Brain teasers

What makes an aircraft turn?

August 20 2005 edition
Steve Seibel
steve at aeroexperiments.org
www.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 reference frame.

 

* 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 earth.

 

--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"

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