Value chain · CLM-1193
In plain terms
A 1979 study for NASA drew the pilot transmitter's beam about three-quarters of a degree wide, a few hundred kilometres across by the time it reaches the satellites, and argued that with 100 satellites spread along a sixth of the orbit only one would sit in each pilot beam; the others would see a site's pilot only through its much weaker side lobes.
The claim as recorded
Raytheon's 1979 pilot-beam study for NASA draws the ground pilot transmitter's pattern (Figure 4-11, "RFI in Orbit due to Multiple Pilot Transmitters") with a 45.4 dBi main lobe of half-power width about 0.73 deg, annotated as 3.8 x 10^5 m at 3.8 x 10^7 m, and sidelobes of 20, 11 and 2 dBi falling at 9 dB per octave; from a spread of 100 SPS over a 60 deg equatorial arc it concludes that there is approximately one SPS in each pilot main beam, so another site's pilot reaches a given SPS only through its sidelobes, and that with pilot sidelobes below 20 dB the interfering pilots together cannot deliver as much power at an SPS as its own pilot.
Evidence behind this: T3, a Raytheon contractor report to NASA Marshall (ER79-4032, NASA-CR-161161, January 1979); the beamwidth and the one-per-beam result are annotations on a sketched pattern, not a measurement.
Scope and limits
THE FIGURE'S TWO BEAM FIGURES DO NOT AGREE, AND THE PAGE DOES NOT SAY WHICH IS MEANT. Own arithmetic, not the page's: 0.73 deg (0.0127 rad) at 3.8 x 10^7 m spans about 4.8 x 10^5 m, while the 3.8 x 10^5 m printed beside it is about 0.57 deg at that range. The page does not say what the 3.8 x 10^7 m is. It is longer than the GEO altitude (3.58 x 10^7 m) and close to a ground-to-GEO slant range, but the page also uses it as the radius of the 60 deg arc, where the GEO orbit radius would be 4.22 x 10^7 m (own reading). The one-per-beam result rests on the assumed 100 SPS over 60 deg of arc (about 4 x 10^5 m apart, own arithmetic); closer spacing puts more than one in a beam. SRC-085 PDF 57 [45] takes that other case, "multiple SPS satellites will be illuminated by a single pilot beam", and codes the pilot so each satellite recognises its own; SRC-085 gives no spacing on that page, so the two reports state different cases rather than disagree on a measurement. The pattern is a sketch: no aperture is stated on these pages.
What it assumes
No assumptions are recorded against this claim.
Where it comes from
PDF 77 [4-17], Figure 4-11 at render: "45.4 dBi"; the half-power width is printed as theta-3 "~ 0.73" with a degree sign (the symbol is "approximately equal"); "3.8 X 10^5 M AT 3.8 X 10^7 M" (superscripts); "SIDELOBES DELAY AS 1/X^3/2" (sic, for decay), "9 dB/OCTAVE"; lobes labelled "20 dBi", "11 dBi", "2 dBi"; "SPS SPREAD OVER 60" (degree sign) "IMPLIES" Delta ~ 2 pi (3.8 X 10^7) / 6 ~ 3.8 X 10^7, "APPROXIMATELY ONE IN MAIN BEAM". PDF 76 [4-16] at render: "Only one pilot beam is actually aimed at that SPS but the sidelobes of the other pilot beams are an interference source."; "Figure 4-11 shows that 100 SPS systems can be spread over a 60" (degree sign) "equatorial arc with only one SPS in a given pilot beam. If the pilot beam peak sidelobes are less than 20 dB, all the interference pilot beams cannot create as much power at a particular SPS as its dedicated pilot beam."
Basis: half-power beamwidth in degrees; beam width in m at a range in m; gain in dBi; number of SPS in one pilot main beam
Cite this
energyaperture.com/c/clm-1193
CLM-1193, Energy Aperture, as of 1979-01.