Value chain · CLM-1092
In plain terms
The famous 23 milliwatts per square centimetre is measured face-on to the beam, which is how the receiving panels are tilted, and is the same number the beam carries through the upper atmosphere. Spread over flat ground at the reference site in the southern United States, where, if the satellite is due south of the site, the beam comes in at about 50 degrees above the horizon, the same beam delivers about a quarter less per square metre of ground, 17 to 18 rather than 23.
The claim as recorded
The 1978 reference system's 23 mW/cm2 (230 W/m2) peak is a beam-normal density: the density in the plane perpendicular to the beam, incident on rectenna panels tilted to face the satellite, and equal to the on-axis in-beam value the ionosphere sees. The document states it as "a peak power density limitation in the ionosphere", puts its 5 km radius "perpendicular to boresight", and says the rectenna is "still only intercepting the circular power beam" while "the ground footprint is changed from a circle to an ellipse". Its printed ground ellipse, 13 km north-south by 10 km east-west at 34 deg N, is the 10 km beam-normal circle divided by cos z at that latitude (12.96 km); its 102.1 km2 of site area is pi x 6.5 x 5; its 78.54 km2 rectenna at the equator and 78.2 km2 "active intercept area" are pi x 5^2; its panels "tilted 40 degrees from the horizontal" face a satellite at zenith angle 39.5 deg. The horizontal ground-plane equivalent of the peak at the 34 to 35 deg N reference site is 17.4 to 17.7 mW/cm2 (174 to 177 W/m2), a factor of 1.30 to 1.32 below the beam-normal figure.
Evidence behind this: T0-calculation on the document's own printed geometry, each step a one-line check against a number the document prints.
Scope and limits
The finding is about the 1978 reference document's own frame. It says nothing about whether 23 mW/cm2 is a safe or achievable peak, and nothing about the collection term (CLM-0870). A reader converting the 23 to a per-hectare or per-km2 ground figure must multiply by cos z for the site; a reader comparing it with an ionospheric threshold need not (CLM-0865's comparability holds and its unresolved 32 per cent closes in the beam-normal direction). The document's "as much as 35 km2, or a factor of 50 percent" for higher latitudes is loose (35 km2 is 44.6 per cent of 78.54 and corresponds to 40 deg N; 50 per cent to 41.7 deg N).
What it assumes
A satellite on the rectenna's meridian, which SRC-085 does not state; a 15 deg offset moves cos z by 0.036 and the ground-plane figure by about 1 mW/cm2 (CALC-115 section 5).
Where it comes from
This is the project's own working, shown in full:
PDF p.37, render: "a peak power density limitation in the ionosphere of 23 mW/cm2" (the layer prints "23.1mW/cm2" with a stray dot) and, normalised, "88% of its energy within a 5 km radius perpendicular to boresight". PDF p.138, render: "The basic area of the rectenna is 78.54 km2 at the equator" and "(Even though the rectenna is still only intercepting the circular power beam, since the beam arrives at the Earth at greater angles at the higher latitudes, the ground footprint is changed from a circle to an ellipse.)". PDF p.204 and p.230, normalised: "covers an elliptical area 13 km in the north-south direction by 10 km in the east-west direction"; p.230: "750 rows of rectenna panels tilted 40 degrees from the horizontal, providing an active intercept area of 78.2 km2". PDF p.49, normalised: "the rectenna is a series of serrated panels perpendicular to the incident beam"; p.146, raw: "rows of panels oriented normal to the incoming beam". PDF p.235 Table R-4, render: "AREA AVAIL. (TOTAL) 102.1 km2". Arithmetic at CALC-115: cos z = 0.771 at 34 N and 0.759 at 35 N for a satellite on the meridian; 10 / 0.771 = 12.96 km; pi x 6.5 x 5 = 102.1 km2; pi x 25 = 78.54 km2; 23 x 0.771 = 17.7 and 23 x 0.759 = 17.4 mW/cm2. The converse fails: were 23 the horizontal figure, the in-beam peak would be 30.3 mW/cm2 at 35 N, above the limit the document says it designs to.
Basis: mW/cm2 and W/m2; km; degrees
Related records
- Answers question
- QST-001 not published in this release
Cite this
energyaperture.com/c/clm-1092
CLM-1092, 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.