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Needlessly click-baity article title. TLDR: We don't have a full solution that models flight. We also don't have a full understanding of how bicycles work.

FabHK 7y ago
> TLDR: We don't have a full solution that models flight. We do, actually. It's just hard to explain.
- NikolaeVarius 7y ago
  There is a Millennium Challenge problem to provide a solution to the Navier Stokes Equations which are a fundamental component of modeling flight. The entire article about how none of the current models fully explain how a plane stays in the air. So what is this full solution you are talking about because my Aero professors must have done a bad job teaching the topic to me
  - FabHK 7y ago
    I'll let the article (which we are discussing here) speak for itself (my highlighting though): > accounts of lift exist on two separate levels of abstraction: the technical and the nontechnical. [... The former] exists as a strictly mathematical theory, a realm in which the analysis medium consists of equations, symbols, computer simulations and numbers. There is little, if any, serious disagreement as to what the appropriate equations or their solutions are.
    - NikolaeVarius 7y ago
      You are misunderstanding what a full solution means and what the article is saying. There are a systems of equations that allow us to model flight. But they are NOT a full model of flight characteristics, as a consequence of, like mentioned, lack of a full solution to the Navier Stokes equations > The solutions of those equations and the output of the CFD simulations yield pressure-distribution predictions, airflow patterns and quantitative results that are the basis for today’s highly advanced aircraft designs. Still, they do not by themselves give a physical, qualitative explanation of lift.
- diffeomorphism 7y ago
  Speaking as a mathematician, no. We have the Navier-Stokes equations, which we are fairly certain are a good model and which work well in practice/numerically. So an engineer might agree with your view. However, mathematically these equations are difficult, we have very few explicit solutions and the question of whether solutions to these equations are well-behaved in all circumstances is a famous open problem. Indeed, it is one of the Millenium problems and solving it will make you very famous. Also, your "I'll let the article speak for itself" is rude and naive.

FabHK 7y ago

> TLDR: We don't have a full solution that models flight. We do, actually. It's just hard to explain.

NikolaeVarius 7y ago
There is a Millennium Challenge problem to provide a solution to the Navier Stokes Equations which are a fundamental component of modeling flight. The entire article about how none of the current models fully explain how a plane stays in the air. So what is this full solution you are talking about because my Aero professors must have done a bad job teaching the topic to me
- FabHK 7y ago
  I'll let the article (which we are discussing here) speak for itself (my highlighting though): > accounts of lift exist on two separate levels of abstraction: the technical and the nontechnical. [... The former] exists as a strictly mathematical theory, a realm in which the analysis medium consists of equations, symbols, computer simulations and numbers. There is little, if any, serious disagreement as to what the appropriate equations or their solutions are.
  - NikolaeVarius 7y ago
    You are misunderstanding what a full solution means and what the article is saying. There are a systems of equations that allow us to model flight. But they are NOT a full model of flight characteristics, as a consequence of, like mentioned, lack of a full solution to the Navier Stokes equations > The solutions of those equations and the output of the CFD simulations yield pressure-distribution predictions, airflow patterns and quantitative results that are the basis for today’s highly advanced aircraft designs. Still, they do not by themselves give a physical, qualitative explanation of lift.
diffeomorphism 7y ago
Speaking as a mathematician, no. We have the Navier-Stokes equations, which we are fairly certain are a good model and which work well in practice/numerically. So an engineer might agree with your view. However, mathematically these equations are difficult, we have very few explicit solutions and the question of whether solutions to these equations are well-behaved in all circumstances is a famous open problem. Indeed, it is one of the Millenium problems and solving it will make you very famous. Also, your "I'll let the article speak for itself" is rude and naive.