Why things fly, and why the usual explanation is wrong.
A wing lifts because there is circulation round it, not because the air over the top has further to travel. That story is in a great many textbooks and it is simply false, and it can be shown to be false by computing the two quantities it equates. These are essays about how air and water actually move, one idea at a time, with every flow solved and checked rather than sketched.
Start anywhere
the essay that opens each part of the subject, of 460
Flows and fields
Streamlines are not the paths particles take
Three different curves get drawn through a flow and they are routinely treated as one. In steady flow they coincide, which is why the confusion survives; in unsteady flow they are as different as a photograph and a long exposure.
Ideal flow
The theory that solves everything
Throw away viscosity and assume nothing is spinning, and fluid mechanics collapses into a linear problem with closed-form answers. The price is one term, and the term turns out to matter more than everything kept.
Circulation and lift
What actually holds a wing up
Not the shape, and not the story about air meeting up again behind. A wing lifts because there is circulation round it, and the sharp trailing edge is what decides how much.
Viscosity
Everything happens in a layer you cannot see
Air has so little viscosity that ignoring it works almost everywhere. Almost everywhere leaves out a film next to the surface, perhaps a millimetre thick, and that film decides drag, stall and whether an aircraft flies at all.
Regimes and numbers
One number decides which physics applies
A bacterium and a whale both swim, and they are not doing the same thing at different sizes. The ratio of inertia to viscosity separates them, and crossing it changes the rules rather than the magnitudes.
Compressible flow
What a signal travels at
Air finds out that an aeroplane is coming, and it finds out at a definite speed. That speed does not depend on how hard the air is squeezed or on how much of it there is — only on how hot it is — and every result in compressible flow is downstream of that one fact.
Transition and turbulence
The solutions stop being chosen
Hagen and Poiseuille's pipe profile is an exact solution of the Navier–Stokes equations at every Reynolds number, and it is linearly stable at every Reynolds number. Something else happens at 2300 anyway, and it is not that the solution stopped being one.
Fluids at work
The most a disc can take
A wind turbine cannot extract more than sixteen twenty-sevenths of the energy passing through the circle its blades sweep. That is not a limit on turbines — it is a limit on anything at all, and it follows from three conservation laws and no engineering.
What is taught wrongly
The story about air meeting up again
The most repeated explanation of lift says that air parting at the nose must rejoin at the tail, so the longer upper path forces a higher speed. The premise is false, and the speed it predicts is wrong by a factor of twenty.
Just added
- A choked throat buys time, not silence — what is taught wrongly
- The drift that turns a current into rolls — flows and fields
- The nozzle that is best at one thing — fluids at work
- The pulse that has to travel — regimes and numbers
- The floor that gives the drift back — flows and fields
- The pulse that grows as it leaves the heart — regimes and numbers
- The spot a local theory cannot see — what is taught wrongly
- The wall the suction puts in the curve — fluids at work
- A boom is aged in the thin air it starts in — compressible flow
- A choke that belongs to two streams — fluids at work
- A lighter spar turns a box wing into a biplane — circulation and lift
- Four cameras and a field they cannot see — what is taught wrongly
- The decay inside the four-fifths law — transition and turbulence
- The heat the eddies do not carry — regimes and numbers
- The pump that is better the more it squeezes — flows and fields
- Past three, an ellipse is a shear layer — ideal flow
- Two rings leapfrog only if they start alike — circulation and lift
Three ways through
none of them a list of essays
Series
One idea taken as deep as it goes — each essay a distinct argument with its own figures, in the order they have to be read.
Every figure, by regime
Sorted by the hypothesis each one states — the Reynolds band, the Mach band, or the declaration that viscosity is absent and the answer holds at all of them.
What is refuted here
Every wrong explanation this collection tests, with the computation that settles it and the verdict it returned.
The parts of the subject
Flows and fields
Streamlines, particle paths and the field that carries them. What is conserved, what a picture of a flow can show, and what it cannot.
Ideal flow
The exact theory of a fluid with no viscosity — closed-form, elegant, and predicting no drag at all. Its failure is the most useful thing in the subject.
Circulation and lift
Where lift actually comes from. The Kutta condition, the Joukowski aerofoil, and lift derived rather than asserted.
Viscosity
The thin layer next to a surface that ideal flow ignores, and which supplies drag, separation and the wake.
Regimes and numbers
Reynolds, Mach, Froude, Strouhal. One number decides whether a flow creeps, separates or shocks, and the same shape behaves differently at each.
Compressible flow
What changes when density stops being a constant. Shocks, expansion fans, nozzles that work backwards, and the one place on this site where an inviscid flow has drag.
Transition and turbulence
Where the laminar solutions stop being the ones the flow takes, and what can honestly be said about what follows — which is less than the textbooks imply and more than nothing.
Fluids at work
Turbines, pipes, weirs, balls, sails, arteries and blades. What the conservation laws say about machines, which is more than a designer expects and less than a brochure claims.
What is taught wrongly
Equal transit time, Bernoulli misapplied, and the rest. Each stated fairly, then tested against a solved flow and found false.
Threads running through
The exact theory is wrong
Ideal flow is closed-form, elegant and predicts that an aeroplane needs no engines. Every honest account of this subject is organised around what that failure reveals.
One number decides the regime
The same shape in the same fluid behaves completely differently at different Reynolds numbers. The shape is not the question; the ratio is.
Lift is circulation
Not shape, not equal transit times, not air pushed down in the way usually claimed. Lift is the circulation round the body, and the Kutta condition is what fixes it.
Everything happens in a thin layer
Viscosity is negligible almost everywhere and decisive in a film a millimetre thick, and that film decides drag, stall and the wake.
What is conserved
Mass, momentum, circulation, vorticity. Every result worth having is a statement that one of them cannot go anywhere, and every check in this site's solver is a test that it did not.
A smooth picture proves nothing
Streamlines are smooth whatever nonsense produced them. A flow figure is only worth as much as the conservation laws it was checked against.
Taught wrongly, everywhere
Some of the most repeated explanations in physics education are in this subject, and they are false. Stating them fairly and then testing them is more useful than ignoring them.