Re: pedagogical use of helicopters

[William Beaty <billb@ESKIMO.COM>]

On Sat, 14 Aug 1999, John Denker wrote:

>  1) A hovering helicopter is a strange beast.
>    1a) From a distance, from a black-box point of view, a hovering
> helicopter is rather similar to a rocket, hovering on pure thrust.  It is
> not analogous to an airplane.

Ah, you've cut to the central point in the Newton/Bernoulli lifting-force
controversy.  How can any aircraft remain suspended above the ground (or
remain in level flight)?

It can either push upon the earth, or it can employ action/reaction in the
way a rocket does.  A helium balloon pushes indirectly upon the earth.  So
does an aircraft in "ground effect" flight.

But when an aircraft is far from the earth, its only option is to employ
action-reaction to produce a net downwards acceleration of massive gasses.
In other words, the air within the wake-vortex pair behind an aircraft has
been given a net downwards motion and this acts like a "rocket exhaust."
WHen far from the earth, this is the "pure thrust" on which the aircraft
rides.  At the same time the aircraft is thrust upwards against gravity.
The wings of an airplane do not simply create a spinning pair of
wake-vorticies, they also project those vorticies downwards.  When the
aircraft is far from the earth, this is the only source of lift.  Without
those downwards-moving vortices, aircraft could not remain aloft.


Once we accept all of the above, it becomes obvious that helicopters are
very much like conventional airplanes in that they both ride ENTIRELY upon
thrust.  True, we can reduce the energy losses in an airplane by makings
its wings longer.  We can also do the same thing with the rotor of a
helicopter. If the wings (or rotor blades) can intercept enough mass per
second, then they need not deflect the mass by much, and so the energy
loss is reduced.  An infinite wing (or rotor blade) can produce a lifting
force without any induced drag.




I've seen many arguments over the years which focus upon the circulation
surrounding a 2D airfoil.  One facet of this has not been examined here:
if the circulation extends to a great distance around an airfoil, then it
necessarily interacts with the ground.  As a result, a 2D simulation
depicts ground-effect flight, not the normal high-altitude flight of a
real-world aircraft.  In ground-effect flight there is need for any
"exhaust" flung downwards.  If the airfoil is interacting with the surface
of the earth, then we now have the "bouncing baseballs" analogy in
operation, and the mass of the "trampoline" has essentially become
infinite.  This only works for ground-effect flight.  In a 3D aircraft the
circulation pattern which surrounds various parts of the wing cancels at a
distance from the aircraft.  The circulation cannot reach the ground.  A
3D aircraft is fundamentally different than a stack of 2D airfoil
simulations.


Another problem with the 2D models:  in two dimensions the net upwash MUST
equal the net downwash.  In other words, in two dimensions the streamlines
around the airfoil form circles.  In a 2D-world there can be no trailing
vortex.  A 2D-world lacks the degrees of freedom required to create a
downwards "exhaust".   If we follow a parcel of air, we will see it
accelerated upwards as the airfoil approaches, then accelerated downwards
as it passes the airfoil, then accelerated upwards once more.  There has
been no *net* force applied to the parcel of air.  In three dimensions
things are different: each parcel of air is accelerated upwards to become
upwash, then is accelerated downwards as the airfoil passes, then *remains
moving downwards* as part of the wake-vortex pair.  The parcel of air has
experienced a net downwards accleration, and the aircraft has been
accelerated upwards.


In a 3D world, the air which is far in front of the aircraft is
undisturbed, but the air which is far behind it has been given a net
downwards motion.  This change in momentum is the source of the lifting
force.  In 3D the streamlines of circulation do not form circles, instead
it's possible for the "circulation" streamlines to break free of the wings
and go spiralling downwards as the wake-vortex moves downwards.  This
demonstrates that a real wing is NOT just a stack of 2D airfoils, and if
we concentrate on the lessons of 2D circulation, then we will miss some
vital phenomena which only arise in a 3D system.

It might profit students to learn first how a 3D wing works, and only
later to examine the strange world of "flatland aerodynamics."  I find
that it's far easier to understand the features of 2D simulations *after*
I've seen some clear explanations of the physics of wings in three
dimensions.


Another problem with 2D models: in an inviscid 2D simulation the
circulation can continue forever once it has been established.  In an
inviscid three-D situation, things are different: there is a massive
leakage of circulation in the form of the wake-vortex pair.  The books
I've examined point out that a sheet of vorticity flows from the trailing
edge of wings as well as from their tips. In a 3D wing, energy must be
expended continously in order to re-establish the circulation, and this
cannot occur if the air has zero viscosity.  This is not true in 2D.  In
2D an airfoil can essentially fly forever, and the circulation need only
be created once during takeoff.  In 2D, the "starting vortex" assumes an
importance which is totally lacking in a 3D airplane.

If we concentrate too much on 2D simulations, we will come to believe that
real-world airplanes should be able to fly forever, that
pressure-differences are the central concept, that action-reaction is
unimportant and there is zero net deflection of air by the wing, and that
the wake-vortex pair which trails behind the aircraft has little to do
with the generation of the lifting force.


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