Appendix G — Key Thresholds & Critical Numbers
The book's load-bearing numbers in one place — the quick-reference card for workshops, classrooms, and field decisions. Each entry links to its full context.
Temperature Ladder (°C)
| Temp | What happens | Ch |
|---|---|---|
| ~260 | Fire-piston ignition by compression; ember from friction coal | 1 |
| 250–400 | Heat-treating chert improves knappability; low-temp charcoal for powder | 2/21 |
| 300–350 | Fast-charcoal grade for black powder | 21 |
| 150–600 | Hot-blast preheat range (Neilson pipe stoves upward; Cowper regenerators later exceed 1,000) | 22 |
| ~600 | Dull-red glow; open-fire pottery hardening begins | 5 |
| 63/72 | Milk pasteurization (30 min / 15 s) | 30 |
| ~700 | Cherry-red; reliable earthenware kilns | 5 |
| ~770 | Steel loses magnetism (transformation point — hardening reference) | 14 |
| 800–1,000 | Updraft kiln territory; soda-lime glass melts with flux | 5/17 |
| ~900 | Lime calcination (CaCO₃ → CaO); case-hardening carburizing heat | 17/14 |
| ~900–1,250 | Bloomery operating range (below iron's melt point) | 14 |
| ~950 | Hall-Héroult cryolite bath for aluminum | 38 |
| 900–1,200 | Charcoal + forced draft; copper smelting zone | 1/10 |
| 1,085 | Copper melts | 10 |
| ~1,300 | Sparking-white forging heat (welding) | 14 |
| 1,414 | Silicon melts (semiconductor purification world) | 35 |
| 1,450 | Portland cement clinker sintering | 27 |
| 1,538 | Pure iron melts (cupola territory needs forced blast) | 22 |
| ~1,700 | Incandescent lamp filament glow | 26 |
| ~3,500 | Carbon arc crater | 26 |
Ratios & Compositions
| Item | Numbers | Ch |
|---|---|---|
| Black powder | 75 : 15 : 10 KNO₃/S/C, grained, dry | 21 |
| Lime mortar | 1 lime : 3 sand | 17 |
| Concrete water/cement | 0.4–0.5 structural (more water = always weaker) | 27 |
| Type metal | ~60 Pb / 25 Sn / 12 Sb | 18 |
| Bronze classic | 88–90 Cu / 10–12 Sn (+Pb variants) | 10 |
| Steel carbon window | 0.2–1.4 % C useful; >2 % = cast iron | 14 |
| Stainless threshold | ≥ ~10.5 % Cr passive film | 27 |
| Saltpeter leach → crystallize | KNO₃ salts out first on cooling; recrystallize once | 21 |
| Chlorine residual | 0.2–0.5 mg/L after 30 min contact = protected water | 30 |
| Grain storage moisture | <13 % or mold/weevils win | 7 |
| Hay safe moisture | <18 % before baling/storing | 8 |
| ORS formula scale | ~75 mmol/L glucose with matched sodium salts | 30 |
| Haber-Bosch conditions | ~200 atm, ~450–500 °C, Fe catalyst, recycle loops | 32 |
| Bloomery reference smelt | 2 kg charcoal : 1.5 kg roasted ore per charge (~45 kg ore, ~90 kg charcoal total) → 8–12 kg raw bloom (30–45 % slag) → 4–5 kg consolidated bar; blast 800 L/min | 14 |
| Photolithography first cycle | spin 4,000 rpm/30 s ≈1 µm resist · soft bake 95 °C/60 s · g-line dose 100–200 mJ/cm² · develop TMAH 2.38 %/60 s · BOE etch ~100 nm/min | 35 |
Power & Energy Arithmetic
| Fact | Number | Ch |
|---|---|---|
| Ox sustained draft | ~0.5 kW (~6 humans) | 8 |
| Horse draft | ~0.7–1 kW bursts | 8 |
| Overshot waterwheel | 60–70 % efficiency; 1 m³/s × 3 m ≈ ~20 kW delivered | 16 |
| Newcomen → Watt efficiency | ~0.5 % → ~3–4 % (separate condenser saves ~75 % fuel) | 23 |
| Reference 10 kW steam unit | Ø180 mm × 200 mm stroke, 300 rpm, 7 bar gauge, mep ≈240 kPa, double-acting → ~12 kW indicated / ~10 kW brake; Ø400 mm boiler shell at 7 bar needs 6 mm plate (computed min 3.1 mm, SF 5, joint η 0.70) | 23 |
| Hot blast fuel effect | ~⅓ less fuel per ton pig from ≥150 °C blast (Neilson, 1828); enables raw-coal smelting | 22 |
| Steam duty trajectory | Newcomen ~4–6M → Watt ~20–30M → best Cornish compounds ~90–100M ft·lb per 84-lb bushel; 2 kg coal/kWh ≈ 50M duty | 23 |
| Marine triple-expansion | 15–20 % thermal | 23 |
| Diesel slow-speed marine | >50 % thermal | 29 |
| Gasoline energy density | ~45 MJ/kg (battery c.1900: ~0.2) | 29 |
| Petroleum energy density | ~42 MJ/kg | 28 |
| Modern battery cost fall | ~90 % decline since commercialization | 43 |
| PV module learning rate | ~20 % cost drop per doubling | 43 |
| Betz limit | 59.3 % max wind extraction | 43 |
| Pumped hydro round-trip | ~75–80 % | 43 |
| Hydrogen round-trip | ~30–40 % (use for industry, not bulk grid) | 43 |
| Aluminum smelting | ~13–15 kWh/kg; recycling ~5 % of that | 38 |
| Fission per fission event | ~200 MeV | 37 |
| Abundance threshold | <$0.03/kWh system-level electricity | 43 |
Motion, Space & Navigation
| Fact | Number | Ch |
|---|---|---|
| Δv to LEO | ~9.4 km/s incl losses; mass ratio e^(Δv/ve) | 39 |
| LEO orbital speed | ~7.8 km/s; GEO altitude 35,786 km | 40 |
| GPS relativistic drift | ~38 μs/day uncorrected ≈ 10 km/day error | 40 |
| Longitude arithmetic | Earth rotates 15°/hour; 1 s chronometer error ≈ 0.4 km at equator | 20 |
| Fiber loss target | ≤20 dB/km viable (1970); modern ~0.15–0.2 dB/km @1550 nm | 41 |
| Hull speed intuition | ~1.34×√waterline(ft) knots (displacement hulls) | 24 |
| Sewer self-cleansing velocity | ≥ ~0.6 m/s keeps solids moving | 30 |
Health & Food Security
| Fact | Number | Ch |
|---|---|---|
| Semmelweis handwashing effect | ~90 % childbed-fever mortality cut | 30 |
| Sanitation-first result | Urban life expectancy doubled pre-antibiotics | 30 |
| Agriculture land yield | 1 ha managed grain supports ~4–10 people | 7 |
| Pre-mechanized farm labor | ~1–2 ha per person hand-farming | 7 |
| Green Revolution yields | ~1–2 t/ha → 6–10 t/ha cereals | 32 |
| Nitrogen dependency | ~half of humanity's fixed N via Haber-Bosch | 32 |
| Medical dashboard | Maternal+infant mortality <1 % of births = functioning system | 31 |
| Cold chain vaccines | 2–8 °C; freeze OR heat both destroy potency | 31 |
Process Discipline Constants
| Rule | Statement | Ch |
|---|---|---|
| √N law | Averaging N repeats shrinks random error by √N | 20 |
| Learning curve | Costs fall ~25–30 % per cumulative production doubling | 35/43 |
| I²R doctrine | Doubling voltage quarters line loss — buy distance with voltage | 26 |
| N-1 contingency | Grid survives any single component loss instantly | 43 |
| Stewardship rule | Antibiotics: right drug/dose/duration, narrow spectrum, complete courses | 31 |
| Jump legality test | Physics permits + knowledge exists + failure recoverable | Appendix C |
| X̄–R chart constants | n=5: A₂=0.577, D₃=0, D₄=2.114, σ̂=R̄/d₂ (d₂=2.326); baseline 20–25 subgroups; act only on signals | 47 |
| Limit-gauge budget | gauge tolerance ≤10 % of work tolerance; ~10 % wear allowance on GO member, audited monthly | 15 |
| Capability gate | tolerance ÷ 6σ̂ ≥ 1.33 before promising interchangeable parts | 15/47 |
| Interface standardization | Container loading: ~$5.86/t break-bulk → ~$0.16/t containerized (lock the interface first; ISO 668) | 47 |
| First-fab cleanroom | ISO Class 7 room + ISO Class 5 laminar bench (≥60 air changes/h) | 35 |
| Zone-refining plan | 6–8 passes at ~2 mm/min, zone ≈ ingot diameter; boron (k≈0.8) resists zoning — remove chemically first | 35 |
| Dead-end alarm | Enthusiasm without falsification path = consult Appendix B | B |
Usage: print/laminate this appendix alongside Appendix A. A carries the sequence; G carries the numbers that keep each step honest.