How PlaneRange Calculates Aircraft Range

Every range ring, runway limit and fuel figure on PlaneRange comes from one model, fitted to the payload-range charts Boeing and Airbus publish for airport planners. This page covers where the data comes from, how I turned the charts into numbers, the equations, and how far off the result is for each aircraft. If something here is wrong, I want to know.

Who built this

I'm Daniel Gauthier, and PlaneRange is a one-person project. I've worked as a software engineer for five years and have a Master's in Computer Science, focused on CS education and cybersecurity. I've run an ADS-B receiver since 2018, feeding FlightAware, Flightradar24 and adsb.lol, and I upload aircraft photos to FlightAware. The aircraft photos on this site are mine.

The source: ACAP documents

Boeing calls them Airplane Characteristics for Airport Planning (ACAP). Airbus calls them Aircraft Characteristics. Airports use them to plan gates, taxiways and runways, and I use two sections of each:

Section 2.1, weights. Maximum takeoff weight (MTOW), maximum zero fuel weight (MZFW) and usable fuel for each weight variant. I model the variant most common in service.
Section 3.2, payload-range. Range against payload (Airbus) or against operating empty weight plus payload (Boeing), usually with extra lines for reduced takeoff weights.

The first version of PlaneRange started from brochure ranges instead, and that was a mistake. A brochure range is quoted for a typical cabin, but the old model treated it as the range at maximum payload. For the Boeing 737 MAX 8 it used 3,550 nm where the ACAP chart shows about 2,500 nm at MZFW, so a full aircraft could reach up to 40% farther on the map than it really can.

Digitizing the charts

The charts are pictures in a PDF, so the first job is turning lines back into numbers. There are two kinds of page:

Vector pages (most Airbus documents, some Boeing). The curves are stored as PDF drawing commands, so I read their coordinates straight out of the file and map them to the axes using two labeled gridlines per axis. There is no tracing error.
Raster pages (most Boeing documents). These are images. I locate the gridlines by pixel, follow each curve from a starting point I place by hand, and check every trace against an overlay drawn on the original image. Where curves crowd together a trace can slide onto its neighbor, and the overlay is where that shows up.

Boeing plots zero fuel weight directly. Airbus plots payload, so I convert it using the chart's own empty weight: MZFW from the weight table minus the chart's maximum payload.

I trace the reduced takeoff weight lines as well as the outer envelope. On the envelope alone, a more efficient aircraft and one with smaller fuel reserves push the curve out by about the same amount, so the fit can't tell them apart. The reduced-weight lines separate the two, and they are also what a departure from a short runway uses.

So far that is 42 charts, 143 lines and 11,445 points. Some types have one chart per engine.

The model

Specific range, the distance an aircraft flies per kilogram of fuel, falls as the aircraft gets heavier. I model it as:

SR(W) = K / W × (W / Wref)1 − n

W is the current weight and W_ref is the chart's MTOW. With n = 1 this is the Breguet range equation. The charts don't follow Breguet exactly, so n is fitted as well. For the 787-9 it comes out at 0.92.

Range is the distance flown while the weight falls from takeoff to landing:

ZFW = OEW + payload
TOW = min(MTOW, runway limit, ZFW + fuel capacity)
landing weight = ZFW + reserve fuel + unburned contingency

Reserves follow the chart's own rules. I model them as a distance flown at landing weight (the diversion, hold and approach allowance) plus contingency fuel of 5% of trip fuel that is carried but not burned. The 747-400 chart uses FAR international rules, so its contingency is 10%.

That leaves three constants per chart: K, n and the reserve distance. I fit them by least squares across every traced point on the chart. Points more than four times the RMS error off the curve (100 nm at minimum) are dropped once and the fit is run again. Those are tracing mistakes, usually a trace that snapped onto a label.

The fit runs in Python. The map runs the same equations in TypeScript, and the test suite replays every traced point through the TypeScript version, so a data change that moves an aircraft off its chart fails the tests. Because it is one model, passengers, bags, cargo, fuel capacity and runway length always trade against each other the same way, and flying the ring's full range burns exactly the fuel that fits in the tanks.

Boeing 787-9, Payload/Range for Long-Range Cruise: Model 787-9 (ACAP p. 37). Grey dots are every third point I traced off the chart; blue lines are the fitted model. RMS error 29 nm, worst point 58 nm.

How close the fit is

RMS is the typical miss across all of a chart's points, and "worst" is the single biggest miss. 31 of the 42 fits below are within 30 nm RMS, and all are within 59 nm. The A330 family and the A340-600 are the loosest. Their charts have a kink near maximum payload, where the initial cruise altitude limit takes over, and a smooth curve can't follow it. That costs up to about 3% of range right at MZFW. The biggest single misses are mostly at the ends of a line, where the curve turns sharply.

Aircraft	ACAP chart	RMS	Worst
Airbus A220-100	Figure 1 Zero Fuel Weight (ZFW) vs Range ISA (A220-100), p. 161	19 nm	58 nm
Airbus A220-300	Figure 1 Zero Fuel Weight (ZFW) vs Range ISA (A220-300), p. 175	16 nm	66 nm
Airbus A319-100	Payload/Range - ISA Conditions (A319-100), p. 148	6 nm	15 nm
Airbus A320-200	Payload/Range - ISA Conditions (A320-200), p. 161	6 nm	22 nm
Airbus A320neo	Payload/Range - ISA Conditions (A320neo), p. 163	23 nm	88 nm
Airbus A321-200	Payload/Range - ISA Conditions (A321-100/-200), p. 172	5 nm	17 nm
Airbus A321neo	Payload/Range - ISA Conditions (A321neo), p. 174	35 nm	90 nm
Airbus A330-200 (CF6-80E1)	Payload / Range - ISA Conditions, GE CF6-80E1 (A330-200), p. 266	40 nm	145 nm
Airbus A330-200 (PW4000)	Payload / Range - ISA Conditions, PW 4000 (A330-200), p. 264	44 nm	174 nm
Airbus A330-200 (Trent 700)	Payload / Range - ISA Conditions, RR Trent 700 (A330-200), p. 265	41 nm	146 nm
Airbus A330-300 (CF6-80E1)	Payload / Range - ISA Conditions, GE CF6-80E1 (A330-300), p. 271	59 nm	172 nm
Airbus A330-300 (PW4000)	Payload / Range - ISA Conditions, PW 4000 (A330-300), p. 269	56 nm	168 nm
Airbus A330-300 (Trent 700)	Payload / Range - ISA Conditions, RR Trent 700 (A330-300), p. 270	56 nm	170 nm
Airbus A330-900	Payload / Range - ISA Conditions, RR Trent 7000 (A330-900), p. 273	46 nm	174 nm
Airbus A340-300	Payload / Range - ISA Conditions, CFM56-5C4, 257 t MTOW (A340-300), p. 168	28 nm	73 nm
Airbus A340-600	Payload / Range - ISA Conditions, RB211 Trent 556 (A340-600), p. 175	57 nm	103 nm
Airbus A350-900	Payload/Range - ISA Conditions (A350-900), p. 228	40 nm	134 nm
Airbus A350-1000	Payload/Range - ISA Conditions (A350-1000), p. 229	36 nm	93 nm
Airbus A380-800 (GP7200)	Payload/Range - ISA Conditions, GP7200 (A380-800), p. 127	22 nm	65 nm
Airbus A380-800 (Trent 900)	Payload/Range - ISA Conditions, Trent 900 (A380-800), p. 126	20 nm	63 nm
Boeing 717-200	payload-range capability, p. 7	14 nm	36 nm
Boeing 737-700	Payload/Range for Long Range Cruise: Model 737-700, -700W, p. 63	12 nm	50 nm
Boeing 737-800	Payload/Range for Long Range Cruise: Model 737-800, -800W, p. 65	12 nm	86 nm
Boeing 737-900	Payload/Range for Long Range Cruise: Model 737-900, -900W, p. 66	9 nm	46 nm
Boeing 737-900ER	Payload/Range for Long Range Cruise: Model 737-900ER, -900ERW, p. 67	9 nm	64 nm
Boeing 737 MAX 8	Payload/Range for Long Range Cruise: Model 737-8, p. 41	13 nm	82 nm
Boeing 737 MAX 9	Payload/Range for Long Range Cruise: Model 737-9, p. 43	10 nm	61 nm
Boeing 757-200 (PW2037/PW2040)	Payload/Range for Long-Range Cruise: Model 757-200 (PW2037, PW2040), p. 40	29 nm	228 nm
Boeing 757-200 (RB211-535E4/E4B)	Payload/Range for Long-Range Cruise: Model 757-200 (RB211-535E4, -535E4B), p. 39	29 nm	130 nm
Boeing 757-300	Payload/Range for 0.80 Mach Cruise: Model 757-300 (PW2040, PW2043), p. 42	10 nm	28 nm
Boeing 767-300ER (CF6-80C2B7F1)	Payload/Range: Model 767-300ER, Long-Range Cruise (CF6-80C2B7F1), p. 61	20 nm	86 nm
Boeing 767-300ER (PW4060/PW4062)	Payload/Range: Model 767-300ER, Long-Range Cruise (PW4062), p. 62	23 nm	84 nm
Boeing 767-400ER	Payload/Range: Model 767-400ER, Long-Range Cruise (CF6-80C2B8), p. 65	16 nm	69 nm
Boeing 777-200ER	Payload/Range for 0.84 Mach Cruise: Model 777-200 (High Gross Weight), p. 45	13 nm	69 nm
Boeing 777-200LR	Payload/Range for 0.84 Mach Cruise: Model 777-200LR, p. 43	14 nm	91 nm
Boeing 777-300ER	Payload/Range for 0.84 Mach Cruise: Model 777-300ER, p. 44	12 nm	77 nm
Boeing 787-8	Payload/Range for Long-Range Cruise: Model 787-8, p. 36	17 nm	40 nm
Boeing 787-9	Payload/Range for Long-Range Cruise: Model 787-9, p. 37	29 nm	58 nm
Boeing 787-10	Payload/Range for Long-Range Cruise: Model 787-10, p. 38	11 nm	48 nm
Boeing 747-400 (CF6-80C2B1F)	Payload/Range: Model 747-400, 0.85 Mach Cruise (CF6-80C2B1F), p. 63	19 nm	55 nm
Boeing 747-400 (RB211-524G/H)	Payload/Range: Model 747-400, 0.85 Mach Cruise (RB211-524G), p. 65	10 nm	50 nm
Boeing 747-8 Intercontinental	Payload/Range: Model 747-8, p. 35	22 nm	87 nm

Borrowed charts

These aircraft have no chart of their own but share a wing and engines with one that does. They use that aircraft's fitted constants with their own weights.

Aircraft	Uses the chart of
Airbus A321neo LR	Airbus A321neo
Airbus A321XLR	Airbus A321neo
Boeing 737 MAX 7	Boeing 737 MAX 8
Boeing 737 MAX 10	Boeing 737 MAX 9

No chart available

I don't have a payload-range chart for these aircraft yet: Boeing 727-200, Boeing 707-120B, Douglas DC-8-63, McDonnell Douglas MD-80, Boeing 777X-9, Embraer E170, Embraer E175, Embraer E175-E2, Embraer E190, Embraer E195, Embraer E190-E2, Embraer E195-E2, Bombardier CRJ-700, Bombardier CRJ-900, ATR 72-600, Fokker 70, Fokker 100, Gulfstream G280, Gulfstream G650ER, Bombardier Challenger 650, Bombardier Global 7500, Cessna Citation XLS+, Embraer Phenom 300E, Dassault Falcon 8X, Aérospatiale/BAC Concorde, Ryan Aircraft Spirit of St. Louis, Douglas DC-3, Boeing 314 Clipper. They are calibrated on their published range figures, using the median exponent and reserve distance from the charted fleet. Treat their numbers as less certain than the ones above.

The general aviation aircraft (Cessna 172 Skyhawk, Cessna 208B Grand Caravan, Piper PA-28 Cherokee, Cirrus SR22, Beechcraft Bonanza G36) are calibrated on the full-fuel range from their Pilot's Operating Handbook, with n = 1 and no contingency. They have no zero fuel weight limit, so payload trades directly against fuel up to MTOW.

A few novelty entries have no weight data at all and use a simple curve through their published ranges: Wright Brothers Wright Flyer, Wright Brothers Wright Flyer III, Blériot XI, Goodyear GZ-20A Blimp, Boeing / NASA 747 Shuttle Carrier, Boeing VC-25A (Air Force One), Apple MacBook Neo, Aero Spacelines Super Guppy Turbine.

What the map adds on top

Passengers. 210 lb each including bags, Airbus's 95 kg standard. Seat counts come from real airline configurations, and the slider stops at the cabin's seat count. There is no belly cargo unless you add it.
Extra reserves. The charts already include 5% contingency, a 30 minute hold and a 200 nm diversion. On the map, jets hold for 45 minutes instead of 30, and the diversion is the distance to the nearest real airport rather than a flat 200 nm (only the part beyond 200 nm is added). The 757-200 and 767-300ER charts use US domestic reserves, which already include 45 minutes, so nothing extra is held for them.
Runways. Field lengths from the ACAP takeoff and landing charts at sea level and standard temperature, corrected for airport elevation: 3.5% per 1,000 ft for takeoff and 2% for landing on transport aircraft, 12% and 3.5% for piston aircraft. A short runway caps takeoff weight, not range, so a lightly loaded aircraft can still fly a long way from one.
Wind. Optional. A seasonal average of the west-east wind by latitude, scaled by cruise altitude so turboprops and light aircraft see weaker winds than a jet at FL350. It is not a forecast.
Fuel and CO2. Trip fuel comes from the same model, so the fuel figure can never disagree with the ring.

Known limits

Range is still-air great-circle distance. Real routes are a few percent longer because of airways and tracks.
Temperatures are standard day throughout. Hot days hurt takeoff performance more than the map shows.
Each aircraft has one cruise-average efficiency, so climb fuel on short legs is slightly undercounted, and taxi fuel is left out.
Maximum landing weight isn't checked. For every aircraft here MLW is above MZFW plus reserves, so it never limits range.
ETOPS diversion circles use cruise airspeed with no wind.

PlaneRange is for exploring how aircraft performance works. It is not a flight planning or dispatch tool.

Corrections

If you have an ACAP chart or POH page I'm missing, or a number here looks wrong, email me at [email protected]. The aircraft in the "no chart available" list are the ones I'd most like to move onto real charts.