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Formation flight design via Constructal Law.

Samuel A Savitt1

  • 1Duke University Department of Mechanical Engineering and Materials Science, Durham, 27708-0187, NC, USA.

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|May 29, 2025
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Summary

Formation flight optimizes energy savings by adjusting V-formation designs. The optimal configuration evolves with changing parameters to evenly distribute drag, maximizing energy efficiency.

Keywords:
AerodynamicsAircraftBirdsConstructal lawDesign evolutionDesign optimizationFormation flight

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Area of Science:

  • Aerodynamics
  • Biophysics
  • Fluid Dynamics

Background:

  • Formation fliers conserve energy by flying in the wake of others, reducing drag and increasing lift.
  • The Constructal Law provides a framework for understanding how systems evolve to achieve optimal performance.

Purpose of the Study:

  • To apply the Constructal Law to V-formation flight to determine the optimal configuration for energy savings.
  • To develop an analytical model predicting optimal formation flight based on fundamental parameters.

Main Methods:

  • An analytical model was developed to predict optimal V-formation configurations.
  • The model considers fundamental parameters: velocity, number of fliers, wingspan, weight, and air density.
  • The distribution of induced drag among fliers was analyzed.

Main Results:

  • Optimal V-formation design is not fixed but evolutionary, adapting to changing system parameters.
  • The model predicts that optimal configurations maximize energy savings by adapting to parameter variations.
  • Induced drag is distributed as uniformly as possible among fliers in optimal configurations.

Conclusions:

  • The optimal formation flight configuration is dynamic and adapts to maximize energy efficiency.
  • Constructal Law principles predict a uniform distribution of induced drag in optimal V-formations.
  • Model predictions are supported by observations in natural systems.