What makes an aircraft turn?
August 20 2005 edition
steve at aeroexperiments.org
* An aircraft's "heading" is the direction that the
nose is pointing. A turn is a not a
change in heading.
* A turn is a curvature in the flight path. This curvature can be in any
direction--left, right, up, down, or a combination of these.
* An aircraft will turn whenever the net force acting on the
aircraft is not zero, and has a component that is perpendicular to the flight
path rather than parallel to the flight path.
* By "net force" we mean the sum of all the real,
tangible aerodynamic forces created by the airflow around the aircraft (lift,
drag, thrust, and sideforce), plus gravity.
* The net force that causes a turn can be called a
"centripetal force", because it acts toward the center of the
turn. The centripetal force or turning
force acts on the CG ("center of gravity", or more accurately, center
of mass) of the aircraft and "pushes" the aircraft toward the center
of the turn, causing the flight path to curve.
In the absence of this net force, Newton's laws tell us that the
aircraft would continue moving in a straight line.
* Contrary to intuition, a steady, constant-rate turn does
not involving a net "twisting force" or torque about the aircraft's
yaw axis or any other axis of the aircraft.
In a steady, constant-rate turn the net torque is actually zero. If some part of the aircraft is creating a
torque, that torque is only serving to offset some other torque that is acting
on some other part of the aircraft, bringing the net torque to zero.
* All the above points are true for any vehicle or any other
moving body, not just for aircraft.
* Examples of turns:
--The sun's gravity pulls on the earth, causing the earth to
follow a curving path through space.
--A car's driver turns the steering wheel, causing the car
to position itself so that all 4 wheels (not just the front 2) are meeting the
pavement at a slight sideways angle.
The pavement exerts a sideways force ("sideforce") on the car,
acting at the car's CG. This sideways
force causes the car's path to curve.
--A boat's helmsman turns the wheel, deflecting the boat's
rudder and creating a yaw torque. This
yaws the hull to point in a slightly different direction than the boat is
actually travelling through the water.
This causes the water to impact the side of the hull, generating a
sideways force ("sideforce"), acting at the CG of the boat. This sideways force causes the boat to
follow a curving path through the water.
--An aircraft's pilot applies the rudder to create a yaw
torque, yawing the nose of the aircraft to point in a slightly different
direction than the aircraft is actually travelling through the airmass at any
given moment. The airflow (relative
wind) impacts the side of the fuselage and other components of the aircraft,
generating a sideways force ("sideforce") that acts at the CG of the
aircraft. This sideways force causes
the aircraft to follow a curving path through the air. When an aircraft turns in this manner, the
aerodynamic sideforce created by the impact of the airflow against the fuselage
and other components of the aircraft is felt by the pilot in a real, tangible
way--as the aircraft is "pushed" sideways by the airflow, the pilot
tends to lean in the opposite direction, just as is the case with a person in a
car or a boat. (The slip-skid ball also
deflects to the side--it "feels" the same forces as the pilot's body
does.) This is a very inefficient way
to turn an aircraft--forcing the fuselage to move even slightly sideways
through the air creates excess drag.
--A pilot banks an aircraft. Part of the wing's lift vector is now directed horizontally. The net force acting on the aircraft (i.e.
the sum of gravity plus lift plus all the other aerodynamic forces) now
contains a horizontal component. This
horizontal force, acting on the aircraft's CG, makes the aircraft follow a
curving path through the air. Rather
than using the rudder to "point" the nose of the aircraft in the
direction that he wants to go, the pilot only makes whatever rudder inputs are
needed to keep the nose of the aircraft exactly aligned with the direction that
the aircraft is actually moving through the airmass, so that the nose of the
aircraft points directly into the airflow or relative wind. That's really all there is to a normal,
efficient turn in an aircraft!
* Let's look at the last example (turning an aircraft by banking)
in a bit more detail. This turn is
fundamentally different from the way we turn a car or a boat. This turn is efficient because the fuselage
is not being forced or allowed to plow sideways through the air by even a small
amount. If the net force (which is the sum of gravity plus lift plus
all the other aerodynamic forces) is to act in a purely horizontal direction
with no vertical component, so that the flight path does not curve up or down,
the pilot must increase the magnitude of the lift vector as he rolls the
aircraft into the turn. This increased
G-loading is felt by the pilot in a real, tangible way--the pilot's seat pushes
"upwards" against his body harder than it normally does. Note that the wing's lift vector acts in a
purely "upward" direction in the aircraft's own reference frame, and
does not include any sideways component ("sideforce") in the
aircraft's own reference frame. This is true regardless of whether or not we
increase the wing's lift vector as we roll into the turn. Since we are not allowing the fuselage to
move sideways through the airmass and create an aerodynamic sideforce, and
since the wing's lift vector acts purely "upward" in the aircraft's
reference frame and does not include a sideforce component, the pilot does not
tend to lean toward either side of the aircraft.
* To fully understand this last point, we need to realize
that a pilot does not "feel" gravity. The forces that a pilot "feels" are different from the
forces that affect the flight path and create turns (curvatures in the flight
path). A pilot "feels" only
the real, tangible aerodynamic forces created by the airflow around the
aircraft. These real, tangible aerodynamic forces include lift, drag, thrust
(if present), and aerodynamic sideforce (if present). When we talk about the "G-load" that the pilot feels,
we are talking about the net sum of these real, tangible aerodynamic
forces. Gravity does not contribute to
the "G-loading" that creates stresses on the aircraft structure or on
the pilot's body, and gravity does not pull the pilot's body (or the slip-skid ball) toward the low side of the aircraft. When the pilot's body
(and the slip-skid ball) lean or deflect toward the left side or the right side
of the aircraft, this always signals the presence of a real, tangible aerodynamic
sideforce. If there is no real, tangible aerodynamic sideforce, the pilot's body and the slip-skid ball will stay centered.
On the other hand, the net force that affects the flight path and
creates turns (curvatures in the flight path) is the sum of all the real,
tangible aerodynamic forces, plus gravity.
Note that gravity itself includes a component that acts in the sideways
direction in the reference frame of a banked aircraft, but the pilot (and the
slip-skid ball) do not "feel" this sideforce component in the same
way as they would feel a real, tangible, aerodynamic sideforce. We'll revisit the idea that that the pilot (and the slip-skid ball) do not "feel" gravity a bit later in this article.
* Note that we're not making any reference to
"centrifugal force", because the apparent centrifugal force generated
by the inertia of a moving body following a curving path is not a real force.
*In case it's not clear by now, when we speak of a
"sideforce", we generally mean a real, tangible aerodynamic force
that acts toward the left or right in the aircraft's own reference frame. Although we need a net horizontal force
component to make the flight path curve as viewed from above (for the moment
we're not talking about other types of curvatures such as vertical loops), the
real, tangible aerodynamic forces generated by a turning aircraft need not
include any "sideforce" component.
This is clearly demonstrated by the example of the efficient, banked
turn. In the efficient, banked turn the
only real, tangible aerodynamic forces present are drag, thrust (if there is an
engine), and lift, which acts "straight up" in the aircraft's
* More examples of turns:
--A spacecraft is beyond the earth's atmosphere, with the
engines off. Since aerodynamic and
thrust forces are zero, the pilot experiences an absence of all tangible
forces--this is 0-G "weightlessness". The net force acting on the spacecraft is the 1-G pull of earth's
gravity. If the spacecraft is not
travelling directly toward or directly away from the earth, the pull of gravity
will create a curvature in the flight path.
If spacecraft is travelling parallel to the earth's surface and the
spacecraft's velocity is such that the curvature in the flight path makes the
spacecraft exactly follow the curving surface of the earth, so that the
spacecraft's altitude remains exactly constant, we say that the spacecraft is
"in orbit". Note that we
haven't invoked "centrifugal force" here, because that is not a real
force, and also because that concept would have no application to the case
where the spacecraft was travelling directly toward or directly away from the
--A pilot "unloads" an aircraft's wing to the
zero-lift angle-of-attack. Now gravity
is the only force acting on the aircraft.
The flight path curves downward.
Since the real, tangible aerodynamic forces on the aircraft are zero
(strictly speaking this is only true if there is an engine, and the pilot sets
the thrust to exactly equal drag), the pilot "feels" no force at
all--this is 0-G "weightlessness".
--In wings-level flight, a pilot increases the wing's
angle-of-attack, which increases the wing's lift vector. If we simplify things by assuming that there
is an engine, and that the pilot has set the thrust to exactly equal drag, then
the net force acting on the aircraft is the amount by which the wing's lift
vector exceeds the downward pull of gravity.
The flight path curves upward.
The force that the pilot "feels" is the real, tangible, net
aerodynamic force generated by the aircraft, which is simply the wing's lift
vector. If the pilot has increased the
angle-of-attack enough to double the lift vector so that it equals twice the
weight of the aircraft and contents, the pilot will "feel" a 2-G
force, and will read 2 G's on his G-meter.
The net force acting on the aircraft to create an upward curvature on
the aircraft is different from the force that the pilot "feels". In this example, the net force acting on the
aircraft to create an upward curvature in the flight path is a 1-G upward
force--this is the net vector sum of the 2-G upward aerodynamic force vector,
and the 1-G downward pull of gravity.
* By now it should be clear that gravity is a rather usual
force--because of the way that it acts "from within" and accelerates
every molecule of a system at the same time, it is not "felt" by the
aircraft structure, or by the pilot's body, or by the G-meter, or by the
slip-skid ball, though it does affect the aircraft's path through the airmass.
* Let's return to the subject of rudders. Normally an aircraft's rudder is only used
to counteract "adverse yaw" and yaw rotational inertia (if the yaw
rotation rate is changing rather than constant) and any other aerodynamic yaw
torques that may be present, so that we keep the nose of the aircraft pointing
exactly into the direction of the airflow or relative wind at any given
moment. This is the fundamental purpose
of the rudder. Used in this way, the
rudder is not really playing any role whatsoever in making the aircraft turn,
i.e. in creating a curvature in the flight path. The rudder is simply "helping" the aircraft's inherent
yaw stability characteristics (the "weathervane effect") to keep the
nose of the aircraft pointing directly into the relative wind. This is fundamentally different from the way
we use a rudder when we turn a boat.
* We should emphasize one more time that a change in heading
is not the same as a turn! A turn is a
curvature in the flight path. Many
examples in everyday life cause us to think of a change in heading as being
completely equivalent to a turn. Our
examples of the turning car or boat revealed that as these vehicles turned,
they were actually pointing in a slightly different direction than they were
moving through the water or over the ground.
In winged flight, the relationship between the aircraft's heading and
the aircraft's actual direction of travel through the air is much less constrained
than in the case of a car or a boat.
For example, as an aircraft banks to the left and the flight path starts
to curve to the left, it is very common for the aircraft's nose to initially
swing several degrees to the right, both in relation to the direction that the
aircraft is moving through the air at any given moment, and in relation to the
outside world. As noted above, a pilot
will usually use the rudder to prevent this "adverse yaw" effect, but
if he does not, the flight path will still curve toward the left regardless of
which direction the aircraft's nose is pointing. In no sense does the "adverse yaw" effect actually make
the aircraft turn to the right, although depending on the amount of adverse yaw
and the physical shape of the aircraft, the aerodynamic sideforces produced by
the sideways airflow over the aircraft may cause the turn rate (i.e. the rate of
curvature of the flight path) toward the left to be significantly lower than it
would otherwise be.
* Of course, over the long run, the aircraft's rate of change
in heading must be the same as the turn rate (rate of curvature in the flight
path), or else the nose would end up pointing in a radically different
direction than the aircraft is actually flying through the airmass. An aircraft's inherent yaw stability
characteristics (the "weathervane" effect) will not allow this. But over the short run, the direction and
rate of change in heading can be very different from the actual direction and rate
of change of the flight path.
* Since the main purpose of the rudder is simply to
"help" the aircraft's inherent yaw stability characteristics (the
"weathervane effect") to keep the nose of the aircraft pointing
directly into the relative wind, the rudder is optional. Some aircraft do not have rudders: examples
include hang gliders and trikes, and many 2-channel RC sailplanes. In most cases these aircraft have to put up
with some adverse yaw as the pilot initiates a turn, so that the nose of the
aircraft often points in a slightly different direction than the aircraft is
actually moving through the air, but they still manage to turn quite well. In contrast, some means of roll control is
essential for nearly all aircraft, because most aircraft do not have strong
enough inherent roll stability characteristics to remain wings-level or nearly
wings-level without help from the pilot, and because banking is such an
effective way to make the flight path curve.
In some cases the rudder itself can be an effective roll control--this
is explored in more detail elsewhere on the Aeroexperiments website.
* Many examples from everyday life cause us to think of a
turn as being driven by a "twisting force" or yaw torque. For example, we twist the steering wheel of
a car to make the car turn. However,
we've already noted that whenever the yaw rotation rate is constant, the net
yaw torque is actually zero. The main
reason that we have to apply a constant yaw torque during a turn in many
vehicles (cars, boats, etc) is that we need to overcome the vehicle's inherent
stability characteristics, which create their own stabilizing yaw torque in the
opposite direction, as we force the vehicle to point in a slightly different
direction than it is actually moving through the water or over the pavement,
etc. In an aircraft, we can turn in this
manner, and this will require us to exert a strong yaw torque with the rudder
to overcome the aircraft's inherent yaw stability or "weathervane"
effect, even though the net yaw torque will actually be zero. But as we've already noted, it is much more
efficient to simply bank the wing, and apply whatever rudder inputs are needed
to keep the nose of the aircraft exactly aligned with the flight path and
pointing directly into the airflow or relative wind. Once we have finished increasing the bank angle, and we've moved
the ailerons (or other roll control surfaces, or our own body in the case of a
hang glider) back to a nearly centered position, the largest "adverse
yaw" effects disappear and the remaining aerodynamic yaw torques on the
aircraft are low, and only minimal rudder inputs are needed to neutralize these
remaining aerodynamic yaw torques and keep the aircraft pointing directly into
the airflow or relative wind.
* Even if we don't have a rudder or don't use a rudder, the net yaw torque on the aircraft is zero during a steady, constant-bank, constant-rate turn. Unbalanced torques can exist only briefly. The aircraft will soon find a yaw orientation where all torques are in balance. For example, if something (such as the increased drag experienced by the outside, faster-moving wingtip) is creating a yaw torque toward the outside of the turn, this will cause the nose to yaw toward the outside of the actual direction of the flight path at any given moment. At some point when the yaw angle between the direction of the flight path at any given moment and the direction that the nose is pointing at any given moment is large enough, the yaw torque toward the inside of the turn created by the aircraft's inherent yaw stability or "weathervane effect" will exactly counter the other aerodynamic yaw torque toward the outside of the turn, and the net yaw torque on the aircraft will be zero, and the yaw rotation rate will be constant and equal to the turn rate, even though the nose of the aircraft is pointing in a slightly different direction than the aircraft is actually moving through the air at any given moment. With or without the rudder, in a steady, constant-bank turn an aircraft will find its own equilibrium state where all torques are in balance.
For more on why a pilot does not feel gravity, see the related article on this website entitled "You can't feel gravity!"
For diagrams of the forces we discussed in this article, see the related article on this website entitled "Complete analysis of forces: fully balanced turn, turn with inadequate lift or G-load, slipping turn, non-turning slip, and skidding turn." The first two diagrams are the ones that are relevant to this article, as we haven't yet explored the details of the forces at play during a banked slip or skid, and the diagrams don't yet cover the case of a wings-level skidding turn. In these diagrams, "Na" is the net aerodynamic force, which is the force that the pilot "feels", while "N" is the true net force, which includes gravity.
For much more on adverse yaw and many other aspects of
turning flight, see the related article on this website entitled "Causes of adverse yaw in hang gliders and "conventional" aircraft--with notes on slips, skids, yaw strings, slip-skid balls, rudder usage, yaw rotational inertia, "airflow curvature", aerodynamic "damping" in the roll axis, and flex-wing billow shift"