The New Theory of Flight presented on The Secret of Flight and now being under evaluation by AIAA, can be used as a real time study of a Scientific Revolution in the sense of Thomas Kuhn as the replacement of an Old Theory of Flight developed by Kutta-Zhukovsky-Prandtl 100 years ago (KZP-theory), which has been the ruling paradigm for 100 years, by a new better theory.
- A theory is a good theory if it satisfies two requirements:
- It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements,
- it must make definite predictions about the results of future observations.
Popper has a longer list but Hawking captures the essence. Let us now compare the qualities of the Old Theory and the New Theory according the Hawking’s test. We understand that a theory of physics like fluid mechanics, takes the form of a mathematical model.
OLD: KZP-theory for lift, as the essence of the Old Theory of Flight, is based on a mathematical model consisting of:
- 2d potential flow modified by large scale circulation determined by the Kutta condition of zero velocity at the trailing edge.
NEW: The New Theory is based on a mathematical model consisting of:
- Navier-Stokes equations with vanishingly small viscosity and a slip boundary condition.
- Both OLD and NEW represent ideal models in the sense of Einstein, as models without free parameter.
- OLD makes predictions only for lift and then only for smaller angles of attack before stall.
- NEW predicts both lift and drag for all angles of attack including stall and much more.
- OLD is a very limited mathematical model of fluid flow as invicid, stationary, irritational and incompressible flow plus a circulation modification.
- NEW as Navier-Stokes/slip is a very general model essential describing all slightly viscous fluid dynamics.
- OLD postulates that the velocity at the trailing edge is zero, as a mathematical postulate which cannot be verified experimentally nor be justified from known physics.
- NEW is based on Newton’s 2nd Law and assumptions that the flow is incompressible and satisfies a slip boundary condition, which both agree with experimental observation.
We see that NEW is a good mathematical model, while OLD is very limited, and so according to Hawking’s Test NEW is much better than OLD.
The basic assumptions of a scientific mathematical theory must be possible to verify theoretically or computationally or experimentally. If this is not possible, the theory is not science but a pseudo-science. NEW is science, OLD is pseudo-science.
An example of a pseudo-scientic theory is the Turtles-all-the-way-down-theory based on the assumption that the Earth rests on 4 tortoises which are invisible and cannot be detected in any way, which themselves rest on 4 invisible turtles, and so on. Another is statistical mechanics based on the assumption that atoms play dice.
NEW also opens to understanding exactly how lift and drag are generated by a wing as real physical fluid mechanics phenomenon, while OLD already from start was conceived as a “mathematical trick” with the Kutta condition of zero velocity at the trailing edge as an ad hoc unphysical dictate.
Note that Scientific Revolutions do not take place every year, rather every 100 years or more:
- Newton’s mechanics replaced Aristotle’s mechanics in the 17th century.
- Einstein’s relativity replaced Newtonian mechanics in the beginning of the 20th century, at speeds approaching the speed of light
- Quantum mechanics replaced Newtonian mechanics in the beginning of the 20th century, on atomic scales.
- Digital computing replaced analog computation in the mid 2oth century.