Trajectory Program (Fermat-Torricelli Point System)

Krag

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Nov 24, 2025
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Hello, I am in the process of designing a global trajectory program for civil aircraft. Two aircraft depart from their airports, join together to create a formation, then later separate and land at their destination airports.

A geometric method, that of the Fermat-Torricelli point, is used to determine the optimal point of formation. Through use of weightings, a formation angle can be determined without need for the destination airport.

The longitude and latitude of airports are known, as are the weightings, which represent normalised efficiencies.

Chapter 2, provides a good description of the methodology. Chapter 2.4 onwards is not necessary as I have a fuel burn model, which simply requires the distances of each phase.

https://www.researchgate.net/public...signment_for_Commercial_Formation_Flight#pf23

Could somebody please explain to me how to generate loci of possible join points as illustrated in 2.2.4?

I am using MATLAB to code a trajectory generation for two departure and destination airports over the Atlantic.

If this project interests you I’d be happy to discuss what I have done so far and take any suggestions you may have.
 
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