CALC-135

Launch price per kg to GEO against LCOE: NASA RD1 swept, Frazer-Nash BEIS published cases

REGISTERED 2026-10-14 (ON-476). Drafted for QST-021, checked by a second reader (FIX, all applied before landing), landed by SBSP-coord. The commit that landed it names the draft and the check. Script: qst021-launch-dial.py. verified: VER-2337 CONFIRMED 2026-10-14.

Feeds the launch-price dial (interactive I1) of the QST-021 article. Answers QST-021. Basis: GBP2024/MWh, 20-year life, 10 per cent real, as CALC-062 and CALC-063. x axis: GBP2024 per kg delivered to geostationary orbit (GEO).

Script. qst021-launch-dial.py, run with python -I. It writes the dial's data file, launch-dial.csv. - NASA point: nasa_point() (line 65). It calls restate-lcoe.py rerun_at_life_and_rate() (line 268) on lcoe-model.py clone_params() (line 690), with only starship_cost changed. The x value is build_lifecycle()'s cost_per_kg_geo_delivered (lcoe-model.py lines 334-335). - Currency and price year: restate-lcoe.py to_gbp_2024() (line 148), through usd22_to_gbp24() (line 61). Frazer-Nash rescaling: fn_restate() (line 72), which calls rescale_lcoe() (line 202) and crf() (line 195). - Self-checks: lines 88-103 (CALC-062, and NASA's own Table 26) and lines 133-134 (CALC-063). The script stops and writes no CSV if one fails. A control run with the CALC-062 target set to 930.4 stopped as intended. - Sweep: lines 105-122. Frazer-Nash cases: lines 124-138. Same-price comparison: lines 140-159.

Why it was needed. The dial lets a reader move the launch price and see two estimates move against the British bar (CALC-133). The NASA track needs a model run at each price. The Frazer-Nash track can use only its published cases, because no CASSIOPeiA model is held (CALC-061). One x axis can carry both only if the two per-kg prices mean the same thing.

Do the two per-kg prices mean the same thing? Yes, for this axis. Each is a price per kg moved from the ground to GEO. NASA's is derived from its inputs (first bullet below). Frazer-Nash's is the rate input of its model (item 3 below). Each includes the climb through low Earth orbit (LEO), by refuelled Starship (NASA) or by chemical tug (Frazer-Nash). - NASA does not publish a per-kg price to GEO. The 11,050 USD/kg is derived from NASA's inputs: USD 100M per launch, a 15 per cent block discount, 100 t per launch and 12 tanker launches per payload Starship from LEO to GEO (CLM-0528, CALC-053). - Frazer-Nash's model defines its spacelift term as "The cost of transferring the satellite from earth to GEO" (SRC-018 p.17). Its rate "is the cost per unit mass transferred to GEO" (SRC-018 p.18). The report's sweep of that rate is captioned "Relationship between spacelift cost rate (per unit mass to GEO) and LCOE for SBSP" (SRC-021 p.27, Figure 10). Both of its derivation points are to GEO (SRC-019 p.11, CLM-0716). - The Frazer-Nash model has no separate line for the final climb to GEO. Its thrusters and propellant are sized for station-keeping and decommissioning (SRC-018 p.13-14). It defines the spacelift term as the cost of the whole transfer from earth to GEO (SRC-018 p.17). The two derivation points on SRC-019 p.11 price launches and chemical-tug refuelling. The source does not say how the final climb by on-board electric thrusters is costed.

They differ in four ways. None of them needs a second axis. The first needs a note on the dial. 1. Route (CLM-0531). NASA: 12 tanker launches refuel each payload Starship in LEO, and it flies on to GEO (13 launches per 100 t). Frazer-Nash: chemical tugs raise the payload to about 5,900 km, the satellite is assembled there, and it raises itself to its final operational orbit with on-board electric propulsion (SRC-019 p.11). 2. Price year and currency. NASA: FY2022 USD (CLM-0528). Frazer-Nash: "All cost data are converted into Pounds using an exchange rate from their year of origin [4] and then expressed in 2018 values using gross domestic product (GDP) deflators [3]." (SRC-019 p.3). Both are restated below to GBP2024. 3. Status. NASA's input is a price per launch, and the per-kg value is derived from it (CLM-0528). Frazer-Nash's per-kg value is the model input itself, log-uniform from GBP 358 to 2,410 (SRC-019 p.5). The source derives two points (USD 3,260/kg for Starship, GBP 1,340/kg for SABRE) but does not show how the two bounds were set (SRC-019 p.11; CLM-0716 says this for the lower bound). 4. The mass the rate multiplies. NASA: hardware upmass in 100 t loads (CALC-053). Frazer-Nash: satellite plus assembly-robot mass (SRC-018 p.17).

CLM-0382 and restate-lcoe.py Section 7(d) already compare the two figures as GEO-delivered. This record adds the source wording that supports doing so.

Inputs.

Working, transcribed.

-- Self-checks (script lines 88-103) -- RD1, USD 100M per launch, 20 yr: 3% 564.0 10% 930.3 GBP2024/MWh (CALC-062: 564.0, 930.3) RD1 on NASA's own basis (3%, 30 yr), $/kWh, against SRC-012 Table 26: USD 100M 0.6231 (0.6) USD 50M 0.3977 (0.4) fall from baseline 36.2% (SRC-012 p.18: "about 36%") USD 10M 0.2173 (0.2) fall from baseline 65.1% (SRC-012 p.18: "about 64%")

-- x step, NASA, CALC-062's currency route -- USD2022 11,050.00/kg x 1.0712 (US CPI) = USD2024 11,836.64 / 1.278 = GBP2024 9,261.85/kg

-- NASA RD1, 20 yr, 10% real -- USD/launch USD2022/kg to GEO GBP2024/kg to GEO GBP2024/MWh 10M 1,105.0 926 340.3 NASA case 1b 15M 1,657.5 1,389 373.1 20M 2,210.0 1,852 405.9 25M 2,762.5 2,315 438.6 30M 3,315.0 2,779 471.4 35M 3,867.5 3,242 504.2 40M 4,420.0 3,705 537.0 45M 4,972.5 4,168 569.7 50M 5,525.0 4,631 602.5 NASA case 1a 55M 6,077.5 5,094 635.3 60M 6,630.0 5,557 668.1 65M 7,182.5 6,020 700.8 70M 7,735.0 6,483 733.6 75M 8,287.5 6,946 766.4 80M 8,840.0 7,409 799.2 85M 9,392.5 7,873 831.9 90M 9,945.0 8,336 864.7 95M 10,497.5 8,799 897.5 100M 11,050.0 9,262 930.3 NASA baseline

-- Frazer-Nash BEIS, CALC-063's route -- x: GBP2018 358 x 1.2658 = GBP2024 453.15/kg 2,410 x 1.2658 = GBP2024 3,050.53/kg p50: GBP2018 91.0 x 1.2658 = 115.19 x 0.5848 = 67.4 (each value is restated the same way) case GBP2024/kg p10 / p50 / p90, GBP2024/MWh fifth unit, low spacelift 453 22.1 / 24.7 / 27.6 fifth unit, central none 26.1 / 36.8 / 58.8 (CALC-063: 36.8) fifth unit, high spacelift 3,051 62.0 / 67.4 / 73.3 first unit, central none 38.0 / 49.1 / 71.1 (CALC-063: 49.1)

-- Same price per kg (script lines 140-159) -- GBP2024 453/kg: below NASA's lowest tested price (926); no NASA value GBP2024 3,051/kg = USD 32.94M per launch: NASA RD1 490.7, Frazer-Nash p50 67.4, ratio 7.3 LCOE change per GBP2024 1,000/kg: NASA RD1 70.8, Frazer-Nash p50 16.4 lowest NASA RD1 point (USD 10M per launch): 340.3 = 3.17 x the top of the British bar (107.4)

Result. Over NASA's own launch prices, RD1 at 10 per cent real runs from GBP 340.3/MWh (GBP2024 926/kg to GEO) to 930.3 (GBP2024 9,262/kg). It does not enter the British bar (60.7 to 107.4). Frazer-Nash's fifth unit runs from 24.7 (GBP2024 453/kg) to 67.4 (GBP2024 3,051/kg). At the same price, GBP2024 3,051/kg, NASA's RD1 is 7.3 times Frazer-Nash's fifth unit.

What the numbers show. Within the prices NASA tested, NASA's design does not reach the British bar. Its lowest point is 3.17 times the top of the bar. Launch price closes part of the gap between the studies, but not all of it. At each study's own central price, NASA's RD1 is 25.3 times Frazer-Nash's fifth unit (930.3 / 36.8, our arithmetic from CALC-062 and CALC-063). At one shared price it is 7.3 times. Read with the plus or minus 25 to 30 per cent on the Frazer-Nash figure (CALC-061), the shared-price ratio is 5.6 to 10.4 (our arithmetic: 490.7 / (67.4 x 1.3) and 490.7 / (67.4 x 0.7)). NASA's LCOE also moves about 4.3 times as much per pound per kg (70.8 / 16.4, our arithmetic). This record does not say why. Candidate causes are mass per unit of output and when the mass is launched (NASA relaunches hardware every 10 years, CALC-053; Frazer-Nash launches all propellant during construction, SRC-021 p.25), but neither is tested here.

Where this fails. - NASA track. Every other input stays at NASA's baseline, including the 12:1 refuel ratio. The Dispose lump also stays fixed, and it holds the debris-removal launch cost priced at USD 100M per launch (USD 1.5B of RD1's USD 24.7B; SRC-012 Table 13, p.54). Below USD 100M per launch, the LCOE is therefore slightly high. The size of that effect was not computed. - NASA track inherits CALC-062. The Operate and Dispose lumps keep their 30-year values in the 20-year rebuild. The model was checked against NASA's published totals, not NASA's spreadsheet. These are rebuilds made here, not NASA's published figures. - NASA's per-kg value is an index: launches times price, divided by 100 t. NASA quotes per-kg prices only to LEO (CLM-0528). - Frazer-Nash track. The CRF shortcut carries plus or minus 25 to 30 per cent (CALC-061). The p10 and p90 are rescaled by the same ratio as the p50. That assumes the spread scales like an annuity, which is a further approximation (CALC-063 does the same for the ESA p10 and p90). - In the two spacelift cases the launch price is fixed and the other inputs stay probabilised, so their p10 to p90 spread comes from those other inputs. In the central case most of the spread comes from launch price: "spacelift cost per unit mass is responsible for the vast majority of the output variance" (SRC-021 p.24). - Deflators. All are recalled (CALC-060). For 2018 to 2024, CALC-133 measured the recalled UK CPI multiplier against the fetched GDP deflator and found a 0.19 per cent difference. Frazer-Nash's own 2018 values used GDP deflators (SRC-019 p.3). - The same-price ratio compares two different designs (a mirror swarm and CASSIOPeiA) through two different methods (a rebuild and a shortcut). It carries the limits of CALC-062 and CALC-063 together. - 10 per cent real is a chosen basis and is not benchmarked (CALC-059).

Reading note. SRC-012 Table 26 (p.76) labels RD2's second launch row "$100M", with LCOE 0.5. The text on p.18 gives USD 10M for that case. RD2 is not used here.

Cite this