Value chain · CLM-1093
In plain terms
Working the 1978 antenna design forward gives 25 mW/cm2 straight down from the satellite. The report prints 23. That drop can be explained by the extra distance to a site in the southern United States, or by the report's own allowance for phase errors and failed tubes, but not by both, and each explanation alone is worth the same 7 per cent. The report's own labelling suggests the errors were included, in which case the figure at the actual site is about 21.5.
The claim as recorded
SRC-085's printed 23 mW/cm2 peak is reproduced within 1 per cent by its own ten-step taper in two ways that cannot be told apart: the ideal beam at the slant range to the 34 to 35 deg N site (37,060 to 37,130 km, giving 23.1 to 23.2), or the beam loaded with the document's own error budget (10 deg rms phase and 2 per cent dead tubes, a factor 0.932) at the 35,800 km altitude it states (23.2). The two factors, (d/h)^2 = 1.072 to 1.076 and 1/0.932 = 1.073, are degenerate. The document's caption for the rectenna pattern reads "USING BASELINE ERROR PARAMETER", which points to the second reading; on it, the same beam at the actual site peaks at 21.5 to 21.6 mW/cm2, 6 per cent below the printed figure. The ideal beam at the altitude gives 24.87 mW/cm2. The radiated power from the digitised taper is 6.78 GW against the printed 6.72.
Evidence behind this: T0-calculation: a far-field on-axis sum over the document's own ten-step taper, with the step radii digitised from its plot, compared with the printed peak under four range-and-error combinations.
Scope and limits
SRC-085 does not say which reading it used and this calculation cannot decide it; p.40's caption is evidence, not proof. CALC-088's finding that the ideal peak "requires a range near 37,000 km" is correct for the ideal beam and is here shown to be one of two degenerate explanations, so the register should not carry the 37,000 km as the document's implied range without the alternative. The 2 deg mean edge phase error and the +/- 1 dB amplitude tolerance are under 0.1 per cent on the peak and were not applied; the +/- 3 arc-minute alignment, grating lobes, ionospheric and atmospheric terms were not modelled, as in CALC-088. Nothing here bears on the 88 versus 95 per cent collection question.
What it assumes
The rectenna on the satellite's meridian (a 15 deg offset is worth 1.1 per cent on the density); the error budget applied as uncorrelated rms phase error and a random 2 per cent of dark elements, the standard peak factors; step radii read from the plot to +/- 3 m (worth +/- 1.6 per cent on the peak density and +/- 0.8 per cent on the range that reproduces 23, and the printed 6.72 GW lies inside the band).
Where it comes from
This is the project's own working, shown in full:
CALC-115, sections 4 and 5. Inputs from SRC-085 PDF p.39 (render): "POWER RADIATED FROM TRANSMIT ARRAY 6.72 GW", "TOTAL RMS PHASE ERROR FOR EACH SUBARRAY = 10" deg (raw), "FAILURE RATE OF DC-RF POWER CONVERTER TUBES = 2%" (render; the layer prints "CONVERlER"); p.40 (raw): "ANTENNA PATTERN AT RECTENNA USING BASELINE ERROR PARAMETER: SEE FIGURE 18"; p.43 Figure 16's table of ten step densities 22.14, 18.45, 14.76, 12.30, 9.84, 7.38, 5.54, 4.92, 3.69, 2.46 kW/m2 (render) and its plot, from which the step edges 105, 179, 231, 274, 323, 362, 389, 419, 460 and 500 m were digitised; p.101 (normalised): "Geosynchronous altitude (35800 km) has been used in all studies". Ideal on-axis density 24.87 mW/cm2 at 35,800 km agrees with CALC-088's Route A (24.87) and Route B (248.2 W/m2) from codes sharing no lines. Inverting the printed 23 gives 37,228 km ideal (the slant range to 36.3 deg N) or 35,932 km error-loaded (the altitude to 0.4 per cent).
Basis: physical optics on a 1 km circular aperture at 2.45 GHz; mW/cm2; km
Related records
- Answers question
- QST-001 not published in this release
Cite this
energyaperture.com/c/clm-1093
CLM-1093, Energy Aperture, as of 1978.
Connected records
Other published records linked to this one. A list, not a judgement.
- Also from SRC-085
- CLM-0013The paper that modern UK studies rely on for the beam figure calls anything below 1 kilowatt per square metre safe, with 230 watts per...CLM-0020The original 1978 design set the beam at 230 watts per square metre in the middle of the receiving site, about one twenty-third of that at...CLM-0023In the 1978 reference design, two limits set the size of the transmitter and the receiving site: how much heat the transmitter can shed...CLM-0039The 1978 report set the figure to protect radio and navigation systems from a disturbed ionosphere, called the number theoretical and...CLM-0045The apparent conflict between 12 and 23 was not an error. The underlying study gave a range, and the figure adopted sits near the top of it.CLM-0101The 1978 contract required the researchers to report fixes if ionospheric disturbance pushed the pilot-beam phase error past 2 to 3...CLM-0137In four major space solar power studies from 1978 to 2007, none put a number on how much of the beam's energy would be lost if the beam...CLM-0138The original 1978 government design for beaming power down from space adds up all the expected energy losses to get 63% overall efficiency...More on the source page.