ?
f,
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The actual efficiency of a system will be considerably less than
the geometrical efficiency discussed above because of losses due to
glass absorption imperfect reflection obstructed areas and inter-
stices between the facets that comprise the optical elements, Opti-
mistically assuming two reflections of 0.9 efficiency and other losses
totaling 0.1 we find that an actual efficiency of 41% is unlikely to be
exceeded by any system with a 104-foot aperture, a 5-inch target, and
a 1200 cone of convergence 600).
Four important conclusions can be summarized:
a. If we are interested in a 5-inch target with 8 60? a 104-foot
aperture is not necessarily needed Only 56% of the flux received by a
104 foot aperture can be geometrically utilized. A somewhat smaller
aperture (theoretical minimum = 78 feet) can achieve equal performance
if a suitable and practical optical system can be found. We do not need
o belabor .his possibility its importance is appreciated when one re-
'calls that costs of large constructions vary roughly as the cube of the
aperture
aperture should be capable Of performing efficiently on a target larger
than 5 inches (thebretical maximum 6.6 inches),
b. We noted that all 104.-foot optical systems with continuous un-
obstructed surfaces' and with no spherical 'aberration will .put 56%
of
their unabsorbed or unobstructed flux onto a 5 inch target if 8 = 60?
turning the argument around, we can say that a 104 foot
iThmaraMagt, _
AtAtif MM.= 1:Yr
40`
2
? a,
They are all basically equal: in that respect They differ considerably,
however, in where the 44% spillage goes. A 104-footparaboloid spreads
this spillage over a 13-inch disc whereas an alternative system dis-
,cussedin Section III confines nearly all of the spillage to an 8-inch disc.
In the latter case, the spillage lies close enough to the 5-inch central
disc to be of frequent practical use.
It is possible to design optical systems which not 'only are su-
perior to the paraboloid with respect to a and b above, but which in
addition possess certain advantages with respect to simplicity of opti-
cal fabrication and convenience of adjustment. For example, the cases
discussed in Section III employ surfaces which are either spherical o
nearly spherical over most of their area.
d. A substantial gain in concentration ratio is potentially avail-
able by allowing 8 to exceed 600 Since the concentration. ratio varies
as sin 8, one can theoretically gain a factor of 1 18 by making 8IN
a factor of 1-29 by making or a factor of 1.33 by making
900 which is the absolute limit for a flat target). However, values o
0 beyond 70? are probably not optically practica the
maximum attainable concentration ratio (neglecting losses 40700,
and the associate aplanatic aperture 2h is 84 feet if a 5inch target is
used.
The remainder of this report is divided into four parts. Section,
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C?
?!:
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I \
II concerns the characteristics of a paraboloidal mirror, 'Section III
explores what might be achieved with a two mirror system consisting
of a largeprimarY and a small secondary, Section IVdiscusses a t;1,1,C
tural design suited to the type of optical system presented in Section III,
and Section V presents an alternate arrangement for using a paraboloid
with a heliostat. The structural designs prepared with the excellent
artistic collaboration of Mr. Roger Hayward appear to possess certain
raztical advantages over the proposed heliostat-paraboloid combination.
It should be emphasized that the present report. does not pretend
o be a complete survey of the optical or structural possibilities. Its
primary purpose has been to show that the various possibilities of de-
vising a solar furnace are not yet exhausted.
IL Characteristics of a Paraboloid
Figure 20 is the axial section through a paraboloid of rotation with
'various pertinent quantities labeled n rectangular coordinates the
equation. or this section is siimPl,
ere the origin is at the vertex
2 X
of the paraboloid, and where R is
s radius of curvature in thatzeighborhoo
tex to the focus is
old is
r
Kfirr
Lit?
The distance from the ver-
n polar coordinates the equation if the parabo
21:Qrvitiugg=a4
1 cos 8
11.4
where the pole is at the focus. The normal to the surface at P makes
an, angle 8/2 with the axis, and the radius of curvature at P is given
by
in the meridional plane, and by
cos
in the sagittal plane. A pencil of rays parallel to the axis and incident
z
(
1+ cos 8
at P is brought to an anastigmatic focus at F so that the effective
focal length in both the rneridionalpla.ne and the sagittal plane is simply
If a target surface is placed normal to the axis at F the sagittal
half width of the solar image produced by a single facet at P is the
product of e and the sun's angular radius:
0.004654 R
= 0.00465:4
+
COS
and the projected meridional half width, of the image
absec8.
For paraxial rays a =b 0.0O2327R.f the target is made tocoincde with.this,pa,raxial image, e optical efficiency any annular zone
??? -Po 43 4 rt
Colo v... J.
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0 0023,27
a
6
25 cos cos
t,f
t
4-4
:et
V,
V
'The fraction of the aperture area
width 64Y 3.
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contained within a narroW zone o
LA 2YAY Sin eLe
cos 6)4
where ?Yi is, the radius of the full aperture.. The overall efficiency of
the system is therefore
dA
which yields
0
,
sin 6 cos & d
0.2 (1 + cos 6 )
For a 104 foot paraboloid with a 5-inch pa,ra.xial image, we have
52 feet, R 89 5 feet,
600 and we obtain E 56%. This is in
agreement (as we should expect) with the result derived from the Abbe
sine condition in Section I.
The 44% spillage of a paraboloid having
is spread over a
isc 13.3.inches in diameter, or an area of 14Q square inches. The
distribution
spill light can be computed by finding what fractions
solar image
a long and, 2b wide) form d by facets
o various diame-
?.
hen. the
?at various values of fall inside concentr
c circles
ters between 5 inches and 13 inches at the focal plan.e.
elliptical Image falls entirely inside ?a circle of radius r, the efficiency
for the associated one and for this value of r is 100 Whn-the circle
ut. dzt-ta aa: ? 4 .1 +1.
,
lies entirely inside the elliptical image, the zonal efficiency isr2/ab.
When the circle intersects the ellipse, as sketched in Figure 3, the ef-
ficiency is Skrab where S is the area which the circle and the ellipse
have in common. If r and 1r, it can be shown that the
area in common is
s
?
2cx.(1 arcsin(1
c:46 2
1
'2 arcsin
This expression is rather complex for practical computation, and the
following approximation is more expedient:
a
L.
When b r e ?4 ria; and when a?or, E
Sample results are listed in Table VII and plotted in Figure 24.
These data were assembled primarily for comparison with similar re-
sults for another system discussed n Section III.
'TwoMirror
When only one mirror' participates in the
focusing, it must neces-
sarily be a paraboloid, unless the mirror surface is .a discontinuous
curve. In general, discontinuous curves result in, the utilization of less
solid angl.e for the same peripheral 0 and Y ,and they consequently
offer no gain over continuous curves
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67
4sT
.1?
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IISMOROOMMIMuotontswooProvfvoodoommom409.1,400400,!..woothommawandomA,,,,,ms,,,
When more than one mirror participates in the focusing an infinite
,number of combinations become possible and specific cases must be
selected for investigation. Several combinations involving a large pri-
mary mirror and a small secondary mirror were investigated in vary-
ing degrees of detail. A partjcularly interesting case diagrammed in
Figure 22 ,provides a suitable example for discussion in the present re-
,port. A blend of this case with another one will also be discussed to
show how the good features of two systems might be combined It must
be remembered that these cases are merely examples with arbitrarily
chosen parameters and that they do not represent optimum choices.
Much additional computing and comparing would be required to afford a
basis for the selection of an optimum case
In Figure 22 the primary mirror, which includes about 90% of the
total mirror area of the system s a sphere of radius R. Such a choice
would clearly be convenient both for construction and for adjustment.
Except for the inner zone hidden by the secondary, the facets of the
spherical primary can be adjusted very simply by autocollimation, us-
ing a small light source at the center of curvature
he secondary mirror, which amounts to about 10% of
'mirror
A.
.tne
UIi
area, serves to, correct the spherical aberration of theprirnary.
It is roughly paraboloidal in form and its facets can be adjusted with
adequate precision by means of a template.
XJ.161.1:1114 413 Aul.
?
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d for RI ?
. IA
.1
I
Strangely, the spherical aberration of the primary mirror serves
a useful purpose. It prevents the effective focal length of the combina-
tion from increasing with 0, and it thereby keeps the solar image small
for the outer zones of the system. It is especially effective in the
meridional pla,fte where it also compensates for the sec 8 factor due to
the oblique incidence of the zonal images on the target. As a conse-
qu.ence the outer zones of the system are the most efficient one's and
the spillage around the target is confined to a much smaller disc than
in the case of the paraboloid.
The exact shape of the secondary mirror can be derived byimpo-
sing the condition that optical pathlengths must be the same for all rays
that come to a focus at the center of the target. For any value of
the path is
1 cos
sec
+p sec
d +p tan
where the spherical aberration of the primary is
For paraxial rays, 0 an
-01 043 02500200007-R
d.
'11
0
x
ti
SI
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Setting we obtain
z
2(c?d) + 2 A sec (1) + 2p tan2 0131
?where A =c + d+ p (2 cos
?
sec.
Cr?
It follows that
? x p t n
and the final angle of convergence is
arctan
In terms. of R and c, the coordinates of the primary sphere with the
origin at the vertex are
X R ? cos = R. s ec
The solar image formed by a facet of the primary mirror at Q is
strongly astigmatic the meridional image falling at K and the sagittal
image at Hbut the secondary mirror puts these component images
back together again at F The magn.ification of the secondary mirror
s therefore different for the two axes .of the solar image, and as re-
marked earlier) it has the desirable feature of decreasingwith-increas-
mg
? "h.
a41LL V
^ 14 .1 TN
articular P and n the final,solar image formed
on a plane normal to the optic axis at F is an ellipse simil_rc o that
formed by a facet of a paraboloid, except that its meridional dimension
is now the smaller axis instead of the larger axis of the ellipse. To
vakt'diNallitalit,xXxiif 1'1; IA I,
1,
exis,&4144,
(4
.? ?. ?
..tompUte...th"e? 4Me,riS.On:s of the image ellipses associated with the var.
?
ious zones of the system one Must make use of the following expres-
sions for the pertinent segments of the light path:
(QH) 0' 5 R sec
(QK) .5 R sec 7- 0 5 Y ta.n
(Hp) y csc
(KP) y csc 0.5 Y tan
(GP) y? csc
n a plane normal to the optic axis at F, the meridional half-width o
the image (semi minor axis)
Ira 0.004654 (QK) sec
KP
and the sagittal half width of the image (semi major axis) is
GP
0.004654 ( H)
Some sample data for a optical ...system of this type are listed in Table
VIII. For this Case we adopted c 0. 21R and
10 R, and the
s-
tmhasbeenscaledtoa 100-foot aperture for?a?:. 1165whIch yields d. peripheral ...
of. approximately 600 andof
The spread of the spiii light ur rounding the target can be . reduc-
ed still further by blending the outer 'zones of the sphere-corrector
combination in .Figure 22 with the inner zones o .a system consisting o
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a paraboloidal primary and an ellipsoidal secondary. This blended sys-
tern is sketched in Figure 23. The transition was arbitrarily chosen to
500 and the slope was made continuous across the transi
tion so that neither the primary nor the secondary would have any op-
tical discontinuity. It can be shown that the paraboloidal portion of the
primary is
14,
= 2(R-X ) (X +L) ,
where X0 is the coordi.na e of the junction (0.09369 R) and where 64=
0.00484 R? The ellipsoid is given by
(x +0.08085 11)2
(0.17601 R).2
----- Y2
(0.17357 R)2
Its eccentricity is found to be 0 1657 For 4 < 50? all rays from the
primary pass through the
same axial intercept E, and the
magnifica-
tion of the secondary is found to be
m = 1.0564 + 0.3406 cos
The final images formed on a plane normal to the axis at F have sagit-
tal half,-widths of
iv 0.004654 (QE)
and meridional half-widths o
a b sec 9
where the angle of convergence 9 is given by
arcsin
woo
1 .
--- sin
qt11,0
ott.ttm
7i,t1?4ittatTZ;t1';111 ,titA,15k,1 _:wtiWtr: tit " rd, tstrttltr:
_
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The distribution of the spill light for this blended optical system of Fig-
ure 23 has been calculated as it was for th,e paraboloid; Both distribu-
tions are plotted in Figure 24 for comparison.
r
IV. Mounting for a Two-Mirror System
Figure 25 shows how the two-mirror optical system, described
above, may be embodied with an alt azimuth mounting. Such a mount-
ing has a precedent in large, construction it has been used for the
Manchester radio telescope of 250-foot aperture. The separate angular
motions of altitude and azimuth may be controlled and coordinated by
separate sun trackers with associated servomechanisms or by pro-
grammed drives.
This alt-azimuth mounting has several notable features:
a. Relative immunity to high winds.
b. Protection of optical parts from weather.
c. Facility for optical adjustment.
d. Target plane faces upward.
. Primary movable to a "horizontal" position for maintenance
and repair.
Figure 25 illustrates the general: appearance of the envisioned fur-
nace, while Figure 26 shows three sectional Yiews of the furnace. The
main structure turns in azimuth on a circular track, and this frame
73
'At
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supports the furnace. proper on trunnions that allow it to rotate in alti-
tude.
This construction provides the observing station that is detailed
in Figure 25 and shown. further in Figure 26. Observation directly into
the furnace hot spot is afforded from this station. Observers may work ?
on its cylindrical half-floor when the furnace is tipped, and on the level
half-floor when the furnace pointing vertically. Experience of as-
tronomers with the prime-focus cage of the 200-inch Palomar tele-
scope serves as precedent to show that such an observing system is
practical. Figure 26 shows how the observer enters the observing sta-
tion by an elevator to the trunnion level, and thence by steps.
At the hot spot, when a crucible is exposed it will be inclined up-
ward by at least 300 and it will be nearly vertical at high noon in early
summer. A prearranged set-up for an experiment or for routine ex-
posure may be raised to trunnion level by the elevator indicated. From
there
goes horizontally across the cat-walk to a door in the central
shaft and thence to the hot spot by a lift. This cat-walk may be turned,
during exposure,
a position affording minimum obstruction(a
shown
in Figure 26 upper right).
The artist has shown an ensemble of sloped radial vanes to serve
1 as an attenuator; (2) as the slow shutter; and (3) as a 'protecting
r w."',17.040mt ?
?
74 ?
vo,
o
roof. The vanes are mounted' so that they turn open over the beams that
support the observing station, thereby minimizing light obstruction.
A similar but smaller ensemble of vanes (not shown) could con-
veniently be located radially (to form an inward pointing cone) and reach
from the rim of the secondary mirror to the central shaft. Such
secondary set of vanes could serve as the fast shutter.
For adjusting the facets of the primary mirror, and aligning the
primary with the secondary, we envision the furnace pointed toward a
platform on a nearby tower. By bringing the center of curvature of the
spherical part of the primary within surveillance of an observer there,
the spherical facets can be adjusted by autocollimation as remarked in
Section III.
The facets of the aspheric secondary mirror may be adjusted with
a radial template arm (not shown) which is perpendicular to the optical
axis and rotatable around it.
If the central part of the primary mirror is Paraboloidal as dis-
cussed in the latter part of
Section, III, t may be lined.-up 'simply by
putting a point light source at the focus after preliminary adjustment of
the secondary mirror. The parabolic facets may be observed bymeans
of penta-prisms mounted, one for each zone of facets, on the template
arm mentioned above.
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
75
II
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
Optical line-up may be cairied out during cloudy weather or at
night.
Finally, it is to be noted that this furnace construction is compact,
and that it may be located in a depression of terrain to further protect
it from winds during operation and from damage during storms. This
mounting is certainly more immune to wind than one that has separated
components separately Mounted.
V. Alternative System Usin a Paraboloidal Mirror
Figures 27 and 28 show Mr. Ha.yward's conception of an arrange-
mentusing a "horizontal" rather than the previously proposed "vertical"
heliostat. This arrangement has the disadvantage of requiring a larger
a. The working focal plane faces upward.
By means of bi-parting shutters and a retractable shed, all
optical parts may be protected from wind and weather.
In this arrangement we propose using the bi-parting shutter as
attenuator, with a rotating half-hemisphere for the fast shutter. Access
to the hot spot chamber by a Passage in one of these bi-parting shut-
ters provides for the safety of personnel.
0.1
- I _
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6 --------
- . -
arriple two-mirror system having an all-spherical primary.
21 R, 1 R, aperture = 100 feet, R 93 feet.
50.0
57
8 82 6 24
3.47 5.01 6.82 8.86
10.330 21.060 28.266
47.22 ?47 48 76 49.89
45.79 45.26 44.35 43.34
l0.16 1.89 13.07
11.58 13.56 16.30 19.62
19 19.1 18.98 18.70
8 18 5.24
deg.
feet
11
CZ/01-/? I-0Z JA-OS
CIA-RDP81-01043R002500200002-6
Declassified in Part - Sanitized Copy Approved for Release a 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
411?111.
CIRCLE
RADIUS ra
FIGURE 21
37nsi{,;? kriw, X;
1:1V:
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
SPHERICAL
ZONE-
PARABOLOIDAL
ZONE Thk,
FIGURE ZZ
'4,441.41.4vOrr,:k.,
Declassified in
Part - Sanitized Copy Approved for
Release ? 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
.1
100
ci)
ERCENTAGE
110.7,'Aqr
SYSTEM OF
FIGURE 5 PARABOLOID
PARAXIAL
IMAGE,
? FIGURE 24
PERCENTAGES OF THE TOTAL FLUX
FALLING INSIDE CIRCLES OF VARIOUS
DIAMETERS AT THE FOCAL PLANE.
APERTURE = 100 FEET,.
PERIPHERAL. 9 = 60?.
brk7,6 T
-
,
DIAMETER OF CIRCLE IN INCHES
4
r
T.1
?
. ' ?
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/23: CIA-RDP81-01043R002500200002-6
?
ob 5 cry ing station
phericai
sccondary mirror
lift ts
to h0 t
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observing range
in altitude
step, to 01,3er Wing
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circular track
spherical
primary
cylindrical
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cat walk turned
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clevei tor for
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