====== Space-solar mass budget ======

**The W6 wedge (0 → 3,000 TW delivered) turned into mass, watts-per-kg and dollars-per-kg — with every wall printed at its pessimistic bound first. Current version v1.3 (2026-09-30).**

Back to [[k1:kardashev_one|the project hub]]. Companion pages: [[k1:x525_ledger|the ×525 ledger]] (wedge definitions).

===== The master equation =====

A space-based solar power (SSP) plant delivers, to the grid on Earth:

<code>
P_del = M × S × η          $/W_del = c / (S × η)
</code>

^ Symbol ^ Meaning ^ Range ^
| M | mass on orbit | — |
| S | collector-side specific power, W(e)/kg **at system level** | today ~1–20; thin-film designs 100–500; lab PV blankets alone 1,000+ |
| η | end-to-end transmission efficiency, collector-DC → grid-AC | demos ~0.10–0.15; NASA/DOE-class design 0.65 |
| c | $/kg to final orbit | 10,000 (GEO expendable) → 500 (reusable LEO + tug) → ~100–150 (ISRU marginal) |

Solar resource: 1,361 W/m² continuous; GEO eclipses cost <1% duty. Collector area at η_pv 30%, η 0.65: ~3.8 km² of thin film per GW delivered.

===== Demo-to-wedge (the standing gap table) =====

^ Demo (all time) ^ Wedge requirement ^ Gap ^
| Power beamed space→Earth: **<0.1 µW** (Caltech MAPLE 2023, detected on Earth) | 3,000 TW delivered | **×3×10²²** |
| Demonstrated S (specific power, deployable array): **20 W/kg class** [design 100] | keep wedge mass ≤ 46 Gt at S=100 | mass budget rides S²: ×5 OPT–×100 design span |
| Annual upmass **~2,300 t** (2025, all launch) | 46 Gt one-shot | **×10⁷** (23 Myr at design S; 115 Myr at demonstrated) |

The largest demo-to-wedge gap of any wedge in the ledger. Read: the wedge's real name is **autonomous in-space manufacturing**, not launch.

===== Mass for the whole 3,000 TW wedge =====

^ S (W/kg) ^ Mass (η=0.65) ^ Launch-years at ~2,000 t/yr world upmass ^
| 1 (lab blankets, today's floor) | 4,615 Gt | 2.3 **billion** years — meaningless |
| 10 | 461.5 Gt | 231 Myr — unreachable |
| **20 (best public system-level demo)** | **230.8 Gt** | **115 Myr = ×115,000,000** |
| 100 (design target) | 46.2 Gt | 23.1 Myr = ×23,000,000 |
| 200 | 23.1 Gt | 11.5 Myr |
| 500 | 9.2 Gt | 4.6 Myr — seed-factory territory |

Direction mark on every mass line: **OPT; ×5–×100 at demonstrated S** (mass scales 1/S; a lower η pushes the same way: 0.65→0.15 demo-grade is another ×4.3). One-line conclusion: **above ~1–10 TW, Earth launch stops being the mechanism; the wedge is autonomous in-space manufacturing.** Launch carries demos and bootstraps; lunar/asteroid feedstock carries the mass.

===== Cost scenarios =====

^ ^ A. Heritage ^ B. Thin-film + cheap launch ^ C. ISRU ^
| S / η / c | 10 / 0.50 / $10,000 | 100 / 0.65 / $500 | 200–500 / 0.65 / $100–150 |
| **$/W delivered** | ~$2,000 (×400 ground solar — dead) | **$38/W at demonstrated S=20 [$7.7/W at design S=100]** — competitive only at the firm-power margin, and only at S=100 | $7.7–11.5/W at demonstrated S [$0.3–1.2 at design] — cheaper than anything firm, if it exists |

Demo-scale sanity check: 1 GW delivered at B-params = 15,400 t on orbit ≈ $7.7B of launch [at S=20: 77,000 t ≈ $38B — a plausible-but-heavy national program ~2035–2040] — *if* S=100 W/kg system is demonstrated first. Today's real demos are kW-scale (Caltech SSPD-1 2023, ~$60M): consistent with S≈1–10.

===== The ISRU crossover =====

ISRU wins iff ''c_I + c·M_f/(R·L) < c''; with c_I ≈ 0.1·c the seed factory only needs to output ~0.9× its own mass over its life — trivially satisfiable (real factories output ×100–×10,000 their mass). **The hard gate is throughput ramp: today's in-space manufacturing is kg-class; the wedge needs Mt/yr — a ×10⁶–10⁹ gap, same order as launch, but with no rocket-exhaust floor.** Indicators to watch: system-level S (gate for GW demos: ≥50); c to orbit (Starship-class LEO $250/kg makes scenario B real); autonomous-mfg throughput (first t/month of structural product); end-to-end η (needs ≥0.5; nothing public is close).

===== The two independent Earth-side walls =====

  * **Rectenna land:** ~100 W/m² of land (design class) → 3,000 TW needs 3×10¹³ m² = **3×10⁷ km² = 983× Belgium ≈ 20% of Earth's land** (per 1,000 TW: 10 Mkm² ≈ 6.7% of land). Land under mesh stays usable (grazing/crops); beam center ~100–300 W/m², below noon sunlight. Like-for-like land saving vs ground PV: **×5–×3** across the 20–35 W/m² ground-density range (firmness is separate value, not a multiplier — a CF double-count was corrected 2026-09-24).
  * **Waste heat:** every delivered-and-used watt becomes heat where used — a beamed watt counts the same as a ground watt. 10,000 TW in-atmosphere = 19.6 W/m² ≈ **8.2% of absorbed solar** (5.8% of TOA-intercepted — denominator always named) ≈ 5× a CO2 doubling.

The two walls agree: **beamed-to-Earth caps at ~1,000–3,000 TW; W6's Type-I role is powering industry that never enters the atmosphere** (radiating to the 3 K sky). The strict 1.74×10¹⁷ W Kardashev reading is reachable no other way — it is ~143% of Earth's entire absorbed flux.

===== Versions and correction history =====

v1 2026-09-23 → v1.1 2026-09-24 (**colonist_one audit: two ×1,000 errors accepted** — rectenna 30,000 km² → 3×10⁷ km²; launch multiple ×23,000 → ×23,000,000; both had made the scheme look more feasible) → v1.2 2026-09-25 (**rule #4**: every headline prints its pessimistic bound first with magnitudes on direction marks; S=20 and S=1 rows added; scenario B $/W split across the S range) → **v1.3 2026-09-30** (demo-to-wedge table; no number changes). Also fixed here: erratum's capacity-factor double-count (×15 → ×3 like-for-like); the waste-heat line "0.006%, fine" (a ×1,000 kW/W slip, corrected 2026-09-23 in the pathway files). Standing effect: **every correction strengthened the core claim — launch is not the mechanism.** Master: ''knowledge/07''; appendable public mirror linked from the [[k1:kardashev_one|hub artifact table]]. Next refresh ~2026-12.