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Old September 23rd 03, 06:37 AM
Mark Cherry
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In ,
Dave Daniels wrote:

In article ,
ArtP wrote:


snip

It sounds like you are confusing parasitic drag and induced drag.
Parasitic drag (result of friction) increases as with speed. Induced
drag (result of AOA) decreases with speed (the faster you go the
smaller the AOA required to maintain altitude).


That begins to make more sense. I think that my problem was that
I was assuming that the induced drag decreased with velocity at
any angle of attack or altitude. If the lift is constant, then
higher speeds require a smaller lift coefficient and therefore the
induced drag coefficient is smaller. Am I on the right track here?

Dave Daniels


If you'd typed "If the lift is constant, then higher speeds require a smaller
angle of attack and therefore induced drag {quantity of} is smaller", I'd have
agreed with you immediately. I fail to see how coefficients (of anything) can
become smaller, or larger.

Sorry to be pedantic but, as far as I understand it, 'coefficients' are physical
constants. In this case, they are characteristics of a particular airframe.

The parasitic drag coefficient will go in proportion to a combination of frontal
area and total surface area (note that the frontal area presented to the
relative wind will change with variations in angle of attack, following a pitch
control input). The quantity of parasitic drag increases with the cube of the
airspeed, multiplied by this coefficient, mutiplied by the mass per unit time of
air flowing over it. (in kg.m.s-1 aka Watts, if I' m not mistaken)

I was loose with the definition of airspeed there and since we're cubing it, we
need to be more specific. Whilst TAS is fine for dead reckoning navigation
calculations, I think IAS is a better measure of airflow over the wing because
the stalling speed is the same, expressed in IAS, at all altitudes. (And when
that stalling speed converges with the highest achievable forward speed in level
flight, the plane reaches its 'service ceiling'). IAS falls short of TAS by an
increasing margin, as altitude increases and I think the drag should be
calculated on the basis of the lower, IAS value.

As I see it, a given mass of air (density * volume), moving over a wing in unit
time will produce a given quantity of lift, at a specified AoA, whether you
prefer the Bernoulli principle, or the air-deflection theory (or both) for what
generates it. Therefore, at altitude you *can* fly faster and further (in unit
time) but you also *have to* in order to generate enough lift. (You have to fly
through a larger volume of less-dense air for the mass to be the same, which can
only be done by travelling further forward and, if done in unit time, this
obviously means faster).

As mentioned in previous replies, induced drag is the result of the production
of lift which, by not being perpendicular to the wing (as viewed in
cross-section) retards forward motion to some extent. At higher speeds, the
required amount of lift can be achieved at a reduced angle of attack. This
brings the induced drag vector closer to the vertical and the retardation
component of it is thus minimized (it never totally goes away). A useful side
effect of this is that, by presenting a reduced frontal area to the relative
wind (nearly edge-on), the element of the planes parasitic drag, contributed by
the wings, is reduced and higher speeds become more possible. The induced drag
coefficient, however, remains a constant, for that particular aircraft.


One slight complication (for the programmer) is that real wing profiles are not
uniform across the span - the wingtips may present a slightly different AoA to a
particular relative wind than the wing roots. It can be designed that way so
that *part* of a wing will stall at a slightly higher speed than (and thus in
advance of) the section where the control surfaces are. The turbulence of the
stalled portion causes a vibration which the pilot will be able to feel, as a
warning that a full stall is about to occur and give them time to take action.
Conversely, when no stall is occuring, the fractionally higher AoA means the
wing roots generate more lift than the wingtips, so the strongest part of the
wing takes a larger share of the overall load and wing flexing is minimized.

As far as PC simulators are concerned, modelling multi-modal wings like that, or
the fluid dynamics calculations of air over wings is still far too complex, so
they have to treat a plane as a point mass, with moments of inertia (if that's
not a contradiction in terms) and calculate the forces acting on it. Separate
factors for induced drag, surface area drag etc go into the flight model but
these may be empirically determined values which just happen to make the overall
flight model performance feel 'right', across a range of conditions, rather than
having any resemblance to corresponding factors for the real thing.


--
regards,

Mark