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How do rotorcraft (helicopters, and other rotary aircraft etc.) achieve lift? I mean, obviously the rotor. But who knows the specifics?

What are the physical, mechanical requirements of a rotary blade (propeller?) to achieve sufficient lift to carry

  1. its own weight and
  2. the weight of the vehicle?
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A vehicle moving within a fluid may control its velocity by reaction, by accelerating a mass of that fluid in a convenient direction, and at a convenient rate. Using a wing is an excellent way to achieve that; birds and airplanes are able to fly by using wings that accelerate air down- and rearwards, and a propeller is nothing but a set of slender wings attached to a rotating hub.

In order to achieve a given thrust, that propeller must have a convenient size, and has to rotate at a high enough speed, so that it accelerates a mass of air and the change of momentum of that mass of accelerated air is transformed into a force that we call thrust. The magnitude of that change of momentum is proportional to the mass of air moved and to its change of velocity.

The rotor of a helicopter is just a large propeller that accelerates air downwards (and also rearwards, and sideways too, by means of a control called 'the cyclic')

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To understand this, take a look at Bernoulli's Theorem, or the Theory of Flight.
A helicopter rotor blade is simply an airfoil/aerofoil, and looks much like an aircraft wing (in cross-section).

Look at a diagram of a Venturi tube. Air goes in one end, and the SAME quantity of air has to come out the other end (per unit of time, say per sec). A Venturi tube progressively narrows, then progressively widens again. To get through it, the air has to speed up as the tube narrows (since the mass of air entering and exiting per sec is fixed - what goes in one end must come out the other end).

According to Bernoulli, when the flow of a compressible fluid (in this case air) speeds up, the density of the compressible fluid goes down (and vice versa). Pressure is directly related to density, so pressure also goes down when flow rate (velocity) goes up. The lowest pressure is at the narrowest part of the Venturi tube.

An airfoil/aerofoil cross-section can be looked at as half of a Venturi tube. At the thickest part of the chord, the pressure of the air flowing OVER the airfoil (a.k.a. aircraft wing or helicopter rotor) is lowest. This low pressure (relative to the surrounding air) results in a force called Lift. Lift opposes weight, so if you generate enough Lift (if the helicopter's rotors move through the air fast enough), then there is enough upward force (Lift) for the heli to take-off.

Mathematically, Bernoulli's Theorem is expressed (rho) times v = constant.

Here, (rho) is density, v is velocity.

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    $\begingroup$ Actually while that is always spoken of as a source of lift, it only may account for about 5-10% of th total lift generated. The vast majority of the lift generated comes as a result of altering the momentum of the air moving over an airfoil where it leaves the trailing edge of the airfoil in a downward direction, producing an upward lifting force as a result of Newton’s Third Law of Motion. As for Bernoulli’s principle creating lift, I place that in the category of “Lies my Science Teacher and Flight Instructor Told Me.” $\endgroup$ – Carlo Felicione Sep 15 '18 at 16:33
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    $\begingroup$ note that Bernoulli is not a good explanation of lift: aviation.stackexchange.com/q/44882/1467 $\endgroup$ – Federico Sep 15 '18 at 18:11

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