Fuel, Particulate and the Bound Roll: A Coupled Throughput, Exposure and Replacement Model of Giedi Prime under House Harkonnen, 10120–10191 AG

1. Introduction

Each annual return of the Harkonnen Works Inspectorate ends on the same pair of lines. The first gives the fuel burned in a district's works over the year, in petajoules (PJ). The second, headed "strength", gives the head-count of the district's bound roll on the opening day. The pairing was a clerk's convention and no return comments on it, yet read across seventy-two years the two lines trace the system this paper models. Fuel burned in the last eighteen-year period was about 2.1 times that of the first, the roll that served the furnaces grew only 1.7-fold, and more than half of all who entered that roll came from outside it.

We write c. 10242 AG, some five decades after the fall of House Harkonnen in 10191 AG, when its Giedi Prime records passed into Imperial custody and were opened to the Giedi Prime Industrial Survey. They are the only continuous account of the planet's industry, and they are the House's own: the Inspectorate compiled its returns to allocate fuel and defend output, and the Labour Registry kept its books to keep the roll filled. Nothing in them was written to measure harm, and where harm appears it appears as a cost or a count.

Our question is an engineering one: how did fuel throughput, particulate load, worker exposure and the demography of the bound roll depend on one another, and what did that coupling demand of the system's inputs? We chain fitted relations from throughput to emission, concentration, death rate and replacement, and close the chain with an account of entries and exits. It closes only if the roll is refilled continually from outside, and we estimate by how much.

2. System Description

The returns cover nine works districts, three each of reduction, fabrication, and chemical and refining work, each with a gate where the Inspectorate sited a sampling station. We divide the record into four eighteen-year periods, P1 (10120–10137 AG) to P4 (10174–10191 AG). The bound roll is the population held in hereditary tenure, to which the returns assign the furnace, mill and haulage gangs. Children of bound women enter it at fifteen; external recruits arrive by commitment within the planet, by levy or court order, or by off-world contract carried by the Spacing Guild. Exits are death, release and passage off the roll at sixty-five. Term-contract workers and craftsmen, a smaller roll kept on different conventions, are excluded.

Five record series carry the analysis. The district returns give fuel, feedstock processed, tailings, a feedstock grade index (10120 AG = 1.00) and strength; 445 of 648 district-years survive (69%) (Harkonnen Works Inspectorate, 10120–10191 AG). The gate logs, begun in 10131 AG, give stack emission rate and ambient particulate concentration for 331 of 549 district-years (Harkonnen Works Inspectorate, 10131–10191 AG). We transcribed every hundredth registry number from the Labour Registry's books, which yields 438 district-years with about 465 thousand sampled person-years, 11,900 deaths, 16,300 births and 18,900 entries (Harkonnen Labour Registry, 10120–10191 AG). The Spacing Guild's annual counts of bonded passengers landed at Giedi Prime, released in aggregate for 10138–10191 AG, are the one record the House did not write (Spacing Guild, 10138–10191 AG).

Earlier work on the Great Houses found the Harkonnen records at Giedi Prime unusually full among the twelve Houses it compared, but those were succession notices and ledgers, and about a third of our district-years are missing. We interpolate missing returns on the log scale within each district and treat period totals as approximate. Every series except the Guild's was compiled by the House for its own purposes, so we treat its figures as its claims and test them against the Guild's.

3. Model and Analysis

Reconstructed fuel energy rose from about 450 PJ a year in P1 to about 940 in P4, a factor of 2.1 (Table 1). Feedstock processed rose only 1.7-fold, from 23 to 39 megatonnes (Mt) a year, because the grade index fell from 0.93 to 0.62 and each tonne of feed cost more energy: energy per tonne varies inversely with grade, with an elasticity of 0.53 (95% CI 0.50–0.55) estimated within districts, inside the 0.45–0.65 reported for the heavy-metals trade (Haldrane, 10229 AG).

Emission follows fuel one for one and grade inversely. A log-linear regression of stack emission on fuel energy, grade index and a retrofit indicator, with district intercepts, uses the 235 district-years that have both a return and a gate log. The elasticity to fuel is 0.99 (95% CI 0.86–1.13) and to grade −0.67 (−0.90 to −0.44), so at constant fuel a 10% fall in grade raised emission by about 7%. Emission per PJ rose 18% between P1 and P4, and modelled emission rose 2.5-fold, from about 410 to 1,010 kilotonnes (kt) a year. The pilot retrofits, in the Second Reduction District from 10166 AG and the Second Fabrication District from 10171 AG, cut stack emission by 35% (30–39%).

Concentration at the gate follows emission with an elasticity of 0.76 (95% CI 0.71–0.80; 331 district-years) and, weighted by roll size, rose 1.97-fold between P1 and P4 (95% CI 1.78–2.27). The unweighted gate means in Table 1 rise less, because the P1 mean rests on logs of 10131–10137 AG alone.

We relate deaths to concentration with a log-link count regression, offset by person-years, with age-band and district effects, on the 223 district-years that have both a roll sample and a gate log. The death rate rises with the 0.26 power of concentration, a rate ratio of 1.20 per doubling (95% CI 1.13–1.27), inside the 1.15–1.30 reported for industrial workforces elsewhere (Velloran, 10224 AG). The interval is model-based; a resampling interval over the nine districts was narrower (1.17–1.25), and with so few clusters we do not trust it (Tennerhal, 10227 AG). Setting each district's concentration back to its P1 level lowers P4 deaths by 16% (95% CI 11–22%): of about 32 thousand deaths a year on the roll in P4 (28–35 thousand), some 5,300 are attributable to the rise in load.

Replacement is where the chain closes. Life tables built from the sampled books, by a method set out in earlier work by one of us (Dellacorte, 10233 AG), give expected years on the roll after entry at fifteen of 31.9 (95% CI 30.5–33.9) in P1 and 29.6 (28.6–31.2) in P4. Nursery follow-up shows that 54% of the births of P1 reached fifteen and entered the roll, against 51% for P3. With age-specific fertility, and pooled death rates applied to women because the books tabulate exits by age band and not by sex, these give a net replacement ratio (the daughters a woman entering the roll can expect to see enter it in turn) of 0.67 (0.64–0.70) in P1, 0.62 in P2 and 0.63 in P3 (Table 2). Births of P4 had not reached fifteen by the end of the record, so its ratio, 0.58 (0.56–0.61), is a projection that lets child mortality move with concentration. No resample put any period's ratio at 1 or above.

The roll therefore could not hold its size from within. External entrants were 57% of all entrants in P1 (95% CI 56–58%) and 61% in P4 (59–63%),. Off-world contracts supplied 32% of them in P1 and 57% in P4 (56–59%): commitments within the planet barely grew, from about 11 thousand a year to about 12 thousand, and off-world contracts took up the growth.

A one-year projection of the cohort account from the 10191 AG roll of 1.29 million, with P4 rates, shows what standing still would have cost: about 23 thousand external entrants a year (95% CI 17–27 thousand), against the 27.7 thousand actually received while the roll was still growing.

Abatement was a lever the ledgers priced. The Inspectorate's memorandum of 10158 AG costed a settling-and-filtration retrofit at 38 million solaris per district against a stated hurdle of fifteen years, and recommended two pilots (Harkonnen Works Inspectorate, 10158 AG). Applying the measured cut to the seven unretrofitted districts, which held 75% of the P4 roll, would have lowered gate concentration by 28% and P4 deaths by 8.1% (5.2–11.3%), averting about 1,960 deaths a year. On the ledgers' terms a death costs the price of its replacement, the recorded price of an off-world entrant, about 2,640 solaris in P4, so the 266 million solaris of retrofit pays back in about 51 years (38–81); a fifteen-year payback needed a replacement price of about 9,050 solaris, 3.4 times the recorded price. No further retrofit appears in the returns after 10171 AG.

4. Validation Against Field Data

Table 3 sets out four tests. Three compare the model with the House's own series, and only the Guild comparison checks the House. We refitted the chain on 10120–10180 AG and used it to predict 10181–10191 AG from the returns alone: the gate-concentration forecast beat carrying each district's last three logged values forward (12% error against 19%), 49 of 55 observations fell inside the 90% prediction interval, and held-out deaths were predicted within 2% (ratio 0.98; 95% CI 0.93–1.03).

Off-world entries counted in the registry and scaled to the planet reach 93% of the Guild's count (95% CI 89%–97%) and come within 20% of it in 40 of 54 years. The shortfall is of the size expected if some bonded passengers died in passage or were re-embarked, which neither source marks. The House's books did not inflate off-world intake.

Finally the Registry series close to within 1.5% of entries, with strength rising slightly faster than the books explain.

5. Failure Modes

A halt in recruitment is the system's first failure mode. Projecting the cohort account from 10191 AG with P4 rates, a complete stop to external entry leaves the roll at 91% of its strength after five years and 83% (81–86%) after ten. Nothing in the demography arrests the decline, because the replacement ratio stays below 1.

Amplification is the second. With fuel scaled by ±10% and grade held fixed, the external entrants needed to hold the roll steady change with an elasticity of 1.30 (1.24–1.38), because a larger roll is also exposed to higher concentration: each additional 10% of throughput needed about 13% more recruits, so growth raised the recruitment burden faster than output.

The reconstruction has failure modes of its own. Fuel and grade move together within districts (correlation about −0.93), so their separate elasticities have wide intervals, though their combined effect is better determined. The rate ratio is stable to adding period effects, which gives 1.19 (1.11–1.25), but nine districts remain too few clusters for resampling intervals to be reliable. Concentration is measured at the works gate and not in the residential blocks, which weakens the estimated link by an unknown amount. The P4 replacement ratio assumes that child mortality moves with concentration; with child survival held at its P3 level it would be 0.61, still far below 1.

6. Conclusion

Four conclusions follow from the records. The bound roll could not replace itself in any period: its net replacement ratio lay between 0.58 and 0.67, so the works' growth was supplied by recruitment. External entrants made up 57%–63% of all entrants and numbered about 27.7 thousand a year by P4, over half of them off-world and within 7% of the Guild's own count. The load grew faster than the work: emission rose 2.5-fold against fuel's 2.1, and the rise in concentration accounts for about one death in six on the roll in P4. Abatement cut emission by 35% and lost to replacement on the ledgers' own terms, with a payback of about 51 years against a hurdle of fifteen.

For anyone planning a successor operation the practical implication is a number. Restoring the works to their 10191 AG throughput inherits a requirement of about 23 thousand external entrants a year merely to stand still, and more to grow; that figure belongs in the plan beside fuel and feedstock.