CALC-113

Crew and duration to assemble the 1978 Reference System satellite at Skylab-measured rates, set against its own six months and 555 to 715 crew

The parametric L3 test for in-space assembly: an order-of-magnitude estimate built from a measured per-join time, a source-stated mass rate and the satellite's own mass statement, set against the published six months and 555 to 715 crew, with the gap stated and attributed. 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).

Provenance. The project's working file vc11_assembly_estimate.py, 5,711 bytes, sha256 E9CE2ACE988D0A4F, 98 lines, no dependencies. Inputs: satellite mass by subsystem from SRC-085 Table 1, printed p.48 (PDF 60), whose columns run GaAlAs then silicon - structure 4.957e6 kg silicon and 5.886e6 kg GaAlAs as the sum of array primary and secondary (3.388 and 0.436; 4.172 and 0.581), antenna primary and secondary (0.250 and 0.786, both options) and interface primary and secondary (0.094 and 0.003, both options); totals 50.984e6 silicon and 34.159e6 GaAlAs including the 25 per cent contingency; planform "about 55 km2" (SRC-085 printed p.1); the measured per-join time of 6.2 minutes and projected 2.5 minutes (SRC-451 Vol III p.175, Skylab 3, 22 sections in 137 minutes); the source's own assembly rate of 6 to 12 kg per man-hour and 394 joints per 105 m x 108 m structural bay (SRC-451 Vol III p.188); tri-beam mass 21.4 lb and 78 operations per tri-beam (pp.175 and 177). Published figures under test: six months construction, crew 555 silicon and 715 GaAlAs (SRC-085 printed pp.11 and 14, CLM-0963); two per year (CLM-0962). ASSUMED: 6 to 10 productive hours per crew member per day, and 30.4 days per month. ASSUMED, Route B only: the solar array structure has the same joint density as the antenna bay p.188 describes.

1. The two source pages cohere, which is the check that the inputs are read correctly. p.188 states it derived 6 to 12 kg/man-hr from 394 joints per bay and a per-joint time. Taking p.175's 6.2 minutes: 394 x 6.2 = 40.7 man-hours per bay, implying a bay mass of 244 to 489 kg at the stated rate. At the projected 2.5 minutes, 16.4 man-hours and 98 to 197 kg. A lattice bay built from 21.4 lb tri-beams at a few hundred kilograms is consistent with both. p.188 adds that the rate is "in line with that assumed during Task 1, 11 lb/m-hr", which it calls the rate at which steel workers construct a major building on the ground - so the in-orbit rate is calibrated to terrestrial steelwork, not measured in orbit beyond the one Skylab datum.

2. Route A - structure only, at the source's own rate. Structure mass divided by 6 to 12 kg per man-hour gives 0.41 to 0.83 million man-hours (silicon) and 0.49 to 0.98 million (GaAlAs). To finish in six months:

The published crew sits inside the manual-rate bracket for the structure alone. The 1978 figure is what Skylab-calibrated manual assembly of the primary and secondary structure would need.

3. Route B - joints, from bay density. 394 joints over 11,340 m2 is 0.0347 joints per m2; over 55 km2 that is 1.91 million joints. At 6.2 minutes each, 0.20 million man-hours; at 2.5, 0.08 million. Crew for six months: 44 to 180. Lower than Route A by a factor of 2 to 5, and the difference is the ASSUMED density - the antenna bay is the densest structure on the satellite, and Route B applies its joint count to the whole planform, which overstates joints but omits every non-structural operation. Route B is a floor, not an estimate.

4. Route C - the whole satellite at the same manual rate, which is the part the reference system never states. 50.984e6 kg at 6 to 12 kg per man-hour is 4.2 to 8.5 million man-hours; 34.159e6 kg is 2.8 to 5.7 million. Crew for six months: 2,329 to 7,764 silicon, 1,561 to 5,202 GaAlAs.

5. The gap, and what it implies. Against the published 555 and 715:

Run the other way: at the published crew and manual rates, one satellite takes 13 to 84 months, not six. So the six-month figure is achievable for the structure at Skylab rates and is not achievable for the satellite at any rate the held sources measure or state. The difference is a productivity multiplier of roughly 2x to 14x over manual assembly, which SRC-085 does not state, justify or attribute. SRC-451 Vol III p.175 names the mechanism the 1975 study intended - a free-flying manufacturing "factory" producing structure at 420 lb/hr, eight modules to meet the timetable - which is automation of fabrication, not of the blanket, klystron and subarray installation that carries most of the mass. Whether the multiplier is automation, parallel construction bases, or an assumption never costed, the reference system does not say, and it is carried here as an unstated factor rather than as a plan.

Limits. (1) Hours per crew-day is assumed; the bracket spans 1.7x across it. (2) The kg per man-hour rate is for lattice structure and is applied in Route C to solar blankets, klystrons and waveguides, which are different operations; Route C is an order-of-magnitude device, not a schedule. (3) The single measured datum is a Skylab sunshade pole, not a structural member; everything else on p.175 and p.188 is analysis. (4) The published crew includes LEO staging personnel who do not assemble; removing them narrows the published figure and widens the gap. (5) The p.14 versus Figure 37 LEO crew discrepancy (75 against 225, CLM-0963) is carried, not resolved; using 225 raises the silicon total to 705 and shrinks the multiplier to 3.3x to 11x. (6) The estimate is per satellite and does not test the rate of two per year. SRC-085 printed p.69 (PDF 81) has one base building back to back, with the next satellite's material in transit, so that "once the process is underway, two SPS's are being produced every year". (Corrected 2026-10-22: this item said two per year needed two satellites under construction at once or two bases.)

INDEPENDENTLY REPRODUCED ON LANDING, 2026-09-17, without the script, from the cited pages: Table 1 read at PDF p.60 with its GaAlAs-then-silicon column order (structure sums 4.957 and 5.886; totals 50.984 and 34.159); p.188's "13 to 26 lb/m-hr (6 to 12 Kg/m-hr)", "(394)" and "11 lb/m-hr ... steel worker" read with the text layer's faults ("t}_tca]" for "typical"); 21.4 lb and 78 operations at pp.177 and 175. Recomputed: 394 x 6.2 min = 40.7 h and 244 to 489 kg per bay; 4.957e6 / 12 and / 6 = 0.413 and 0.826 million man-hours; six months = 182.4 days, so 226 and 755 crew at 10 and 6 h; 50.984e6 / 12 / 1,824 = 2,329 and / 6 / 1,094.4 = 7,764; 34.159e6 gives 1,561 and 5,202; multipliers 4.2 to 14.0 and 2.2 to 7.3; 1 - 1/m gives 76 to 93 and 54 to 86 per cent; 4.249e6 / (555 x 10) = 766 days = 25 months and 8.497e6 / (555 x 6) = 2,552 days = 84 months, 2.847e6 / (715 x 10) = 398 days = 13 months; Route B 394 / 11,340 x 55e6 = 1.91e6 joints, 0.197 and 0.080 million man-hours, crew 180 and 44. All match. The script runs clean at its declared digest.

POSTSCRIPT, LATER THE SAME DAY. The multiplier this calc found unstated is stated, in three parts, by the programme documents that arrived from the CDEP corpus that evening: the six months was a ground rule the designs were fitted to, with crews skeletonised and machines slowed to meet it (CLM-0982); machines fabricate and humans handle, with the human share 20 to 30 minutes per beam or a 20 per cent joints allowance (CLM-0984, CLM-0986, CLM-0983); and the crews worked three shifts or ten-hour days with only about two-thirds of those on board on construction (CLM-0983, CLM-0985). Direct labour of Boeing's 259 on construction at 10-hour shifts six days a week (8.6 hours a day over the week) over 180 days is about 400,000 man-hours, just below Route A's structure-only bracket of 0.41 to 0.98 million; NASA's 270, whose shift pattern is not stated, gives about 417,000 at the same hours, just inside it. (Corrected 2026-10-22: this line said about 390,000 and inside the bracket.) Section 5's finding stands as written: the factor was never written down in DOE/ER-0023; it was written down elsewhere.

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