Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Concept

Solidity — where it appears

The ratio of blade chord to blade spacing in a row, or of total blade area to swept area in a rotor. It decides how completely a blade row guides the flow to its own angle and how much lift each blade carries in doing so, and those two move in opposite directions.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Same disc, same solidity, different number of blades, different answer. Thrust and power coefficients for six blade counts at a fixed solidity. They span a factor of 1.101 in thrust, and every one of those rotors is the same actuator disc: same area, same blade area, same tip-speed ratio. The disc theory cannot distinguish them because the blade count is not one of its variables.

A disc that knows no blades

Momentum theory replaces a rotor with a surface across which the pressure jumps, and gets the Betz limit, the induced velocity and the whole energy argument out of it. It has no chord, no section and no number of blades — and at one fixed solidity, two blades and twenty give thrust coefficients ten per cent apart.

circulation · Blade-element Deviation: how far the flow leaves from the blade angle, against solidity. The angle between the outlet flow and the blade, for a row of flat plates at 30° stagger meeting a flow at 45°. An open row barely turns the flow at all and the deviation is nearly the whole of the intended turning; a tight row guides it to within a thousandth of a degree of the blade angle. Nothing about the blade changed between the two ends of this curve.

A row is not a set of aerofoils

An isolated aerofoil's incidence is measured from the free stream. A compressor blade's cannot be, because an infinite row of identical blades above and below it has a circulation that is part of its own free stream — and the velocity the theorem uses is a vector mean that exists nowhere in the machine.

circulation · Cascade

Named alongside it

The objects these essays reach for when they reach for this one.

CirculationModel limitActuator discThe Betz limitBlade-elementCascadeDeviationEfficiencyInduced velocityKutta–Joukowski theoremLift coefficientLift curve slope

All concepts