CALC-114

Solar array area per gigawatt of DC output, reproduced from two held sizings and swept over held ranges

The governing parametric relationship for solar collection at L2: blanket area per gigawatt of DC at the array as a function of solar constant, concentration, cell efficiency, temperature, design, degradation and pointing, reproduced from two held sizings to a stated tolerance and then swept over the ranges the register holds. Producer-computed 2026-09-17; the producer is barred from verifying its own work, and every headline figure was reproduced independently before this landed (recorded at the end). All 14 LIVE records on the layer were read whole first: none carries the relationship; CLM-0201 carries the efficiency range and CLM-0692 the CAST sun-to-grid check, both used below.

Provenance. The project's working file array_area_per_gw.py, 8,824 bytes, sha256 6943987A2E07401C, 122 lines, no dependencies. Inputs: SRC-085 Figure 5 (PDF p.25, printed 13) and p.23; SRC-449 p.268 (printed 246); SRC-171 p.8; CLM-0200, CLM-0201, CLM-0692. Nothing ASSUMED except the choice to hold f_temp and f_design at SRC-085's silicon values through the sweep.

A_blanket = P_dc / ( S x CR_eff x eta_cell x f_temp x f_design x f_rad x f_season x f_solstice )

1. SRC-085 Figure 5, the 1978 reference chain, reproduces exactly. GaAlAs CR2: 71.77 GW solar x 0.9675 summer solstice x 0.91 seasonal x 0.915 reflector-reflectivity equivalent x 0.20 cell at AM0 28 C x 0.908 cell temperature at 125 C x 0.901 array design x 0.96 ultraviolet and radiation = 9.08 GW at the array (figure 9.08); times the downstream chain 0.9368 x 0.9995 x 0.963 x 0.85 x 0.9653 x 0.98 x 0.89 x 0.88 x 0.97 = 0.5508 gives 5.00 GW at the utility busbar; overall 6.97 per cent (figure 6.97). Si CR1: 70.81 GW x 0.9675 x 0.91 x 0.173 x 0.954 (36 C) x 0.951 x 0.9273 = 9.07 GW (figure 9.08, -0.1 per cent); 7.06 per cent (figure 7.06). The solar constant is not stated on the figure; 70.81 GW over the 52.34 km2 Si blanket implies 1353 W/m2, the pre-1980 AM0 value. Blanket areas from p.23: Si 52.34 km2; GaAlAs 26.52 km2 of blanket with 53.04 km2 of reflector.

2. SRC-449 p.268, Rockwell's 1980 GaAs CR2 sizing, reproduces within 1.2 per cent, and the reproduction settles the units of one input. Stated: 1311.5 W/m2 at summer solstice, effective concentration 1.83 at end of life, 20 per cent cell at AM0 and 28 C, operating 113 C, temperature coefficient "0.0282%/C", 4 per cent non-annealable loss, seasonal 0.968, packaging and voltage mismatch 0.89, switchgear 0.997; published result 352.6 W/m2 and 27 x 10^6 m2 for 9.52 GW (the text layer renders the area "2t'il06 m2"; 9.52 GW / 352.6 W/m2 = 27.0e6 m2 confirms it). Reading the coefficient as percentage points per degree gives 348.4 W/m2 (-1.2 per cent); reading it as relative gives 386.3 (+9.6 per cent). The document does not say which; the reproduction does. That is the where-and-why item.

3. The band, km2 of blanket per GW of DC at the array, end of life, CR = 1: 2.3 to 6.3. Anchors from the two sizings: SRC-085 Si 5.77; SRC-085 GaAlAs 2.92 of blanket (5.84 of reflector); Rockwell GaAs 2.84. CLM-0692's CAST figure - 6 km2 for 1 GW delivered at 12.2 per cent sun-to-grid - is about 3.3 km2 per GW at the array once SRC-085's downstream chain (0.551) is applied, inside the band. Per GW at the busbar the figures are about 1.8x larger - 10.5 Si, 5.3 GaAlAs, 5.4 Rockwell on its own 5 GW - and a reader must know which end of the chain a figure is quoted at.

Sweep inputs, each cited: S 1353 (implied, SRC-085) and 1361 (CLM-0692); SRC-449's 1311.5 is a summer-solstice intensity (1311.5 / 1353 = 0.969) and is not swept as S, because the 0.880 below already holds SRC-085's 0.9675 solstice factor; eta 0.173 and 0.20 (both sources), 0.25 (CLM-0200, modelled), 0.31 to 0.37 (CLM-0201's six 2025 designs); f_rad 0.9273 and 0.96 (SRC-085), 0.96 (Rockwell), and SRC-171 p.8's remaining power after electric orbit raising of 85 to 98 per cent by coverglass thickness and trajectory, the register's only measured-environment degradation figure; pointing and seasonal 0.880 (SRC-085's 0.91 x 0.9675) and 0.968 (Rockwell). f_temp and f_design held at SRC-085's Si values.

4. What moves it. Every factor sits in the denominator, so each has elasticity -1. Over the register's own ranges: cell efficiency 0.173 to 0.37 shrinks the array by 0.47 - the only factor-of-two lever. Degradation 0.85 to 0.98: x 0.87. Pointing 0.880 to 0.968: x 0.91. Solar constant 1353 to 1361: x 0.994. Degradation and pointing are ten-per-cent levers and the solar constant is under one per cent. The band's ends: 1353 x 0.173 x 0.85 x 0.880 x 0.954 x 0.951 = 159 W/m2 (6.30 km2/GW) and 1361 x 0.37 x 0.98 x 0.968 x 0.954 x 0.951 = 433 W/m2 (2.31 km2/GW). (Corrected 2026-10-22: the low end paired SRC-449's summer-solstice 1311.5 W/m2 with the 0.880 that already holds the 0.9675 solstice factor, which counts the solstice twice; it was 154 W/m2, 6.49 km2/GW, and the solar-constant lever 0.964. The reproduction record below keeps the figures as first checked.)

Limits. (1) Both sizings are 1978-1980; the cell efficiencies above 0.20 are modelled (CLM-0200) or assumed by design studies (CLM-0201), not achieved, per CLM-0201's own finding. (2) SRC-171's 0.85 to 0.98 is degradation during electric orbit raising before service, not 30-year GEO life; SRC-085's 0.9273 and 0.96 are 30-year figures assuming annealing. The two are different quantities and the sweep uses each as stated. (3) CR > 1 designs need the reflector area too; the band is blanket at CR = 1. (4) The solar constant SRC-085 used is inferred, not read.

INDEPENDENTLY REPRODUCED ON LANDING, 2026-09-17, without the script. Figure 5 rendered at 2.2x and every box read from the render (the text layer lacks 0.915, 0.963, 0.85 and 6.97): the GaAlAs chain 71.77 to 69.44, 63.19, 57.82, 11.56, 10.50, 9.46, 9.08 GW; downstream product 0.5508 and 5.00 GW; 6.97 and 7.06 per cent; 70.81e9 / 52.34e6 = 1353 W/m2. Rockwell: 113 - 28 = 85 C; 0.20 - 0.000282 x 85 = 0.1760, so 1311.5 x 1.83 x 0.1760 x 0.96 x 0.968 x 0.89 x 0.997 = 348.4 W/m2; the relative reading 386.3. Anchors 52.34 / 9.07 = 5.77, 26.52 / 9.08 = 2.92, 53.04 / 9.08 = 5.84, 27 / 9.52 = 2.84; busbar 52.34 / 5 = 10.5 and 26.52 / 5 = 5.3; CAST 6 x 0.551 = 3.3. Band ends 154 and 433 W/m2. Elasticities 0.47, 0.87, 0.91, 0.964. SRC-171 p.8 at the normalised level: "the remaining power increases from 85% to 92% to 95%" and "(94% to 97% to 98%)". All match. The script runs clean at its declared digest.

POSTSCRIPT 2026-09-18. Limit (4) closes: Boeing's Phase II blanket sizing states the solar input as 1,353 W/m2 (CLM-1018), the value this calc inferred from 70.81 GW over 52.34 km2. The programme office's 1981 chain (TM-58236 Figure III-12) is box for box the 1978 Figure 5, so the reproduction in section 1 is of the programme's final chain as well as its first; Boeing's 49.6 km2 for 8.876 GW, 5.59 km2 per GW at the array, is a third anchor inside the band. The 0.85 dc-to-RF factor is labelled "estimated" by the contractor (CLM-1019).

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