Aerodynamics of the AST
During the aerial portion of max zoom the
AST performed as an airplane with lift and drag
resulting from airflow over and around it. Both
are the result of air impacting surfaces which
either change the crafts position, lift, or slow
it, drag. Both are the result of dynamic
pressure (q), which is equal to ½ air density
times the velocity of the aircraft squared.
Thus q is proportional to altitude and to the
square of the velocity, thus doubling speed
quadruples q, etc. Therefore, to achieve
virtually no lift or drag, necessary to achieve
space simulations, required a very low, nearly
zero, q obtained by very slow speed at very high
altitude. The two forces felt by an airplane,
lift and drag, are merely functions of q
multiplied by the surface area affected. A
typical resulting force (drag) is what you feel
when you hold a flat object against the wind in
a speeding car. Thus the force is four times
greater if the speed is doubled and will be
lower at the top of a mountain than at sea level
for the same speed.
Aerial Flight
Airplane flight is the result of air moving
over the lifting surfaces, and the air moves
faster over a curved side, creating a lower
pressure (Bernoulli Principle) than on the other
side. Thus aerodynamic lift pushes toward the
more curved side. That is true for every
lifting surface, wings, ailerons, stabilizers
(i.e. vertical and horizontal) and rudders,
propellers, even the turbine blades of the jet
engine.
It is impossible to get aero lift without
induced drag created by the friction of the air
contacting every surface and added drag
resulting from the energy transferred into the
air as a result of disturbances of the air,
called nonlinear or turbulent flow. Linear
flow, where the air flows in parallel
streamlines, creates far less drag, so the shape
and texture of the surfaces are important, as
well as the angle at which the air approaches
it, called angle of attack (alpha).
Flight performance is affected by the two
major parameters, lift and drag, which are
summed at the aircraft level, where they always
act through the center of gravity (c.g.) where
the entire weight of the aircraft is in
massbalance about all three axes. The
designer’s task is synergy between mass balance
and force balance.
The amount of lift created by an airfoil or
lifting surface depends on the angle at which it
impacts the air, alpha. Actually, the airplane
can be considered stationary and the wind
passing by it, as in a wind tunnel, and all
engineering calculations are the same, whichever
the case. Whenever an airfoil is at an alpha
that creates lift, positive or negative, then a
component of total drag, called induced, is the
result of velocity, air density and the
effective surface area of the airfoil, just as
lift is. Equations used to express
relationships are based on coefficients of lift
or of drag, found simply by testing every new
shape in a wind tunnel over the range of useful
angles of attack and airspeeds. As in this
case, much of design is empirical and it is
interesting to note that the Wright Brothers’
construction of a crude wind tunnel was a factor
in their success. The mathematical
relationships then allow analysis and design
with equations based on the coefficients for
different configurations/designs:

Lift= Coefficient of Lift x ½ air density x
square of the air velocity x the surface area of
the airfoil (or aircraft at the full level). 

Drag (Induced) = Coefficient of Drag x the same
as parameters as above. 

Moment (Roll, pitch or yaw) = Coefficient
of Moment x. 
The enumerable sets of equations required
for analysis and design of modern airplanes are
extremely complex and made practical only
because of the advanced state of computers.
Modern airplanes are sometimes designed with
unstable features to gain performance
advantages, and made flyable by computerized
control systems operating between the pilot and
the control surfaces, since human response is
quite limited. It’s interesting and
argumentative, though a bit discomforting for
pilots that these advances plus many others that
already allow unmanned military drones to
perform attack missions, will toll an end of
pilots in the cockpit, much sooner than we might
expect. Keep in mind that, even with technology
of the 1970’s the computer, not the pilot could
best handle the difficult and critical reentry
and descent on Space Shuttle, and that
capability was never a factor in either
Challenger or Columbia accidents. Oh, by the
way, commercial airline automated flying is the
easiest of all to implement with many more
layers of safety backups than currently
available with human control.
Airplane Performance:
In addition to Lift, the other inherent
parameters of powered flight are: Thrust, the
force to propel the airplane with propeller, jet
or rocket: Weight of the entire airplane, which
of course acts vertically through its center of
gravity and: Profile drag, which is the
resultant drag, exclusive of lifting surfaces,
due to the shape of the vehicle and impact angle
of the air. With thrust acting through the c.g.,
trim is the stable condition at which the
airplane is content to do what it is doing and
will continue, if undisturbed. The pilot has
trim controls for the three axes so it can be
established and no control forces are required
to remain in trimmed flight. Without
disturbances, handsoff flight results, with a
stable aircraft design.

The resulting equations for an airplane in
balance, e.g. trimmed flight are: Lift equals
weight times the cosine of the pitch angle and:
Thrust equals Drag added to Weight and
multiplied by the sine of the Pitch Angle.
Lift = Weight x cosine of pitch angle (=
Effective lift)
Thrust = Drag + Weight x sine of pitch angle
Where: W x sine p. a. is the induced drag
created from total lift.

Steady State Flight: Equilibrium Diagram

Airplane Stability
All of these discussions assume a rigid
airplane, which is never exact. Basically, this
assumption allows only the flight control
movements to affect the aircraft. Especially,
in high speed flight the flexibility of the
vehicle can have dramatic and unexpected
results, catastrophic in the case of individual
airfoils, for example, some of which are even
beyond mathematical predictions and require very
cautious and gradual flight test into the
stability envelope.
Static stability addresses the response of
the vehicle to small disturbances when it starts
in equilibrium (trim) and how it responds
immediately after the disturbance; merely
whether it is stable (moves back toward its
trim) or unstable (moves away from trim), not
what it does thereafter. Though, seemingly
trivial, an airplane that is statically unstable
would be pretty awful to fly no matter its
dynamics, because it could never be trimmed so
the pilot would work constantly to control even
level flight.
The three axes can be considered
independently for static stability with
reasonable accuracy. For example, in the
longitudinal case, the airplane remains in
symmetry to the other two planes. As with lift,
the torque forces required to rotate an airplane
about its three axes are determined for
different configurations in a wind tunnel and
like the Coefficient of Lift are recorded as
Coefficients of Moment, different for each
axis. This allows determination of what occurs
to an airplane when it speeds up or slows down
from the trim or when the stabilizer is moved up
or down to pitch the airplane. Similarly for
roll and yaw. A stable system is when a gust
pitches the nose up and the moments rotate it
back down to trim condition. In such a case the
CM is opposite the change in CL. Thus the
equation;
Static Longitudinal Stability =  dCM/dCL
Conversely, a positive rate of change of
moment coefficient with respect to rate of
change of lift coefficient would be unstable.
Static Longitudinal Instability= + dCM/dCL

Representative Pitching Moment Curves 
The yaw and roll planes, are orthogonal to
the longitudinal plane, but gusts can provide
disturbance in any plane. Both of these are
usually statically stable under anything but
grossly abnormal aft of center of gravity, which
would be outside the safe zone to fly the pitch
axis, in any case. Yaw stability is the result
of the long lever arm from c.g. to vertical tail
and roll is generally provided by dihedral of
the wings, where the tips are a bit higher than
the roots, so if a wing drops a bit a little
sideslip occurs and corrects it.
Dynamic Stability
Dynamic Stability addresses the entire
process of response (long term effects) of an
airplane to any disturbance. The equations for
dynamic motions are very complex, far from the
simple problems of static stability. Dynamics
can also cross over within the 3 axes, in which
cases it involves a much higher degree of
mathematical solutions, requiring simultaneous
solution of three partial differential equations
with calculus.
Dynamic reactions of aircraft vary greatly
but display four possible groupings, with unique
characteristics for each, when combined with the
static stability of the particular aircraft.
1.
Simple Subsidence: statically
stable, dynamically stable.
2.
Damped Oscillation: statically
stable, dynamically stable.
3.
Divergent Oscillation: statically
stable dynamically unstable.
4.
Divergence: statically unstable,
dynamically unstable.

Typical Aircraft Pitching Motions 
Case 4 is absolutely ruled out for
mancontrolled airplane design, since there
could be no trim point and that would be the
source of constant attention to flying the
airplane, far to demanding or even impossible
for the aircrew, whereas the other three might
be considered.
Case 1 is ideal from the standpoint of
requiring the least possible attention from the
pilot, but with some significant drawbacks. No
matter what disturbs the aircraft it hurriedly
returns to trim without oscillations. However
there are inherent disadvantages to having
extreme stability, especially in performance
tradeoffs, because drag, for example can be
greater decreasing many performance features.
Reduced responsiveness of the controls can be
another shortcoming.
Cases 2 and 3 must be evaluated against two
additional and primary parameters of dynamic
stability. Both of these affect the ability for
human control of dynamic responses.
First is the period of the motion created by
a timeconstant; that is the frequency
with which the airplane passes back through its
original position. The other is damping
factor; the rate at which the oscillations
increase or decrease, which is the slope of a
curve drawn so as to touch the maximum
excursions of the respective curves in Fig. 4.
The steeper the curve, the less the system
attempts to remain controlled and the more
correction required by the pilot to avoid
exceeding limits, like stall or to fly precisely
in weather or close formation. Clearly, if the
period is long (large time constant) the ability
of a pilot to cope with instability is improved
significantly, making it less uncomfortable and
disturbing. Likewise strong damping is
preferable and can make such a system
preferable. In the real world of aircraft
design, nothing comes free and everything is a
trade off, even in stability, where a very
stable airplane can be a very poor fighter
because it reduces responsiveness of the
vehicle, and other performance drawbacks.
One of my most unique experiences in flight
test was flying a specially equipped Mc Donnell
Douglas F101A, single seat, twin engine Voodoo,
fighter, in 1963. It was equipped with a side
arm controller, the first of its kind, now
standard in our F16 fighter. A special flight
control system could be turned on to override
normal flight controls and had the unique
capability to allow the pilot to select the
basic type of stability, as above, and to vary
these two primary stability parameters changing
the airplane from very stable to absolutely
uncontrollable. All the factors could thereby
be mixed or matched for a very broad look at
stability. The F101, like the 104 had a high
horizontal stabilizer and thus aerodynamic
pitchup risks, so it was equipped with a “kill”
paddle on the stick for immediate disconnect of
the flight control system whenever the reaction
was headed outside safe limits, which the test
pilots had to use on many occasions, and
pronto! The pilot’s reaction time had a lot to
do with the allowable limits, so we could
contest on how far around a turn we could fly it
before having to abort, but no one can deal with
really bad instability, no matter the skill
level. Lateral, and yaw axis stability
are basically the same in principle, but quite
different in results, but those axes can be
involved in serious stability problems, also.
A couple of very critical dynamics cases are
worthy of mention. One is that of control
surface (rudder, ailerons, etc) flutter, which
occurs suddenly at high speed when the airflow
becomes disturbed and the frequency of that
disturbed air matches the critical frequency
response of the surface at its connections to
the aircraft, or structural joints. The result
can be a sudden disastrous failure of the
airplane’s structure or loss of a critical
control surface. The other is known as
inertial, or sometimes called rollcoupling.
That phenomenon is the result of the moments of
inertia about the roll axis of the airplane. It
occurs as speed and roll rate increase, also
resulting in catastrophic sudden structural
failure of the empennage (tail) from a sudden
extreme yaw induced by a high roll rate. Both
have occurred in test flights, notably before
the advent of fast computers when the known
equations were too complex for automated
analysis. Incremental testing into increased
risk, with data evaluation between flights was
the only test option, which was slow and very
costly, as a result.
But there were a few unstable aircraft that
proved useful. I flew only one such aircraft
that had the problem in the roll axis, the H21,
helicopter. Stick free, it would have rolled on
its back in short order, which was
irrecoverable, and all it took to demonstrate
that was to let go and tap the stick in roll.
But the period was long enough to recover with
the controls, but without hesitation. It meant
you never let go of the controls on the H21,
flying it constantly, so you really didn’t even
notice the instability. 