{"slug": "saving-jet-fuel", "title": "Saving Jet Fuel", "summary": "Airbus's open-source Scikit-decide framework, developed over six years, can optimize flight paths to cut jet fuel consumption, potentially saving a few thousand dollars on a Boeing 787-9 Newark-to-Rome flight that would otherwise burn roughly $68,000 in fuel over 8.5 hours. The framework pairs with the OpenAP aircraft performance model built by Dr. Junzi Sun, a tenured assistant professor at Delft University of Technology, and NOAA wind data to solve optimal routes, and can also reorganize airline workforce schedules and calculate drone swarm paths. The write-up compares two flight paths flown using the Airbus A320 and OpenAP's fuel consumption model, with Scikit-decide version 1.1.1 installed alongside OpenAP and OpenTop 2.6.0.", "body_md": "A Boeing 787-9 Dreamliner flying nonstop from Newark Liberty International Airport (EWR) to Leonardo da Vinci-Fiumicino Airport (FCO) could need $68K in jet fuel over the 8.5-hour flight. Adjusting the flight path for wind conditions could reduce fuel consumption and possibly save a few thousand dollars.\n\nFirms like Jeppesen have offerings in this space, but [Scikit-decide](https://airbus.github.io/scikit-decide), together with a narrow- and wide-body fuel consumption model built by a professor at the Delft University of Technology and wind data from NOAA, offer an open source solution.\n\nScikit-decide has been in development for six years. It's a framework for reinforcement learning, automated planning and scheduling. The project can optimise flight paths, re-organise airline workforce schedules and calculate drone swarm paths.\n\n[OpenAP](https://openap.dev/) is an aircraft performance model and toolkit developed by Dr. Junzi Sun. Dr. Sun has a PhD in air traffic management and, among many other things, teaches a course on the subject as a tenured assistant professor at TU Delft in the Netherlands.\n\nScikit-decide's optimal flight path solver can be configured to use different fuel consumption models. In this post, I'll compare two flight paths flown using the Airbus A320 and OpenAP's fuel consumption model.\n\n## My Workstation\n\nI'm using a 5.7 GHz AMD Ryzen 9 9950X CPU. It has 16 cores and 32 threads and 1.2 MB of L1, 16 MB of L2 and 64 MB of L3 cache. It has a liquid cooler attached and is housed in a spacious, full-sized Cooler Master HAF 700 computer case.\n\nThe system has 96 GB of DDR5 RAM clocked at 4,800 MT/s and a 5th-generation, Crucial T700 4 TB NVMe M.2 SSD which can read at speeds up to 12,400 MB/s. There is a heatsink on the SSD to help keep its temperature down. This is my system's C drive.\n\nThe system is powered by a 1,200-watt, fully modular Corsair Power Supply and is sat on an ASRock X870E Nova 90 Motherboard.\n\nI'm running Ubuntu 24 LTS via Microsoft's Ubuntu for Windows on Windows 11 Pro. In case you're wondering why I don't run a Linux-based desktop as my primary work environment, I'm still using an Nvidia GTX 1080 GPU which has better driver support on Windows and ArcGIS Pro only supports Windows natively.\n\n## Installing Prerequisites\n\nI'll use Python 3.12 along with jq in this post.\n\n``` bash\n$ sudo add-apt-repository ppa:deadsnakes/ppa\n$ sudo apt update\n$ sudo apt install \\\n jq \\\n python3-pip \\\n python3.12-venv\n```\n\nI'll set up a Python Virtual Environment and install scikit-decide, along with the OpenAP open aircraft performance model and OpenTop, a flight trajectory toolkit that was also developed by Dr. Sun.\n\n``` bash\n$ python3 -m venv ~/.flight_planning\n$ source ~/.flight_planning/bin/activate\n$ pip install \\\n 'scikit-decide[all]' \\\n 'openap[all]' \\\n opentop\n```\n\nThe above will need at least 8 GB of storage capacity. These are the packages that were installed.\n\n``` bash\n$ pip install pipdeptree\n$ pipdeptree -d0\nlz4==4.4.5\nopenevolve==0.3.2\nopentop==2.6.0\npip==24.0\npipdeptree==4.2.5\nplado==0.1.6\npygeodesy==26.9.9\npygrib==2.1.8\npyRDDLGym-gurobi==0.2\npyRDDLGym-jax==3.1\npyRDDLGym-rl==0.2\npytz==2026.3.post1\nray==2.37.0\nrddlrepository==2.2\nsb3_contrib==2.3.0\nscikit-decide==1.1.1\nscikit-image==0.26.0\ntensorboardX==2.6.5\ntorch-geometric==2.8.0.post1\ntyper==0.27.2\nunified-planning==1.2.0\nup-enhsp==0.0.27\nup_fast_downward==0.5.2\nup-pyperplan==1.1.0\nz3-solver==5.1.0.0\n```\n\nI'll use DuckDB, along with its [H3](https://github.com/isaacbrodsky/h3-duckdb), [JSON](https://duckdb.org/docs/extensions/json), [Lindel](https://community-extensions.duckdb.org/extensions/lindel.html), [Parquet](https://duckdb.org/docs/data/parquet/overview) and [Spatial](https://duckdb.org/docs/extensions/spatial.html) extensions in this post.\n\n``` bash\n$ cd ~\n$ wget -c https://github.com/duckdb/duckdb/releases/download/v1.5.4/duckdb_cli-linux-amd64.zip\n$ unzip -j duckdb_cli-linux-amd64.zip\n$ chmod +x duckdb\n$ ~/duckdb\nINSTALL h3 FROM community;\nINSTALL lindel FROM community;\nINSTALL json;\nINSTALL parquet;\nINSTALL spatial;\n```\n\nI'll set up DuckDB to load every installed extension each time it launches.\n\n``` bash\n$ vi ~/.duckdbrc\n.timer on\n.width 180\nLOAD h3;\nLOAD lindel;\nLOAD json;\nLOAD parquet;\nLOAD spatial;\n```\n\nThe maps in this post were rendered with [QGIS](https://www.qgis.org/en/site/forusers/download.html) version 4.2.1. QGIS is a desktop application that runs on Windows, macOS and Linux. The application has grown in popularity in recent years and has ~22M application launches from users all around the world each month.\n\nThe boundaries and place names were sourced from [Natural Earth](natural-earth-free-gis-data.html). Maritime Boundaries were sourced from [Marine Regions](https://marineregions.org/downloads.php).\n\n## OpenAP's Aircraft Types\n\nI'll first clone the OpenAP repository.\n\n``` bash\n$ git clone https://github.com/junzis/openap\n```\n\nExcluding unit tests and utility scripts, there are 3,369 lines of Python in this package.\n\nOpenAP's model relies on a large number of datasets that are packaged with its codebase. These cover a wide variety of aircraft. Below are the aircraft manufacturer counts.\n\n``` bash\n$ grep -ho 'aircraft: .*[a-z] ' \\\n openap/data/aircraft/*.yml \\\n | cut -d' ' -f2 \\\n | sort \\\n | uniq -c \\\n | sort -rn\n17 Boeing\n13 Airbus\n 5 Embraer\n 1 Gulfstream\n 1 Cessna\n```\n\nThese are the properties for the Airbus A380-800.\n\n``` bash\n$ cat openap/data/aircraft/a388.yml\naircraft: Airbus A380-800\n\nmtow: 560000\nmlw: 386000\noew: 277000\nmfc: 320000\nvmo: 340\nmmo: 0.89\nceiling: 13100\n\npax:\n max: 853\n low: 410\n high: 620\n\nfuselage:\n length: 72.72\n height: 8.41\n width: 7.14\n\nwing:\n area: 845\n span: 79.75\n mac: null\n sweep: 33.5\n t/c: 0.08\n\nflaps:\n type: single-slotted\n area: null\n bf/b: null\n lambda_f: 0.900\n cf/c: 0.150\n Sf/S: 0.150\n\ncruise:\n height: 12800\n mach: 0.85\n range: 14800\n\nengine:\n type: turbofan\n mount: wing\n number: 4\n default: GP7270\n options:\n A380-841: Trent 970-84\n A380-842: Trent 972-84\n A380-861: GP7270\n\ndrag:\n cd0: 0.016\n k: 0.050\n e: 0.855\n gears: 0.012\n```\n\nThese are its drag coefficients.\n\n``` bash\n$ cat openap/data/dragpolar/a388.yml\naircraft: Airbus A380-800\n\nclean:\n cd0: 0.016\n k: 0.050\n e: 0.855\n\ngears: 0.012\n\nflaps:\n lambda_f: 0.900\n cf/c: 0.150\n Sf/S: 0.150\n```\n\nThese are some additional properties.\n\n``` python\n$ echo \"import pandas as pd; print(\n pd.read_fwf('openap/data/wrap/a388.txt')\n .to_csv(index=False))\" \\\n | python3 \\\n | ~/duckdb \\\n -c '.maxwidth 150' \\\n -c \"SELECT * EXCLUDE(parameters),\n parameters: SPLIT(parameters, '|')\n FROM READ_CSV('/dev/stdin')\"\n┌──────────────────────┬────────────────┬───────────────────────────────────────┬────────┬────────┬─────────┬─────────┬──────────────────────────────┐\n│ variable │ flight phase │ name │ opt │ min │ max │ model │ parameters │\n│ varchar │ varchar │ varchar │ double │ double │ double │ varchar │ varchar[] │\n├──────────────────────┼────────────────┼───────────────────────────────────────┼────────┼────────┼─────────┼─────────┼──────────────────────────────┤\n│ to_v_lof │ takeoff │ Liftoff speed │ 89.9 │ 75.4 │ 104.4 │ norm │ [89.93, 10.07] │\n│ to_d_tof │ takeoff │ Takeoff distance │ 2.56 │ 1.35 │ 3.78 │ norm │ [2.56, 0.74] │\n│ to_acc_tof │ takeoff │ Mean takeoff accelaration │ 1.35 │ 1.04 │ 1.66 │ norm │ [1.35, 0.19] │\n│ ic_va_avg │ initial_climb │ Mean airspeed │ 88.0 │ 80.0 │ 96.0 │ norm │ [88.15, 5.64] │\n│ ic_vs_avg │ initial_climb │ Mean vertical rate │ 5.65 │ 4.4 │ 8.94 │ gamma │ [4.76, 3.22, 0.65] │\n│ cl_d_range │ climb │ Climb range │ 296.0 │ 200.0 │ 446.0 │ beta │ [3.23, 5.18, 179.46, 335.24] │\n│ cl_v_cas_const │ climb │ Constant CAS │ 163.0 │ 155.0 │ 170.0 │ norm │ [163.39, 4.51] │\n│ cl_v_mach_const │ climb │ Constant Mach │ 0.84 │ 0.8 │ 0.86 │ beta │ [12.23, 5.32, 0.72, 0.17] │\n│ cl_h_cas_const │ climb │ Constant CAS crossover altitude │ 3.3 │ 1.3 │ 5.3 │ norm │ [3.29, 1.24] │\n│ cl_h_mach_const │ climb │ Constant Mach crossover altitude │ 8.9 │ 8.2 │ 9.7 │ norm │ [8.94, 0.47] │\n│ cl_vs_avg_pre_cas │ climb │ Mean climb rate, pre-constant-CAS │ 7.85 │ 5.95 │ 9.75 │ norm │ [7.85, 1.16] │\n│ cl_vs_avg_cas_const │ climb │ Mean climb rate, constant-CAS │ 7.51 │ 5.2 │ 9.82 │ norm │ [7.51, 1.40] │\n│ cl_vs_avg_mach_const │ climb │ Mean climb rate, constant-Mach │ 5.56 │ 3.23 │ 7.91 │ norm │ [5.57, 1.42] │\n│ cr_d_range │ cruise │ Cruise range │ 4348.0 │ 892.0 │ 20565.0 │ gamma │ [2.81, 246.73, 2274.81] │\n│ cr_v_cas_mean │ cruise │ Mean cruise CAS │ 136.0 │ 130.0 │ 145.0 │ beta │ [3.32, 5.27, 126.00, 29.75] │\n│ cr_v_cas_max │ cruise │ Maximum cruise CAS │ 145.0 │ 134.0 │ 164.0 │ beta │ [2.02, 3.21, 130.38, 46.65] │\n│ cr_v_mach_mean │ cruise │ Mean cruise Mach │ 0.84 │ 0.82 │ 0.86 │ norm │ [0.84, 0.01] │\n│ cr_v_mach_max │ cruise │ Maximum cruise Mach │ 0.87 │ 0.85 │ 0.9 │ gamma │ [16.14, 0.80, 0.00] │\n│ cr_h_init │ cruise │ Initial cruise altitude │ 11.55 │ 9.3 │ 12.23 │ beta │ [3.82, 1.66, 7.49, 5.01] │\n│ cr_h_mean │ cruise │ Mean cruise altitude │ 11.73 │ 10.87 │ 12.28 │ beta │ [7.22, 3.92, 9.59, 3.14] │\n│ cr_h_max │ cruise │ Maximum cruise altitude │ 12.06 │ 11.52 │ 12.6 │ norm │ [12.06, 0.33] │\n│ de_d_range │ descent │ Descent range │ 310.0 │ 238.0 │ 528.0 │ gamma │ [4.73, 213.47, 25.87] │\n│ de_v_mach_const │ descent │ Constant Mach │ 0.83 │ 0.8 │ 0.87 │ norm │ [0.83, 0.02] │\n│ de_v_cas_const │ descent │ Constant CAS │ 154.0 │ 142.0 │ 167.0 │ norm │ [154.84, 7.74] │\n│ de_h_mach_const │ descent │ Constant Mach crossover altitude │ 10.1 │ 8.6 │ 11.5 │ norm │ [10.06, 0.88] │\n│ de_h_cas_const │ descent │ Constant CAS crossover altitude │ 6.6 │ 3.9 │ 9.4 │ norm │ [6.64, 1.69] │\n│ de_vs_avg_mach_const │ descent │ Mean descent rate, constant-Mach │ -6.06 │ -11.9 │ -2.97 │ beta │ [3.43, 2.08, -15.98, 14.36] │\n│ de_vs_avg_cas_const │ descent │ Mean descent rate, constant-CAS │ -8.36 │ -11.74 │ -4.97 │ norm │ [-8.36, 2.06] │\n│ de_vs_avg_after_cas │ descent │ Mean descent rate, after-constant-CAS │ -5.48 │ -6.93 │ -4.02 │ norm │ [-5.48, 0.88] │\n│ fa_va_avg │ final_approach │ Mean airspeed │ 73.0 │ 68.0 │ 77.0 │ norm │ [73.28, 3.02] │\n│ fa_vs_avg │ final_approach │ Mean vertical rate │ -3.71 │ -4.13 │ -2.92 │ gamma │ [9.49, -4.74, 0.12] │\n│ fa_agl │ final_approach │ Approach angle │ 2.9 │ 2.42 │ 3.38 │ norm │ [2.90, 0.29] │\n│ ld_v_app │ landing │ Touchdown speed │ 70.0 │ 62.1 │ 78.0 │ norm │ [70.00, 5.52] │\n│ ld_d_brk │ landing │ Braking distance │ 2.26 │ 0.73 │ 3.8 │ norm │ [2.26, 0.93] │\n│ ld_acc_brk │ landing │ Mean braking acceleration │ -1.01 │ -1.51 │ -0.52 │ norm │ [-1.01, 0.30] │\n└──────────────────────┴────────────────┴───────────────────────────────────────┴────────┴────────┴─────────┴─────────┴──────────────────────────────┘\n```\n\nThese are the aircraft type synonyms list.\n\n```\n$ ~/duckdb -c \"FROM READ_CSV('/dev/stdin')\" \\\n < openap/data/aircraft/_synonym.csv\n┌─────────┬─────────┐\n│ orig │ new │\n│ varchar │ varchar │\n├─────────┼─────────┤\n│ a124 │ b744 │\n│ a306 │ a332 │\n│ a310 │ a318 │\n│ at72 │ e145 │\n│ at75 │ e145 │\n│ at76 │ e145 │\n│ b733 │ b734 │\n│ b735 │ b734 │\n│ b762 │ b763 │\n│ b77l │ b77w │\n│ c25a │ c550 │\n│ c525 │ c550 │\n│ c56x │ c550 │\n│ crj2 │ e145 │\n│ crj9 │ e75l │\n│ e290 │ e190 │\n│ glf5 │ glf6 │\n│ gl5t │ glf6 │\n│ lj45 │ glf6 │\n│ md11 │ b773 │\n│ pc24 │ c550 │\n│ su95 │ e170 │\n└─────────┴─────────┘\n```\n\n## Aircraft Engines\n\nAircraft often have the option of at least two different engines to choose from. There are 427 engines listed in this package's dataset.\n\n``` bash\n$ wc -l openap/data/engine/engines.csv # 427\n```\n\nThese are the details for the Trent 970-84.\n\n``` bash\n$ echo \"FROM 'openap/data/engine/engines.csv'\n WHERE name = 'Trent 970-84'\n LIMIT 1\" \\\n | ~/duckdb -json \\\n | jq -S .\n[\n {\n \"bpr\": 8.45,\n \"cruise_alt\": null,\n \"cruise_mach\": null,\n \"cruise_sfc\": null,\n \"cruise_thrust\": null,\n \"ei_co_app\": 1.16,\n \"ei_co_co\": 0.31,\n \"ei_co_idl\": 13.38,\n \"ei_co_to\": 0.32,\n \"ei_hc_app\": 0.08,\n \"ei_hc_co\": 0.12,\n \"ei_hc_idl\": 0.04,\n \"ei_hc_to\": 0.02,\n \"ei_nox_app\": 12.09,\n \"ei_nox_co\": 29.42,\n \"ei_nox_idl\": 5.44,\n \"ei_nox_to\": 38.29,\n \"ff_app\": 0.72,\n \"ff_co\": 2.157,\n \"ff_idl\": 0.255,\n \"ff_to\": 2.605,\n \"fuel_lto\": 965.0,\n \"manufacturer\": \"Rolls-Royce plc\",\n \"max_thrust\": 338700.0,\n \"name\": \"Trent 970-84\",\n \"pr\": 38.0,\n \"type\": \"TF\",\n \"uid\": \"18RR081\"\n }\n]\n```\n\nThese are the engine manufacturer counts.\n\n```\n$ ~/duckdb\nCREATE OR REPLACE TABLE a AS\n FROM 'openap/data/engine/engines.csv';\n\nSELECT COUNT(*),\n manufacturer\nFROM a\nGROUP BY 2\nORDER BY 1 DESC;\n┌──────────────┬────────────────────────────┐\n│ count_star() │ manufacturer │\n│ int64 │ varchar │\n├──────────────┼────────────────────────────┤\n│ 108 │ GE Aircraft Engines │\n│ 94 │ CFM International │\n│ 85 │ Pratt & Whitney │\n│ 62 │ Rolls-Royce plc │\n│ 13 │ International Aero Engines │\n│ 12 │ Pratt & Whitney Canada │\n│ 11 │ Rolls-Royce Corporation │\n│ 8 │ Rolls-Royce Deutschland │\n│ 8 │ Honeywell │\n│ 7 │ Aviadvigatel │\n│ 5 │ Textron Lycoming │\n│ 4 │ KKBM │\n│ 3 │ IVCHENKO PROGRESS ZMBK │\n│ 2 │ PowerJet S.A. │\n│ 2 │ Allied Signal │\n│ 1 │ Engine Alliance │\n│ 1 │ Garret AiResearch │\n└──────────────┴────────────────────────────┘\n```\n\nThese are the engine-type counts for Turbofan (TF), Mixed-flow Turbofan (MTF), Turboprop (TP) and Piston (PS) engines in this dataset.\n\n```\nSELECT COUNT(*),\n type\nFROM a\nGROUP BY 2\nORDER BY 1 DESC;\n┌──────────────┬─────────┐\n│ count_star() │ type │\n│ int64 │ varchar │\n├──────────────┼─────────┤\n│ 322 │ TF │\n│ 98 │ MTF │\n│ 5 │ TP │\n│ 1 │ PS │\n└──────────────┴─────────┘\n```\n\nThis is the engine list ranked by their maximum thrust.\n\n```\nSELECT manufacturer,\n name,\n type,\n max_thrust\nFROM a\nORDER BY 4 DESC\nLIMIT 25;\n┌─────────────────────┬───────────────┬─────────┬────────────┐\n│ manufacturer │ name │ type │ max_thrust │\n│ varchar │ varchar │ varchar │ double │\n├─────────────────────┼───────────────┼─────────┼────────────┤\n│ GE Aircraft Engines │ GE90-115B │ TF │ 513900.0 │\n│ GE Aircraft Engines │ GE90-113B │ TF │ 504900.0 │\n│ GE Aircraft Engines │ GE90-110B1 │ TF │ 492600.0 │\n│ Rolls-Royce plc │ Trent XWB-97 │ TF │ 436748.0 │\n│ GE Aircraft Engines │ GE90-94B │ TF │ 430920.0 │\n│ GE Aircraft Engines │ GE90-92B │ TF │ 426720.0 │\n│ GE Aircraft Engines │ GE90-90B │ TF │ 419250.0 │\n│ Rolls-Royce plc │ Trent 895 │ TF │ 413050.0 │\n│ Rolls-Royce plc │ Trent 892 │ TF │ 411480.0 │\n│ Pratt & Whitney │ PW4090 │ TF │ 408300.0 │\n│ GE Aircraft Engines │ GE90-85B │ TF │ 397210.0 │\n│ Rolls-Royce plc │ Trent 884 │ TF │ 390100.0 │\n│ Pratt & Whitney │ PW4084D │ TF │ 385900.0 │\n│ Rolls-Royce plc │ Trent XWB-84 │ TF │ 379000.0 │\n│ Pratt & Whitney │ PW4084 │ TF │ 369600.0 │\n│ GE Aircraft Engines │ GE90-77B │ TF │ 366750.0 │\n│ Rolls-Royce plc │ Trent 1000-R3 │ TF │ 363900.0 │\n│ GE Aircraft Engines │ GE90-76B │ TF │ 363220.0 │\n│ Rolls-Royce plc │ Trent 877 │ TF │ 361640.0 │\n│ Rolls-Royce plc │ Trent 1000-M3 │ TF │ 358100.0 │\n│ Rolls-Royce plc │ Trent 1000-N3 │ TF │ 358100.0 │\n│ Pratt & Whitney │ PW4077D │ TF │ 355700.0 │\n│ Rolls-Royce plc │ Trent XWB-79B │ TF │ 355200.0 │\n│ Rolls-Royce plc │ Trent XWB-79 │ TF │ 355200.0 │\n│ Rolls-Royce plc │ Trent 970B-84 │ TF │ 352900.0 │\n└─────────────────────┴───────────────┴─────────┴────────────┘\n```\n\nThese are the fuel model defaults and overrides.\n\n```\n$ ~/duckdb -c \"FROM READ_CSV('/dev/stdin')\" \\\n < openap/data/fuel/fuel_models.csv\n┌──────────┬─────────────┬────────────────────┬────────────────────┬────────────────────┐\n│ typecode │ engine_type │ c1 │ c2 │ c3 │\n│ varchar │ varchar │ double │ double │ double │\n├──────────┼─────────────┼────────────────────┼────────────────────┼────────────────────┤\n│ A318 │ CFM56-5B9/3 │ 0.7769784596099123 │ 1.765377288174942 │ 2.5349134936316693 │\n│ A319 │ V2524-A5 │ 0.8694169413032631 │ 1.9542690629047836 │ 2.5028187026860103 │\n│ A320 │ CFM56-5B4/P │ 1.0453208160586924 │ 2.3633720747416573 │ 1.2378127479131922 │\n│ A321 │ V2533-A5 │ 1.3979999999999444 │ 2.054028451829268 │ 1.0008941993511127 │\n│ A332 │ Trent 772 │ 2.886430057340283 │ 1.0960397632560752 │ 2.3772585567580293 │\n│ A333 │ Trent 772 │ 3.1199999999999997 │ 1.0365152289922772 │ 1.950599421257047 │\n│ B737 │ CFM56-7B26 │ 1.0237419750954273 │ 1.4670109921175798 │ 3.2566140275646456 │\n│ B738 │ CFM56-7B26E │ 1.075484518912494 │ 1.8777303165419037 │ 1.8895522140156369 │\n│ B739 │ CFM56-7B27E │ 1.3079999999999998 │ 1.5986016771932572 │ 1.2789091908108752 │\n│ CRJ9 │ CF34-8C5 │ 0.6437136288905128 │ 1.9690234662778772 │ 1.4375859706162741 │\n│ E170 │ CF34-8E5 │ 0.6341784688704629 │ 2.778729428440142 │ 1.0149695061665696 │\n│ E190 │ CF34-10E5 │ 0.8339999999998783 │ 2.3343013671118475 │ 0.4847704716061958 │\n│ E195 │ CF34-10E5A1 │ 0.911999999999993 │ 1.929664699695295 │ 0.8452746256489131 │\n│ E75L │ CF34-8E5 │ 0.6340709359225759 │ 2.614653287356019 │ 0.8714282723568036 │\n│ default │ default │ 0.937564901246902 │ 1.9767611682280135 │ 1.3954794843472482 │\n└──────────┴─────────────┴────────────────────┴────────────────────┴────────────────────┘\n```\n\n## Toulouse to Berlin\n\nBelow, I'll find an optimal flight path from Toulouse-Blagnac Airport (LFBO / TLS) to Berlin Brandenburg Airport (EDDB / BER).\n\n``` bash\n$ python3\npython\nimport numpy as np\nfrom openap.aero import cas2mach, ft, kts\nfrom openap.extra.nav import airport\nfrom pygeodesy.ellipsoidalVincenty import LatLon\n\nfrom skdecide.hub.domain\\\n .flight_planning\\\n .aircraft_performance\\\n .bean.aircraft_state \\\n import AircraftState\n\nfrom skdecide.hub.domain\\\n .flight_planning\\\n .aircraft_performance\\\n .performance.performance_model_enum \\\n import PerformanceModelEnum\n\nfrom skdecide.hub.domain\\\n .flight_planning\\\n .aircraft_performance\\\n .performance.phase_enum \\\n import PhaseEnum\n\nfrom skdecide.hub.domain\\\n .flight_planning\\\n .aircraft_performance\\\n .performance.rating_enum \\\n import RatingEnum\n\nfrom skdecide.hub.domain\\\n .flight_planning\\\n .domain \\\n import FlightPlanningDomain, \\\n WeatherDate\n\nfrom skdecide.hub.domain\\\n .flight_planning\\\n .flightplanning_utils \\\n import plot_network_adapted\n\nfrom skdecide.hub.solver.astar import Astar\n```\n\nThe heuristic parameter can be either \"time\", \"distance\", \"lazy_fuel\", \"lazy_time\", or None. If nothing is passed, A* will use a Dijkstra-like search algorithm.\n\n```\norigin = \"LFPG\"\ndestination = \"LFBO\"\naircraft = \"A320\"\nweather_date = WeatherDate(day=1, month=5, year=2026)\nheuristic = \"lazy_fuel\"\ncost_function = \"fuel\"\n\nacState = AircraftState(\n model_type=\"A320\",\n performance_model_type=PerformanceModelEnum.OPENAP,\n gw_kg=80_000,\n zp_ft=10_000,\n mach=cas2mach(250 * kts, h=10_000 * ft),\n phase=PhaseEnum.CLIMB,\n rating_level=RatingEnum.MCL,\n cg=0.3)\n\ndomain_factory = lambda: FlightPlanningDomain(\n aircraft_state=acState,\n mach_cruise=0.78,\n mach_climb=0.7,\n mach_descent=0.65,\n nb_forward_points=20,\n nb_lateral_points=10,\n nb_climb_descent_steps=5,\n flight_levels_ft=list(np.arange(30_000, 38_000 + 2_000, 2_000)),\n graph_width=\"medium\",\n origin=LatLon(43.629444, 1.363056),\n destination=\"EDDB\",\n objective=cost_function,\n heuristic_name=heuristic,\n weather_date=weather_date)\n\ndomain = domain_factory()\n```\n\nWhen the above runs, if weather data hasn't been fetched from NOAA and if the date of the flight is within the past six months, GRB2 files will be downloaded.\n\n``` bash\n$ du -hs ~/skdecide_data/weather/grib/nowcast/*/*.grb2\n144M /home/mark/skdecide_data/weather/grib/nowcast/20260501/gfs_4_20260501_0000_000.grb2\n144M /home/mark/skdecide_data/weather/grib/nowcast/20260501/gfs_4_20260501_0600_000.grb2\n143M /home/mark/skdecide_data/weather/grib/nowcast/20260501/gfs_4_20260501_1200_000.grb2\n143M /home/mark/skdecide_data/weather/grib/nowcast/20260501/gfs_4_20260501_1800_000.grb2\n```\n\nEach file has data covering the entire planet. These are the contents of `gfs_4_20260501_1800_000.grb2` rendered on a globe in QGIS.\n\nThis is the solver's altitude and geographical search space.\n\n```\nplot_network_adapted(\n graph=domain.network,\n p0=LatLon(43.629444, 1.363056),\n p1=LatLon(\n airport(\"EDDB\")[\"lat\"],\n airport(\"EDDB\")[\"lon\"],\n airport(\"EDDB\")[\"alt\"] * ft))\n```\n\nThis is the optimal flight path according to the solver.\n\n```\nsolver = Astar(\n domain_factory=domain_factory,\n heuristic=lambda d, s: d.heuristic(s),\n parallel=False)\n\nsolver.solve()\nA* finished to solve from state ... in 0.28 seconds\ndomain.custom_rollout(solver=solver, make_img=True)\nGoal reached after 19 steps!\n({'time': 7666.281474928903, 'fuel': 5855.093906205222}, None)\n```\n\nI'll format each of the flight plan's steps so they're easier to read.\n\n```\ndomain.observation.trajectory.to_csv('TLS-BER.csv', index=None)\n$ ~/duckdb\nSELECT phase: UPPER(phase),\n time_: ts::INT,\n alt: alt::INT,\n mass: mass::INT,\n mach: ROUND(mach, 2),\n cas: cas::INT,\n fuel: fuel::INT,\n geom: ST_POINT(lon, lat)\nFROM 'TLS-BER.csv'\nORDER BY ts;\n┌─────────┬───────┬───────┬───────┬────────┬───────┬───────┬────────────────────────────────────────────────┐\n│ phase │ time_ │ alt │ mass │ mach │ cas │ fuel │ geom │\n│ varchar │ int32 │ int32 │ int32 │ double │ int32 │ int32 │ geometry │\n├─────────┼───────┼───────┼───────┼────────┼───────┼───────┼────────────────────────────────────────────────┤\n│ CLIMB │ 28800 │ 0 │ 80000 │ 0.45 │ 154 │ 0 │ POINT (1.363056 43.629444) │\n│ CLIMB │ 29183 │ 12000 │ 79402 │ 0.7 │ 194 │ 598 │ POINT (1.3614644301412264 44.431571122861556) │\n│ CLIMB │ 29767 │ 18000 │ 78717 │ 0.7 │ 173 │ 685 │ POINT (0.8028803270337778 45.54329961845038) │\n│ CLIMB │ 30367 │ 24000 │ 78104 │ 0.7 │ 154 │ 2 │ POINT (0.22308186850312028 46.64860136322122) │\n│ CLIMB │ 30369 │ 24000 │ 78102 │ 0.7 │ 154 │ 2 │ POINT (0.2213600223765711 46.65181397470445) │\n│ CLIMB │ 30691 │ 30000 │ 77808 │ 0.7 │ 135 │ 294 │ POINT (0.781910701674247 47.146798229437145) │\n│ CRUISE │ 31222 │ 30000 │ 77331 │ 0.78 │ 152 │ 477 │ POINT (0.18057649919536045 48.254448220756515) │\n│ CRUISE │ 31515 │ 30000 │ 77070 │ 0.78 │ 152 │ 262 │ POINT (0.7571242215277763 48.74964861278412) │\n│ CRUISE │ 31805 │ 30000 │ 76812 │ 0.78 │ 152 │ 258 │ POINT (1.3446668642885302 49.24219441171162) │\n│ CRUISE │ 32093 │ 30000 │ 76555 │ 0.78 │ 152 │ 256 │ POINT (1.943586016571517 49.732000774167815) │\n│ CRUISE │ 32382 │ 30000 │ 76298 │ 0.78 │ 152 │ 257 │ POINT (2.554285524033502 50.218985517421046) │\n│ CRUISE │ 32672 │ 30000 │ 76041 │ 0.78 │ 152 │ 257 │ POINT (3.1771982015706532 50.70307279893911) │\n│ CRUISE │ 32961 │ 30000 │ 75786 │ 0.78 │ 152 │ 256 │ POINT (3.812797488711077 51.18419969012497) │\n│ CRUISE │ 33252 │ 30000 │ 75529 │ 0.78 │ 152 │ 257 │ POINT (4.461619033936127 51.66232853895605) │\n│ CRUISE │ 33547 │ 32000 │ 75270 │ 0.78 │ 146 │ 259 │ POINT (5.1243038676232 52.13747186609129) │\n│ CRUISE │ 34103 │ 30000 │ 74794 │ 0.78 │ 152 │ 476 │ POINT (7.006628090474678 51.93831668841654) │\n│ DESCENT │ 34458 │ 24031 │ 74503 │ 0.65 │ 142 │ 290 │ POINT (7.7011825929472675 52.40044729715865) │\n│ DESCENT │ 35058 │ 18063 │ 73995 │ 0.65 │ 160 │ 51 │ POINT (9.423199233939213 52.1821111144618) │\n│ DESCENT │ 35114 │ 18063 │ 73944 │ 0.65 │ 160 │ 51 │ POINT (9.580613666598857 52.160789987133924) │\n│ DESCENT │ 35714 │ 12094 │ 73388 │ 0.65 │ 179 │ 13 │ POINT (11.398384342445423 51.895274115132494) │\n│ DESCENT │ 35727 │ 12094 │ 73375 │ 0.65 │ 179 │ 13 │ POINT (11.435080901553494 51.88959204464927) │\n│ DESCENT │ 36063 │ 6126 │ 73023 │ 0.65 │ 199 │ 352 │ POINT (12.17769156482302 52.32776873134525) │\n│ DESCENT │ 36466 │ 48 │ 72534 │ 0.65 │ 221 │ 488 │ POINT (13.48503 52.36769) │\n└─────────┴───────┴───────┴───────┴────────┴───────┴───────┴────────────────────────────────────────────────┘\n```\n\nI'll export the flight plan to Parquet and render it on top of the ground-level wind data in QGIS.\n\n```\nCOPY (\n SELECT * EXCLUDE(lon, lat),\n geometry: ST_POINT(lon, lat)\n FROM 'TLS-BER.csv'\n ORDER BY ts\n) TO 'TLS-BER.parquet' (\n FORMAT 'PARQUET',\n CODEC 'ZSTD',\n COMPRESSION_LEVEL 22,\n ROW_GROUP_SIZE 15000);\n```\n\n## Toulouse to Warsaw\n\nBelow, I'll find an optimal flight path from Toulouse-Blagnac Airport (LFBO / TLS) to Warsaw Chopin Airport (EPWA / WAW).\n\nThe initial target altitude will be much higher than in the previous example. The result is a flight that is able to take a much more direct route.\n\n```\nacState = AircraftState(\n model_type=\"A320\",\n performance_model_type=PerformanceModelEnum.OPENAP,\n gw_kg=80_000,\n zp_ft=18000.0,\n mach=cas2mach(250 * kts, h=10_000 * ft),\n phase=PhaseEnum.CLIMB,\n rating_level=RatingEnum.MCL,\n cg=0.3,\n x_graph=5,\n y_graph=5,\n z_graph=10)\n\ndomain_factory = lambda: FlightPlanningDomain(\n aircraft_state=acState,\n mach_cruise=0.78,\n mach_climb=0.7,\n mach_descent=0.65,\n nb_forward_points=20,\n nb_lateral_points=10,\n nb_climb_descent_steps=5,\n flight_levels_ft=list(np.arange(30_000, 38_000 + 2_000, 2_000)),\n graph_width=\"medium\",\n origin=LatLon(43.629444, 1.363056),\n destination=\"EPWA\",\n objective=cost_function,\n heuristic_name=heuristic,\n weather_date=weather_date)\n\ndomain = domain_factory()\n\nsolver = Astar(\n domain_factory=domain_factory,\n heuristic=lambda d, s: d.heuristic(s),\n parallel=False)\n\nsolver.solve()\nA* finished to solve from state ... in 29.45 seconds.\ndomain.custom_rollout(solver=solver, make_img=True)\nGoal reached after 14 steps!\n({'time': 6153.660431613251, 'fuel': 5600.171145693044}, None)\n```\n\nWarsaw is 500 KM further away from Toulouse than Berlin. But the faster climb to cruising altitude under the given wind conditions meant the aircraft could take a more direct route. It made it to Warsaw almost 45 minutes faster and only needed 76% of the fuel that the Berlin flight needed.\n\nThese are the steps in the above flight plan.\n\n```\ndomain.observation.trajectory.to_csv('TLS-WAW.csv', index=None)\n$ ~/duckdb\nSELECT phase: UPPER(phase),\n time_: ts::INT,\n alt: alt::INT,\n mass: mass::INT,\n mach: ROUND(mach, 2),\n cas: cas::INT,\n fuel: fuel::INT,\n geom: ST_POINT(lon, lat)\nFROM 'TLS-WAW.csv'\nORDER BY ts;\n┌─────────┬───────┬───────┬───────┬────────┬───────┬───────┬───────────────────────────────────────────────┐\n│ phase │ time_ │ alt │ mass │ mach │ cas │ fuel │ geom │\n│ varchar │ int32 │ int32 │ int32 │ double │ int32 │ int32 │ geometry │\n├─────────┼───────┼───────┼───────┼────────┼───────┼───────┼───────────────────────────────────────────────┤\n│ CLIMB │ 28800 │ 30000 │ 80000 │ 0.45 │ 85 │ 0 │ POINT (6.321780309765473 45.78957852956533) │\n│ CRUISE │ 29196 │ 32000 │ 79639 │ 0.78 │ 146 │ 361 │ POINT (7.274006698354081 46.275553205520794) │\n│ CRUISE │ 29604 │ 34000 │ 79276 │ 0.78 │ 139 │ 363 │ POINT (8.243146568075773 46.75332543362598) │\n│ CRUISE │ 30018 │ 36000 │ 78915 │ 0.78 │ 133 │ 361 │ POINT (9.229481862337197 47.22261290149568) │\n│ CRUISE │ 30436 │ 38000 │ 78555 │ 0.78 │ 127 │ 360 │ POINT (10.23327610333648 47.68312559281413) │\n│ CRUISE │ 30861 │ 38000 │ 78191 │ 0.78 │ 127 │ 365 │ POINT (11.25477083484032 48.13456566890824) │\n│ CRUISE │ 31297 │ 36000 │ 77819 │ 0.78 │ 133 │ 371 │ POINT (12.29418112454121 48.57662718213212) │\n│ CRUISE │ 31732 │ 34000 │ 77449 │ 0.78 │ 139 │ 370 │ POINT (13.351689351409924 49.00899540355703) │\n│ CRUISE │ 32161 │ 32000 │ 77082 │ 0.78 │ 146 │ 367 │ POINT (14.427435465032865 49.431345252175966) │\n│ CRUISE │ 32589 │ 30000 │ 76710 │ 0.78 │ 152 │ 372 │ POINT (15.521498988740307 49.843337488922174) │\n│ DESCENT │ 33101 │ 24066 │ 76280 │ 0.65 │ 142 │ 429 │ POINT (16.633858546975723 50.2446086742223) │\n│ DESCENT │ 33589 │ 18131 │ 75861 │ 0.65 │ 160 │ 420 │ POINT (17.764276668345886 50.63474030548783) │\n│ DESCENT │ 34046 │ 12197 │ 75433 │ 0.65 │ 179 │ 428 │ POINT (18.91184798374883 51.01313503252613) │\n│ DESCENT │ 34472 │ 6262 │ 74984 │ 0.65 │ 199 │ 449 │ POINT (20.071843186874247 51.378167839584854) │\n│ DESCENT │ 34954 │ 100 │ 74400 │ 0.65 │ 221 │ 584 │ POINT (20.94663 52.17147) │\n└─────────┴───────┴───────┴───────┴────────┴───────┴───────┴───────────────────────────────────────────────┘\n```\n\n## Airbus A320 vs Boeing 737\n\nOpenTop can be paired with OpenAP and used to figure out flight trajectories between two airports.\n\nIts optimiser requires a grid cost file. I'll first download an example 142 MB NetCDF file provided by the project.\n\n``` bash\n$ wget https://opendap.4tu.nl/thredds/fileServer/data2/djht/bea8a3fe-e34c-4598-9f94-c5a5c63348e5/1/contrail_original.nc\n```\n\nThe cost file can be either in Casadi or Parquet format. I worked from an [example](https://openap.dev/optimize/contrails.html) in its documentation, which produced a 246 KB Casadi file.\n\n``` python\nimport openap\nimport pandas as pd\nfrom scipy.ndimage import gaussian_filter\nfrom opentop.tools import cached_interpolant_from_dataframe\nimport xarray as xr\n\nds = xr.open_dataset('contrail_original.nc')\\\n .sel(time='2015-12-18')\n\nlevel_pressure = [\n 0.0000,\n 10.0000,\n 30.0000,\n 50.0000,\n 70.0000,\n 90.0787,\n 110.6606,\n 132.3968,\n 155.7909,\n 181.1544,\n 208.6494,\n 238.3258,\n 270.1530,\n 304.0465,\n 339.8891,\n 377.5467,\n 416.8789,\n 457.7442,\n 500.0000,\n 543.4970,\n 588.0685,\n 633.5144,\n 679.5799,\n 725.9285,\n 772.1102,\n 817.5241,\n 861.3757,\n 902.6287,\n 939.9520,\n 971.6610,\n 995.6532,\n 1009.3396]\n\ndf = (\n ds.to_dataframe()\n .reset_index()\n .assign(lev=lambda x: x.lev.astype(int))\n .merge(\n pd.DataFrame(level_pressure, columns=[\"hPa\"]).reset_index(names=\"lev\"),\n on=\"lev\",\n )\n .assign(height=lambda x: openap.aero.h_isa(x.hPa * 100).round(-2))\n .assign(longitude=lambda x: ((x.lon + 180) % 360 - 180))\n .query(\"height<15000\"))\n\ndf_cost_world = df.rename(\n columns={\n \"lat\": \"latitude\",\n \"atr20_contrail\": \"cost\",\n }\n)[[\"time\",\n \"latitude\",\n \"longitude\",\n \"hPa\",\n \"height\",\n \"cost\"]]\n\ndf_cost = df_cost_world.query(\n \"-20