Technical evaluation · for FMS / avionics engineers
A mathematical rail for the sky.
For trajectory-management engineers at airframers, operators and avionics suppliers evaluating en-route fuel, comfort and after-action posture. The patent's Subsystem D-2 claims a pre-laid medium-map database (M t ) acting as a "mathematical rail" the aircraft follows. Below we run a 200 km en-route segment through a synthetic Lamb-vortex turbulence field with two autopilots — blind great-circle vs M t -aware path planner — and seal each M t snapshot into an HMAC transition chain. All numbers from a reproducible Python pipeline.
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§0 · Reader's note — what is and is not claimed
Two independent value props on this page. Evaluate them separately.
(1) Turbulence-aware routing primitive (§3 – §4). That a pre-laid medium-map M t + α-blended memory hop produces a usable "rail" through a turbulence field. The trajectory comparison in §3 is against a blind great-circle baseline — a deliberately weak reference that isolates the planner from confounding gains. Modern production flight management (FMS + cost-index + WAFS turbulence grids + ATC-mediated re-clearance) is a much stronger baseline against which the marginal value of the M t rail must be measured in a pilot. See §3 caveat and §8 limitations.
(2) Tamper-evident flight-history chain (§5 – §7). The FPGA-PUF sealed transition hash chain + multi-party offline verification is independent of which planner produced M t . It bolts onto today's FMS, tomorrow's AI-planner, or any third-party trajectory stack and still gives operator / met-service / accident investigator a cryptographically-verifiable atmospheric annotation of every minute of flight. This is the primary licensable portfolio asset.
An operator who is sceptical of (1) on toy-simulator grounds can still adopt (2) standalone.
⚡ Signal / Data Restoration
Turbulence-corrupted measurements → atmospheric M t rail recovered.
Patent core claim: "recover original modal information from broken received signal via medium forward model + integrity-anchored prior" . Eight Lamb-Oseen vortices corrupt raw sensor reads along a 200 km en-route segment. The atmospheric forward model + α-blended memory hop reconstructs the underlying field for a 50 km look-ahead slab planner — 35.6% fuel reduction + 35.4% comfort improvement vs. great-circle. Multi-party verifier (operator / met-service / investigator).
§1 · Why a trajectory-management team should read this
Three value axes: fuel, comfort, and tamper-evident flight history.
A 200-km en-route segment through a moderate-turbulence field shows two effects. First, an autopilot that knows the medium-map M t ahead can deviate around high-intensity cells — fuel and passenger comfort improve by tens of percent at no airframe-level cost. Second, every M t snapshot is signed inside an FPGA and chained, so the flight's atmospheric history becomes audit-grade evidence for after-action review, weather-service validation, and incident investigation.
En-route fuel
Routing around turbulence pockets reduces drag-equivalent fuel consumption — measured 35 % on the synthetic 200-km segment below.
Passenger comfort
RMS lateral acceleration drops in proportion to time spent inside turbulence cores — direct correlate of seat-belt-sign minutes.
After-action / incident review
Sealed M t chain replaces "we trust the FDR" with "we cryptographically verify the FDR's atmospheric annotations".
Weather-service validation
Operator and meteorological service can independently verify the chain — settles "was the forecast wrong or the routing wrong?" disputes.
§2 · Experimental setup
2-D point-mass, 200-km en-route, eight Lamb vortices.
We use a 2-D top-down model deliberately — no 6-DOF rigid-body, no flight-dynamics integration with JSBSim / X-Plane, no FAA-grade turbulence model. The point is to isolate the trajectory-planning primitive (the rail of Subsystem D-2) from confounding gains from a production autopilot, weather service, or FMS. Porting onto a higher-fidelity sim is straightforward and is the next step of any pilot.
Domain
200 km along-track × 80 km cross-track, en-route segment at fixed altitude
Aircraft
2-D point mass, 70 t (narrowbody class), cruise 240 m/s (~ Mach 0.8), max heading slew 3°/s
Turbulence field
8 Lamb-Oseen vortex cores (Γ ≈ 1.2 – 2.0 × 10⁶ m²/s, core radius 4.5 – 7.5 km), slow time drift, plus a sinusoidal thermal band
Sensor
Forward-looking cone, 30 km range, ±15° FOV, 40 samples / scan, σ = 0.06 noise on relative intensity
Integration step
5 s — en-route resolution, fine enough for path replanning
Blind autopilot
Great-circle direct to destination — no air-field knowledge
M t -aware autopilot
Noisy a-priori medium map (σ = 0.18 per cell) refined in real time by the forward sensor; planner minimises integrated turbulence over the next 50 km slab
Memory hop weight
α mem = 0.30 — operator trusts 30 % in each new sensor sample, 70 % in the propagated map
§3 · Trajectory comparison
Same field, same noise, two autopilots. The rail is visible.
Both autopilots receive identical sensor noise streams and fly through the identical turbulence field. The only difference is the M t -aware autopilot's access to the pre-laid medium-map database. The blue trajectory is the "rail" predicted by the patent.
Metric
Blind great-circle
Modern FMS + WAFS †
M t -aware (this work)
Relative cruise fuel (arb. units, ×10⁶)
60.7
~ 42 – 46 (est.)
39.1
RMS lateral acceleration (m/s²)
0.590
~ 0.44 – 0.48 (est.)
0.382
Segment time (s)
≈ 850
≈ 855 – 865 (est.)
≈ 870
Time inside high-intensity cells
~ 45 % of flight
~ 12 – 18 % (est.)
~ 6 % of flight
Δ vs blind great-circle
~ 25 – 30 % (FMS baseline)
−35.6 % fuel / −35.4 % comfort
Δ vs modern FMS + WAFS
~ 7 – 15 % (modal marginal)
† The blind-great-circle baseline is the weakest reference, not the production reference. Modern commercial flight uses FMS + cost-index optimisation + WAFS turbulence grids + ATC-mediated re-clearance and already captures most of the easy turbulence avoidance. The middle column is a published-literature estimate of what a modern FMS recovers (Pejovic / ICAO data suggests 25 – 30 % fuel and comfort improvement over great-circle on representative routes). Our marginal value vs modern FMS — the number a Tier-1 avionics evaluator actually cares about — is the ~ 7 – 15 % range in the last row, and it must be measured in a JSBSim / X-Plane pilot with the OEM's actual FMS in the loop. The headline 35 % figure should be read as "vs the deliberately weak reference," not "vs production."
Fuel accounting here is drag-equivalent (proxy units); a production engine model is needed to translate to kg-of-Jet-A figures. The +2.4 % segment-time increase is a deliberate planner trade — the cost-index analogue that a real FMS exposes as a tunable knob.
§3.5 · 4-class severity classification under sensor noise
Before deciding the route, decide which severity bracket you're in.
A complementary view of the same problem: classify each 200 km segment as smooth / light / moderate / severe so that dispatch and air-traffic systems can route around or coordinate diverts. Receiver A is the NOAA-style gridded-wind statistics baseline (mean, std, peak gust) — what most current EFB / dispatch tools use. Receiver B is the 6-coefficient Chladni modal projection of the full 200 km × 30 km M t slab. Same LDA classifier; only the feature representation differs.
Fig. — Modal + sealed prior holds 94 – 98% across the clean-to-moderate SNR regime, with smaller gains at very low SNR. Where it matters most for routing decisions (0 to +10 dB sensor SNR), B is +7 to +9 pp ahead.
SNR (dB)
Receiver A — NOAA grid stats
Receiver B — modal + sealed prior
85.7%
94.4%
+8.8 pp
87.6%
95.0%
+7.4
89.9%
98.2%
+8.3
91.6%
98.1%
+6.5
71.2%
74.6%
+3.4
Fig. — Wind-speed M t fields for each severity class with both autopilots' planned trajectories overlaid. The slab-planner steers around vortex cores; the great-circle does not.
Numbers from running the published Python pipeline: 200 km × 30 km atmospheric slab with 2 – 13 Lamb-Oseen vortices per scenario, severity-driven by vortex-to-track proximity. 300 scenarios per class per SNR. Both classifiers use LDA on an SNR-mixed training set. Reproducible from fixed seeds.
§4 · Memory hop · M t map evolution
The rail gets sharper as the flight progresses.
Each sensor scan refines the operator's medium map via an exponential blend. By mid-flight the M t map closely matches the ground-truth turbulence field ahead; by late flight the entire en-route segment is well-localized. This is the "rail-pre-laid" loop: successive flights feed back into the database that informs the next flight's planner.
predict : M̂ t|t−1 (x, y) = M̂ t−1 (x, y) (slow field, no propagation model) update : M̂ t (x, y) = (1 − α mem ) · M̂ t|t−1 (x, y) + α mem · s t (x, y) (where sensor observes (x, y)) plan : τ̂ k = argmin y ⟨M̂ t ⟩ slab (y) + λ |y − y now | (50 km look-ahead slab)
§5 · Sealed flight history
Each M t is signed by an FPGA-resident PUF key, then chained.
One M t snapshot per minute, HMAC-SHA256 signed against the previous transition hash with a key derived from a PUF inside an FPGA. A 10 % alteration to a single cell in any historical snapshot breaks every downstream signature — both the operator and the meteorological service can independently verify offline.
Fig. — 14-minute flight chain. 10 % alteration to M 6 in storage: 6 / 14 links validate (clean baseline = 14 / 14). All H k for k ≥ 6 reject.
σ t = HMAC K PUF (H t−1 ‖ M t )
H t = SHA256(H t−1 ‖ M t ‖ σ t )
verify HMAC K PUF (H t−1 ‖ M t ) ≟ σ t ∀ t
MAC primitive
HMAC-SHA256, 256-bit PUF-derived key
Key custody
AWS F2 FPGA (AFI agfi-085919c09c35982c3 ) in the lab today; production target = a DAL-A-certified card in the IMA cabinet
FDR / QAR integration
Each sealed M t persisted in the QAR data stream alongside the existing parameters; FDR-grade compatibility
Tamper sensitivity (measured)
10 % change to a single cell → 100 % of downstream links reject
Multi-party verification
Operator, meteorological service, and accident investigator each hold the public verification key
§6 · Operational scenarios
Where the rail pays back.
Commercial en-route
Long-haul carriers — a 3 % fuel reduction across a fleet rolls up to nine-figure annual savings. The rail compounds over years as the M t database grows.
NTSB / AAIB / ARAIB
Accident investigators get a cryptographically-sealed atmospheric narrative — closes the gap between "FDR says we hit turbulence" and "we can verify the operator knew".
Defense / contested airspace
EW spoofing of mid-air weather services would today silently degrade routing; the chain detects it and falls back to sensor-only.
eVTOL / urban air mobility
Microweather inside a city corridor changes per-flight. The rail database, built up by the fleet, gives a fresh per-flight M t the FMS can plan against.
Drone fleets
Delivery / surveillance UAS already share telemetry; signing each M t turns that shared telemetry into adversary-resistant evidence and prevents weather-poisoning attacks.
Insurance / re-insurance
Hull and passenger-liability underwriters can price flights based on chain-verified turbulence exposure rather than ex-post reporting alone.
ATC integration
The chain is small enough (≪ 1 kB per snapshot) to ride existing CPDLC data-link channels; ATC and operator share the same M t ground truth.
FMS / autopilot upgrade
The planner attaches downstream of the existing FMS as a Flight-Path Optimiser; no change to the certified autopilot itself.
§7 · Integration paths
Three deployment shapes.
In-FMS optimiser
Onboard FMS module that consumes the M t database via ACARS / SwiftBroadband / Inmarsat link. Tight integration with autopilot. DAL-A path, longer cycle.
Operations-centre optimiser
Dispatcher-side planning service that publishes signed route advisories. No avionics-cert impact; suitable for retrofit. Pairs naturally with cabin-Wi-Fi turbulence-warning apps.
Black-box log signer
Sealed M t records produced alongside existing FDR / QAR data. The chain integrates with whichever planner the operator uses (or none).
Standards alignment
ARINC 718A (flight-data acquisition), ICAO Annex 6 (operations), Annex 13 (accident investigation), DO-178C / DO-254 for any avionics path
Licensing model
Per-aircraft IP block, per-fleet software license, or per-flight-hour optimiser-as-a-service — negotiated via the lead financial advisor
§8 · Honest limitations
What this page does not show.
2-D point mass. No 6-DOF rigid-body, no banked-turn dynamics, no propulsion model, no fuel-flow integration with engine thrust. Production planners need a 6-DOF simulator (JSBSim, X-Plane, or the airframer's own) before any fuel claim can be defended in absolute kg-of-Jet-A.
Synthetic Lamb-vortex turbulence field. A handful of analytic vortices is a stylised stand-in for a real atmospheric turbulence field. Pilot studies on NOAA/ECMWF turbulence forecasts or operator-supplied in-situ EDR datasets are the right next step.
The sensor is an abstraction. In practice the "forward-looking sensor" maps onto Ka-band weather radar, LIDAR clear-air-turbulence sensors, or in-situ EDR reports from preceding aircraft. The numbers here will shift in either direction with a more realistic sensor budget.
Path planner is a 1-D slab argmin. The §3 / §4 planner picks one cross-track value per replanning interval. A production planner would do RRT* or sample-based optimisation with banking constraints. The chain primitive is independent of the planner choice.
FPGA is software-emulated in this demo. The chain in §5 is computed in Python against the same PUF-key constant the real FPGA uses. A separate program of work has the same HMAC running on an AWS F2 FPGA AFI. A DAL-A certified target is the production deployment.
Chain content vs chain attestation. The chain attests which M t was produced when . It does not encrypt the field map nor attest to crew or platform identity. Identity binding and confidentiality are separate primitives that stack on top.
No simultaneous traffic. A real en-route environment has other aircraft, ATC constraints, and dynamic SUAs. Multi-aircraft separation and conformance to ATC routing is out of scope for this page.
§9 · For your flight-management team
Run it on your own segments.
The Python pipeline that produced every figure on this page is available under NDA. The recommended first step is to repeat §3 against your operator-specific EDR / CIT-radar data — replace the Lamb-vortex field with a real-data raster and re-measure fuel and comfort deltas against your in-house planner. The chain primitive (§5) is field-independent and can be evaluated separately from the planner work.
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