Aircraft travel in well defined airways, at different flight levels depending on direction and also have specific rates of ascend, descend and turn (e.g 2-min turn).

Are there any known models that take these spatial constraints into account and produce a plausible route between two points in space for a given aircraft?

My specific use case is straightforward: I have the current position of an aircraft and a number of alternative endpoints on that route. Instead of drawing straight lines between these alternatives, I would like to draw plausible routes taking into account as many real constraints as it is possible.

I haven't look into how this is implemented in computer games yet (e.g. flightgear) and I could write a simple enough auto-router taking into account the rate constraints. I would however like to know if there are any widely accepted or recommended existing auto-routing models.

Additional Information

In view of comments to this question I would like to clarify the following:

  1. I am not looking for flight-planning algorithms or constrained routing in the sense of optimal paths that are sometimes sought by algorithms such as those used in this paper.

  2. I am looking for routing algorithms whose output is the actual path that if set on an autopilot will bring the aircraft through an endpoint at a specific bearing, level and speed. Ideally, I am looking for "names" in the same sense that the paper linked above states "...some auto-routers for military aircraft do exist including CLOAR, OPUS and JRAPS...".

  3. As a secondary question, do ATC systems have some sort of auto-routing as an aid to operators at busy areas? If yes, then perhaps it would be worth checking if the algorithms are published because I expect they would have to be standardised and validated.

  4. As an example, consider an aircraft that is approaching an airport to land. The aircraft is on a specific course, flight level and speed and it is to be directed to enter the landing pattern at a specific point. An approach would be to extend the entry point's bearing and aircraft's bearing and fit a cycle that corresponds to the 2-min turn to bring the course of the aircraft on the entry point bearing (i.e. smooth the corner of the intersection). If such an intersection is undefined (e.g. the bearings are parallel, or they intersect at a really long distance) then a new leg needs to be added which a) intersects with the current course of the aircraft b) intersects the entry point bearing and c) satisfies other constraint (e.g. shortest distance, no sharp angles, etc). If that is undefined on the side of the entry point a new leg must be added, this leg should a) intersect the given leg at...and so on. This approach will result to a path (not THE path) that respects specific constraints...But obviously the question here is how realistic it will be both for an aircraft to fly but also would a human operator produce a path with similar qualities or reject it altogether? Hence, the question...are there any auto-router algorithms out there already?


  1. If the general consensus veers more towards a situation where it is very hard to get acurate information on routing models for civilian aircraft, is there a set of minimal parameters that would have to be taken into account when designing a simplistic auto-router that would be more likely to generate plausible paths given two points in space? "Plausible" is defined as "similar to what a human ATC would have directed the airplane to do" or "a path that appears sensible to an average pilot". At the moment I would be considering the rates of ascend, descend and turn.
  • $\begingroup$ Intuitively, when I read your question, I think the answer should be somewhere in the region of dynamic programming algorithms. Perhaps that can help your search. $\endgroup$
    – Sanchises
    Commented Apr 12, 2015 at 16:00
  • $\begingroup$ Thank you for the pointer, dynamic programming definitely has a place in the solutions to this problem but I am looking for established models (or algorithms) at a first instance. Not sure if ATC equipment has auto-routing functionality (?), that must have been standardised and validated so far. $\endgroup$
    – A_A
    Commented Apr 12, 2015 at 16:09
  • $\begingroup$ Airlines do the routing, so you'd be looking for their models. $\endgroup$ Commented Apr 12, 2015 at 16:49
  • $\begingroup$ Thanks. Just to clarify that I am not interested in the broad flight plan. I am interested in what happens, for example, when an aircraft is about to land and it is rerouted to a holding pattern due to high traffic. So, given current aircraft, route and speed and endpoint data (entry bearing, entry level, entry velocity), solve for a plausible route. $\endgroup$
    – A_A
    Commented Apr 12, 2015 at 20:28
  • 1
    $\begingroup$ I for one am certain that routing problems like this are actually NP hard and are undoubtedly very unpleasant multidimensional nonlinear optimisation problems. It might be interesting to consider a "2D ish" toy model as an illustration -- say, routing electrical traces on a printed circuit board, which, as Wikipedia lovingly says, is far from straightforward! $\endgroup$
    – Landak
    Commented Apr 12, 2015 at 21:09

3 Answers 3


I am looking for routing algorithms whose output is the actual path that if set on an autopilot will bring the aircraft through an endpoint at a specific bearing, level and speed

There are indeed models for moving between waypoints: I remember siting on the flightdeck of an A320 and noticing the airspeed increase as we descended towards the airport. I asked the pilot and he responded that this was in preparation for a turn coming up as to not loose airspeed. Not a huge differences perhaps but will make a difference over a year with a lot of aircraft.

Most airlines have company routes detailing which waypoints to use to a destination. To the best of my knowledge, these are fairly standard (you might have few) and not too weather dependant, unless there is a big storm for instance. One exception to this are transatlantic tracks that are changed daily depending on weather. At least for most flights, possible variations are few and will be in busy airways. Changing airways is normally a larger deviation so it is just good to bare with it, and the weather is unlikely to be considerably better for just a slight detour.

As a secondary question, do ATC systems have some sort of auto-routing as an aid to operators at busy areas?

ATC have normally no real incentive to cut down routes, at least in cruise. They might help you skip some waypoints and get the aircraft down a little quicker if the airspace is calm during arrival. To also put things into perspective, I was on the flightdeck into a moderately large european airport where we were put first into a hold due to bad planning and then told to speed up after we left it to catch up again. Arlanda airport had something going on however with green approaches.

I am looking for routing algorithms whose output is the actual path that if set on an autopilot will bring the aircraft through an endpoint at a specific bearing, level and speed.

The issue here is that there is no incentive for aircraft manufacturers to release such algorithms to the public. If Airbus uses algorithm A, and Boeing algorithm B, each with a different inputs, you neither would want the other to make algorithm C that works with both inputs and being more efficient. The bottom line however is that everybody remains constrained by the infrastructure already in place that is pretty rigid.

  • $\begingroup$ Thank you for your response which to an extent it is useful and I guess, lined up to be accepted in the end, in the absence of a more accurate one. I have amended the question without any intention to be a pig about it but if there appears to be nothing relevant out there, I might as well put together something simplistic, yet plausible. $\endgroup$
    – A_A
    Commented Apr 13, 2015 at 16:09
  • $\begingroup$ Note that most of the routing actually happens in a computer on dispatcher's desk. It does have auto-routing and it is really sophisticated, because it takes into account not just fuel burn, but also overfly charges and any restrictions that apply to the plane on the particular day—it's base ETOPS rating, but also any MEL items that have additional restrictions—and of course forecast winds aloft. The on-board system basically just recalculates the top-of-descent. $\endgroup$
    – Jan Hudec
    Commented Feb 12, 2017 at 16:16

Both ForeFlight and DUATS provide airway auto-routing.

From the comments in your question, I suspect this is not what you want, but I'm offering it as an answer just in case.

  • $\begingroup$ Indeed not exactly what I am after but +1 for what appears to be routing web services from Lockheed Martin. $\endgroup$
    – A_A
    Commented Apr 13, 2015 at 21:20

I'm with ForeFlight and wanted to let you know we have a commercial API that offers exactly this service. As @thunderstrike said, I'm afraid you'll find most services like this are commercial in nature as the formulas are proprietary and the potential cost savings can be very high.


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