CALC-118

Rectenna land per gigawatt, with and without the exclusion zone, from the 1978-81 reference-system figures

REGISTERED 2026-10-03 (ON-332). Drafted by 3d-02 (9f98023), checked by 3d-01 (d1d4812, re-check pass), Table 35 notes re-read at the page by 3d-01 and 3d-02; landed by SBSP-coord.

What it computes. Land per GW of delivered power for the 1978-81 reference system: rectenna only, then rectenna plus the buffer or exclusion zone, then the stricter-boundary case OTA gives. Each figure is a stated site area divided by the stated 5 GW per site (delivered to the utility interface, as CALC-117 row 1). Nothing is scaled to another design: no held record gives a rectenna area for any modern design (CALC-117 section 2).

Inputs (all LIVE and CONFIRMED). - CLM-1092 (DOE/ER-0023, 1978): rectenna 78.54 km2 at the equator (pi x 5^2); site area 102.1 km2 at 34 deg N (pi x 6.5 x 5). - CLM-1052 (DOE/ER-0054, 1980): - site including a 2 km buffer, 2 x 10^8 m2; - rectenna proper about 50 per cent of that; - 1480 m2 per MW-yr at 0.9 and 30 years; - ER-0055 Table C.7, 79 km2 at the equator and an expected average of 200 km2. - CLM-1283 (OTA, 1981): - 174 km2 per site with the exclusion boundary at 0.1 mW/cm2; - rectenna edge at 1.0 mW/cm2 and 2 km of buffer on each side; - almost 1,700 km2 per site if the edge could not exceed 0.01 mW/cm2.

1. Results.

OTA's own per-GW figure. OTA's Table 35 prints 35.0 km2 per 1,000 MW and 1,280 m2/MW-yr for this site (SRC-601 PDF p.200, printed 198, as read by 3d-01; CLM-1283 carries only the 174.0, so citing these needs a record update or a direct page citation at landing). L5's 34.8 is our division; OTA's printed 35.0 is the figure to quote. The 1,280 against DOE's 1480 (CLM-1052) is the 174 against 200 km2 difference, and 174 km2 at 1,280 m2/MW-yr fits a 0.9 capacity factor (our arithmetic: 174e6 / (5,000 x 30 x 1,280) = 0.906; OTA's note a states 30 years and 0.9, and 174e6 / (5,000 x 30 x 0.9) = 1,289, so the printed 1,280 is rounded).

Arithmetic, to reproduce. - Columns 4 and 5: area / 5 and area / (5 x 0.9). - Column 6: 5e9 W / (area in m2). L6: 5e9 / 2e8 = 25.0. This is delivered power per unit of land at 5 GW, not beam density; at 0.9 the L6 equivalent is CLM-1052's 22.5 W/m2. - L6 per MW-yr: 2e8 / (5,000 x 0.9 x 30) = 1481, CLM-1052's 1480. - L7 over L5: 1,700 / 174 = 9.8 (CLM-1283's limits already give it).

2. The 174 is OTA's 13 by 17 km ellipse, and the 200 is an approximate or average figure. - A 13 by 17 km ellipse is pi x 6.5 x 8.5 = 173.6 km2, which matches OTA's 174 (our arithmetic on printed axes): Table 35 note b gives a 9 by 13 km rectenna with 2 km added on each side. Its printed "117 km2" is the 9 x 13 bounding rectangle; the ellipse is 91.9 km2. - CLM-1052 names the 13 by 17 km buffered ellipse as "about 2 x 10^8 m2". ER-0055 Table C.7 says the total is "expected to average 200 km2". Both DOE figures are approximate. - So the 200 km2 is probably a rounding, or a latitude average, of the same geometry: about 15 per cent above the ellipse it names. - CLM-1052's limits note the 13 by 17 km figure is the 9 by 13 km ellipse plus 2 km each side. The 10 by 13 km rectenna plus 2 km would give 14 by 17 km, which is 186.9 km2. That is still below 200. - The 34 deg N rectenna ellipse (L3, 10 by 13 km) is 102.1 km2 on the same formula. - For a per-GW figure with buffer, 35 (OTA's printed 35.0) to 40 km2 per GW is the range the held figures support. It is a 2 km buffer at one latitude band, not a general rule.

3. What moves it. - The exclusion criterion, by an order of magnitude. - Moving the boundary from 0.1 to 0.01 mW/cm2 multiplies the land about 9.8 times (L5 to L7). - OTA's Table 42 gives a Soviet public value ten times lower again, 0.001 mW/cm2. OTA states no land figure at that level (CLM-1283 limits), so none is computed here. - Latitude. - The ground footprint is the beam-normal circle stretched by 1 / cos z (CLM-1092), where z is the satellite's zenith angle, 39.5 deg at 34 deg N for a geostationary satellite on the meridian, not the latitude (which would give 1.21): about 1.30 times at 34 deg N (L1 to L3: 78.54 to 102.1 km2). - A site further north grows further. CLM-1092's limits give "as much as 35 km2" more at higher latitudes, and call that loose. - The beam-edge density. - L5 assumes the 1.0 mW/cm2 rectenna edge and the reference beam. - A design with a different peak or taper, such as SRC-169's simulated 460 W/m2 (CLM-0403), would have a different rectenna and buffer. No held record sizes one, so this calc does not extend to modern designs.

Limits. 1. Receiving-site land only: transmission lines, mining, launch sites (20 to 850 km2, unallocated in CLM-1052) and manufacturing are outside. This is the boundary CLM-1052 and CLM-1283 state. 2. All figures are 1978-81 reference-system design values, not measurements. 3. The per-GW figures use 5 GW delivered per site, and the 0.9 column uses CLM-1052's capacity factor. NASA OTPS RD2's 0.6 (CLM-1349) shows the factor is design-specific. 4. L7's 1,700 km2 is OTA's citation of a 1978 siting report (SRC-512) that was not checked (CLM-1283 limits). 5. The ellipse areas in section 2 are our arithmetic on the stated axes. 6. A buffer is land that is fenced or restricted. Whether it can be farmed is not stated in these records and is not assumed. 7. Comparators on the same km2/GWav basis are in outputs/review/landuse-comparators-2026-10-08.md (ON-343), recorded as CLM-1398 to CLM-1400. Rectenna-only (L1, L3) is about 17-23 km2/GWav; the UK 2021 design (CALC-001, rectenna only) is 34.2, a design value that assumes continuous delivery (CF 1.0, a design assumption, CLM-0177; no SBSP plant has operated); with the 0.1 mW/cm2 boundary or 2 km buffer (L5 at OTA's 35.0 / 0.9, L6) about 39-44; ground PV direct 110-175 (Ong direct; CLM-1398) and total 128 (Ong, CLM-0317); wind 11 (footprint) to about 1,050 (spacing); nuclear 0.6-1.0; gas including fuel land 36-167. Only like-for-like footprint types may be compared.

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