Value chain · CLM-1191
In plain terms
The study sized its transmitting and receiving antennas with a standard beam formula, assumed about half the transmitted power would be caught on the way down, and found that above 35 GHz the antennas are small enough that they stop mattering much to the total mass, and that going beyond 100 GHz gains little.
The claim as recorded
The study sized antenna and rectenna with the near-field relation Pr/Pt = 1 - exp(-At Ar / (lambda R)^2), taking a 15% space transmission loss (Pr/Pt = 0.85) with the satellite overhead, and applied a 54% transmitter-to-rectenna link efficiency to all cases, from a numerical integration for an ideal tracking antenna at variable distance. Comparing 2.45, 35, 100 and 300 GHz, it found that altitude and frequency strongly drive antenna and rectenna area, that the transmission system is not a significant share of system mass above 35 GHz, and that little is gained above 100 GHz. Its Figure 5 gives the antenna and rectenna only as the square root of their product, which at 100 GHz and 2,459 km reads just above 10,000 m2.
Evidence behind this: T3, a NASA Lewis Research Center conference paper (25th IECEC, Reno, August 1990) that calls itself a "zero-th order" feasibility analysis (PDF 3 [1]) and "an initial scoping document": spreadsheet projections, not built hardware.
Scope and limits
THE 54% IS ASSUMED, AND THE RECTENNA ALONE IS NOT STATED. The link efficiency comes from an idealised integration, and the transmitter efficiencies "were assumed constant for all frequencies" (PDF 4). Figure 5 is a figure reading. Its axis is the square root of antenna area times rectenna area; the unit, m2, is read from the rotated axis label at render. OWN ARITHMETIC, NOT THE PAPER'S: with lambda = 3.0 mm at 100 GHz and R = 2,459 km, Equation 1 at 0.85 gives At Ar = 1.03 x 10^8 m4, whose square root, 10,160 m2, agrees with Figure 5; with Figure 3's 58 x 58 m antenna (3,364 m2, PDF 5) that implies a rectenna of about 30,700 m2, a square about 175 m on a side.
What it assumes
No assumptions are recorded against this claim.
Where it comes from
PDF 6 [4]: "Transmission frequencies of 2.45, 35, 100, and 300 GHz were investigated in this study."; "A near field approximation equation was used to size the antenna and rectenna"; Equation 1 at render: "Pr/Pt=1-exp{-AtAr/(LR)2}" with L the wavelength and R the separation distance; "a 15% space transmission loss was assumed in the calculations (i.e. Pr/Pt is set equal to 0.85)"; "A simple numerical integration for an ideal tracking antenna at variable distance yielded a 54% link efficiency, which was used for all cases." PDF 7 [5]: "Altitude and frequency have a large effect on antenna/rectenna areas and tend to drive the satellites to a lower orbit to minimize the antenna/rectenna size and mass."; "the transmission system does not contribute significantly to the system mass at greater than 35 GHz and little is gained at frequencies above 100 GHz for the cases investigated." Figure 5 "Antenna/Rectenna Area vs Altitude", render at zoom 4: the 100 GHz point at about 2,450 km sits just above the 10,000 gridline.
Basis: frequency in GHz; fraction of transmitted power received; link efficiency in per cent; square root of antenna area times rectenna area in m2 against altitude in km
Cite this
energyaperture.com/c/clm-1191
CLM-1191, Energy Aperture, as of 1990-08.
Connected records
Other published records linked to this one. A list, not a judgement.
- Also from SRC-393
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