Dickerson, E. T.

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11176-H098-R0-00
APOLLO SPACECRAFT SYSTEMS MIALYSIS PROGRAM
TECHNICAL REPORT
TASK E-34D
NAS9-8166	 31 DECEMBER 1968
PRELIMINARY Lk REFLECTIVITY MODEL
Prepared by
KATIONAL AERONAUTICS AND SPACE ADMINISTRATION
MANNED SPACECRAFT CENTER
HOUSTON, TEXAS
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APOLLO SPACECRAFT SYSTEMS ANALYSIS PROGRAM
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PRELIMINARY LR REFLECTIVITY MODEL
TASK E-34D
31 DECEMBER 1968
i
Prepared by:
Tr—. F. T. Dickerson
Approved by: ^.
C.	 Blakely,  ask nager
1
Approved 
by
ier, Manager
omnbnication and Sensor Systems
Department
'	 T^
In order to facilitate the Guidance and Control Division of NASA
in making computer simulated performance estimates of the landing radar,
it was necessary to specify an interim reflectivity model. This model
is based on theoretical reflectivi` curves as well as measured radar
data [1].
Measured data from White Sands Missile Range gives a good estimate
of how the landing radar will perform in the lunar environment. This
statement is-supported by the similarity of the electrical properties of
the 'lunar surface and the reflectivity sites at WSMR. The dielectric
constant of the lunar surface is reported to be 3.0 + 0.2 by G. L. Taylor
[2]. This value of the permittivity is very close to the-value of the
permittivity measured for the three reflectivity sites at WSMR [3].
Theoretical results were compared to measured data in a previous
report [4]. That report presented a reflectivity curve based on the
Beckmann-Smith reflectivity function. Data supporting this model presented
in reference [4] were obtained from earth based radar data.
The following curves presented in this report give an estimate of
the lunar reflectivity for various altitudes above the lunar surface based
on the above studies and measured data from WSMR. In each case a band nr
uncertainty is specified. This band of uncertainty can be considered as
a three sigma value of each of the reflectivity curves.
To date theory and data are inadequatE to specify a single reflectiv-
ity curve for all altitudes above the lunar surface without a large variance.
For this reason it was necessary to specify several reflectivity curves to
cover the wide range of altitudes. The altitude above the lunar surface
was broken down into three regions as follows: 40,000 ft. to 8000 ft.,
8000 ft. to 2000 ft., and 2000 ft. to the lunar surface. Reflectivity
curves for these regions are presented below.
Figure 1 is an estimate of the lunar reflectivity for LM altitudes
between 40,000 ft. and 8000 ft. based on theoretical and measured data.
Since preliminary data indicate that the variance is smaller at high altitudes
0
the band of uncertainty was chosen to be ± 2 db about the mean. Note that
the uncertainty is ±6 d1:6 for incidence angles less than 5 degrees. This
uncertainty is due to the absence of data to adequately determine the contri-
bution from the specular component near normal incidence.
Figure 2 is an estimai-. of the lunar reflectivity for LM altitudes
between 8000 ft. and 2000 ft. It should be noted that a wider band of
uncertainty is specified in this region. When supporting data from WSMR
become available this band will be reviewed and updated as required.
Figure 3 and 4 are estimates of the lunar reflectivity for-LM
altitudes below 2000 ft., and different local terrain roughness. -Figure
3 gives-an estimate of the lunar reflectivity when the local large scale
roughness is in the range-of 25 to 40 ft. Figure 4 gives an estimate of
the reflectivity when the large scale.roughness_is in the range of 2-4
feet. - For a.smooth terrain below 2000 ft. it is recommended that the
mean curve of Figure 2 be used. A band of uncertainty of +3 db was
chosen for all reflectivity carves below 2000 ft.
I
20
10
0
m -10b
H
J -20
U-WW
-30
-40
-50
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1
L
r^
J ^^ 2 d
0	 10	 20	 30	 40	 50	 60	 70	 80	 90
ANGLE OF INCIDENCE 9 (DEG)
Fiuure 1. Reflectivity Cu-vr for Altitudes Between 8,000 Feet
and
	 Feet
S
b
}
_H
F-VWJ
LL
W
ce
-10
-20
20
10
0
-30
-40
I
-50
0
Earth Based Reflectivity Data
`ftmift
1—
"Wft
s ti \
10	 20	 30	 40	 50	 60	 70	 80	 90
ANGLE OF INCIDENCE 0 (DEG)
Figure 2. Reflectivity Curve for Altitudes Between 2000 Feet and
8000 Feet.
I
20
10
0
CUTOFF AT 5 DEG
m
} -10
vWJ
w -20Ce
-30
-40
I
-50 L
0
	
10	 20	 30	 40	 50	 60	 70	 80	 90
ANGLE OF INCIDENCE 0 (DEG)
Figure 3. Reflectivity Curve for Altitudes Below 2000 Feet With
25-40 Feet Surface Roughness.
5
mS
b -10
}
F-
F-
U
U . - 20-
W
ESTIMATE
20
10
CUTOFF AT 5 DEG
0
-30
-50 L
0 10	 20	 30	 40	 50	 60	 70	 80	 90
ANGLE OF INCIDENCE 8 (DEG)
-40
r
Figure 4. Refiectivity Curve for ;altitudes Below 2000 hoot With
-4 Feet Surface !toughness.
5
REFERENCES
1. Dickerson, E. T., "Comparison of Surveyor Data With Beckmann-Smith
Reflectivity Model", TRW Report Number 05952-HSO5-RO-00, 15 May 1968.
2. Tyler, G. L., "Brewster Angle of the Lunar Crust", Nature, Volume
219, Number 5160, pp. 1243-1244, September 21, 1968.
3. Gonzales, H. F., "Terrain Dielectric Constants", U. S. Army Technical
Report, 15 November 1968.
4. Dickerson, E. T., "Interim LR Reflectivity Model", TRW Report Number
11176-HO18-TO-00, 9 August 1968.
7


Apollo spacecraft systems analysis program. Preliminary LR reflectivity model

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