# How can I calculate a flightpath given a set of waypoints?

I have made a GUI that allows the user to create waypoints defined by latitude, longitude, altitude, and time-of-arrival. I'm looking for some software that can generate a flightpath between the waypoints.

For example, say that I have placed 5 waypoints. All that I know is that I want my aircraft to be at those five points in space at the times specified. To create my 'flightpath', I want to calculate the latitude, longitude, altitude, pitch, roll, yaw, and velocity of the aircraft as it moves from one waypoint to the next. I'd like to calculate those values for time intervals of, say, one second.

I've made a hackish solution, but it isn't very realistic. Someone must have tackled this problem before. Does anyone have any suggestions on software or algorithms I can use?

• What do you mean by "simulates a flightpath"? Do you mean drawing lines between them, or animating the progression through them over time?
– fooot
Apr 28, 2015 at 18:44
• I hope I addressed what is needed. I do not mean drawing straight lines between then, I mean a progression through them over time. Apr 29, 2015 at 19:35
• It's more related to maths than to aviation. An actual flightpath has other constraints (performance, weather / wind, ATC rules...) that are not part of this geometry problem.
– mins
Apr 29, 2015 at 19:59
• It is a very math heavy problem; however, I thought that aviation folks would be more likely to know if such software exists. If my question is not appropriate for the aviation overflow, then I understand, and my apologies. Apr 29, 2015 at 20:07
• Nice question, I 've done this in the past. How realistic does it need to be? What are your requirement on accuracy. what is the purpose of the program. What kind of aircraft are you trying to do this for, do you have access to an aircraft performance model for the aircraft? Do you take wind into account, and other meteorological aspects? May 5, 2015 at 7:03

The Haversine equations will calculate the bearing and distance between any latitude/longitude pair, and can calculate the location and next bearing for points along a Great Circle.

They go back to the days of sail, shortly after the invention of the marine chronometer, which allowed calculation of the current longitude. As such they assume that the points are on the surface of an idea sphere; as Earth is slightly oblate, there is an error of upto 0.6% in calculations of locations. For any realistic altitude, the oblateness (23 km difference between polar and equatorial radius) is likely to be larger than the change in altitude.

A discussion of them is here http://www.movable-type.co.uk/scripts/latlong.html

If all you're looking for is calculations of ETE, ETA, headings, fuel burn, and other such items you can make use of the FAA's DUATS platform. Skyvector has some basic capability in this area as well.

You'll have to chase down the actual aircraft performance data to input into the software if you want realistic estimates, but the internet is awash with information manuals and operating handbooks for the more widespread families of light aircraft. Google is your friend for this one. As for numbers between waypoints, the simple and lazy, but often sufficient, solution is to simply interpolate.

Commercial solutions exist as well such as ForeFlight and AOPA's FlyQ, but I doubt they would add anything of substantial value for your particular needs.

• Thanks those are some great leads! I think this is the closest answer that I'm gonna get. Thank you so much. May 7, 2015 at 14:12
• @StephenHartzell - something occured to me. Are you trying to implement a program where the user inputs a series of waypoints and times that they want to be over those waypoints at and the program returns the parameters that they must fly at in order meet those times? In this case, there would be several ways that you can go about this. If you wanted to build everything from scratch, you could look into linear programming (maybe nonlinear too) techniques. Gradient techniques might also be helpful if you can efficiently piggyback off existing flightpath calculation solutions.
– habu
May 7, 2015 at 14:48
• Also, if that's the case, this question might be more appropriate for the math, DataScience, or SO SEs, depending on your focus.
– habu
May 7, 2015 at 14:49
• You are correct, but I was also searching for any known software that does that. That's why I thought it was appropriate for this the aviation stackexchange. My current approach is very mathy, and like i said it works ok'ish. I was just searching to see if there was already a solution (which probably does use advanced mathematical techniques). May 8, 2015 at 15:43
• @StephenHartzell - a perfectly reasonable assumption to make. I suggested the other SEs if you were looking for specialized knowledge to help develop the solution. With respect to figuring out airspeed and flightpath, I would imagine that proprietary software does exist, or at least the capability might be embedded in dispatch software packages, as both the airlines and the military need to engage in a certain amount of flight profile optimization to make schedules work, and it would be time consuming to figure it all out by hand. Not sure how that would be helpful to you, unfortunately
– habu
May 8, 2015 at 16:46