THEORY
Steve Seibel
www.aeroexperiments.org
steve at aeroexperiments.org
Material from April 2003
Preface and brief revisions August 11 2004
Brief revisions August 7 2005
Preface: This "theory" section lays the foundation for an
understanding of the forces at play during "coordinated" turns,
slipping turns, and skidding turns, including the relationship between a
sideways airflow component and a sideways aerodynamic force component, yaw
strings, slip-skid balls and bubbles, why you can't "feel" gravity,
"centrifugal force", and more. This "theory" section also
addresses dihedral, anhedral, sweep, yaw stability or the "weathervane
effect", positive and negative coupling between yaw and roll, and roll
stability. The "theory" section also addresses many common
"myths" around the physics of turning flight. I've explored many
ideas in the "theory" section via hands-on real-world aerodynamic
explorations in hang gliders and other aircraft, including putting a rudder on
a flex-wing hang glider to create a yaw input, putting a wingtip drogue chute
on a flex wing hang glider to create a yaw input, and more--see other portions
of this aeroexperiments website for more on these in-flight tests.
This material was prepared for an earlier version of this website. Some of
this content is still rather rough-cut but it will provide the reader with some
idea of the questions I've been interested in. Look for this content to be
revised, completed, and incorporated into the main site map at a later date.
One interesting topic not yet discussed in detail in this "theory
section" is the relationship between billow, washout and the amount of
effect aerodynamic anhedral contained in a swept wing, and why applying a VG
decreases the amount of effective aerodynamic anhedral contained in the sail of
a flex-wing hang glider. That will be examined on this website in the near
future.
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THEORY:
Index to theory section:
PART 1: Some brief notes on dihedral, anhedral, sweep,
and coupling between yaw and roll
PART 2: Notes on how a positive coupling between yaw and
roll, due to dihedral or sweep, contributes to roll stability and allows an
aircraft to be turned by rudder inputs
PART 3: Notes on how a negative coupling between yaw
and roll, due to anhedral, contributes to roll instability and roll
responsiveness
PART 4: Basic explanation of turns, slips, and skids
PART 5: More notes on coordinated turns, slips, skids,
and the nature of aerodynamic sideforces
PART 6: How to (correctly) diagram the force vectors at
play during "coordinated", "slipping", and
"skidding" turns:
PART 7: Practical use of the rudder to prevent slips or
skids
(Or: when do we expect to see slips or skids in a
rudderless aircraft?)
PART 8: Some myths regarding turns
PART 9: "You can't feel gravity!"
PART 10: Notes on the July 2000 article "Turning
flight and sideslip in hang gliders"
PART 1: Some brief notes
on dihedral, anhedral, sweep, and coupling between yaw and roll:
This "Theory" section mostly addresses the real and apparent forces
at play during slips, skids, and "coordinated" flight. In later
updates we'll delve into many, many more topics, such as the "airflow
curvature" effect. (For some notes on the airflow curvature effect, check
out the long article that I created several years ago.) In later updates we'll
also focus heavily upon the coupling between yaw and roll, particularly in the
case of a swept wing with anhedral. Very briefly: a wing with dihedral tends to
have "positive" coupling between yaw and roll. By this we mean that
if the nose of the aircraft gets yawed to the left in relation to the
aircraft's actual direction of travel through the airmass, or if the aircraft
is struck by a sudden crosswind gust from the right, then the aircraft will
tend to roll to the left. The reason for this has nothing to do with one wing's
lift vector being "more vertical" and the other wing's lift vector
being "less vertical", as is sometimes alleged. This would not create
any roll torque. Rather, the "upwind" wing experiences a greater
angle-of-attack than the "downwind" wing, so that the upwind wing
creates more lift than the downwind wing, creating a roll torque. Anhedral
works the opposite way: a wing with anhedral tends to have "negative"
coupling between yaw and roll. By this we mean that if nose of the aircraft
gets yawed to the left in relation to the aircraft's actual direction of travel
through the airmass, or if the aircraft is struck by a sudden crosswind gust
from the right, then the aircraft will tend to roll to the left. The reason for
this is that the "upwind" wing experiences a lower angle-of-attack
than the "downwind" wing. Anhedral and dihedral effects are
relatively independent of the angle-of-attack of the aircraft as a whole.
Another important factor is sweep. A swept wing tends to have
"positive" coupling between yaw and roll--just like a wing with
dihedral. Here is the reason for this: when the relative wind includes a
sideways component, then the "upwind" wing experiences an airflow
that hits the leading edge nearly squarely head-on, while the "downwind"
wing experiences an airflow with a large component parallel to the leading
edge, blowing from root to tip. Therefore the "upwind" wing produces
more lift than the "downwind" wing. This sweep effect is highly
dependent on lift coefficient, i.e. on angle-of-attack. If the pilot unloads
the wing to the zero-lift angle-of-attack, so that the lift coefficient is
zero, then there will be no roll torque even if there is a strong sideways
airflow component. If the pilot puts the wing at a high angle-of-attack---which
will correspond either to a high G-loading, or to normal 1-G flight at a low
airspeed--then a sideways airflow component over the wing will generate a very
strong roll torque. The upshot of all this is that it is very possible for a
swept, anhedral wing to show slight positive or neutral yaw-roll coupling at
high angles-of-attack (when the pilot flies at trim or pushes out on the bar),
and to show strong negative coupling at low angles-of-attack (when the pilot
pulls the bar all the way in). The positive coupling seen at low airspeeds and
high angles-of-attack is created by sweep, and the negative coupling seen at
high airspeeds and low angles-of-attack is created by anhedral. I suspect that
many modern hang gliders exhibit these characteristics. And here's one more
twist in the whole picture: the anhedral in a hang glider wing is created in
large part not by the droop in the leading edges relative to the keel, but
rather by the washout built into the wing. Much more on this in later editions
of this webpage!
PART 2: Notes on how a
positive coupling between yaw and roll, due to dihedral or sweep, contributes to
roll stability and allows an aircraft to be turned by rudder inputs
We'll explore in detail the relationship between the yaw-roll coupling due
to sweep, dihedral, or anhedral, and the aircraft's resulting stability or
instability in the roll axis, in a future update of this section. Again, this
relationship has nothing to do with one wing's lift vector being "more
vertical" than the other wing's lift vector when the aircraft banks, as is
sometimes alleged. Rather, when the aircraft banks, the flight path starts to
curve. If the nose does not yaw to keep pace with the changing direction of the
flight path, then a sideways component will start to appear in the airflow over
the wing. In other words the aircraft will start to slip sideways through the
airmass. This will happen regardless of whether the pilot has intentionally banked
the aircraft, or the aircraft has tipped a bit due to turbulence. Anytime the
aircraft banks, it starts to slip sideways for at least a few seconds, until
the aircraft's intrinsic yaw stability--the "weathervane"
effect--applies enough yaw torque overcome the aircraft's yaw rotational
inertia, and to overcome adverse yaw effects which will be present whenever the
bank angle is changing, and to start the nose smoothly tracking around the
horizon in a full-fledged non-slipping turn with the nose of the aircraft
constantly pointing directly into the airflow. (Of course in an aircraft with a
rudder, the pilot can bypass this slip by applying inside rudder to keep the
nose pointing directly into the airflow right form the start, as the flight
path starts to curve). Whenever the aircraft is experiencing a slip--i.e. a
sideways component in the airflow--then sweep and dihedral or anhedral will all
be acting to create a roll torque as described above. In an aircraft with
dihedral or sweep, this roll torque will have a stabilizing effect. Here's why:
if the left wing drops, then the tilted lift component from the banked wing
starts pushing the aircraft toward the left. The flight path starts to curve,
but it takes a little while before the aircraft's intrinsic yaw stability (the
"weathervane effect") generates enough yaw torque to overcome the
aircraft's yaw rotational inertia and increase the yaw rotation rate enough to
keep the nose pointing squarely into the changing direction of the airflow as
the turn continues. (Eventually this will happen, if the aircraft stays banked
at a constant angle, and then the aircraft will be in a fully-fledged
non-slipping turn). During these moments while the aircraft is slipping
sideways through the air, the left wing is creating more lift than the right
wing, either because the airflow is moving more "squarely" across the
left wing than the right wing as seen from above (in the case of a wing with
sweep) or because the left wing is at a higher angle-of-attack than the right
wing (in the case of a wing with dihedral). This imbalance in lift tends to
return the aircraft to wings-level.
If an aircraft with dihedral or sweep has too much yaw stability--i.e. too
large a vertical tail fin--then if the aircraft gets tipped to one side, it
will quickly "weathervane" into a full-fledged, non-slipping turn
before the dihedral or sweep have any chance to roll the aircraft back toward
wings-level. The large fin decreases the roll stability that would normally be
created by the sweep or dihedral. By the same logic, if an aircraft has a lot
of dihedral or sweep, then when the pilot makes an intentional roll input, it
will be important for him to also use the rudder to keep the nose pointing
directly into the airflow so that there is no sideslip. If the aircraft slips
sideways due to adverse yaw or yaw rotational inertia when the pilot makes a
roll input to bank the wing, and a lot of sweep or dihedral is present, then an
unfavorable, opposing roll torque will be created and the roll rate will be very
sluggish. And by the same logic, if an aircraft has a lot of dihedral or sweep,
then the rudder can be used to generate a roll torque by yawing (skidding) the
nose of the aircraft in the direction that the pilot wants to turn. The
resulting sideways airflow will interact with the dihedral or sweep to roll the
aircraft in the desired direction. (This is precisely why many light aircraft
can be steered with the rudder, without using the ailerons.)
PART 3: Notes on how a
negative coupling between yaw and roll, due to anhedral, contributes to roll
instability and roll responsiveness
Anhedral has a destabilizing effect, and makes the aircraft more responsive
to the pilot's roll inputs (except in cases where adverse yaw is not an issue
because the roll inputs are in accomplished via spoilerons). If an aircraft
with a lot of anhedral gets tipped to one side, the resulting slip will tend to
make the aircraft keep rolling to an ever-steeper bank angle. Here's why this destabilizing effect occurs:
if the left wing drops, then the tilted lift component from the banked wing
starts pushing the aircraft toward the left. The flight path starts to curve,
but it takes a little while before the aircraft's intrinsic yaw stability (the
"weathervane effect") generates enough yaw torque to overcome the
aircraft's yaw rotational inertia and increase the yaw rotation rate enough to
keep the nose pointing squarely into the changing direction of the airflow as
the turn continues. (Eventually this will happen, if the aircraft stays banked
at a constant angle, and then the aircraft will be in a fully-fledged
non-slipping turn). During these moments while the aircraft is slipping
sideways through the air, the right wing is creating more lift than the left
wing, because the anhedral geometry is increasing the angle-of-attack of the
right wing. This imbalance in lift tends to roll the aircraft to a steeper bank
angle.
On an aircraft with anhedral, a large vertical fin can help to reduce this
roll instability by increasing the aircraft's yaw responsiveness or
"weathervane effect" so that there is less sideslip when a wing
drops.
When the pilot makes a roll input, if the aircraft sideslips due to adverse
yaw or yaw rotational inertia, this will actually create a favorable roll
torque if anhedral is present. This is why anhedral is important in hang
gliders. Anhedral actually "harnesses" adverse yaw (and yaw
rotational inertia) in a way that increases the roll rate of the aircraft when
the pilot makes an intentional roll input. Applying rudder along with the roll
input, or having a large fixed vertical fin, can negate this effect and
decrease the roll rate, though drag will naturally be decreased if the aircraft
is not allowed to slip sidewise through the airmass. By the same token, over-use
of a rudder, so that the nose of the aircraft skids over to point too far in
the direction of the desired turn, will actually create an unfavorable or
"wrong-way" roll torque if anhedral is present.
Obviously, the characteristics of a wing with both sweep and anhedral will
be complex. In some cases, which of these two effects will dominate may depend
on the wing's angle-of-attack (more on this later). This can create some very
interesting stability and rudder-response characteristics.
Now we're going to change gears away from the subject of coupling between
yaw and roll, and focus on the basic physics of slips, skids, and
"coordinated" turns.
PART 4: Basic
explanation of turns, slips, and skids:
Consider a banked aircraft. The wing's lift vector acts "square"
to the wingspan (i.e. perpendicular to the wingspan) as seen in a head-on view.
Therefore the wing's lift vector contains a horizontal component. This
horizontal force component acts on the aircraft to create a curve in the flight
path, as viewed from above--i.e. a turn. The horizontal component of lift is
the "centripetal force"--i.e. the inward-pointing force--which is the
fundamental cause of the turn. "Centripetal" means that this force
component is always pointing toward the center of the circle described by the
turning aircraft, which also means that the force component is always acting
perpendicular to the direction that aircraft is actually travelling at any
given moment. (Another familiar example of a "centripetal force" is
the earth's gravity, which acts on a spacecraft, or on a satellite, or on the
moon, to produce a continual curve in the orbiting body's trajectory, yielding
a circle or an ellipse. Every time a moving body describes a curving path of
travel, a centripetal force is at work.)
There are only two situations in which a banked aircraft would not end up
following a curved flight path, as viewed from above. Case 1: if the pilot
moves the control stick forward to "unload" the wing all the way to
the zero-lift angle-of-attack, reducing the wing's lift vector to zero, then
there will be no turn. (There's really no equivalent in hang-gliding, since
even when the control bar is pulled all the way in, with the pilot's weight
shifted all the way forward, the wing is not unloaded all the way to the
zero-lift angle-of-attack, unless it is in the midst of a tumble after an upset
in turbulence.) Case 2: if the aircraft is somehow generating additional
aerodynamic forces which include a horizontal component acting toward the
outside of the turn, exactly equal and opposite to the horizontal component
pointing toward the inside of the turn which was created by the banked wing, so
that the net horizontal force on the aircraft ends up being zero, then there
will be no turn.
Coordinated (non-skidding, non-slipping)
flight:
In the case of a normal, coordinated, non-slipping, non-skidding turn, the
wing's lift vector is essentially the only aerodynamic force present. (In a
powered aircraft in level flight thrust and drag are also present but cancel
each other. When an aircraft is in a steady glide or a steady climb there will
in fact be an excess drag vector or an excess thrust vector, respectively, but
these aren't very significant for our discussion here. More specifically, these
thrust and drag forces don't include any sideways components, in the aircraft's
reference frame. We'll deal with them in more detail later.) For now the key
points of interest are these: relative to the outside world, the wing's lift
vector contains a horizontal component which provides the centripetal force
that drives the turn. If the aircraft is to turn, it makes no sense at all to
"balance" the horizontal forces by introducing an "centrifugal
force" vector. "Centrifugal force", in the sense that it is
usually used in diagrams relating to turning flight, is just an
"apparent" force created by inertia, not a real force. In other words
"centrifugal force" is a myth--it doesn't really exist--and it really
shouldn't be included on vector diagrams relating to turning flight. A turning
aircraft is in an unbalanced condition, not a balanced condition; the
horizontal forces cannot add up to zero. So why does the pilot feel no sideways
load on his body in a normal, "coordinated", nonslipping, nonskidding
turn? Here's why: relative to the aircraft's reference frame, the wing's lift
vector points squarely "upward", i.e. it is "square" to the
wingspan, or perpendicular to the wingspan. And no other sideways aerodynamic
forces are present, in the reference frame of the aircraft and pilot. Therefore
the aircraft and the pilot experience no "sideways" force, in their
own reference frame. If we introduce an additional, mythical, horizontal force
called "centrifugal force", then we create the illusion that the
pilot and the slip-skid ball will in fact "feel" a net sideways
force, in their own reference frame, even in a normal, "coordinated",
turn. This makes no sense.
At this point the reader may be asking "But what about gravity? If we
get rid of centrifugal force, won't gravity pull the pilot, and the slip-skid
ball, toward the inside of the turn?" An excellent question. Gravity is a
real force and certainly helps to determine that the aircraft, and its
contents, follow through space. Any vector diagram that is intended to explain
the path taken through space by the aircraft must certainly include gravity.
However, because gravity acts on every molecule of the aircraft, the pilot's
body, the slip-skid ball, etc, all at the same time, it does not tend to pull
the slip-skid ball toward the low side of the aircraft, nor does it tend to
pull the pilot's body toward the low side of the aircraft. Instead all of these
items move through space together, each being accelerated by gravity in exactly
the same way. Nor can gravity be "felt" by the pilot--every molecule
of each of his bones, muscles, etc are pulled by gravity in exactly the same
way and no internal sensations of stress or strain can arise. So vector
diagrams which are intended to illustrate the forces "felt" by the
pilot's body, and to illustrate the forces which tend to roll the slip-skid
ball toward the low side or the high side of the aircraft during a slip or a
skid, should not include gravity. These vector diagrams should only include the
aerodynamic forces generated by the aircraft. These real, aerodynamic,
forces--or perhaps their mirror image--are exactly what we mean when we speak
of a "G-load". If the wing is lifting with a force equal to 1G, the
pilot will feel this 1G lift force, or perhaps we may prefer to say that the
pilot feels an apparent 1G downward force due to the inertia of his body. By 1G
we mean a force equal to the body's normal weight on earth. And if the wing is
producing 1G of lift, then this 1 G force is exactly what the pilot will feel,
regardless of whether he is flying near the surface of the Earth, or near the
surface of Mars, or through a cloud of gas somewhere in deep space. Gravity has
nothing to do with it. (Of course, the aircraft will be accelerating upward
into a loop, rather than following a level flight path, in some of these
scenarios!)
One often encounters the idea of a "balance between centrifugal force
and gravity". This idea comes up in relation to "coordinated"
turning flight, and also in relation to 0-G ballistic or orbital flight where
the pilot or astronaut is weightless. This idea is extremely
misleading--"centrifugal force" doesn't exist, and you can't
"feel" gravity. Zero-G conditions exist whenever the total
aerodynamic and thrust forces add up to zero. End of story. Here's a nail in
the coffin of the idea of a "balance between centrifugal force and
gravity". Imagine an astronaut, stationary in space with respect to the
earth, just a bit beyond the earth's atmosphere. Of course he immediately
begins to freefall toward the earth. In this particular situation there is no
curvature of any kind in his flight path, and therefore we cannot explain his
0-G experience in terms of a "centrifugal force" which
"balances" the pull of gravity.
The forces that a pilot feels in flight are the real, aerodynamic forces created
by the aircraft, not gravity or "centrifugal force".
For more, go to the subsection entitled "You can't feel gravity!"
This subsection is located at the extreme end of the "Theory"
section.
Here are just a few more comments on the idea of "centrifugal
force". We've stated that when the aircraft exerts an upward lift force on
the pilot--let's say 2 G's for the sake of this example--then for inertial
reasons the pilot's body seems to feel a 2-G force in the "downward"
direction, and so the normal convention is to think of a "positive"
G-loading as somehow acting in the "downward" direction. Again, this
is just an inertial effect--the only real force involved is the upward 2-G lift
force that aircraft is creating. The mirror-image, "downward"
reflection of this lift force--the 2-G "downward" force that the
pilot seems to "feel"--is only an inertial effect and doesn't really
belong in a vector diagram of the actual forces at play. However, for the
moment we can go along with the convention that the pilot is somehow
"feeling" the apparent downward inertial effect rather than the real
upward force. As seen in by an observer in the external world, this apparent
downward force, acting on the banked aircraft includes a horizontally outward
component, i.e. a "centrifugal" component. So in a very narrow sense
it is valid to go along with the convention that the pilot is somehow
"feeling" a centrifugal force, not a centripetal force. However, this
opens the doorway to many errors. The central point is that this apparent
"centrifugal force" is only one component of a larger "apparent
force" vector which is simply the mirror image of the vector sum of all
the real, aerodynamic and thrust forces (but not the gravitational forces) that
are acting on the aircraft. The real net aerodynamic force vector and the
mirror-image "apparent force" vector represent two different ways of
thinking about the world and really don't belong on the same vector diagram.
When we draw the real, net, aerodynamic force and the mirror-image "apparent
force" on the same vector diagram, then we are giving mixed signals. What
is the message supposed to be? That these forces, being equal and opposite,
cancel each other out, so that the pilot is "feeling" a net force of
zero, i.e. that he is weightless? That the net horizontal forces add up to
zero, i.e. that the aircraft is not turning, even if it is banked? It's really
much more accurate to limit our vector diagrams to the real forces at play,
without including the "apparent force" vector. Worse yet are the
ubiquitous vector diagrams that include the horizontal component of the real
aerodynamic force generated by the aircraft, and the "apparent"
centrifugal force component which really should just be the horizontal
component of the mirror-image "apparent" force vector, equal and
opposite to the real aerodynamic force vector--yet in so many of these
diagrams, the horizontal component of the real aerodynamic force vector, plus
the apparent "centrifugal force" vector, do not add up to zero. What
conclusion are we supposed to draw from this? If the apparent "centrifugal
force" is really just the mirror-image of the horizontal component of the
real aerodynamic forces at play, then how can the apparent "centrifugal
force" vector, and the horizontal component of the real aerodynamic force
vector, not be equal in magnitude? Again, it's really much better to limit our
vector diagrams to the real forces at play, without including the
"apparent force" vector components. If we want to include all of the forces
that are affecting the acceleration of the aircraft and pilot through space,
then we include gravity, and if we want to include only the forces that are
"felt" by the pilot or affect the motion of the slip-skid ball, the
pilot, etc, in relation to the rest of the aircraft, then we omit gravity, and
only show the real aerodynamic forces. Since the mirror image "apparent
force" vector is related to the way that the pilot "feels" the
real aerodynamic forces, and we've learned that the pilot cannot
"feel" gravity, and that gravity alone cannot simulate a
"weighted environment" by pulling objects against the low side of an
aircraft or spacecraft, then it makes little sense to speak of an apparent
"centrifugal force" vector in the case of 0-G spaceflight where
gravity is the only real force present. Yet this is often done, especially in
the case of orbital flight.
We've strayed rather far from our summary of the forces at work in
coordinated, slipping, and skidding turns! Let's continue.
Slipping flight:
A slip occurs when the pilot allows the nose of the aircraft to be yawed in
relation to the aircraft's actual direction of travel, so that the nose points
toward the high side or outside of the turn, in relation to the direction that
the aircraft is actually travelling through the air. During a slip, a pilot in
an open-air cockpit who turned his face to point directly into the airflow or
relative wind would notice that the nose of the aircraft was yawed toward the
high side or outside of the direction that the pilot was actually facing.
Since the fuselage and other aircraft components are being forced to plow
through the air in a sideways manner, they generate an aerodynamic sideforce
which acts to push the whole aircraft toward the high side or outside of the
turn. For a given amount of slip--for example imagine that the nose of the
aircraft is yawed to point 10 degrees toward the outside or high side of the
turn, in relation to the direction that the aircraft is actually travelling at
any given moment--the amount of aerodynamic sideforce that will result is
highly dependent upon the fuselage shape and size. For example, imagine 2
sailplanes, each flying at a 10 degree slip angle, as indicated by the telltale
or yaw string at the nose of each aircraft. (The telltale or yaw string moves
freely in the wind and so indicates the difference between the direction that
the nose is pointing, and the actual direction of the airflow or relative wind,
which is equal in magnitude and opposite in direction to the aircraft's actual
path of travel through the airmass. So the yaw string indicates whether the
nose is pointing directly into the airflow and parallel to the aircraft's
actual direction of travel, or is yawed off to one side or the other in
relation to the airflow and the actual direction of travel.) If one sailplane
has a large, slab-sided fuselage and the other has a slender rounded fuselage,
the former will generate a much stronger aerodynamic sideforce than the latter.
So for a given yaw string deflection, the pilot in the sailplane with the boxy
fuselage will feel a much larger sideforce on his body than the pilot in the
sailplane with the slender fuselage. The slip-skid ball will also deflect much
further in the boxy aircraft than in the slender aircraft.
In flying-wing aircraft such as hang gliders, there is no fuselage to
generate these sideforces, so the sideforces will be very small indeed. Also, a
hanging pilot is free to swing from side to side, so instead of
"feeling" a force acting against his body, he'll simply note that he
tends to hang slightly on the high side or the low side of the aircraft
centerline when he relaxes his grip. For these reasons, a slip or skid will
feel very different--and will likely be much harder to detect--in a hang glider
than in a "conventional" airplane or sailplane.
The aerodynamic sideforce from a slip acts parallel to the aircraft's
wingspan. In other words in the aircraft's own reference frame it acts purely
in the "sideways" direction, parallel to the wingspan and
perpendicular to the wing's lift vector, but in the reference frame of the
outside world it contains a significant vertical (upward) component when the
bank angle is steep. In fact some aerobatic aircraft can be held indefinitely
in a 90-degree bank. To do this, the pilot holds lots of "top rudder"
which yaws the nose upward--i.e. skyward-- and generates enough sideforce off
of the aircraft fuselage--acting sideways in the aircraft's reference frame and
acting vertically upward in the reference frame of the outside world-- that the
entire aircraft weight can be supported. (In actual practice the tilted engine
thrust also helps support a portion of the aircraft weight).
At more normal bank angles, the aerodynamic sideforce component generated by
the slipping fuselage contains a large horizontal component which points toward
the outside of the turn. (This is a genuine, real, "centrifugal
force" which should not be confused with the "apparent", fake,
centrifugal force that is generated by inertial effects when a body follows a
curving flight path). This horizontal, centrifugal, aerodynamic force component
reduces the net horizontal, centripetal, aerodynamic force that is being
generated by the aircraft, so the turn rate is decreased. In extreme cases the
pilot applies so much rudder (in relation to the bank angle) that the fuselage
creates so much aerodynamic sideforce that the turn rate falls to zero--this is
the non-turning, constant-heading slip which is useful for crosswind landings,
for increasing drag on final approach, for seeing around the nose of a
radial-engined aircraft on final approach, etc.
At extreme bank angles, the aerodynamic sideforce component generated by the
slipping fuselage contains a large vertical component which points skyward, as
we've already seen. To keep the vertical forces in balance, the wing's lift
must be reduced--the sustained 90-degree bank maneuver discussed immediately
above is the extreme example of this. Again, the net horizontal, centripetal
force ends up being reduced, and the turn rate is decreased.
Skidding flight:
A skid occurs when the pilot allows the nose of the aircraft to be yawed in
relation to the aircraft's actual direction of travel, so that the nose points
toward the low side or inside of the turn, in relation to the direction that
the aircraft is actually travelling through the air. During a skid, a pilot in
an open-air cockpit who turned his face to point directly into the airflow or
relative wind would notice that the nose of the aircraft was yawed toward the
low side or inside of the direction that the pilot was actually facing.
Since the fuselage and other aircraft components are being forced to plow
through the air in a sideways matter, they generate an aerodynamic sideforce
which acts to push the aircraft toward the low side or inside of the turn. Again,
for a given amount of skid, as measured with the yaw string, the resulting
aerodynamic sideforce will vary according to the shape and size of the aircraft
fuselage and other components. An aircraft with a large, boxy fuselage will
generate much more sideforce than an aircraft with a small, streamlined
fuselage.
The aerodynamic sideforce from the skid acts parallel to the aircraft's
wingspan. In other words in the aircraft's own reference frame it acts purely
in the "sideways" direction, perpendicular to the wing's lift vector,
but in the reference frame of the outside world it contains a significant
vertical (downward) component when the bank angle is steep. This is one of
several reasons why a pilot tends to move the control stick aft to increase the
wing's angle-of-attack whenever he executes an accidental skidding turn. And
this is one of the reasons why an accidental skidding turn can be an invitation
to a spin.
The aerodynamic sideforce component generated by the skidding fuselage
contains a large horizontal component which points toward the inside of the
turn. This horizontal force component increases the net horizontal,
centripetal, aerodynamic force being generated by the aircraft, so the turn
rate is increased, compared to a non-skidding turn at the same bank angle.
However, as a general rule it is far more efficient to yaw the nose back into
alignment with the actual direction of flight at any given moment, and then
increase the turn rate as desired by increasing the bank angle.
PART 5: A few more notes
on coordinated turns, slips, skids, and the nature of aerodynamic sideforces:
The aerodynamic sideforce generated during a slip or a skid is really a form
of lift, not drag--it is a force acting perpendicular to the flight path. Of
course drag will also increase as the aircraft flies sideways through the
air--both the profile drag, and the induced drag associated with producing
lift. It is not efficient to fly sideways! However a flying-wing aircraft will
experience much less of a drag penalty than an aircraft with a big, boxy
fuselage, for a given angle of sideslip through the airmass.
We've already emphasized that a pilot "feels" only the real,
aerodynamic force created by the aircraft, not gravity or "centrifugal
force". If a turn is "coordinated", then the only net
aerodynamic force of interest is the wing's lift vector, acting
"square" or perpendicular to the wing and "straight up" in
the aircraft's own reference frame, and the pilot will feel no sideforce and
the slip-skid ball will stay centered. The net aerodynamic force vector acts
"straight up" in the aircraft's reference frame, and this is what the
pilot feels. Unfortunately, common convention is to express the apparent G-load
as if it were created by some mysterious force within the body, not by the
external force of the wing's lift, and therefore we imagine that the usual
positive 1-G loading is somehow acting in the "downward" not the
"upward" direction. But no matter, this is just a convention. The key
point is that whenever there is no aerodynamic sideforce present, then the
pilot will not feel any sideforce, regardless of what we may read in books
about gravity and "centrifugal force".
We've already seen that a slip occurs when the aircraft is allowed to fly
through the air in a sideways manner, with the nose yawed to point toward the
high side or the outside of the turn. And we've already seen that as the
fuselage and other components plow sideways through the airmass, they create an
aerodynamic sideforce that acts toward the outside or high side of the turn.
This sideforce directly influences the acceleration and trajectory of the
aircraft, but is transmitted to the pilot and the slip-skid ball only in an
indirect manner. Therefore the aircraft tends to move toward the outside or high
side of the turn in relation to the pilot and slip-skid ball. Or put the other
way, the pilot and the slip-skid ball seem to fall to the inside or low side of
the turn, as they tend to continue on their own, independent, inertial
trajectories. Again, we have an aerodynamic force component acting toward the
high side or the outside of the turn, in the reference frame of the aircraft,
and the usual convention is to say that the pilot and the slip-skid ball are
experiencing a net G-loading which is oriented not quite exactly in the usual
"downward" direction, in the aircraft's reference frame, but rather
is tilted slightly toward the inside or low side of the turn in the aircraft's
reference frame. In a skid the reverse is true--the aircraft generates an
aerodynamic sideforce component which is angled toward the inside or low side
of the turn, and the pilot and slip-skid ball tend to move toward the outside
or high side of the turn.
In either a slip or a skid, the aerodynamic sideforce eventually ends up
being transmitted through the aircraft structure into the seatbelts and then
into the body of the leaning-over pilot. Also the sloping floor of the tube of
the slip-skid ball is able to transmit this sideforce into the ball, once the
ball has rolled to the side a bit. Then everything is in equilibrium--the
aircraft, the tilted-over pilot, and the displaced ball are all moving through
space together as a unit, despite the slip or skid. Despite what you may read
in books about "unbalanced" forces on the pilot or the slip-skid
ball, the pilot does end up "feeling" exactly the same forces as the
aircraft itself "feels". Aircraft and pilot accelerate together and
the pilot is not ejected out the side of the aircraft, which is what is implied
if the usual comments in the hang gliding and airplane and sailplane literature
are taken too literally!
In the literature for airplanes and sailplanes, most
"explanations" put the "cart before the horse" by saying
that the rudder somehow (mysteriously) changes the turn rate, and this creates
a mismatch between "centrifugal force" and the other forces at play,
and then these mismatched forces throw the slip-skid ball and the pilot to one
side of the aircraft. Changes in the amount of lift generated by the wing are
sometimes thought to be able to create the same effects, by affecting the
balance between the vertical component of lift, and gravity, and
"centrifugal force", and the other forces at play--this is approach
that is usually taken by authors writing about turns in hang gliders and
trikes. It is much better to simply recognize that the rudder (or the lack of
rudder, when rudder is needed to combat adverse yaw etc.) makes the aircraft
fly sidewise through the air, and this generates real aerodynamic sideforces,
and these aerodynamic sideforces are the direct, fundamental cause both of the
sideways tilting of the pilot's body and the slip-skid ball, and of the change
in turn rate. Again the key point: the pilot feels only the real, tangible,
aerodynamic forces that are being generated by the aircraft. Not
"centrifugal force", and not gravity. Any "explanation" of
slips and skids which emphasizes the "imbalance between gravity and
centrifugal force", or the "imbalance between the horizontal component
of lift and centrifugal force", or the "imbalance between the
vertical component of lift and weight", is missing the point
completely--and doubly so if the "explanation" fails to make any
reference to the real, aerodynamic sideforce that is generated as the fuselage
and other aircraft components are allowed to fly sideways through the air
during a slip or skid.
What happens if, during a turn, the pilot shoves the control stick forward
to unload the wing to the zero-lift angle-of-attack? (Or what a happens if a
hang glider pilot abruptly pulls in the bar to decrease the wing's
angle-of-attack?) If we are basing our analysis on gravity, "centrifugal
force", etc., then the answer is quite unclear; at first glance it appears
that the pilot and the ball will tend to fall toward the low side or the inside
of the turn due to "excess gravity" or "inadequate centrifugal
force", in relation to the actual vertical and horizontal force components
that the wing is generating. However if we realize that the only thing that
matters is the direction of the net aerodynamic force created by the aircraft,
then we know that reducing the lift vector--which always acts
"square" to the wing and "straight up" in the pilot's
reference frame--will not create any imbalanced forces on the pilot or the
slip-skid ball. Unless, of course, the aircraft then starts moving earthward in
such a manner that the fuselage slides sideways through the airmass, thus
creating an aerodynamic sideforce. As long as the pilot uses the rudder to keep
the nose pointing directly into the airflow, this cannot happen. What if the
pilot is flying a rudderless aircraft, or keeps his feet of the rudder pedals
as shoves the stick forward? Repeated experiments in a variety of aircraft show
that no discernable slip results in this situation. Possible reasons for this
will be discussed in great detail in another section! (Hint: consider the fact
that "unloading" the wing will decrease the turn rate, but yaw
rotational inertia is still carrying the nose of the aircraft around at the
original rate of yaw rotation, which would seem to promote a skid not a slip.
Perhaps this "excess" yaw rotation ends up being exactly what is
needed to yaw the nose down into the airflow as the flight path curves downward
due to the inadequate G-loading.)
PART 6: How to (correctly)
diagram the force vectors at play during "coordinated",
"slipping", and "skidding" turns:
1. "Coordinated" turn
Start by drawing the weight or gravity vector. (Our initial diagrams will
show all the forces at work on the aircraft and contents; later we'll erase the
gravity vector to leave only the forces that are actually "felt" by
the pilot). Now draw the wing's lift vector, "square" or
perpendicular to the banked wing. For the time being make the lift vector of
such a length that its vertical component is equal to the gravity vector. The
diagram is now complete. The unbalanced horizontal component of the wing's lift
vector is the horizontal, centripetal force which drives the turn. Now let's
alter the diagram to show only the forces that are "felt" by the
pilot. We simply erase the gravity vector. The only remaining vector is the
wing's lift vector. Since it acts "square" to the wingspan, and
"straight up" in the aircraft's own reference frame, the pilot feels
no sideforce, and the slip-skid ball shows no tendency to fall toward the low
side or the high side of the aircraft.
Admittedly we've ignored the drag vector, which will bear a small part of
the aircraft weight in the case of gliding flight. Similarly, in climbing
powered flight the thrust vector will bear a small part of the aircraft weight.
These vectors don't involve any sideforces, and so for the sake of our
discussion it's simpler to focus on constant-altitude, powered flight where
thrust and drag cancel each other.
2. Slipping turn
Again start by drawing the weight or gravity vector. Now draw the wing's
lift vector, "square" or perpendicular to the banked wing. For the
time being make the lift vector of such a length that its vertical component is
equal to the gravity vector. Now add the aerodynamic sideforce created as the
fuselage and other aircraft components fly sideways through the airmass. This
vector should be drawn parallel to the wingspan, and pointing toward the high
side or outside of the turn. Now shorten the wing's lift vector slightly, so
that the vertical force components (including gravity) still add up to zero.
The diagram is now complete. The vector sum of the horizontal component of the
wing's lift vector, plus the horizontal component in the aerodynamic sideforce
vector from the slip, yields the (now reduced) net horizontal, centripetal
force which drives the turn. Now let's alter the diagram to show only the
forces that are "felt" by the pilot. We simply erase the gravity
vector. The remaining forces--the actual aerodynamic forces--include a
sideforce component that pushes the aircraft toward the outside or high side of
the turn. In response, the pilot will tend to fall toward the low side or
inside of the turn. If we wish, we can add an "apparent G-force" vector
which is equal in magnitude and opposite in direction to the real aerodynamic
forces being created by the aircraft, but we should remember that this
"apparent G-force" is really just a reflection of the inertia of the
pilot's body, the slip-skid ball, etc., and so this "apparent" force
doesn't really belong in the vector diagram.
3. Skidding turn
Again start by drawing the weight or gravity vector. Now draw the wing's
lift vector, "square" or perpendicular to the banked wing. For the
time being make the lift vector of such a length that its vertical component is
equal to the gravity vector. Now add the aerodynamic sideforce created as the
fuselage and other aircraft components fly sideways through the airmass. This
vector should be drawn parallel to the wingspan, and pointing toward the low
side or inside of the turn. Now lengthen the wing's lift vector slightly, so
that the vertical force components (including gravity) still add up to zero.
The diagram is now complete. The vector sum of the horizontal component of the
wing's lift vector, plus the horizontal component in the aerodynamic sideforce
vector from the slip, yields the (now increased) net horizontal, centripetal
force which drives the turn. Now let's alter the diagram to show only the
forces that are "felt" by the pilot. We simply erase the gravity
vector. The remaining forces--the actual aerodynamic forces--include a
sideforce component that pushes the aircraft toward the inside or low side of
the turn. In response, the pilot will tend to move toward the high side or
outside of the turn. If we wish, we can add an "apparent G-force"
vector which is equal in magnitude and opposite in direction to the real
aerodynamic forces being created by the aircraft, but we should remember that
this "apparent G-force" is really just a reflection of the inertia of
the pilot's body, the slip-skid ball, etc., and so this "apparent"
force doesn't really belong in the vector diagram.
4. Vertical accelerations
In the above diagrams we made the vertical forces, including weight or
gravity, add up to zero. But there's no reason that we can't extend or shorten
the wing's lift vector, in any of the diagrams, so that we end up with a net
upward or downward force and acceleration. This will also affect the horizontal
balance of forces, and the turn rate. However, just changing the length of the
lift vector does not create a sideforce in the reference frame of the aircraft
and pilot. Therefore, just changing the length of the lift vector will not make
the pilot, and the slip-skid ball, tend to move toward the low side of the
aircraft. The "coordinated" turn will remain "coordinated",
and the slipping turn will remain a slip, and the skidding turn will remain a
skid, if only the length of the lift vector has changed. Of course, when we
introduce a vertical acceleration, it's a fair question as to whether this will
make the aircraft move through the airmass in such a way that the fuselage
meets the air in a sideways manner and creates aerodynamic side forces where
none existed when the vertical forces were in balance. Experimental tests in a
wide variety of aircraft suggest that this does not occur; we'll give some
possible reasons why in another section of this website. For now we'll repeat
the hint that we gave above: at first glance, "unloading" the wing
would appear to make the aircraft slide downward (earthward) through the
airmass in a sideways slip, with the nose pointing toward the high side or
outside of the actual flight path through the airmass. But consider the fact
that "unloading" the wing will decrease the turn rate, but yaw
rotational inertia will still tend to carry the nose of the aircraft around at
the original rate of yaw rotation, which would seem to promote a skid not a
slip. Perhaps this "excess" yaw rotation ends up being exactly what
is needed to yaw the nose down into the airflow to meet the airflow squarely
head-on, even as the flight path curves downward due to the deficiency in the
vertical component. If this is the case, then there will be neither a slip nor
a skid.
PART 7: Practical use
of the rudder to prevent slips or skids:
(Or: when do we expect to see slips or skids
in a rudderless aircraft?)
By now we've talked a great deal about slips and skids without any attention
to how a pilot uses the rudder in actual flight. The goal is to keep the nose
of the aircraft pointing directly into the airflow, not yawed to the high side
or low side in relation to the airflow, i.e. in relation to the relative wind,
which simply blows equal in velocity and opposite in direction to the
aircraft's actual direction of travel through the airmass. In other words we
are keeping the nose pointing in the same direction as we actually going,
through the airmass.
As a pilot starts to roll an aircraft into a turn, the drag on the outboard,
rising, wing tends to increase. This is adverse yaw. The usual explanation is
that the outboard wing is creating more drag "because it is creating more
lift" than the inboard wing. However, adverse yaw continues to act even
when the roll rate becomes constant. If the roll rate is constant, not
accelerating, then both wings are in fact creating the same amount of lift. The
real cause of adverse yaw has to do with the way that the upward motion of the
rising wing makes it experience a change in apparent airflow direction in a
manner that increases drag. For full details take a look at the "See How
It Flies" webpage in the "Links" section of this website.
At any rate, because of adverse yaw, the pilot has to apply inside rudder
pressure as he rolls the aircraft into a turn, or else adverse yaw would tend
to yaw the nose toward the outside of the turn, creating a temporary slip. This
is not desirable--what we really want is to get the nose yawing around the
horizon in the opposite direction, toward the inside of the turn, since a turn
involves a steady rotation in both the yaw and pitch axes. (And even in the
roll axis, surprisingly, if the turn is climbing or descending--more on this
later). In fact, even if the aircraft were designed with "perfect" ailerons
that ended up creating no adverse yaw at all, the pilot would still have to
apply some inside rudder to supply the needed yaw torque to start the nose
yawing around the horizon. Otherwise we would see some slip as the nose of the
aircraft tended to remain on its initial heading for a few moments, even as the
banked wing started to produce a sideforce and the flight path started to
curve. In aircraft that use spoilers for roll and yaw control, the spoilers
provide this yaw torque, as well as the yaw torque needed to overcome adverse
yaw. In this case the aircraft may be able to enter a turn, without slipping,
even without using any rudder. But in most cases we expect to see some slip as
we enter a turn in a rudderless aircraft.
Once the aircraft settles into a steady turn, very little rudder is needed.
If the airspeed is low, yielding a tight turn radius, and the wingspan is large
and the fuselage is long and the tail is large, a bit of inside rudder may be
needed to compensate for "airflow curvature" effects. The curvature
of the airflow in the turn increases the airspeed experienced by the outboard
wing, which increases both lift and drag on the outboard wing, and the curving
airflow also creates an inward airflow in the vicinity of the rear of the
aircraft, which pushes the tail inwards and yaws the nose outward. All these
effects tend to create a slight slip, if inside rudder is not applied. In a
rudderless aircraft we will like see just a touch of slip in a steady turn at a
low airspeed.
As the pilot rolls outside of the turn, the situation is basically the
mirror-image of the turn entry, and outboard rudder is generally needed to
combat adverse yaw and to stop the aircraft's yaw rotational inertia, both of
which tend to keep swinging the nose around in the direction of the turn,
creating a skid as the wings roll back toward wings-level. In a rudderless
aircraft we'll typically see a bit of skid as we roll out of the turn--a yaw
string will blow toward the inside or low side of the turn--though again we may
be able to avoid this by using well-designed spoilers for roll control.
In a wide variety of aircraft, I've found that hauling aft on the control
stick, or pushing the control stick forward, or pushing out the bar (shifting
body weight aft), or pulling in the bar (shifting body weight forward) has no
noticeable effect on the aircraft's tendency to slip or skid, either while
flying at a constant bank angle or while rolling into a turn or rolling back to
wings-level. The average airspeed--as opposed to the change in airspeed and the
G-loading--is a significant factor; in general adverse yaw is more pronounced
at low airspeeds. However some hang gliders with a fair amount of anhedral may
have significantly higher roll rates--and therefore significantly more adverse
yaw--at high airspeeds and low angles-of-attack.
Most aircraft can be rolled into a turn and back to wings-level without any
use of the rudder, as long as the pilot is willing to accept a bit of slip and
skid. However these slips and skids generally decrease the roll rate, for
reasons that will be discussed later. However in the case of aircraft with a
lot of anhedral, it is possible for the slip or slid to actually help to
increase the roll rate as the aircraft enters or exits a turn.
PART 8: Some myths
regarding turns:
Myth #1: Banking an aircraft permits a turn, but does not cause a turn.
Myth #2: If a pilot banks an aircraft, but does not make a nose-up pitch
input—i.e. if the pilot banks the aircraft but does not move the control bar
forward (in a hang glider) or does not move the control stick or yoke aft (in
conventional airplane or sailplane)—the aircraft will not turn. Instead, it
will slip sideways (earthwards), without turning.
Myth #3: A slip is caused by inadequate lift in relation to the bank angle,
which allows gravity to pull the pilot, the slip-skid ball, and perhaps also
the entire aircraft, toward the low side of the banked aircraft, i.e. toward
the low side of the turn. (Much less common is the logical compliment: that a
skid is caused by excess lift in relation to the bank angle.)
Myth #4: A slip is caused by an inadequate turn rate in relation to the bank
angle, so that there is not enough "centrifugal force" in relation to
the bank angle. This allows gravity to pull the pilot, the slip-skid ball, and
perhaps also the entire aircraft, toward the low side of the aircraft. A skid
is caused by an excess turn rate in relation to the bank angle, so that there
is too much "centrifugal force" in relation to the bank angle.
"Centrifugal force" overpowers "gravity" and this throws
the pilot, the slip-skid bubble, and perhaps also the entire aircraft, toward
the outside of the turn. A turn is "coordinated" when the amount of
"centrifugal force" is "right" for the bank angle, so that
"centrifugal force" and "gravity" are in the proper
balance.
Myth #5: This is a variation of myth #4. A slip is caused by an inadequate
turn rate in relation to the bank angle, so that there is not enough
"centrifugal force" in relation to the horizontal component of lift.
The resulting vector sum of "centrifugal force" plus the
"horizontal component of lift" yields a net side force toward the
inside of the turn, which throws the pilot, the slip-skid ball, and perhaps
also the entire aircraft, toward the low side or the inside of the turn. A skid
is caused by an excess turn rate in relation to the bank angle, so that there
is too much "centrifugal force" in relation to the horizontal
component of lift. The resulting vector sum of "centrifugal force"
plus the "horizontal component of lift" yields a net side force
toward the outside of the turn, which throws the pilot, the slip-skid ball, and
perhaps also the entire aircraft, toward the outside of the turn.
Myth #6: The amount of curvature in the flight path influences the amount of
"centrifugal force" that is "felt" by the aircraft (and the
pilot, and the slip-skid ball), and the airspeed influences the amount of
curvature in the flight path that will be present for any given bank angle. A
slip or skid is created by an imbalance between "centrifugal force"
and other forces such as gravity, the vertical component of lift, the
horizontal component of lift, etc.. Therefore too much airspeed in relation to
the bank angle can create a skid, and too little airspeed in relation to the
bank angle can create a slip.
Myth #7: As the bank angle increases toward 90 degrees, the G-loading
increases toward infinity and the stall speed also increases toward infinity.
At 90 degrees of bank, G-loading and stall speed are infinite.
Myth #8: A pilot must use extreme caution while entering a turn, due to the
increase in stall speed. Banked flight is intrinsically more dangerous than
wings-level flight. If an aircraft's stall speed is 40 mph, then its 2-G stall
speed is 56 mph. If the pilot started at 50 mph and rolled to a 60-degree bank
angle, he would be in great danger of stalling, even if he didn't move the
control stick aft (or even if he didn't push the control bar forward, in a hang
glider).
PART 9: "You can't
feel gravity!"
You can't feel gravity, because it simultaneously pulls on every molecule of
your body. Since gravity works "from the inside", not by pressing
against a few external surfaces, no internal stresses or strains are created.
So you can't feel gravity. If you are travelling in a vehicle, gravity
simultaneously acts on every molecule of the vehicle, and every molecule of all
the contents of the vehicle, so gravity can never pull contents of the
vehicle--including the driver or pilot--up or down toward the "high
side" or the "low side" of the vehicle. Also, you can't
"feel" centrifugal force--because it doesn't exist! You only can
"feel" the genuine, external forces that are imposed upon your body
by your surroundings. In an aircraft, you "feel" only the real,
aerodynamic and thrust forces created by the aircraft. In a car, you only
"feel" the real, tangible traction forces created by the tires on the
pavement, plus any significant aerodynamic forces. And so on and so forth.
(Note: for convenience we're going to be a bit sloppy and use
"1-G" as a measure of force--equal to the weight in pounds of the
object of concern--as well as a measure of acceleration).
Examples:
1. Person standing on ground. Forces at play: 1-G downward force of gravity
pulling down on body, 1-G upward force of earth pushing up on feet. Net force:
0 G's. Net acceleration: 0 G's. Forces "felt" by the person: all of
the above except gravity. Net force "felt" by person: 1-G upward
force of earth pushing against their feet. Unfortunately, common convention is
to express the apparent G-load as if it were created by some mysterious force
within the body, not by the external force of the floor pressing upward, and
therefore we imagine that the usual positive 1-G loading is somehow acting in
the "downward" not the "upward" direction. Intuitively this
seems to make some sense, until we realize that this apparent G-load is caused
entirely by the floor pushing upwards on the body, and really has nothing whatsoever
to do with downward pull of gravity. Read on for more! But no matter, this is
just a convention. The true force "felt" by the person is actually
1-G in the upward direction.
2. Pilot in normal 1-G flight. Forces at play: 1-G downward force of gravity
pulling down on pilot and on aircraft, and 1-G upward lift force created by
wings. Net force: 0 G's. Net acceleration: 0 G's. Forces "felt" by
the pilot and by the aircraft structure: all of the above except gravity. Net
force "felt" by pilot and by the aircraft structure: 1-G upward lift
force created by wings.
3. A pilot has "unloaded" his aircraft's wing to the zero-lift
angle-of-attack, and has set thrust exactly equal to drag, achieving momentary
"zero G" flight or weightlessness. Forces at play: 1-G downward force
of gravity, plus a forward thrust force, plus a rearward drag force. Net force:
1-G downward. Net acceleration: 1-G downward. Forces "felt" by the
pilot: all of the above except gravity. Net force "felt" by the
pilot, and by the aircraft structure: zero G's.
4. Pilot has rolled to a 90-degree bank, and has shoved the control stick
forward to "unload" the wing to the zero-lift angle-of-attack. He is
using the rudders (if needed) to keep the nose pointing directly into the
airflow; i.e. the aircraft is not slipping sideways through the airmass. He has
set the engine to create a thrust force that exactly equals drag, achieving
momentary "zero G" flight or weightlessness. Forces at play: 1-G
earthward pull of gravity, plus a forward thrust force, plus a rearward drag
force. Net force: 1-G earthward pull of gravity. Net force: 1-G earthward. Net
acceleration: 1-G earthward. Forces "felt" by the pilot: all of the
above except gravity. Net force "felt" by the pilot, and by the
aircraft structure and contents: zero G's. The pilot doesn't "fall"
toward the low side of the aircraft and the slip-skid ball doesn't
"fall" toward the low side of the aircraft.
5. Pilot beginning a 2-G pull-up to enter a loop. Forces at play: 1-G
downward pull of gravity, 2-G upward pull of wings. Net force: 1-G upward. Net
acceleration: 1-G upward. Forces "felt" by the pilot: all of the
above except gravity. Net force "felt" by the pilot and by the
aircraft structure: 2-G upward.
6. A pilot, inverted at the top of a loop, has set the wing at the
angle-of-attack which will produce "positive" 1-G, in the aircraft's
reference frame, at that airspeed. Forces at play: 1-G earthward pull of
gravity, 1-G earthward pull of wing's lift. Net force: 2-G earthward. Net
acceleration: 2-G earthward. Forces "felt" by the pilot: all of the
above except gravity. Net force "felt" by the pilot: 1-G earthward,
which is 1-G downward as seen by an external observer, and 1-G
"upward" in the reference frame of the aircraft and pilot. This is the
exactly the same G-loading, in the reference frame of the aircraft and pilot,
as exists in normal, "upright", unaccelerated flight.
7. Astronaut near earth, but beyond earth's atmosphere; rocket motor is
producing 10 G's of thrust. Forces at play: 1-G downward pull of gravity, 10-G
thrust from motor. Net force: vector sum of thrust plus gravity; here we
haven't specified the direction of travel of the rocket so we can't quite
finish the math. Net acceleration: again this will be determined by the vector
sum of thrust and gravity. Forces "felt" by astronaut: all of the
above except gravity. Net force "felt " by the astronaut: 10-G.
8. Astronaut far from earth, at some hypothetical point in space where the
gravitational pull of all the stars, planets, etc happens to be completely negligible;
rocket motor is producing 10 G's of thrust. Forces at play: 10-G thrust from
motor. Net force: 10-G. Net acceleration: 10-G. Forces "felt" by
astronaut: all of the above except gravity. Net force "felt " by the
astronaut: 10-G.
9. Astronaut near earth, but beyond earth's atmosphere; rocket motor is
switched off. Forces at play: 1-G downward pull of gravity. Net force: 1-G
downward pull of gravity. Net acceleration: 1-G downward. Forces
"felt" by astronaut: all of the above except gravity. Net force
"felt " by the astronaut: 0-G. If the spacecraft is in orbit, the
resulting downward motion is precisely matched to the craft's forward velocity
in such a way that the flight path curves in such a way that the distance from
the craft to the earth remains exactly constant. On the other hand if the
spacecraft is completely stationary with respect to the earth, then it will
immediately begin plunging earthwards. In this case there is no curvature in
the flight path, so we are not tempted to "explain" away the
astronaut's 0-G perceptions by saying that "centrifugal force" is
"balancing" the pull of gravity.
10. Diver in water, ballasted to neutral buoyancy, and not moving with
respect to water. Forces at play: 1-G downward force of gravity pulling down on
body, 1-G upward force of water pushing up on body. Net force: 0 G's. Net
acceleration: 0 G's. Forces "felt" by the person: all of the above
except gravity. Net force "felt" by person: 1-G upward force of water
pushing up on body. Since this buoyant force is dispersed over the entire
surface of the body, it does not create very much stress or strain within the
body, and the resulting sensation is somewhat like 0-g weightlessness.
PART 10: Notes on the
July 2000 article "Turning flight and sideslip in hang gliders"
This is another long article I wrote a few years ago on the topic of turning
flight and slips and skids, especially in hang gliders. It covers all my early
experiments on the relationship between pitch inputs and slips and skids in
hang gliders and sailplanes and airplanes. In the future that material will
also appear in the main body of this website. This older article also contains
a lot of theory; in particular the subject of "airflow curvature" is
explored in detail. The article is a few years old and in need of updating. The
main conclusions about pitch inputs and sideslips and skids are still
completely valid. None of the experiments on yaw-roll coupling had been carried
out at the time when this paper was written. The main point in need of change
is this: I now believe that most modern hang gliders show negative coupling
between yaw and roll, not positive coupling between yaw and roll. In other
words if a glider gets yawed to the left in relation to the glider's actual
direction of travel through the airmass, or if a glider is struck by a sudden
crosswind from the right, then the glider will tend to roll to the right,
except at the lowest airspeeds, when the coupling between yaw and roll may be
neutral. At higher speeds, most modern gliders have enough anhedral to
overpower the normal "positive" coupling between yaw and roll which
would normally be created by the swept or delta-shaped wing, so that the
yaw-roll coupling ends up being negative. This anhedral is created in large
part not by the droop in the leading edges relative to the keel, but rather by
the washout built into the wing. The older article assumed that most hang
gliders would show positive coupling between yaw and roll at all airspeeds, due
to sweep. The comments that I made based on these particular assumptions are
still relevant to rigid-wing hang gliders, which typically have sweep and little or no anhedral (in fact these aircraft usually have dihedral). They are not relevant to modern flex-wing gliders, except in some cases at airspeeds near or below min. sink. Several places in the article I refer to a "hypothetical blade-wing hang glider" with so much anhedral that there is a negative coupling between yaw and roll. I now realize that this is a good description of nearly all modern flex-wing hang gliders, at least at airspeeds above min. sink--I've seen clear evidence of a negative coupling between yaw and roll on a Wills Wing Raven, Skyhawk, and Spectrum, as well as an Airborne Blade. Some of the sections of this long July 2000 article that are affected by this error include the sections that deal with the effect of a vertical fin on the handling characteristics of a hang glider, the sections that deal with the total balance of roll torques in a stabilized, constant-bank turn, and the sections that address towing and lockout dynamics. One other area where I have changed my thinking--at several points in the older article I allowed for the possibility that some hang gliders might show a slight skid, rather than a slight slip, in a stabilized, constant-bank turn. I now feel that it is quite unlikely that any rudderless aircraft would skid in a stabilized, constant-bank turn. Again, all of this is completely peripheral to the main question addressed in
the older article, which was "Does a hang glider tend to slip toward the
low wing if the pilot pulls in the bar while banked, or if the pilot banks the
glider without letting out the bar in the usual nose-up pitch 'coordination' input"?
Turning flight and sideslip in
hang gliders
