CALC-053

Physics chain, mass, launch count and unit cost, from the design parameters alone

Feeds CLM-0242, CLM-0243, CLM-0245, CLM-0466. SHARED - four claims, one re-runnable section. Answers QST-004.

Script: the LCOE model. - physics chain: SECTION 3, verify_power_chain(), line 262 - mass and launches: SECTION 4, build_lifecycle(), lines 293-300 - launch cost: build_lifecycle(), lines 534-537 as printed by print_trace() - learning curve: SECTION 1, learning_curve_total_cost(), line 110

Why it was needed. This is the launch point of the whole independent model. If delivered power cannot be reproduced from area and physics alone, nothing downstream is independent - it is just NASA's numbers rearranged. A mismatch here would have invalidated everything.

Inputs.

Working, transcribed.

-- Delivered power (CLM-0242) --
efficiency chain = 0.35 x 0.90 x 0.70 x 0.90 x 0.98 x 0.95 x 0.78 x 0.90 = 0.12970

RD1  incident = 11,473,000 m2 x 1367.5 W/m2 = 15,689.3 MW
     nameplate = 15,689.3 MW x 0.12970       =  2,034.9 MW
     delivered = nameplate x CF 0.997        =  2,028.79 MW
     [report's own "power delivered": 2028.79 MW - matches to 5 s.f.]

RD2  incident = 19,000,000 m2 x 1367.5 W/m2 = 25,982.5 MW
     nameplate = 25,982.5 MW x 0.12970       =  3,369.9 MW
     delivered = nameplate x CF 0.60         =  2,021.95 MW
     [report's own figure: 2021.95 MW - matches to 5 s.f.]

-- Launch count, RD1 (CLM-0243) --
in-space mass   = 4.00 kg x 1,463,000        = 5,852,000 kg
develop upmass  = in-space + servicers       = 5,899,600 kg
hardware launches = ceil(5,899,600 / 100,000)          =    59
refuel launches   = 59 x 12                            =   708
Assemble launches = 59 + 708                           =   767
refurb batches    = round(30 / 10) - 1                 =     2
Maintain launches = 767 x 2                            = 1,534
Dispose launches  = 20  [SOURCED, not re-derived]      =    20
TOTAL lifecycle launches = 767 + 1,534 + 20            = 2,321
     [report's own figure: 2,321 - exact]
RD2 by the same route: 3,973 against the report's 3,960, 0.3 per cent high.

-- Cost of mass delivered (CLM-0245) --
effective $/launch = $100,000,000 x (1 - 0.15)         = $85,000,000
$/kg to LEO        = $85,000,000 / 100,000 kg          =        $850 /kg
$/kg landed at GEO = $850 x (1 + 12)                   =     $11,050 /kg
Multiple:            11,050 / 850 = 13 x

-- Manufacturing learning curve (CLM-0466) --
Integrated Wright power-law form:  T(N) = C1 x N^(1+b) / (1+b),  b = ln(LR)/ln(2)
RD1 modules  : $6.9073B modelled  against $6.9B published
RD1 servicers: $11.4B   modelled  against $10.9B published
Agreement 1 to 5 per cent on both.

Result. Delivered power reproduces to five significant figures from physics alone, with no cost figure as an input. Launch counts reproduce exactly for RD1 and to 0.3 per cent for RD2 from mass, capacity, refuel ratio and refurbishment cycles alone. Delivered mass costs $11,050/kg to GEO against $850/kg to LEO, a factor of thirteen, and that single multiplier is the clearest explanation of why launch is 71-77 per cent of lifecycle cost in the source study.

Where this fails. - The power chain confirms the internal arithmetic consistency of the design description, not that the efficiency figures are achievable or correctly sourced from Rodenbeck et al. - The launch count confirms the arithmetic, not the engineering feasibility of 100-plus Starship-class launches a year sustained for a decade. - The $/kg figure is a single multiplier for one propulsion architecture. It does not model how launch cost and refuel ratio might fall together under a different architecture; see CALC-056 and CALC-080 for the case where they are varied together.

TWO RECORDED DEFECTS IN CLM-0466 THAT THIS RECORD MUST CARRY, BOTH ALREADY REPAIRED IN THE CLAIM AND NEITHER SILENTLY DROPPED.

1. The claim's premise was false and is withdrawn. CLM-0466 described NASA's Crawford-model formula as unpublished and said it had been reverse-engineered by testing candidate formulas. SRC-012 prints the exact Python code in full at p.45-46, and it is a discrete cumulative sum, not the continuous integral the model substituted. The two agree to within 0.02 per cent so no figure moves. Inventing a difficulty that did not exist is a close cousin of inventing a quotation, and the reverse-engineering narrative must not be repeated in this record or any output built on it. 2. A worked example was cited that the script does not compute. The claim originally offered three worked examples: modules, ADR vehicles, servicers. `lcoe-model.py` computes no ADR cost line. I checked this independently: adr appears three times in the file, at lines 32, 33 and 106, and all three are inside comments or the module docstring. There is no computed ADR cost. The figure existed only as hand-arithmetic in a write-up whose own text claimed every number came from an actual run. The ADR line is removed; the other two examples do reproduce.

One low-severity reading note, offered as a reading and not as an error. CLM-0242 calls the chain a "seven-stage conversion-efficiency chain" and then lists eight factors. Eight is what the script uses and eight is what multiplies to 0.12970, so the arithmetic is unaffected. "Seven stages" is consistent if the solar cell is counted as capture rather than conversion, and two of the eight (atmospheric_eff, beam_collection_eff) are transmission losses rather than conversions either way. More likely a loose label than a miscount, which is why it is recorded as a reading note and not as a defect.

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