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Copyright © 1996-2001 jsd
6 Angle of Attack Stability, Trim, and Spiral Dives
Maintain thine airspeed,
lest the ground arise and smite thee.
— Aviation proverb.
This chapter discusses how you should use the trim
wheel, how the airplane responds to changes (or attempted changes)
in angle of attack, and how you should recover from a spiral dive.
6.1 The Basic Stability PrincipleTo control pitch attitude, conventional pilot technique
is to push or pull on the yoke until the airplane is doing what
you want, and then to use the trim wheel to ``trim off''
the yoke forces — thereby telling the airplane to remember that
the current aircraft behavior is what you prefer.
But let's look into this a little more closely.
What aspect of the behavior is the trim wheel supposed to ``remember''?
The last answer is far and away the best: the airplane
is trimmed for a definite angle of attack. As we shall see, knowing
this has important safely implications. Trim for angle of
the preferred rate of climb?
- the preferred pitch attitude?
- the preferred airspeed?
- the preferred angle of attack?
As discussed in section 2.12, the airspeed
indicator is the closest thing you have to an angle-of-attack
indicator in typical light aircraft; therefore at standard weight
(and load factor), trimming
for airspeed is almost as sensible as trimming for angle of attack.
Angle of attack stability is crucial to well-behaved flight. It can
be achieved without any complicated moving parts; even a balsa-wood
toy glider maintains a definite angle of attack. To see how it works,
let's start by considering the forces on the teeter-totter shown in
In the top panel of the figure, we have an ordinary
playground teeter-totter with two buckets of water on it. Each bucket contains
a four-inch depth of water. The left bucket has half as much
horizontal area, so it contains half as much volume as the right
bucket. Since the smaller bucket is twice as far away from the
pivot, the torque from the small bucket is just equal (and opposite)
to the torque from the big bucket; all the torques cancel.1
Now let's consider what happens if an inch of rain falls on our
teeter-totter. The new situation is shown in the bottom panel of
figure 6.1. In both buckets, the depth of water increases by
one inch, and in both buckets this represents a 25% increase. The
system remains in equilibrium.2
We now contrast this with the slightly different
teeter-totter arrangement shown in figure 6.2. The initial
situation is shown in the top panel. This time, the small-area
bucket (the one on the left) is filled to a depth of only one
inch. The other bucket is filled to a depth of four inches.
In order to get things in balance, the large bucket must be moved
much closer to the pivot — four times closer than it was previously,
and all-in-all eight times closer than the small bucket.
Let's consider what happens if an inch of rain falls
on this new arrangement. Once again, the depth of water increases
in both buckets by one inch. This still represents a 25% increase
for the right-hand bucket, but it now represents a 100% increase
in the left-hand bucket. The same additional depth has a disproportionate
effect. The system is no longer in equilibrium; it will tilt
down to the left.
You may be wondering what all this has to do with
airplanes. Well, this sort of reasoning is exactly what is needed
to explain the angle-of-attack stability of an airplane. The
situation is shown in figure 6.3.
In the top panel, the airplane is just cruising along
in still air. The wing is flying at a normal cruise angle of attack
(four degrees), while the tail is flying at a much lower angle
of attack (only one degree). This is in analogy with the two
buckets, one having four inches of water and the other having
only one inch.3
The torques are in balance because the even though the tail is
``loafing'' (producing much less lift than it is
capable of) it is much, much farther away from the pivot point. You
can check the balance mathematically: the tail has one-quarter as much
coefficient of lift and one-half as much area, but it has eight
times as much lever arm — so all the torques cancel.
The bottom panel of figure 6.3 shows what happens if the
airplane flies into an updraft. Because of the
updraft, the relative wind is no longer
coming from straight ahead, but is coming from a point one degree
below the forward horizon. In the first instant after the airplane
enters the updraft, the pitch attitude will not have changed (it won't
have had time to change) so at least for a moment both the tail and
wing will be flying at an angle of attack one degree higher than
previously: two degrees and five degrees, respectively. This
represents a 100% increase for the tail but only a 25% increase for
the wing. This creates a pitching moment. The aircraft will pitch
nose-down into the updraft. The pitch-axis torque budget will return
to equilibrium only when the original angle of attack has been
The same logic applies to any other situation where
the airplane finds itself flying at an angle of attack different
from its trimmed angle of attack. Any increase or decrease in
angle of attack will have a disproportionate effect on the
tail. The airplane will pitch up or down until it
restores its trimmed angle of attack.
Angle of attack stability results from this simple
principle: ``the thing in back flies at a lower angle of attack
than the thing in front''. Aircraft designers have a special
word for any situation where two airfoils have different angles
of incidence, namely
decalage,4 from the
French word for
``shift'' or ``offset''.5 The more wing/tail decalage
you have, the more vigorously the airplane will oppose any attempted
deviation from its preferred angle of attack.
* Other Flying Objects Are Not SimilarThis property of being trimmed for a particular angle
of attack is truly remarkable. It is not shared by other so-called
``aerodynamic'' objects such as darts, arrows or bombs. They can't
be trimmed for any angle of attack other
than zero. If you drop a bomb from a great height, it will (to
an excellent approximation) wind up pointing straight down and
going straight down, with a velocity essentially as large as could
possibly be obtained from an object of that size and weight.
In contrast, an ordinary airframe in ordinary gliding flight goes
horizontally 10 (or more) feet for every foot of descent. Its
airspeed is tenfold less than the terminal velocity that would
be expected for an object of that size and weight, and its vertical
speed is at least a hundredfold less than terminal velocity.
If you reduce the amount of drag on the bomb, it
will fall faster. If you reduce the amount of drag on the airframe,
it will be able to descend slower.
Don't let anybody tell you the tail on an airplane works ``just like''
the feathers on an arrow.
6.1.1 Center of Mass Too Far AftLet's consider what happens to an airplane that has
insufficient decalage. It is all too easy to create such a situation,
by violating the aft limit of the airplane's weigh-and-balance
envelope. Suppose you are hauling a bunch of husky skydivers.
Suppose initially the loading is within the weight-and-balance
envelope, but one by one all the jumpers wander to the very back
of the cabin. As more and more weight accumulates in the back
of the plane, the center of mass (center of gravity) moves aft,
and you have to dial in more and more nose-down trim. The tail
has to fly at a higher and higher angle of attack to support the
added weight back there. Eventually you reach the point where
the wing and the tail are flying at the same angle of attack —
no decalage. At this point the airplane will not necessarily
immediately fall out of the sky, but you'd better be careful.
The airplane will no longer have any angle of attack
stability. It won't maintain its trimmed
airspeed. (There are lots of things that could disturb the angle of
attack, such as (a) an updraft, as depicted in figure 6.4, in
analogy to the previous subsection, or (b) a speed change, which would
cause a loss of lift — which in turn would cause an angle of attack
change as discussed in section 5.2.) If you think
you've got the airplane trimmed for 100 knots and 4° angle of
attack, it will be equally happy to fly at 200 knots and 1° angle
of attack, or 50 knots and stalling angle of attack!
In such a situation, you will need to keep very close
watch on the angle of attack. You will need to constantly intervene
to prevent the airspeed from wandering off to a dangerously high
or dangerously low value — above VNE or below
VS — leading to in-flight structural failure
or a nasty stall. This is in marked contrast to a normal airplane
with a normal amount of angle-of-attack stability which will maintain
a definite angle of attack (and therefore a more-or-less constant
airspeed) all by itself.
Not only is our aft-loaded airplane much more likely
to stall than a normal airplane, the resulting stall will be the
worst stall you've ever seen. In a normal stall, only the wing
stalls; the tail keeps flying normally. The nose then drops,
and the stall recovery begins automatically. Pushing on the yoke
helps things along. But in our aft-loaded
plane, notice that the tail is flying at just as high an angle
of attack as the wing. It is perfectly possible that the
tail will stall first. When this happens, the nose will pitch
up! This guarantees the wings will stall shortly after the tail
does. Now you've got an airplane with both the wing and
the tailplane stalled. Pushing forward on the yoke will only
make the tailplane more stalled. This is not a good situation.
At this point, the jumpers won't have to be asked
twice to leave the plane. After they've left, you may be able
to recover from the stall.
The stall is not the only thing you need to worry
about with an aft-loaded airplane. You could just as easily get
an airspeed excursion to a very high airspeed. That in turn could
lead to structural failure.
The moral of the story: don't mess with the weight-and-balance
envelope. The airplane's manufacturer did extensive analysis
and testing so they could put the largest possible weight-and-balance
envelope in the Pilot's Operating Handbook.
6.1.2 Center of Mass in the MiddleNow let's take another look at what happens when
the center of mass is in the middle of the allowed envelope.
Suppose you get another group of passengers (since the skydivers
from the previous scenario are unwilling to fly with you anymore,
and have taken up basket weaving instead).
Once again, suppose the center of mass starts out
in the middle of the weight-and-balance envelope, as was depicted
back in figure 6.3. Now suppose a few of the passengers
move somewhat toward the front of the cabin. The center of mass
will move forward. The tail will have less weight to support.
If you don't do anything, the nose will drop and the airspeed
will increase. Your first impulse will be to maintain altitude
and airspeed by pulling back on the yoke. If the passengers promptly
returned to their original positions, you would promptly be able
to release the yoke pressure. But let's imagine that they stay
forward. Rather than hold a steady back pressure on the yoke,
you will dial in some nose-up trim to relieve the pressure.
As the center of mass moves farther and farther forward,
you will need to dial in more and more nose-up trim to maintain
the desired angle of attack. At some point the center of mass
will move ahead of the center of lift of the main wing. The tail
will then need to provide a negative amount of lift in order for
the torques to be in balance, as shown in figure 6.5.
There is nothing wrong with this; indeed most aircraft operate with
negative tail lift most of the time.
The wing will have to generate enough lift to support
the entire weight of the airplane, plus a little bit extra to
overcome the downward force on the tail. (We have to have the
forces in balance as well as the torques.) This in turn implies
the wing will generate a little more induced drag, but the loss
in performance is so small that you ordinarily won't notice it.
You will have lots and lots of decalage, so the airplane
will have plenty of angle of attack stability. You can check
this in the figure.
Some people are under the misimpression that the tail must fly at
a negative angle of attack for the airplane to be stable. That's
just not true. The real rule is just that the thing in back needs
to fly at a lower angle of attack than the thing in front.
If the angle is so much lower that it becomes negative, that
is just fine, but it is not required.
The amount of stability you have depends on the angle
of attack of the tail relative to the wing, not relative to zero.
6.1.3 Center of Mass, Lift, and AreaAn amusing consequence of the decalage rule involves
the center of area and center of lift of the
airplane. To find the center of area non-mathematically, make
a top-view picture of the airplane (on reasonably rigid paper).
Cut away the background, leaving just the airplane itself, and
see where it balances. The balance-point will be precisely the
center of area.
The mathematical rule involved is a generalization
of the rule you use to calculate the location of the center of
mass. Various examples of the rule include:
All distances in these calculations are measured from some arbitrarily
chosen reference point, called the datum. (The choice of datum
doesn't matter, as long as you use the same datum for all
To locate the center of mass: total up the product
of mass times distance, summing over all elements of mass in the
airplane. Divide by total mass; the result is the distance from
the datum to the center of mass.
- To locate the center of area: total up the product
of area times distance, summing over all elements of area. Divide
by total area; the result is the distance from the datum to the
center of area.
- To locate the center of lift: total up the product
of lift times distance, summing over everything in the airplane
that produces lift. Divide by total lift; the result is the
distance from the datum to the center of lift.
6.1.4 Pitch-Axis EquilibriumIn steady flight the airplane must be in equilibrium. All torques must cancel, as discussed in
section 19.7. There are various ways pitch-axis torques
can arise; an extreme example is shown in figure 6.6.
The engine is mounted high up on a pylon. (Seaplanes commonly do
this.) In particular, the thrust is created some distance above where
the drag is created. This means we have two forces and a lever
arm — i.e. a torque.
: Thrust Not Aligned With Drag Makes Torque
: Weight Not Aligned With Lift Makes Torque
The obvious way to cancel this torque is to have
the center of lift (of the whole airplane) slightly offset from
the center of mass (of the whole airplane). This causes a pitching
moment — a torque around the pitch axis — as shown in figure 6.7.
The amount of torque produced by the thrust/drag
misalignment will depend on the throttle setting. Specifically,
when you open the throttle such a seaplane will tend to pitch
down and accelerate; you will need to pull back on the yoke and/or
dial in lots of nose-up trim to compensate. This is a rather
undesirable handling characteristic. Airplane designers try to
minimize the thrust/drag lever arm. Indeed, given a choice, it
is better to put the thrust slightly below the drag, in which
case opening the throttle causes the airplane to pitch up slightly
and reduce its trim speed.
In all cases, the lift/weight lever arm (figure 6.7)
is always very, very short compared to the thrust/drag lever arm
(figure 6.6), since weight and lift are huge
compared to thrust and drag.
There are other miscellaneous contributions to the pitch-axis torque
budget. For one thing, any airfoil (even a barn door) produces a
certain amount of torque —
not just pure lift. The amount of torque grows with angle of attack,
but some airfoils have the obnoxious property that the amount of
torque is not strictly proportional to the amount of lift. Changing
the airfoil (e.g. by extending flaps) changes the amount of torque.
The horizontal tail has a huge amount of leverage,
and its coefficient of lift is adjustable over a very wide range.
This means that by moving the yoke and/or trim, the pilot can
move the center of lift (of the whole airplane) over a wide range.
This in turn produces lots of torque to overcome the various nonidealities
I reiterate: the center of lift of the whole airplane
is always very, very nearly aligned with the center of mass of
the whole airplane. Otherwise the aircraft would not be in equilibrium.
On the other hand, because of the decalage rule,
the center of area will always be behind the center of
lift (and hence behind the center of mass). This is because the
tail is ``loafing''. It is not doing its share of the
lifting. The tail is a long way behind the center of mass, so
it has a whole lot of leverage. It has a lot of area, out of
proportion to the lift it is producing. This means the center
of area will be aft of the center of lift.
To reiterate: the center of mass is significantly
ahead of the center of area, not the center of lift.
Another misconception that is more nearly true is
the notion that the center of mass of the whole airplane
has to be ahead of the center of lift of the wing alone.
This condition will occur if the tail is producing a negative
amount of lift. As we have seen, this is possible, but not necessary.
Here's an explicit example. I've actually done the
The easiest way to determine whether the tail lift
is positive or negative is to observe the direction of motion
of the tip vortices. This can be done using yarn contraptions
that dangle from the tips of the horizontal tail.
I took a Cessna 172 Skyhawk and put a couple
of large pilots in the front seats, with no luggage and no other
passengers. That meant the center of mass was right at the front
of the envelope, so the tail had to produce considerable negative
lift in order to maintain equilibrium. There was lots and lots
of angle of attack stability.
- I took the same Skyhawk and put a small pilot
in the front seat, a large mad scientist in the back seat, and
120 pounds of luggage in the rear cargo area. That put the center
of mass right at the rear of the envelope, so the tail had to
produce considerable positive lift in order to maintain equilibrium.
The airplane still had plenty of stability. (As far as the pilot
could tell, it was just as stable as it ever was.)
6.1.5 Canards Operate on the Same PrincipleSome airplanes have the main wing in the back. They
get their stability from a much smaller wing (called
a canard) in the front. Anybody who believes that ``the
thing in back always has to fly at a negative angle of attack''
will have a hard time understanding how this works. The thing
in back is the main wing! It had better be flying at a normal,
positive angle of attack.
In fact, you can build a whole sequence of planes,
gradually transforming a canard configuration into a normal configuration
by making the rear wing smaller and the forward wing larger.
If you do it right, all of them will have positive lift from the
tail, and all of them will be stable — all for the same reason.
According to the decalage rule, the thing in front
must be flying at a higher angle of attack. The canard configuration
is analyzed in figure 6.8.
In the top panel, the airplane is buzzing along in
still air. The main wing (in the back) is operating at a normal
cruise angle of attack, 4°. The canard is operating at 10°
angle of attack. This gives us 6° of decalage, which should
be plenty. All the forces and torques are in balance.
Then, as shown in the lower panel, the airplane flies
into an updraft. The updraft affects the canard and the main wing
equally, increasing both angles of attack by one degree. This
represents a 25% change for the main wing, but it represents only
a 10% change for the canard. The airplane will pitch nose-down,
as it should. The system will return to equilibrium only when
it returns to the original (trimmed) angle of attack.
In a canard-type airplane, the center of mass is
clearly always ahead of the main wing, but this is not what creates
stability. The center of mass has to be ahead of the center of
area (including the area of the canard). The only way this can
happen is if the canard produces a huge amount of lift, out of
proportion to its area. The next time you see such an aircraft
parked on the ramp, take a look. You will see that the canard
is installed at a tremendously large angle of incidence.6
Since the canard must fly at a higher angle of attack
than the main wing, stalling of the canard is always a concern
during maneuvers that involve a high angle of attack — e.g. landing.
This explains why canard airplanes tend to have high landing
speeds (which in turn requires rather long runways) — to land
at a nice slow speed you have to fly the main wing at the highest
possible coefficient of lift. Now for stability the canard has
to fly at an even higher coefficient than that, which calls for
some compromises and/or some very tricky designs.
6.1.6 Beyond DecalageDecalage is the main issue but not the only issue
affecting the airplane's angle of attack stability. The following
points are mentioned only briefly, because they are of more interest
to airplane designers than to pilots.
To reiterate: decalage is the primary means for creating angle
of attack stability. The other effects mentioned in this subsection
determine how much decalage will be needed.
In maneuvers where the airplane is rotating around its pitch
axis, pitch damping must be taken into account, as discussed in
- The tail flies in the propwash (to a greater extent than
the wing). This reduces stability, because it reduces the steepness
tail's lift versus angle of attack curve. Remember that stability
depends on the torque due to the tail increasing more steeply
than the torque due to the forward wing when an overall angle
of attack change occurs. Alas, the propwash hits the tail at
the same angle regardless of what the relative wind is doing,
so stability is reduced.
- The tail flies in the downwash of the wings. This
again because it reduces the steepness of the tail's lift versus angle
of attack curve. The air flowing off the back of the wing tends to
flow straight off the trailing edge, regardless of the angle at which
it approached the wing. Also, when the airplane's overall angle of
attack changes, the aft wing can move in or out of the forward wing's
wake. This changes the lift curve of the stabilizer in ways that are
hard for designers to predict. Further, any change in the downwash
pattern can move the angle of attack to a new equilibrium point.
Therefore, on most aircraft, extending the flaps perturbs the trim
speed, as discussed in section 5.5.
- In a steep turn, the trimmed angle of attack will decrease
slightly, because rotations are not commutative, as discussed
in section 19.6.5.
- A propeller disk in front of the airplane reduces stability,
because of the way the airflow through the disk changes with angle
of attack. (Pusher props increase stability.)
- A cambered
wing reduces stability. Conversely, you can make an airfoil that
doesn't need a tail to be stable, if you give it enough reverse
camber; flying-wing aircraft use this trick.
- The aspect ratio of an airfoil affects the steepness of its lift versus
angle of attack curve. You get more stability if you have a short
fat wing and a long skinny tail.
- Sweepback affects the lift versus angle of attack curve.
- Ground effect changes everything. This
is important because you
want the airplane to be well behaved during takeoff and landing,
not just during cruise.
- As discussed in section 6.1.7, designers can
use springs and/or bobweights to pull the airplane slightly away
from its purely aerodynamic trim point.
6.1.7 Springs and BobweightsIn addition to the purely aerodynamic contributions discussed at the
section 6.1, some airplanes have non-aerodynamic
contributions. Imagine an aircraft that is not quite in trim from a
purely aerodynamic point of view, so that you must apply pressure to
the yoke. Now imagine that you relieve this pressure using a spring
connected to the yoke. The airplane is now in trim in an overall
sense. It is trimmed approximately, but alas not exactly, for a
definite angle of attack. This is because at a higher airspeed, the
aerodynamic force on the yoke is larger. This force overpowers the
spring, changing the angle of attack.
Designers can also use weights (called bobweights) to
pull the airplane slightly off its aerodynamics trim point. That makes
the angle of attack depend on load factor as well as airspeed.
Designers generally try to design an airplane to use aerodynamic trim
alone, but sometimes adding springs and/or bobweights are the
expedient way to create an acceptable ``control feel''.
6.1.8 Pitch DampingLet's consider what happens during a maneuver where the aircraft is
rotating around the pitch axis. This includes loops, phugoids (as
discussed in section 6.1.12), and steep turns. Note that for
any bank angle steeper than 45 degrees, a turn involves more
pitch-axis rotation than yaw-axis rotation.
Figure 6.9 shows what the relative wind does during an
upward-pitching maneuver. The angle of attack of the tail is
increased relative to the angle of attack of the wing. The
aerodynamic effect is similar to the effect you would get by applying
some nose-down trim. That is, the airplane wants to fly at a lower
angle of attack than it would in the corresponding situation without
the pitching motion. This effect is the main contribution to pitch
damping. It is helpful because it makes phugoid oscillations die out
after a few cycles. On the other hand, it makes graveyard
slightly more dangerous.
6.1.9 Center of Mass Too Far Forward Let's finish our discussion of the pitch axis torque
budget by considering what happens if the center of mass is too
far forward. The airplane in figure 6.10 has too much weight in the forward cargo area. In order for the torques
to be in balance, the tail must be flying at
a tremendous negative angle of attack.
Stability is not the problem here. The aircraft
has vast amounts of decalage and will be exceedingly stable.
If the situation is not too extreme, the aircraft will be flyable
until the time comes to raise the nose for the landing flare.
When you pull back on the yoke, the tail will stall. This is
the mirror image of the usual stall: the tail stalls because its
angle of attack becomes too negative. The more stalled it gets,
the less (negative) lift it produces. The nose of the airplane
will snap down like a mousetrap.
This can definitely happen any time you exceed the
forward limit of the weight-and-balance envelope; please don't
get the idea that you are OK unless you actually put anvils in
the forward baggage locker.
Some aircraft have very tight restrictions on the
center of mass. Beechcraft Sundowners and V-tailed Bonanzas are
notable examples; a Sundowner with just two pilots and full fuel
is well beyond the forward limit of the center-of-mass envelope.
The correct solution to this problem is to use ballast. For the Sundowner, 50 pounds of ballast
at the back of the luggage compartment typically suffices.
I once knew some people who liked to fly a Sundowner
but didn't like to bother with the ballast; they complained that
the airplane was tricky to handle in the flare and they wondered
why it had to go into the shop for nose gear repairs three times
in a six-month period. The airplane was destroyed in a crash
so they don't have this problem anymore.
Ballast may seem low-tech, but it does the job.
I recommend using jugs of water as your ballast. That way if
you need ballast on the outbound leg but need full load-carrying
capacity on the return leg (satisfying the balance requirement
with cargo and rear-seat passengers) you can dump out the water
and keep the jugs; with other forms of ballast you'd need to worry
about how to replace or retrieve it.
Here's a dirty trick that might save your neck in
an emergency. If you need to land an airplane that is too nose-heavy,
use soft-field technique. That is, carry some engine power during
the flare. The propwash over the tail will give you a little
more control authority and delay the tailplane stall. On the
other hand, if you are smart enough to anticipate this situation,
you ought to be smart enough to load the airplane properly so
that the situation doesn't arise.
6.1.10 Other Failure ModesThere are lots of ways to violate the weight-and-balance
envelope. As discussed above,
Additional things that you need to worry about include:
If the center of mass is too far aft, the airplane
will lose its angle of attack stability. The airplane will not
maintain its trimmed airspeed.
- If the center of mass is too far forward, you
run the risk of a negative-alpha tail stall.
Compliance with your airplane's official weight-and-balance
limits is required by FAR 91.9(a). The regulators take violations
pretty seriously, as indeed they should.
- There is always a limit to how far you can deflect
the yoke. You may run out of control travel before you reach the
stall or the zero-stability point. This is not entirely good
news, because it means you lose control of the pitch axis sooner
than you otherwise would.
- Of course, if you put too many anvils in the
baggage compartment you need to worry about structural
failure of the compartment floor — in addition to whatever stability
and control problems you have.
- As the center of mass moves forward, the phugoid
oscillations (as discussed in the section 6.1.12) tend to
become more pronounced.
- Et cetera, et cetera.
6.1.11 Practical ConsiderationsAirline crews are required to check the weight and
balance in detail for every flight. In practice, general
aviation pilots often pre-calculate typical cases. For instance,
I know that in one of the planes I commonly fly, two pilots (of
any reasonable size) and full fuel is well within the envelope,
so I know I don't need to check the details.
If I am flying an unfamiliar airplane, or an unusual
mission (e.g. taking three linebackers as passengers in a Skyhawk)
then I will check the weight and balance very carefully.
I have a computer program that makes it quick and
6.1.12 Phugoid Oscillations As we have seen, it is a good thing for the airplane
to have plenty of stability of angle of attack, and this is relatively
easy to arrange.
In fact, the airplane's desire to return to its trimmed
angle of attack is so strong that it generally returns too quickly,
and overshoots. To say it in slightly more technical terms, airplanes
essentially never have as much damping of the pitch axis
as you would like.
You can do the experiment yourself easily enough: Trim the airplane
for straight and level flight at some reasonable airspeed. Pull back
on the yoke until the airplane slows down about ten knots, and then
let go. The airplane will not just return to its trimmed condition
(pitch attitude, airspeed, and angle of attack) but will pitch down
and speed up too much. Of course, the airplane will shortly
discover this, and will pitch up and slow down again — but will
overshoot in the other direction. This is shown in figure 6.11.
This phenomenon is called
phugoid oscillations (pronounced fyoo'goid). After a few
cycles, the oscillations will die out7 and
the airplane will return to the previous trimmed condition.
As the center of mass moves forward, you get more
and more stability, but less and less damping of the pitch axis
— therefore worse phugoids.
Fortunately, the phugoid oscillation is so slow that
you can easily arrest the oscillation. If at point (1) in the
figure you push the nose down to level pitch attitude, the airplane
will be on altitude, on airspeed, and level — and the phugoid
will be over. Similarly, if at point (3) you pull the nose up
to level pitch attitude, the phugoid will be over instantly.
If starting at point (2) you hold level pitch attitude, the airplane
will take a while to accelerate to its trim speed; you will need
to maintain back pressure on the yoke until it does. Similarly,
starting at point (4) you can push on the yoke until the airplane
decelerates to its trim speed.
You may find this recovery procedure counterintuitive at first, so
it's good to practice it a few times. See also section 10.6.2 for a general discussion of how to recognize
oscillations and how to respond.
You can expect a phugoid whenever the airplane's airspeed or pitch
attitude is disturbed from the trimmed equilibrium condition. Rough
handling of the controls will do it for sure. Even if you leave the
controls alone, a series of updrafts
and downdrafts can easily initiate a
phugoid (if you are not paying enough attention to the pitch
attitude). This will result in much larger altitude and airspeed
excursions than would have occurred if level pitch attitude had been
On July 19, 1989, the #2 engine of a DC-10 disintegrated,
disabling the hydraulic systems that operate the
flippers.8 The pilots managed to fly the beast to the Sioux City
airport, controlling it with just the #1 and #3 throttles — the
only controls still available. Every power change provoked a
few cycles of phugoid oscillation. The pilots had never been
taught about phugoids; they had to figure it out on the fly (so
to speak). The captain of this flight, Al Haynes,
has given a
number of lectures recounting the experience. A videotape exists,
too — highly recommended.
If you think the word ``phugoid'' looks strange, you're right. The
origins of the word are highly amusing. Apparently
Lanchester (who was the first to analyze
these oscillations) wanted to coin a fancy name, based on Greek roots.
He started with the English word ``flight'', which is, unfortunately,
a homonym. From there, he stumbled onto the Greek word for
fleeing instead of flying. The same root
``fugh'' has come down to us in the words
``fugitive'' and ``centrifuge''. So a term that was meant to
translate as ``aeronautical oscillation'' actually comes out as
``fugitive oscillation''. Oh well.
6.2 Spiral Dive
6.2.1 Which Way Is Up?People think they know which way is up, but they don't. The
semicircular canals in your inner ear will tell you which way is up
for a few seconds, but after that, you don't know. Not without
If you can see the horizon, that tells you which way is up. If you can
see the ground below you, that tells you which way you are turning. If
you have a horizon gyro and a rate-of-turn gyro, and you are skilled
at interpreting them, that's fine. But suppose you are flying in
clouds, or over an unlighted area on a dark, overcast evening. If you
look away from the instruments, you have no idea which way is up, or
which way you are turning.
Sooner or later you will get into a bank, and then the bank angle will
increase rather rapidly (due to the overbanking tendency,
The result is called a spiral
dive. It has a well-deserved
nickname: graveyard spiral. Except for running into something,
a spiral dive is almost the only way you can inadvertently destroy an
This will be a good application and illustration
of what we have just learned about angle of attack stability.
This subsection gives a quick overview of the situation; a more
detailed discussion is presented in subsection 6.2.3.
Imagine that you are initially trimmed for straight
and level flight at, say, 100 knots. Then you inadvertently enter
a steeply banked turn.
Figure 6.12 shows the forces acting
on the plane in level flight and in the turn. Let's imagine that
the plane weighs exactly one ton. In level flight the downward
force of gravity is exactly canceled by the lift produced by
the wings, so the wings must be producing one ton of lift.
In the turn, though, the wings must produce enough
force not only to support the weight of the airplane (vertically),
but also to change the airplane's direction of motion (horizontally).
The total force can be quite large: In a 60° turn, two tons
of force is required. In a 75° turn, almost four tons of
force is required, as shown in figure 6.13.
In order to produce 4 tons of lift, the airplane must fly at roughly
200 knots — twice the wings-level trim speed.
Now let's imagine that after spiralling for a while, you discover
what is going on. The first thing you should do is to roll back
to wings-level attitude. That solves your most urgent problem, but
does not get you completely out of danger.
So let's think about the new situation. The airplane is still going
roughly 200 knots. (It is going to slow down, but it hasn't yet done
so.) It is still trimmed for cruise angle of attack. Therefore, the
wings are still producing 4 tons of lift. You've got a real
problem. Previously, you had 4 tons of lift pointing mostly
horizontally, pulling you around the turn. Now you've got 4 tons of
lift, pointed vertically — pulling you into a loop! This situation
is illustrated in figure 6.14.
Note that a properly-executed aerobatic loop-de-loop
involves only 4 Gs of force at the bottom. There is no doubt that
an airplane rolling out of a 75°-banked spiral has enough
energy to flip right over onto its back — unless you do something.
This is the phugoid from hell.
Therefore, when rolling out of a steeply-banked turn,
plan on pushing on the yoke, to prevent a dangerously nose-high
6.2.3 General DiscussionSpiral dives are really important. Now that we've
learned the ``lay of the land'', let's go through the
scenario again in a little more detail.
The first step in the scenario is to have one wing down. There are
lots of ways this could happen. If the airplane is not in good
lateral trim (perhaps because you've burned more fuel from one tank
than another, or because the passengers and cargo are not
symmetrically distributed) one wing might drop as soon as you let go
of the controls. Even if the trim is perfect, turbulence certainly
can make one wing go down.
Having a wing down produces a whole series of
consequences.10 The earliest step in this series
is shown in figure 6.15. The airplane has just entered
a bank. The airspeed is the same as it was before the bank began,
simply because it has not yet had time to change.
We see that the vertical component of lift is insufficient to balance
the weight of the airplane. (Compare this figure with
figure 6.12 or figure 6.13.) The unbalanced force will
cause the airplane to drop straight down. This is the same as the
``albatross effect'' discussed in
Then, as soon as any appreciable downward velocity develops, the
airplane will pitch down and speed up — because the airplane wants
to maintain its trimmed angle of attack11 as discussed in section 6.1.
The combined effect of vertical damping and angle
of attack stability will cause the airplane to speed up until
the lift vector is long enough that its vertical component balances
the weight of the airplane, as depicted in figure 6.12.
The load factor is defined to be
the ratio of the lift the wing is actually producing, relative
to the lift required for unaccelerated flight.
To say it yet another way, the load factor specifies how many G you
pull in a steady turn. It grows explosively at large bank angles,
as shown in figure 6.16.
The trim speed increases almost as dramatically, as shown in figure 6.17. In a 60° bank, the airplane will want to
maintain a speed that is roughly 141% of its wings-level trim speed.
In a 75° bank, the trim speed is roughly 200% of the wings-level
trim speed. In every airplane I know of, if you start out at cruise
and then double the airspeed, you will be well beyond VNE (never-exceed
airspeed). This creates the risk of immediate structural failure,
especially if you do something foolish like pull back on the
The trim speed grows in proportion to the square
root of the load factor. There is a simple reason for this.
Recall (from e.g. section 4.4) the key
When you enter a spiral dive, the wing area of the airplane doesn't
change, the density of the air (r) doesn't change, and the
coefficient of lift12 doesn't change
coefficient of lift × wing area
Consider the following scenario: imagine you are not proficient at
instrument flying, but you find yourself flying through clouds or
flying on a dark night over the desert. You will very soon lose track
of which way is up.
At some point you perceive that something is wrong, because you are
being pushed into your seat by unusual G loads. Four Gs will
definitely get your attention. You should also be able to hear the
unusual wind noises, as the airplane accelerates to roughly 200% of
its normal cruise speed. You will not have any sensation that
you are turning. Even if you suspect you are in a turn, you will not
be able to tell which direction you are turning, without referring to
outside references or gyroscopic instruments.
Because of the overbanking tendency, the bank angle
will continue to increase. The airspeed, descent rate, and load
factor will increase accordingly. There will be no significant
6.2.4 Recovering From a Spiral DiveIf you find yourself in an unusual turning, descending
situation, the first thing to do is decide whether you are in
a spiral dive or in a spin. In a spiral dive, the airspeed will
be high and increasing; in a spin the airspeed will be low. Also,
the rate of rotation in a spiral is much less; the high speed
means the airplane has lots of momentum and can't turn on a dime.
Here is the correct procedure for recovering from
a spiral dive.13
If you have good outside references, by all means
use them to re-establish wings-level attitude and then to re-establish
a reasonable pitch attitude.
Smoothly roll the wings level.
- Simultaneously use your other hand to retard
the throttle. This is not an essential step, but it might prevent
the engine RPM from going beyond redline.
- Do not pull on the yoke at all. When you finish
rolling out of the turn, the airplane will have 15 degrees or
so of nose down pitch attitude, but it will immediately pitch
up all by itself, at the rate of roughly 15 degrees per second.
You should just wait a second or so until the airplane
returns to level flight attitude, and then push on the
yoke to maintain a reasonable attitude.
- As the airspeed returns to normal, the amount
of pushing you need goes to zero. You can re-open the throttle
and fly away.
If you don't have good outside references, you should
not rely on the attitude indicator (artificial horizon).
The attitude indicator contains a gyro mounted on ordinary mortal
gimbals, which can only accommodate a limited range of pitch and
bank angles. A steep spiral can easily cause the gyro to tumble,
whereupon it will need several minutes of relatively straight
and level flying before it can re-erect itself. Military aircraft
have non-tumbling attitude indicators, but you're not likely to
find such things in a rented Skyhawk. Therefore, you should roll
the wings level by reference to the rate-of-turn gyro.14 Being a rate gyro (as opposed to a free gyro)
it has no gimbals, and therefore can't possibly suffer from gimbal
Remember: to recover from an unusual attitude, use
the rate-of-turn gyro to level the wings.15 This is a good example of the
sort of information you have to get from books. Presumably during
training you will never do anything bad enough to tumble the attitude
Controlling the pitch attitude without relying on
the artificial horizon requires thoughtful use of the airspeed
indicator. At the point where the wings have just been returned
to level, the airspeed will be something like twice what it ought
to be. It will decrease slowly at first, then faster and faster.
Your job is to keep the airspeed from unwinding too quickly.
Pick some rate like 5 knots per second, and push on the yoke enough
to keep the airspeed needle from moving faster than that.
Don't worry that pushing on the yoke will cause the airplane to fly
into the ground. The airplane will climb and it will pitch up all by
itself; your job is to keep it from pitching up too much.
the law of the roller coaster: 9 feet per knot, per hundred knots
(section 1.2.1). As you slow down from the high-speed
dive, most of that airspeed energy will be converted back to altitude.
Wait until the airspeed returns to a reasonable value before you worry
about returning to your exact intended altitude.
You can also use the altimeter
to help manage the pitch attitude. As soon as the altimeter needle
starts moving upward, you should push on the yoke to keep the needle
from moving too quickly.
Unless you know you are proficient on instruments, you should not rely
too heavily on the vertical speed indicator. It has weird built-in
delays that can be hard to interpret.
Very, very few pilots have been taught how to handle
a spiral dive correctly. In fact, the official FAA Flight
Training Handbook (reference 21) currently17 says not once but four times (on pages 65, 187, and 188)
that the procedure for recovering from a spiral dive calls for pulling
back on the yoke. It says that you shouldn't pull back too
much, but nowhere does it say that you might need to push forward.
The FAA Instrument Flying Handbook also discusses spiral dives
without giving the slightest hint that forward pressure might be
necessary. The vast majority of other pilot training books suggest
the same wrong procedure.
In some aircraft, including many trainers, retarding
the throttle produces a nose-down pitch change which helps with
the recovery, just like a small push on the yoke. Although this
helps, it is definitely not sufficient in all cases. What's worse,
there are some aircraft (as mentioned in section 6.1.4)
in which retarding the throttle produces a nose-up pitch
In a not-very-steep spiral, it hardly matters what
recovery procedure you use, but the more serious the spiral, the
more crucial it is to use the correct procedure.
Let's look again at what happens if you use the wrong
procedure. You are buzzing along in the clouds, and you get into
a spiral dive. You smoothly roll the wings level (so far so good).
The next thing you know the plane pitches up into a ridiculous
nose-high attitude. If we are talking about a really high-speed
spiral dive, the airplane will loop right over on its back. If
the spiral was more moderate, you will ``only'' do a tail
slide or hammerhead or something.
This is just about the last thing you need. You
were in a spiral dive, which was bad enough — but now you are
in some horrendous unusual attitude, stalled and/or upside down,
still in the clouds.
If you use the correct procedure, recovering from
the spiral dive is straightforward. If you use the wrong procedure,
the ensuing unusual attitude could be very hard to recover from.
If you use the widely-taught ``standard'' procedure and pull back on
the yoke, it can only make things worse. Pulling back will increase
the angle of attack, and therefore the coefficient of lift. This might
make things much worse, for several reasons:
The correct recovery procedure is rather counter-intuitive. Because
the airplane is descending and because it is going too fast, your
instincts will tempt you to raise the nose. The problem is that
the airplane's instincts tell it to do the same
thing — and it will pitch up too much unless
It will make you more likely to wind up in an
- Since the wings were already developing 4 Gs,
you don't need to increase that very much before you snap the wing
- Even if you don't break the airplane, you might
break the pilot. It varies a lot from person to person, but 6
Gs, especially suddenly and unexpectedly, is enough to
drain the blood from your head and collapse some of the blood vessels
in your brain. Even if the G load is removed, it will take a
while for you to regain consciousness. Furthermore, even after you
regain consciousness you will not be as smart as you used to be. Your
thought processes will be severely impaired for a couple of minutes if
not longer. Since you were already in an emergency situation
before you blacked out, this is really the last thing you
6.2.5 Try It YourselfYou don't need to take my word for what happens —
you can go out and do some experiments yourself.
You probably want to take an instructor
along, but it is not absolutely necessary if you are careful.
Experiment with shallow banks before messing with really steep
Start by trimming the airplane for level flight at
a low-cruise airspeed, say 100 knots, and clearing the area.
Roll the airplane into a 45° bank and let
it descend and
accelerate. Leave the throttle alone, leave the trim alone, and
don't push or pull on the yoke. Apply enough aileron to keep
the bank from getting steeper than 45°. Wait a few seconds
for the airspeed and descent rate to stabilize, then roll the
wings level and watch what happens.
After you know what happens in a 45° bank, try
it again at 50°, and work your way up to 55°. Don't
even think about exceeding 60° without having an aerobatic-qualified
instructor on board. The margin between an ``interesting''
spiral and a genuine emergency becomes small, as you can see in
When you roll out of the 55° or 60° banked
spiral, the nose will be pointed about 15 degrees below the horizon.
If you count off one second, the pitch attitude will be level.
After two seconds, it will be 15 degrees nose up. After three
seconds, it will be 30 degrees nose up, which is an awful lot.
You will be quite happy to grab the controls at that point and
push the aircraft back to a reasonable pitch attitude.
Repeating the experiment under the hood is also edificational.
Normally when you demonstrate a steep turn, the airspeed does not
increase — in fact it decreases. That is because you retrim and/or
pull back on the yoke, causing the angle of attack to increase. In
contrast, our explanation of the spiral dive assumed that it was an
inadvertent spiral dive, so the angle of attack stays nearly the
same and may even decrease18 slightly. One
thing is certain: the wings have to create enough lift to support the
effective weight of the airplane (real weight times load factor). If
the coefficient of lift stays the same, the speed has to increase; if
the speed stays the same, the coefficient of lift has to increase.
The airplane has considerable angle of attack stability. The
airplane is trimmed for a definite angle of attack.
- Speaking of pitch stability is less accurate than speaking of
angle of attack stability.
- The biggest contribution to angle of attack stability
is decalage. The thing in back flies at a lower angle
of attack than the thing in front. The thing in back may, but
need not, fly at a negative angle of attack. A canard obviously
requires the thing in back (the main wing!) to have positive angle
Angle of attack stability is reduced as the center
of mass moves aft.
- The trim wheel is used to choose what the trimmed
angle of attack will be. The yoke is a convenient extension of
the trim wheel, for temporary changes in angle of attack.
- The trimmed angle of attack corresponds to a
definite airspeed (assuming constant load).
- Configuration changes (flap extension, power
changes etc.) have side-effects on the trim speed.
- In a turn, the load factor increases. In order
to maintain its trimmed angle of attack, the airplane pitches
down and speeds up. In a steep turn (assuming you don't change
the angle of attack using the yoke and/or trim), the speed-up
- When you roll out of a steep turn, the airplane
tends to pitch up all by itself. You may need to push on the yoke
to maintain control.
- For a general discussion of the concepts of force,
torque, and moment, see section 19.7.
- For a general discussion of
the principles and terminology of equilibrium stability, and damping,
see chapter 10.
- We find it convenient
to use the center of mass of the airplane as our pivot point,
measuring all lever-arms from that point, so the
force of gravity
contributes nothing to the pitch-axis torque calculations. Of
course, the answers come out the same no matter what pivot is
chosen. See also section 6.1.4 for a discussion
of sundry additional pitching moments.
- ...rhymes with
``day-garage'', with the accent on the last syllable.
word can equally well refer to a difference in angle of attack
between the two wings of a biplane.
- One famous exception: the Wright brothers' original airplane (``Flyer I'') on display in the
Smithsonian does not have enough decalage to produce positive
angle of attack stability. It must have required a goodly amount
of skill and constant attention during flight.
section 6.1.8 for a discussion of why it dies out.
- ... not to mention the ailerons, rudder, flaps,
- Other disasters such as in-flight
fires are vanishingly improbable by comparison.
- Among other things, airplane
turn, pitch down, speed up, and experience a load of more than
one G. Also, once the airplane is substantially banked (more than
30 or 40 degrees) the overbanking tendency will cause the bank
to get steeper and steeper.
angle of attack remains constant to a good approximation, but because
of the pitch damping discussed in section 6.1.8 and other
nonidealities discussed in section 6.1.6, it won't be
- Remember, coefficient of
lift is determined by angle of attack — and the airplane is trimmed
for definite angle of attack. We are assuming an inadvertent spiral
dive, so you presumably haven't changed the angle of attack by pushing
or pulling on the yoke, or by messing with the trim.
from a spin is discussed in section 18.7.
- That is, the turn needle or turn coordinator, whichever
you happen to have.
- When the wings are level, you will observe zero rate of
turn on the rate gyro. Remember that this instrument indicates rate
of turn, not bank angle per se.
- See section 1.2.1.
- Mid-1997. The FAA is working on a revision of the
Flight Training Handbook. Let's hope these sections are the first to
- ... due to pitch
damping, as discussed in section 6.1.8.
[Comments or questions]
Copyright © 1996-2001 jsd