The Secret

This site presents a New Theory of Flight revealing the Secret of Flight in an explanation in mathematical terms why it is possible for a bird and airplane to fly at an affordable expense of energy, that is with a lift to drag quotient bigger than 10.

The New Theory shows in particular that the classical theory of Kutta-Zhukovsky-Prandtl does not capture true physics, and as such is misleading.

The New Theory also opens for the first time to computational simulation from first principle physics at affordable cost in the form of Direct Finite Element Simulation DFS.

DFS allows simulation of the full dynamic flight characteristics of an airplane with readily available computational power in close accordance with observations.

DFS uses a slip/small friction boundary condition in agreement with observations and thus does not fall into the trap of Prandtl’s boundary layer theory asking for computational resolution of thin boundary layers, which has made Computational Fluid Dynamics into an impossibility with foreseeable computer power.

The New Theory is thus intimately connected to computation which unlocks the Secret of Flight and makes the true magic of flight understandable in mathematical terms.

You will be able to discover the SECRET OF FLIGHT by going through the following steps connecting to Basic Mantra of Flight and Basic Principle;

  1. Watch a movie of real flow around and airfoil to see key features of the flow.
  2. Recall Bernoulli’s Principle \frac{1}{2}V^2 + P = Constant.
  3. Understand the formation of lift and drag from leading edge flow attachment.
  4. Understand trailing edge separation without stagnation and pressure rise.

1. Recording of Real Flow

Key features to observe as the angle of attack changes:

  • The flow attaches smoothly to the leading edge and stays attached until trailing edge before stall.
  • The flow leaves the the trailing edge smoothly without retardation.

2. Bernoulli’s Principle

Real Flow Around a Wing

The above picture shows the secret of flight:

  • Low pressure (blue) on top of the leading edge giving lift L about 3 times as big as
  • the high pressure at the front of leading edge giving drag D
  • resulting in blue area/red area = L/D > 10.
  • The flow leaves the wing at the trailing edge without high/low pressure
  • in a downward motion as downwash creating lift as reaction force.

Potential Flow Around a Wing

We compare with zero potential flow without downwash with high/low pressure at the trailing edge destroying lift to zero and reducing drag to zero:

Potential Flow Around a Circular Cylinder

We compare with the pressure distribution P(\theta ) over the front and top of a circular cylinder given as

  • P(\theta ) = -1 + 2 \cos (2\theta )

where the angle \theta =0 in the front (P = 1) and \theta =90 on top as illustrated in the following picture (P = -3):

Revealing the Secret

The secret of a wing is to not destroy the L/D > 10 created at the leading edge, by separating at the trailing edge without the high/low pressure of potential flow, by 3d rotational slip separation with point stagnation as explained in Separation.

The secret of flight is to explain why the real flow is not potential flow, when potential flow solves the Navier-Stokes equations describing real flow.

The secret of flight is to understand what is wrong with the potential solution as a solution of the Navier-Stokes equations.

Prandtl’s answer was the boundary condition, which showed to be wrong:

  • The potential solution does not satisfy a no-slip boundary condition requiring both the normal and tangential flow velocity to vanish on the boundary.

The New Theory shows that it is instead stability:

  • The potential solution is unstable at separation and thus is unphysical.
  • The zero lift and drag of the potential solution is unphysical and is not observed.
  • The instability of the potential solution makes the flow separate without high/low pressure and thus generate both lift and drag from the leading edge.

The Real Thing

After this introduction we are ready to face the reality of the secret reveal in the following Navier-Stokes/slip plots of velocity and pressure for angles of attack ranging form 4 to 20 degrees  (with comparison to measurements in Experiment vs Computation):

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