# How is the length of a leg calculated?

Here are few facts:

• A flight is basically climbing, staying high, then descending toward a runway

Changes in altitude increase the distance an aircraft flies. Given the climb/descent angle, this increase may be insignificant, but it still exists.

Given many elements (TSA, other traffic,...) I imagine an airliner can almost never take a direct route. Not to mention the path leading to the approach.

• An airport may have several runways whose length may not be the same

The departure point may be the parking position, the beginning of the runway, the end of the runway, the point where the aircraft reaches $V_2$,... The same goes for the arriving point.

• The precision of the maximum range of an aircraft is really precise

When looking at ailiners' performances, one key figure seems quite strange: the range. It seems quite precise (few miles). Lets take the ERJ-140ER as example. Its maximum range is 1250nm. Given this number, I imagine the precision is less than 10nm (3 significant digit), i.e. about 3 to 4 times an international airport's runway length (4km for dubai international airport).

Given all those elements, how is a leg length (distance of 1 flight between 2 airports) calculated for an airliner?

• If you are planning to fly the maximum range to land at your destination, then you are planning to die. Maximum range minus time to divert minus 30 minutes minus minimum "in the tanks" on landing reserve. – Simon Oct 28 '15 at 13:21
• @Simon I thought at least the 30min reserve and the minimum in the tanks were taken into account in max range calculation. Otherwise, this is only a marketing figure with no realistic meaning. – Manu H Oct 28 '15 at 13:57
• @ManuH I don't know how Boeing and Airbus do it, but Piper and Cessna "range" figures are from full tanks to empty tanks (zero fuel). – voretaq7 Oct 28 '15 at 15:38
• Along the inseam. – user19474 Oct 28 '15 at 17:55
• The gap between marketing and practical application is usually large. As voretaq says, maximum range is full to empty. Maximum usable range is therefore something less. – Simon Oct 28 '15 at 19:58

Many of the 'variables' you mention, are in fact fixed, and in large determined by dispatch (the smart folks at the company). For commercial flight, the flight plan will be filed in advance (generally by the company dispatch), and will contain all the waypoints en route, including expected flight levels. Dispatch makes the calculation for the most efficient flight in close collaboration with ATC authorities, for example by reserving slots on certain airways.

Deviations from the flight plan are not common - you won't hear ATC tell an airplane mid-flight to suddenly take the long way round - instead, any route alterations are communicated to the pilots when they are still on the ground, and if necessary, extra fuel is taken on board.

This flight plan is then given to the pilots, and programmed into the FMC. The FMC is a very sophisticated piece of software, and can in fact calculate the required fuel for this leg all by itself - you can even program it to calculate the best trade-off between efficiency and speed (see this KLM video at 1:40). I'm not entirely sure about the details, but you can probably program the SID and STAR of the departure and destination airports respectively as well.

On top of this, extra fuel is taken on board for things like taxi, expected holding patterns (your dispatcher will know how busy you can expect it to be at your destination airport; e.g., Heathrow is generally very busy and you might want to take some extra fuel on board), and enough fuel to at least be able to perform a few go-arounds or a diversion if circumstances call for it. In the end, the pilot is responsible for taking enough fuel on board, but will rely on the FMC and dispatch to make an educated guess.

• The FMC absolutely does have the capability to navigate the SID and STAR, at least for a reasonably modern FMC. Also, changes to the planned routing happen all the time: shortcuts, vectors off course for traffic or weather, changing the arrival due to runways being closed or "turned around" as winds change, etc. The changes aren't drastic (+/- a few miles, usually), but they are perfectly commonplace. – Ralph J Oct 28 '15 at 20:35
• @RalphJ Mostly, I wasn't sure whether the STAR would be programmed on departure, since the approach might be assigned during later stages of the flight. Also, I meant to refer to substantial changes in the flight path, not minor deviations (you won't be asked by ATC to cross the Atlantic ocean on a different track 5000 feet lower) – Sanchises Oct 28 '15 at 20:54
• The STAR can change, but yes, you'll put whatever arrival you were filed for in the FMC during the preflight. One benefit of this is that the arrival contains your descent profile (cross THISS at FL240, cross THATT at 250 knots & 10,000'), so your fuel predictions from the start are working from the best known Top of Descent point. – Ralph J Oct 28 '15 at 23:51

Calculating the exact amount of fuel necessary to make a trip is an inexact science, for exactly the reasons you mentioned. The reported range is calculated for an ideal trip. Your mileage may vary.