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Open Aircraft Drag Polar Model
Junzi Sun, Jacco M. Hoekstra, Joost EllerbroekDelft University of Technology
Sesar Innovation Days 2018Salzburg, Austria
Why are we talking about the Drag Polar now?
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What is a drag polar?
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1. It is an aircraft aerodynamic model
2. It describes the relationship between Lift and Drag
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Theory
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Aircraft dynamics
α: angle of attack
θ: pitch angle
γ: flight path angle
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Aircraft control surfaces
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Lift and drag coefficients
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The drag polar
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Current problems (Challenges)
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Challenge 1: Point-mass model
- “angle of attack” removed
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Point-mass model
α: angle of attack
θ: pitch angle
γ: flight path angle
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Challenge 2: Lack of openness
- Missing public data from manufacturer- The closed-source “go-to” model (BADA 3/BADA 4)
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Can we / How to estimate them?
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The drag polar
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Problem formulation
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/ V
/ V
/V
Problem formulation
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/ V
How to solve this using optimization?
10 Variable N Time steps
10 x N Dimensions
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Bayesian computationMarkov chain Monte Carlo with Metropolis algorithm
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Bayesian representation - the hierarchical model
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1 - Monte Carlo
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Monte Carlo
Source: Chuck Huberhttps://blog.stata.com/2016/11/15/introduction-to-bayesian-statistics-part-2-mcmc-and-the-metropolis-hastings-algorithm/
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Monte Carlo
Source: Chuck Huberhttps://blog.stata.com/2016/11/15/introduction-to-bayesian-statistics-part-2-mcmc-and-the-metropolis-hastings-algorithm/
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2 - Markov chain Monte Carlo (MCMC)
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MCMC
Source: Chuck Huberhttps://blog.stata.com/2016/11/15/introduction-to-bayesian-statistics-part-2-mcmc-and-the-metropolis-hastings-algorithm/
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MCMC
Source: Chuck Huberhttps://blog.stata.com/2016/11/15/introduction-to-bayesian-statistics-part-2-mcmc-and-the-metropolis-hastings-algorithm/
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2 - Markov chain Monte Carlo with Metropolis algorithm
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Source: Chuck Huberhttps://blog.stata.com/2016/11/15/introduction-to-bayesian-statistics-part-2-mcmc-and-the-metropolis-hastings-algorithm/ 29
Source: Chuck Huberhttps://blog.stata.com/2016/11/15/introduction-to-bayesian-statistics-part-2-mcmc-and-the-metropolis-hastings-algorithm/
MCMC with Metropolis
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Can this be solved?
10 Random variable N Time steps
10 x N Dimensions
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MCMC sampling of several states
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An easy way to ensure the convergence: Multiple MCMC chains
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Posterior distributions
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Verify with basic CFD results
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Verify with basic CFD results
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From
one AC type, one flight to Many AC types, many flights
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Flight data
- 20 aircraft types- FL30 to FL150, clean flaps configuration- High resolution (update rate) data.- Accurate real-time wind and temperature data (Meteo-Particle model *)
* Weather field reconstruction using aircraft surveillance data and a novel meteo-particle modelhttps://journals.plos.org/plosone/article?id=10.1371/journal.pone.0205029
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Drag polar of multiple aircraft types (Clean configuration)
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Comparison with BADA 3
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Open Drag Polar
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Challenge 2: Lack of openness
- Missing public data from manufacture- Closed-source “go-to” model (BADA)
Challenge 2: Lack of openness
- Missing public data from manufacturer- Closed-source “go-to” model (BADA 3 / BADA 4)
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Conclusion
Limitations
- Mass uncertainty
- Thrust uncertainty
- Fixed aspect ratio
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- Better model for span efficiency e
- Incorporate fuel flow model
- Add more aircraft types
- Independent ways to validate and
refine the drag polar coefficients
Future work
