[Comments or questions]
Copyright © 1996-2001 jsd
5 Vertical Damping, Roll Damping, and Stalls
The really good pilots use their superior judgment
to keep them out of situations where they might be required to
demonstrate their superior skill.
5.1 Introduction and OverviewThe purpose of this chapter is to examine how the airplane responds to
pure vertical motions and to pure rolling motions. We will see that
(except near the stall) the airplane vigorously resists such motions.
For a non-aerodynamic object like a pompom, if you
wave it through the air, it will resist the motion, due to ordinary
air friction. An airplane has friction, too, but we will see that
there is another process (``aerodynamic damping'') that
is enormously more powerful than friction.
This strong aerodynamic damping should not be taken
for granted, since you can certainly get an airplane into situations
where the damping goes to zero or becomes negative. This is why
the airplane is hard to fly near the stall. We will discuss how
to deal with and/or prevent such situations.
5.2 Vertical Damping
5.2.1 Origins of Vertical DampingNormally, the airplane is in equilibrium — all forces
are in balance.1 Let's consider the vertical forces in particular,
and see how the airplane maintains its equilibrium.
To see how the wing reacts initially2 to eliminate any unbalanced
vertical force, consider the scenario in figure 5.1.
Initially, the airplane is buzzing along in straight-and-level
flight and is nicely trimmed. Vertical forces are in balance.
Then we imagine there is sudden change in the weight of the airplane,
relative to the lift. A sudden excess of lift over weight could
happen in several ways, such as the departure of a skydiver.
Conversely, a sudden excess of weight over lift could happen in
at least three ways:
Since we are analyzing the initial reaction,
so we will assume there has not yet been any change in the pitch
The lift decreases if you lose airspeed because
of a sudden windshear.
- The load on the airplane (the effective weight)
increases in a steeply banked turn.
- The weight increases if an albatross flies in
the window and sits on the seat beside you.
For a brief instant after the weight increase, there
will be an unbalanced downward force. According to Newton's second
law, this will result in a downward acceleration. This in turn
means the airplane will begin to descend.
If the downward force remained unbalanced, the airplane
would continue to accelerate downward. It would not just go down,
it would go down faster and faster and faster. This is not what
happens, for a very interesting reason. As soon as the wing picks
up an appreciable downward velocity, its angle of attack will
As we discussed in section 2.2, angle of
attack is just the angle at which the air hits the wing. In figure 5.2 we see that the air hits the wing at a
larger angle during the descent; the pitch attitude of the airplane
has not changed, but the relative wind is coming from a new direction,
ahead of and below the airplane. This increase in angle
of attack normally results in an increase in coefficient of lift.
The extra lift balances the new weight, and equilibrium is restored.
is called vertical damping. As we shall see, an airplane
normally has very strong vertical damping, and this is crucial
for normal flight.3
The process is depicted in figure 5.3.
The steps involved are:
If the extra weight were removed, the airplane would
return to level flight at the original angle of attack.
Unbalanced downward force
makes downward acceleration.
- Downward acceleration leads to downward velocity.
- Downward velocity causes increased angle of attack.
- Increased angle of attack causes increased upward
- This continues until upward force equals downward
force. The final state is a steady descent, with no further acceleration
because the forces are once again in balance.
This strong vertical damping is the reason why we
almost always assume that lift equals weight.4
If the forces were out of balance, the airplane would accelerate
upward or downward, and the angle of attack would change until
balance was restored. In practice, balance is restored so quickly
that weight is never significantly different from lift.
I reiterate that this chapter considers only the
initial response of the wing alone; the longer-term response of
the airplane as a whole (including the horizontal stabilizer)
is discussed in chapter 6.
5.2.2 Loss of Vertical DampingVertical damping may seem obvious — but it is not.
You should not take vertical damping for granted, because it doesn't always exist. It goes
away at the stall.
Let's repeat the previous experiment, but this time
let's imagine that the airplane was flying at a rather low airspeed
(higher angle of attack) when it picked up the added weight.
This is analyzed in figure 5.4; note the higher
angle of attack when compared with figure 5.3.
Now we find ourselves in a really nasty situation.
Even if the extra weight were removed, the airplane would continue
to fly at the new angle of attack — the very high angle of attack
depicted on the right-hand side of figure 5.4.
The airplane would continue to descend, and even accelerate downward.
As before, the added weight causes a downward
- As before, this leads to downward velocity.
- As before, this causes increased angle of attack.
- Surprise! the increased angle of attack causes
no increase in upward force, because the coefficient of
lift does not increase forever as a function of angle of attack.
- Equilibrium is not restored. The airplane
continues to accelerate, descending faster and faster....
5.3 The Stall
5.3.1 Definition of StallThe situation just described is called a stall. A number of
peculiar things happen at the stall, including a loss of vertical
The stall occurs at a special point on the coefficient
of lift curve. Not coincidentally, this corresponds to a special
point on the power curve, as was indicated back in figure 1.13. It is worth exploring this relationship.
Figure 5.5 shows two curves: the vertical speed versus
airspeed, and the coefficient of lift versus angle of attack.
As discussed in section 2.12, there is a deep relationship
between airspeed and coefficient of lift; if the coefficient of
lift is small the airplane has to fly at a higher speed to support
The stall occurs at the critical angle
- The critical angle of attack is the point where further
increases in angle of attack do not result in a further increase in
coefficient of lift.
- The unstalled regime refers to angles of attack below
the critical angle of attack; the stalled regime refers to
angles of attack beyond the critical angle of attack.
: Power Curve related to
Coefficient of Lift Curve
The coefficient of lift has a maximum; therefore
the airspeed has a minimum. This minimum airspeed is called the
stalling speed, and is denoted VS.
5.3.2 Flying Beyond the Stall?We are now in a position to answer a question that
used to cause a lot of confusion: can you fly ``beyond''
the stall? Some people say yes, some people say no. The answer
depends on which curve you are talking about.
In figure 5.5, the coefficient of lift
curve does not end at the stall, it just turns downward. Similarly,
the power curve does not end at the stall, it just hooks back
under. The rightward hook in the latter is related to the downturn
in the former.
Yes, it is definitely possible to fly at an angle of
attack higher than the critical angle of
attack. (It may require super-human skill to overcome the
pathological handling characteristics in this regime, but it is
possible in principle to maintain a stalled angle of attack
- No, it is not possible to sustain flight at airspeeds
below the stalling speed.
To say it another way: in the stalled regime, the
coefficient of lift decreases with increasing angle of attack,
so the airspeed required to support the weight of the airplane
must actually increase as the airplane becomes more and more deeply
In the stalled regime the aircraft has a high and increasing
coefficient of drag.5 Therefore it takes a lot of power to maintain level flight in
this regime. At constant power, the rate of climb decreases (or, more
likely, becomes more negative) as the aircraft becomes more deeply
A typical point in the stalled regime is indicated
by the black six-pointed star in figure 5.5. Flight
in this regime — flying beyond the stall — is very peculiar.
If some disturbance gives the airplane a slight upward velocity,
it will accelerate upward and become less and less stalled. Conversely,
if some disturbance produces a slight downward velocity, the airplane
will accelerate downward and become more and more stalled. If
you lower the nose the airplane will ascend; if you raise the
nose it will descend. This sort of flying is no fun at all.
However, even in the stalled regime, the wings are
producing enough lift to support the weight of the airplane.
Lift does not go to zero at the stall. Indeed, the coefficient
of lift is maximized at the stall!
The stall is a problem not because of loss of lift,
but because of loss of vertical damping. Vertical damping is
In some aircraft, the stall occurs quite suddenly,
because there is a rather sharp corner in the coefficient of lift
curve, as shown in figure 5.6. Just below the critical
angle of attack, there is good vertical damping; just above the
critical angle of attack there
is strongly negative vertical damping.
Most aircraft are not so nasty. For the coefficient
of lift curve shown in figure 5.5, the vertical damping
goes away gradually as you approach the stall. The aircraft will
handle about the same one degree below the critical angle of attack
or one degree beyond the critical angle of attack.
We will defer until chapter 18 a discussion
of what causes the stall, i.e. what properties of the airflow
cause the coefficient of lift curve to bend over.
5.4 Roll Damping
5.4.1 Origins of Roll DampingIn section 5.2 we considered how the airplane would
respond to an unbalanced force that was purely vertical. Now let's
consider how it responds to an unbalanced force
that causes a torque around the roll axis.6
For instance, imagine several large passengers suddenly got up
and moved to the left side of the airplane. This scenario is
depicted in figure 5.7.
To understand this situation, we use the same logic
as in the previous section. Remember, the angle of attack is
defined to be the angle between a reference pointer (welded onto
the wing, shown in red in the figure) and the direction of flight
through the air. Although the nose of the airplane is still moving
straight ahead, the left wingtip is moving ahead and down,
while the right wingtip is moving ahead and up. This means
the left wingtip is operating at an increased angle of attack,
while the right wingtip is operating at a reduced angle of attack.
In any normal (i.e. unstalled) situation, this difference
in angle of attack results in the downgoing wingtip producing
more lift than the upgoing wingtip. These forces oppose the rolling
motion. We describe this situation by saying the rolling motion
of the airplane is heavily damped
Consider the following contrast:
The front wheel of a bicycle
is only lightly damped (assuming the bearings
are in good shape and the wheel is not touching the ground). If you
give the wheel a shove, it will keep going around and around for a
The rolling motion of an airplane is quite heavily damped (in
the unstalled regime). If you give an airplane a shove (e.g. by
briefly deflecting the ailerons) it will not keep rolling. The rate
of roll goes away almost as soon as the roll-inducing forces go
If you keep shoving on the bicycle wheel,
it will accelerate: rolling faster and faster. This is the rotational
version of Newton's second law: angular acceleration is proportional
to angular force (i.e. torque).
If you deflect the
ailerons, the airplane will accelerate around the roll axis,
but only for a short time. Thereafter, if you maintain the same
deflection, the wingtip-to-wingtip difference in angle of attack will
generate forces that prevent any further angular acceleration. The
airplane will roll at a steady rate, proportional to the aileron
A light, single-engine airplane has so little inertia around the roll
axis that you can hardly notice it. Therefore the roll
rate is essentially always proportional to aileron
deflection. The ailerons' job is to overcome the roll damping.
A twin-engine airplane has a lot more rotational inertia (because
it has those heavy engines mounted way out on the wing, and maybe
tip-tanks also). You may notice that it does not respond as quickly
to aileron deflection. To initiate a roll, you have to overcome
inertia; during this time the rotational acceleration is proportional
to the aileron deflection. Eventually the roll rate builds up
to the point where roll damping becomes effective — that is, the
wingtip-to-wingtip difference in angle of attack prevents further
acceleration and the final roll-rate is proportional to the aileron
5.4.2 Loss of Roll DampingRoll damping is crucial to normal flight.
It should not be taken for
granted, since it goes away at or near the stall. (This is analogous
to the loss of vertical damping discussed in section 5.2.)
As depicted in figure 5.8, the damping goes away as
we approach the stall:
The left side of the figure shows an airplane in a roll, at a
normal airspeed. Because of the rolling motion, the left (downgoing)
wingtip is flying at a higher angle of attack, which (in this regime)
produces more lift, compared to the right wingtip. Large forces are
generated opposing the rolling motion.
The right side shows
the same thing, except that the angle of attack is much higher — at or
just beyond the critical angle. Once again because of the rolling
motion, the left (downgoing)
wingtip is flying at a higher angle of
attack, but alas this no longer means it is producing more lift. In
fact, it could well be producing less lift than the right wingtip.
The aerodynamic forces do not oppose the initial rolling motion, but
could well amplify it.
The loss of roll damping that occurs at the stall is quite a
departure from normal behavior. This is
precisely how you enter a spin or a snap roll: you arrange that one
wingtip is flying above the critical angle of attack while the other
is flying below the critical angle of attack.
5.4.3 Schemes to Increase Roll DampingSince an unintentional loss of roll damping (spin
or snap roll) is even more obnoxious and dangerous than an unintentional
loss of vertical damping (straight-ahead stall), aircraft designers
go to some trouble to increase the roll damping. They make use
of the following two facts:
1) All bits of wing contribute equally to the lift,
and to the vertical damping.
2) Bits of wing near the root contribute less to
the roll damping, while bits of wing near the tips contribute
more (because of leverage).
So the trick is, we want the roots to stall first.
If we set the roots at a higher angle of incidence than the tips,
when the wing as a whole attains its maximum coefficient of lift,
the roots will be stalled and the tips will be unstalled, and
there will still be a positive amount of roll damping. At the
stall, the airplane will drop its nose straight ahead, rather
than dropping one wingtip. This is a very desirable handling
This design trick (decreasing incidence along the
span from root to tip) is called washout.
The opposite notion (having less incidence at the roots than
the tips) is called washin.
Nobody would design a plane with washin.7
To help compensate for propeller drag effects (as discussed in
section 9.5), sometimes one wing is given more washout
than the other. This is called simply asymmetric
Finally: Deploying the flaps has the effect of increasing the washout.
That's because the flaps are only installed on the inboard sections of
the wings. When they are deployed, they increase the incidence of
that section, as discussed below.
5.5 The Effect of FlapsFlaps are important. They are used during landing
(section 12.7.1), takeoff (section 13.2)
and other low-speed maneuvers (section 12.10 and
So, the question is, what do flaps do? Well, that question has no
less than five different good answers:
Extending the flaps lowers the stalling speed.
- Extending the flaps increases the wing section's
angle of incidence.
- Extending the flaps effectively increases the washout, since
on most planes the inboard sections have flaps while the outboard
sections do not.
- Extending the flaps increases drag. This is
helpful during landing, but unhelpful during climb and cruise.
- Extending the flaps perturbs the trim speed. This is an
undesirable side effect. See below, and see also section 12.10.
5.5.1 Effect on Stalling SpeedExtending the flaps gives the airfoil a shape that is more resistant
to stalling. It can fly at a higher angle of attack without stalling.
This is shown in figure 5.9, especially in the
left-hand panel thereof. More importantly, it can produce
a higher coefficient of lift, perhaps as high as 2.5, whereas
the same wing without flaps would stall before its coefficient
of lift got higher than 1.3 or thereabouts. This higher coefficient
corresponds to a lower stalling speed (assuming other things like
weight are held constant).
: Flaps Affect Coeff. of Lift and Incidence
5.5.2 Effect on IncidenceExtending the flaps increases the incidence of the wing as a whole.
You have effectively rotated the whole wing by a few degrees. Its
leading edge is in the same place, but its trailing edge is lower,
relative to the rest of the plane. This is shown in the right-hand
panel in figure 5.9. You need to account for this
change in incidence, so you can judge angle of attack by looking out the
window, as discussed in section 2.4.
I always wince a little when I hear someone say ``when we extend the
flaps it increases the lift''. Well, I hope not. I hope that lift
equals weight throughout the flap-extension process. Of course lift
would increase if you kept the same pitch attitude while
increasing the incidence, but proper technique involves lowering the
nose while the flaps are extending, to maintain lift equal to weight.
It's also true that at some later time, we will reduce airspeed,
and at that time we will need more coefficient of lift for the
same amount of lift. A correct way to say it is this: extending
the flaps permits a higher coefficient of lift. The best way to
say it is quite simple: extending the flaps lowers the stalling speed.
5.5.3 Effect on WashoutExtending the flaps raises the incidence of the wing-roots relative to
the rest of the wing. That is, it increases the washout.
It turns out that this increase in incidence is in some sense larger than
the increase in the stalling angle of attack. This has important and
rather surprising consequences. Consider the typical situation where
flaps are installed only on part of each wing. When flaps are
extended, the affected part of the wing is flying at a higher angle of
incidence, and therefore a higher angle of attack, compared to the
unflapped part of the wing. Therefore the flapped section will stall
I know this sounds paradoxical, but it is 100% true:
even though the flapped section has a shape that is intrinsically
more stall resistant, it will stall before the unflapped section
This stalling behavior is actually quite useful. As discussed in
section section 5.4, to get good low-speed handling, we
want the wing-roots to stall first. That ensures we don't run out of
roll damping before we run out of vertical
damping. Therefore designers typically install flaps only on the inboard part of the wings.
To see how the flapped section can be producing more lift (even though
it may be operating near, or even beyond, its critical angle of
attack), please refer9
to figure 5.10.
In this figure, the horizontal axis is not angle of attack, but rather
angle of attack minus incidence. This quantity has a simple
physical interpretation: it is the angle at which the relative wind
hits the fuselage. It has the nice property that it doesn't depend on
which part of the wing is being considered, and it doesn't change when
the incidence is changing due to flap extension.
Before the flaps are extended, the wingtip and root
have the same shape and the same performance, as shown by the
blue curve. When the flaps are extended, the back part
of the airfoil rotates down. This means that the flapped section
has been rotated to a higher angle of incidence. To measure the
incidence, you can look at where each coefficient-of-lift curve
crosses through zero. You will see that the magenta curve has
been shifted to the left. Another way to see this is at the top
of the figure: the zero-lift-direction (marked ZLD) of the flapped
section now points more nose-up. The max-lift-direction (marked
MLD) has rotated in the same direction by an even larger amount.
In the situation shown in the figure, the flapped
section is flying beyond its critical angle of attack (magenta
curve) while the wingtip is flying below its critical angle of
attack. This corresponds to a fairly low airspeed, such as might
be used for a short-field approach.
In this situation, even though the flapped section
is stalled, its coefficient of lift is still quite high, indeed
higher than what the unflapped section could produce at any
angle of attack.
5.5.4 Effect on DragDeploying the first notch of flaps (on most airplanes) adds relatively
little drag. Deploying the last notch adds much more.
5.5.5 Effect on TrimOn most airplanes, extending the flaps tends to lower the trim speed,
just as if you had dialed in some nose-up trim. You will need to dial
in some nose-down trim to compensate. (On most Mooneys, extending the
flaps actually raises the trim speed, and you will need to dial in
some nose-up trim to compensate.)
The main contribution to the nose-up trim change is that the tail
flies in the wake of the wing. The extended flaps give a more
downgoing angle to the downwash, which then hits the tail. On
aircraft with a high T-tail, such as a Seminole, the tail is much less
affected by the downwash from the wings, and there is typically very
little trim change with flap extension.
Another contribution comes from the drag. On a low-wing airplane,
the extended flaps tend to drag the bottom of the plane backward,
forcing the nose down. This partially cancels the previously-mentioned
effect of the downwash on the tail.
Conversely, on a high-wing airplane, the drag of the flaps tends to
drag the top of the airplane backwards, forcing the nose up. This
adds to the previously-mentioned downwash effect. Therefore we expect
high-wing aircraft to have more trim change with flap extension.
If you set up for level flight at 90 knots and gradually10 extend the flaps (leaving the power and trim
controls alone), you can expect to see the following reductions in
|| C-152 (2200 RPM)
|| 5 knots
|| 10 knots
|| 10 knots
|| 25 knots
|| 5 knots
|| 15 knots
|| 40 knots
In a C-152, extending the flaps with the engine at low power
causes much less trim change, so in everyday operations you will not
become familiar with the large changes shown in the table. However,
when you start a go-around, you will have full power and full flaps,
and therefore a dangerously low trim speed (something like 45
KIAS). Watch out for nasty pitch-up on go-around! The Skyhawk
(C-172) and Skylane (C-182) behave about as badly the C-152. See
- The stall occurs at the critical angle of attack,
which is the point where a further increase in angle of attack
does not create a further increase in coefficient of lift.
- Lift does not go to zero at the stall. In fact,
the coefficient of lift reaches its maximum at the stall.
- Vertical damping goes to zero at the stall.
- Roll damping goes to zero at about the same point
and for similar reasons. However, a well-designed airplane will
maintain a little bit of roll damping even after it has lost vertical
- The airplane is very ill-behaved near the stall
because of the loss of vertical damping and roll damping.
- It is possible to fly at an angle of attack above
the critical angle of attack, but it is not possible to maintain
steady flight at an airspeed below the stalling airspeed.
- Flaps affect the airplane in five different ways: stalling
speed, drag, incidence, washout, and trim.
- See chapter 10.1
for a general discussion of equilibrium, stability, damping, and
- This chapter concentrates on the airplane's initial
reaction, taking into account just the wing. In the longer term, the
airplane reacts to an increased load by pitching down and speeding up,
but this occurs after and because of the effects discussed here, and
because the tail gets into the act, as discussed in chapter 6.
- See chapter 10
for a discussion of damping in general.
more on the relationship of lift and weight, see chapter 4.
- The induced drag
will be about the same as in unstalled flight at the same airspeed,
but the form drag will be much
increased. See section 4.3 for a discussion of types of
- For simplicity, will consider pure rolling motion.
More complicated motions such as Dutch roll can make a (negative)
contribution to the damping budget. See section 10.6.1.
can experience washin by flying upside down. A plane that has
washout in normal flight will effectively have washin during inverted
flight. For this reason, high-performance aerobatic aircraft
are often built with essentially zero washout.
- Because of an ambiguously-worded passage in the
FAA Flight Training Handbook, some people seem to have gotten the
impression that the term washin was a fancy term for asymmetric
incidence. It is not; no engineer (or well-informed pilot) would use
the term that way. You should stick with the definitions given here.
- In books such as
reference 5, you will see curves that resemble
figure 5.10, in that the coefficient-of-lift curve
intercepts the x-axis somewhere to the left of the origin.
Figure 5.10 chooses the x-axis so that intercept is equal
and opposite to the incidence, but in those other books they choose
the x-axis differently. Their intercept is not related to the
incidence except possibly by coincidence. See section 2.14
for a discussion of the choices involved.
the C-152, VFE, the max speed for operating with flaps fully
extended, is 85 knots. You can briefly pull on the yoke to get the
speed below 85 before extending the first notch of flaps. After that,
you won't need to pull anymore, because of the trim-speed change which
is the point of this demonstration.
[Comments or questions]
Copyright © 1996-2001 jsd