--- marp: true theme: default paginate: true --- # Landing-Ellipse Contraction as a Technology Learning Curve Quantifying the precision-landing improvement rate across Mars missions *A measurement offered in stewardship of the capability that many hands have built, and in service of the missions still to come.* **A design-stage doctoral defense** **Candidate:** JPL_AUTONOMY_EDL_06 **Program:** COLLEGIUM 1st Battalion **Category:** NORTH STAR / JPL, Entry, Descent, and Landing Systems **Anchors:** Joel Mokyr (mechanism); Simon Kuznets (measurement) **Date:** 2026-06-15 --- ## The contribution **Primary hypothesis (H1):** the three-sigma Mars landing-ellipse area contracts along an exponential, roughly log-linear learning curve driven primarily by onboard EDL-guidance technology, guided entry, the range trigger, and terrain-relative navigation (TRN), not by launch-vehicle injection accuracy. **Null hypothesis (H0):** ellipse contraction is unrelated to onboard EDL-guidance technology generation; any apparent learning curve is a generic time trend or is driven by approach navigation. This is a single falsifiable proposition with a fixed decision rule. The dissertation specifies the complete design to test it; the regression has not yet been executed. --- ## H1 and H0 stated exactly - **H1:** the three-sigma landing-ellipse semi-major axis (equivalently, ellipse area) for Mars surface missions declines along an exponential learning curve in which the dominant explanatory variables are onboard EDL-guidance technology generations (guided entry, range trigger, TRN), and in which launch-vehicle and interplanetary injection accuracy, once the standard approach-navigation corrections are accounted for, is not the binding constraint on ellipse size. - **H0:** ellipse contraction is unrelated to onboard EDL-guidance technology generation; the technology covariates carry no explanatory power once mission sequence or a time trend is included. The proposition predicts a specific sign and ordering of effects that the data can contradict. --- ## The problem - Every Mars surface mission commits, years before launch, to a landing ellipse: a three-sigma region inside which the vehicle is expected to touch down. - A large ellipse forces selection of bland, uniformly safe sites and excludes the best science; a small ellipse lets a project target a specific feature and accept local hazards. - The ellipse has contracted by more than two orders of magnitude: from Viking's hundreds of kilometers to a few kilometers of effective targeting for Mars 2020. - It is the most consequential number in Mars mission design, and it has never been treated as one measurable series. --- ## The gap - The EDL engineering literature documents each mission and each guidance technology in depth, but mission by mission, never as one series. - The technology-economics literature has a mature learning-curve apparatus for performance and cost metrics. - The two have never been joined. - No study fits a learning-rate model to the cross-mission ellipse series, or formally attributes the contraction to identifiable technology insertions while controlling for the rival explanation that vehicles are simply delivered to the atmosphere more accurately. --- ## Why it matters for NASA and JPL - **Requirements-setting:** read an expected ellipse off a given guidance suite, instead of negotiating the requirement qualitatively years before launch. - **Investment valuation:** compare the marginal precision return of TRN against approach navigation on a common quantitative basis. - **Honest extrapolation:** separate a genuine secular trend from a one-time level shift before a future architecture commits to a precision assumption. - Direct consumers: Mars Sample Return retrieval and the human-Mars EDL architecture studies. --- ## Theoretical framework: two anchors, not decoration - **Joel Mokyr (mechanism).** A learning curve is what extensibility looks like when a technique rests on a deep propositional base. Guided entry, the range trigger, and TRN are discrete additions to the prescriptive landing-technique base. This generates the decision to model technology generations as separate covariates rather than fit one smooth trend. - **Simon Kuznets (measurement).** An aggregate is meaningless without a stated boundary, valuation convention, and netting rule; decompose before theorizing; separate a level shift from a secular trend. This generates the decision to construct the series before fitting any slope. --- ## The three levers attack distinct error sources | Lever | Error source attacked | Mokyrian class | |---|---|---| | Guided lifting entry | Hypersonic downrange/crossrange dispersion | Macro-invention | | Range-to-go trigger | Parachute-deploy dispersion | Incremental | | Terrain-relative navigation | Position-knowledge error; enables divert | Macro-invention | Because the levers are physically separable, they are coded as three distinct indicators, not one index of modernity. Prediction: largest fit steps at guided entry (MSL) and TRN (Mars 2020), smaller at the range trigger. --- ## Data: three named public datasets - **NTRS landing-accuracy reconstructions:** the per-mission design ellipse and reconstructed performance (primary dependent variable). - **TechPort insertion records:** the flight on which each guidance technology first appeared (the three technology indicators), corroborated by the flight-reconstruction literature. - **PDS landing-site localization:** the achieved miss distance, an independent accuracy check on the design ellipse (secondary dependent variable). - All three are open access; no credential required. --- ## Population and unit of analysis - **Unit:** the mission landing event. - **Population:** U.S.-led successful Mars surface landings, Viking 1 (1976) through Mars 2020 (2021): a census of nine to eleven events, not a sample. - **Held out:** Tianwen-1 (2021) for external-validity discussion. - **InSight (2018)** is the pivotal case: a late mission that deliberately flew an unguided ballistic entry into a large ellipse. - The smallness of the sample is the central statistical-conclusion threat, and it is irreducible: only future missions enlarge it. --- ## The Kuznetsian measurement burden - The design ellipse is not a measurement; it is a simulation product whose conventions (sigma level, atmosphere model, Monte Carlo fidelity, target definition) drifted across forty-five years. - A naive regression of log area on mission sequence would conflate genuine capability gain with convention drift. - Mitigation: every value carries its sigma level and simulation-convention provenance; all values are normalized to a common three-sigma area; any value whose convention cannot be pinned down is carried with a provenance band, not silently harmonized. - Comparability: high for the modern missions, low for the Viking pair, which is reported with a with-and-without sensitivity check. --- ## The model **Baseline:** `ln(EllipseArea_i) = beta_0 + beta_1 * Sequence_i + epsilon_i` **Augmented:** `ln(EllipseArea_i) = beta_0 + beta_1*Sequence_i + gamma_1*GuidedEntry_i + gamma_2*RangeTrigger_i + gamma_3*TRN_i + delta*ApproachAccuracy_i + epsilon_i` - Log-linear OLS: the learning rate is `exp(beta_1) - 1`; the form is multiplicative, variance-stabilizing, and matches the physics of fractional error-source removal. - H1: the gamma terms are jointly significant and negative; delta is small and insignificant. --- ## Identification: where the leverage comes from Identification rests on two design features the historical record happens to contain, not on sample size: 1. **The InSight counterfactual.** A late mission with the calendar of MSL and Mars 2020 but the guidance of Viking and Phoenix. If contraction were a pure time trend, InSight should have inherited a small ellipse for free; it accepted a large one by design. Its residual from the trend is the central identifying quantity. 2. **The approach-accuracy control.** Holds constant the delivered entry-state dispersion, so any residual contraction loading on the technology indicators is net of launch and interplanetary navigation. The delta coefficient is the direct test of H0. The identification claim is exactly as strong, and as fragile, as the InSight case. --- ## The nested-specification hierarchy - The full augmented equation is over-parameterized for nine to eleven points; it is not fit as one multicollinear horse race. - Instead, technology generations are added one at a time, in frozen historical order, reporting incremental adjusted R-squared and an exact test on each added term. - This is the cliometric decomposition: attribute the aggregate contraction to its components in a stated order rather than asserting them jointly. - The order is pre-registered and cannot be reverse-engineered to a result. --- ## Threats to validity, paired with mitigations - **Internal (time-technology collinearity):** the InSight counterfactual and the approach-accuracy control; nested reporting exposes any residual confound. - **External (U.S.-Mars only):** Tianwen-1 and lunar precision landing are reference points, never in-sample evidence; confidence beyond the population is low. - **Construct (design ellipse vs achieved precision):** the PDS achieved-miss-distance series is the parallel dependent variable. - **Statistical-conclusion (n = 9 to 11):** permutation and exact inference, not asymptotic p-values. --- ## Pre-registered analysis plan 1. Assemble the ellipse series from NTRS, recording the simulation convention behind each value. 2. Compute log ellipse area and, separately, log achieved miss distance from PDS. 3. Code the three technology indicators from TechPort and the approach-accuracy control. 4. Fit baseline, then nested augmented specifications, with permutation-based inference. 5. Run the robustness battery: achieved-miss-distance DV, drop-InSight, program-as-experience-unit, linear-in-levels. The specifications, the order of entry, the decision rule, and the reporting are frozen before estimation. --- ## The fixed decision rule - **Support for H1** requires both: the gamma coefficients jointly significant and negative under the permutation test, and the delta on approach accuracy small and insignificant, surviving the drop-InSight and achieved-miss-distance re-fits in sign and ordering. - **Failure to reject H0:** the technology terms lose joint significance once the sequence trend or the approach control is present, or the approach control absorbs them, or the InSight residual sits on the trend. - **Tie-break (the likely small-sample case):** a correctly-signed but not jointly significant block is "consistent with but not confirming H1," with the InSight residual given decisive weight. The null is reported with the same prominence as a confirmation. --- ## Expected results (illustrative, design-stage) | Specification | Sequence | Technology terms | Approach control | |---|---|---|---| | Baseline | negative, large | none | not entered | | + Guided entry | smaller | negative | not entered | | + Range trigger | smaller | negative, small | not entered | | + TRN | smaller | negative, largest | not entered | | + Approach control | little changed | retain sign (H1) | small, insignificant (H1) | **Every value is illustrative. The regression has not been run on the assembled dataset. The results template is specified but, by design, unpopulated.** --- ## The decisive reading: the InSight residual - Under H1, InSight sits visibly above the fitted trend: a late mission that did not inherit a small ellipse because it lacked the guidance suite. - Under H0, InSight sits on the trend: time and generic maturation explain the contraction. - What InSight proves: it discriminates the technology hypothesis from the pure-time hypothesis. - What it does not prove: it cannot apportion credit among the three levers, because it lacks all three at once and is one point. - The drop-InSight re-fit measures exactly how much of the conclusion rests on this single case. --- ## Confidence and uncertainty - **The contraction is real and large:** very high confidence (it is the premise, not the inference). - **Under H1, onboard guidance is the dominant lever:** moderate confidence, set by small-n and collinearity; rises if the achieved-miss-distance series reproduces the contraction and the InSight residual sits above the trend; falls if the approach control absorbs the technology terms. - **Any single lever's separate rate:** low confidence by construction. - The strongest defensible claim is a signed, order-of-magnitude, counterfactual-surviving attribution, never a precise rate. The minimum detectable effect is large, and the design says so. --- ## Rival explanations, confronted not dismissed - **Pure time trend** (generic maturation): bounded by the InSight counterfactual. - **Approach accuracy** (this is H0 itself): bounded by the delivered-entry-state control; it may win, and that would be a finding, not a defeat. - **Site-selection endogeneity** (easier targets over time): partly the reverse of the truth, since later missions chose harder sites, and bounded by the achieved-miss-distance dependent variable, which is independent of site forgiveness. None is eliminated; all three are bounded, which is more than any single-mission study can claim. --- ## How the argument fits together **The thesis:** the ellipse contracted along a technology-attributed learning curve, and this dissertation specifies the falsifiable design to test it. | Step in the argument | Where | |---|---| | The problem is real | Ch. 1, 3, 4 | | The problem is material | Ch. 1, 3, 7 | | The design addresses the causal mechanism | Ch. 2, 4, 5 | | The design discriminates the technology account from its rivals | Ch. 5, 6, 7 | | The residual risk is acceptable | Ch. 5, 6, 8 | **Residual risk:** identification leans on one observation (InSight); the lever apportionment is weakly identified; the earliest ellipses are provenance-fragile. Bounded, not eliminated; the design is informative whichever way the coefficient falls. --- ## Scope decision: no architecture traceability - The contribution is a cliometric measurement-and-attribution account of a constructed performance series, not the design of a real capability, system, or data exchange. - A formal architecture traceability (strategic objective to capability to system function to data exchange to measure to decision) is deliberately omitted. - The decision relevance, requirements-setting and investment valuation, is carried in plain prose, not forced into a capability-architecture vocabulary the contribution does not concern. --- ## What holds even if H1 is rejected - **A defined measurement:** log of three-sigma ellipse area, with provenance, and a parallel achieved-miss-distance construct, where the literature had only mission-by-mission numbers. - **A stated boundary:** the population, the experience axis, the held-out case, all fixed in advance. - **A falsifiable hypothesis:** a specific sign and ordering the data can refute, where the literature offered only narrative. If H0 wins, the dissertation establishes that the contraction is generic maturation or delivery-driven, which redirects where a future program should invest. The design is informative either way. --- ## Contribution, restated - The novelty is not that landings grew more precise (well documented), nor a new guidance algorithm. - It is the joining of two literatures: the EDL engineering record and the technology-economics learning-curve apparatus, into one constructed series, fitted with a learning-rate model, with the contraction attributed to identifiable technology insertions under Mokyr's mechanism and Kuznets's measurement discipline. - Executed, it gives NASA and JPL a quantitative, technology-attributed basis for landing-accuracy requirements and guidance-investment valuation. - Not executed, it still contributes a defined measurement, a stated boundary, and a falsifiable hypothesis. --- ## Defense questions invited - Is mission sequence the right experience axis, or should it be cumulative landings or calendar time? - With nine observations, what inference do you actually trust, and how much rests on the single InSight case? - How comparable are ellipse definitions across missions, given changing simulation conventions? - Could site-selection endogeneity mask or mimic the learning curve? - What is the smallest result that would still count as confirming the contribution? --- ## Selected references - Steltzner et al. (2007), MSL EDL System Performance [S01]; Way (2011), range trigger for MSL EDL [S05]; Johnson et al. (2022), Mars 2020 Lander Vision System Flight Performance [S08]. - Golombek et al. (2016), Selection of the InSight Landing Site [S15]; Karlgaard et al. (2007), Statistical Reconstruction of Mars EDL Trajectories [S07]. - Alberth (2008), experience-curve forecasting [S18]; Ziegler and Trancik (2021), lithium-ion improvement rates [S19]. - Mokyr dossier, propositional vs prescriptive knowledge [S23]; Kuznets dossier, boundary-valuation-netting measurement [S24]. Full reference list (130 entries, all with resolvable DOI/URL) in the dissertation backmatter.