The sideslip paradox
Last updated June 27, 2014
Alert readers will notice that the following theme appears throughout many of the articles on this website:
When a banked aircraft is generating "too little" lift in relation to the bank angle, this does not necessarily mean that the aircraft will slip sideways through the air toward the low wingtip, or that the pilot will tend to fall toward the low side of the fuselage or control frame.
How is this possible?
Before we start to explore the "why" of this, we should emphasize that any interested hang glider pilot can mount a yaw string to his hang glider, as described in the related article on this website entitled "Flying with a yaw string". The little tuft of yarn will tell the story! In general, pulling in the bar while banked or while rolling into a turn does not make the glider slip sideways toward the low wing.
Coming back to theory-- again, how is this possible?
Let's do a simple thought experiment where we suspend a glider from a string in a banked attitude with zero airspeed, and then cut the string. The vertical component of lift (plus the vertical component of drag) is much less than weight. In fact, lift and drag are both initially zero. Gravity will certainly accelerate the glider earthwards. As the glider gains downward speed, it will certainly be moving sideways through the airmass, toward the low wingtip. A yaw string will blow toward the high wingtip. This is a case where a "shortage of lift" is indeed causing a sideslip.
But then what happens? The slipping flow will generate a "weathervane" yaw torque that swings the nose down into the airflow. When the nose yaws to face the airflow, it's very common for it to "overshoot" a little bit-- to go too far-- and then come back to face directly into the wind. If we pay close attention we might see actually several "wobbles" before the nose settles down to point directly into the wind.
To understand this more clearly, imagine what would happen if we had an actual weathervane, made of heavy metal with a significant amount of mass and yaw rotational inertia, and we moved it to point 90 degrees cross to the wind and then let it go. As it started to swing into the wind, it would pick up enough rotational speed and inertia that it would "overshoot" and wobble back and forth a few times before settling down to point directly into the flow. The same dynamic is often visible when an aircraft yaws back into the airflow after slipping or skidding strongly sideways.
If we watched yaw strings on the glider during this whole process, we'd see the strings initially stream strongly toward the high wingtip as the glider started to "fall", and then they would swing to point slightly toward the low wingtip, and then "wobble" slightly back and forth a few more times before settling down to stream more or less straight back. Meanwhile, during this whole process, the glider is continuing to accelerate earthwards and gain airspeed, because the glider has not picked up quite enough speed to make the vertical component of lift (plus the vertical component of drag) equal weight.
So this is one case where a steady earthward acceleration, and a continual earthward motion, does not create a steady sideslip. Why? Because we're changing the orientation of our reference frame-- we're changing the direction that the glider's nose is pointing-- as we go. The glider is continuing to accelerate earthwards and continuing to move earthwards, but the low wing is not always the "upwind" or "leading" wing, and the high wing is not always the "downwind" or "trailing" wing. The yaw string does not always stream toward the high wingtip.
We can't really say that a banked aircraft must be sideslipping if it is accelerating earthwards or moving earthwards. Sideslip is not a matter of which direction an aircraft is accelerating or moving relative to the earth. Sideslip is matter of which direction an aircraft is moving in relation to the direction that the nose is pointing. Earthward acceleration, earthward motion, and sideslip are really three completely different things.
Yet our thought experiment above seems to suggest a powerful correlation between earthward acceleration and sideslip, at least initially. When we cut the string and let the aircraft fall, it initially slipped very strongly toward the low wingtip.
At their core, most discussions of sideslip in flight training manuals are really based on this sort of thought experiment. But it is realistic to imagine that we're going to start a maneuver by hanging in space with zero airspeed? Rarely!
What happens if we make our thought experiment more realistic by not starting with zero airspeed and zero turn rate and zero yaw rotation rate? Instead, we'll start with the aircraft flying at a normal airspeed in a normal turn, with a yaw rotation rate appropriately matched to the bank angle and airspeed. The nose may be pointing slightly toward the high side of the flight path, so that the low wing is the "leading" wing or "upwind" wing, and the yaw string streams slightly toward the high wingtip. This is a slip. Or the nose may be pointing slightly toward the low side of the flight path, so that the high wing is the "leading" wing or "upwind" wing, and the yaw string streams slightly toward the low wingtip. This is a skip. Or the nose may be pointing directly into the airflow. In any case, the slip or skid angle (if any) will remain constant, because the yaw rotation rate is correct for the turn rate-- the nose is "keeping up" with the turn.
Let's light a smoke flare on each wingtip to trace our path though the air. Now let's abruptly pull the control bar aft to "unload" the wing, so that the vertical component of lift (plus the vertical component of drag) becomes much less than weight. Now what happens?
If we look at the aircraft in a side view, again we'll see that the flight path will curve earthward. This would seem to create a strong demand for a nose-down yaw rotation, just as when we cut the string and dropped the aircraft with zero airspeed. Note that is the same direction as the yaw rotation that we had before we pulled in the bar-- but we seem to need more of it now. This would seem to suggest that we'll see a strong sideslip until the yaw rotation rate increases, so that the nose yaws down to point more directly into the airflow. A yaw string (and the smoke trails) would seem likely to blow sideways toward the high wingtip, just like when we "cut the string" in the earlier experiment.
But what if we look at the aircraft from above? When we pulled in the bar and "unloaded" the wing, we instantly decreased the turning force and the turn rate-- the rate of curvature of the flight path, in degrees per minute. We also increased the radius of curvature of the flight path as viewed from above. The smoke trails are tracing larger circles now, as viewed from above. For the moment, the airspeed is still low, but rising-- that's what it means for the wing to be "unloaded". What happens if the nose keeps yawing around at the original rate of yaw rotation? Since the turn rate has decreased, won't the nose swing to point too far toward the inside of the turn, so that the high wing becomes the "leading" or "upwind" wing, and the low wing becomes the "trailing" or downwind wing? This is a skid, not a slip. To avoid an ever-increasing skid angle, don't we need to slow the yaw rotation rate? In other words, haven't we created a demand for a reduction in the yaw rotation rate, not an increase in the yaw rotation rate? To the extent that yaw rotational inertia is significant and the yaw rotation rate takes some time to increase or decrease, won't we see some skid, not some slip, when we pull the bar in? Won't the yaw strings blow toward the low wingtip, not the high wingtip?
Consider also that in the long run, as we keep the bar pulled-in, the glider will eventually come to equilibrium at a higher airspeed and a lower turn rate than it had with the bar further forward. There's no question that in the long run, there has been a net decrease in the aircraft's yaw rotation rate. Doesn't this imply that on the whole, as the airspeed increased, the glider experienced a skidding airflow (from the high wingtip toward the low wingtip), not a slipping airflow? Wouldn't this be needed to generate the "weathervane" yaw torque that is needed to slow the yaw rotation rate?
Our intention here is not give a complete answer to this question-- perhaps the full details of the dynamics depend on the initial bank angle and other variables. After we abruptly pull in the bar, perhaps the aircraft experiences both some moments of slight slip and some moments of slight skid before it finally settles into equilibrium. Our intention here is simply to point out that we get opposite answers if we only take the "side view" and consider only the forces tending to accelerate the aircraft downward, or if we only take the "top view" and consider only the forces that tend to change the turn rate.
That's why our intuition that we'll always "slip" sideways through the air whenever lift is "too small" for the bank angle isn't based on a solid foundation. It's only based on a "side view" of the problem, and it neglects the importance of the change in turn rate.
When we actually observe of a yaw string in flight, we see that very little slip or skid results when we abruptly pull in the bar while holding the bank angle constant.
When we roll briskly from wings-level into a turn without moving the bar forward to immediately "load up" the wing, the situation is a bit different. Now both the "side view" and the "top view" suggest that yaw rotational inertia is tending to promote a slip. Both "views" show that we have a demand for a yaw rotation toward the low wingtip, and until that happens, the nose is going to be "left behind" on a constant heading as the direction of the flight path changes. Both "views" suggest that the low wing will become the "leading" or "upwind" wing and the high wing will become the "downwind" or "trailing" wing. But how do things change if we move the bar forward as we roll into the turn to immediately "load up" the wing with the proper lift force (G-loading) for the bank angle, holding the airspeed exactly constant? We've greatly reduced the downward curvature in the flight path-- the "side view" suggests that our pitch "coordination" input has caused a smaller demand for yaw rotation than we had when we made no pitch "coordination" input. Yet by "loading up" the wing promptly, we've caused the turn rate to be higher, at any given instant, than when we made no pitch "coordination" input. The "top view" suggests that our pitch "coordination" input has caused a greater demand for yaw rotation than we had when we made no pitch "coordination" input! Again the "side view" and the "top view" are giving us conflicting results.
When we actually observe a yaw string in flight, for any given roll rate, we see about the same amount of slip as we enter a turn regardless of whether we move the bar forward as we roll to hold the airspeed nearly constant and promptly "load up" the wing, or we keep the bar in a constant position in the fore-and-aft sense so that the glider has to pick up extra airspeed by diving, or we pull the bar aft as we roll to keep the G-load very low so that the glider has to pick up a great deal of extra airspeed by diving.
Also, our line of discussion up to this point seems to suggest that yaw rotational inertia tends to promote sideslip as we roll in to a turn. The picture gets more complicated when we realize that any rolling motion creates a powerful aerodynamic adverse yaw torque that tends to swing the nose to point toward the rising wing. In light of this, a glider with lots of yaw rotational inertia might actually tend to show less sideslip when entering a turn, not more! In general, aerodynamic adverse yaw torque, not yaw rotational inertia, appears to be the main driver of sideslip in hang gliders and many other aircraft. This is all the more reason to question our intuitive idea that "insufficient lift" will make a glider slip sideways through the air.
Even if we accept the idea that "insufficient lift" while banked doesn't generally drive the glider sideways through the airmass, we still may have an intuitive sense that the pilot will tend to fall toward the low side of the fuselage or control frame whenever the lift vector or G-loading is too small for the bank angle. This idea comes from a conception that the forces "felt" by the pilot are the result of some sort of battle between gravity and the aerodynamic forces generated by the aircraft. This idea appears throughout many flight training manuals, including hang gliding training manuals. Let's look at this in more detail. If we want to fix our reference frame on the aircraft and look to see whether the pilot will tend to accelerate in any particular direction in relation to this reference frame, we'll need to create a "centrifugal force" vector to represent the apparent forces caused by the curvature of the flight path in the horizontal and vertical dimensions. There are two ways to handle gravity. We can include the curvature of the flight path due to gravity when we calculate our "centrifugal force" vector, and then also draw a force vector to represent the pull of gravity on the pilot's body. In this conception, horizontal flight would be represented by a 1-G downward centrifugal force component representing the way that lift is trying to curve the flight path upward, plus a 1-G upward centrifugal force component reprenting the way that gravity is trying to curve the flight path downward, plus a 1-G downward force component representing the actual pull of gravity on the pilot's body. Or we can omit the curvature in the flight path due to gravity when we calculate our "centrifugal force" vector, and also omit the force vector representing the pull of gravity on the pilot's body. We get the same answer either way. Gravity exerts an equal acceleration on every molecule of the aircraft and pilot, and creates no tendency for the pilot to fall toward one side of the aircraft or the other, regardless of the bank angle. So it's simplest to leave gravity out of the picture entirely. In this case, our "centrifugal force" vectors are nothing more than the mirror image of the real aerodynamic force vectors generated by the aircraft. After all, these real aerodynamic force vectors are the only things-- apart from gravity-- that can cause the flight path to curve and create "centrifugal forces" that act on the pilot.
Let's state that more simply. To consider whether a pilot will have any tendency to fall toward the high side or the low side of the aircraft, we only need to consider the direction of the aerodynamic force vectors generated by the aircraft. Nothing more. If the aircraft is only generating positive lift, he'll only feel his seat pushing "straight up" on his body, parallel to the lift vector, in proportion to the lift force or G-loading. Or he'll naturally hang "straight down" in the center of the control frame, with the hang strap parallel to the lift vector. When we add drag into the picture (or in the case of a powered aircraft, when drag is greater than thrust), the net aerodynamic force or G-loading acting on his body will be tilted slightly-- he'll tend to fall forward against his seat belts, or his body will tend to ride further forward relative to the control bar. (The control bar will tend to trim further aft.) If we have a motor and thrust is greater than drag, the pilot will tend to be pushed back in his seat, or he'll tend to ride further back relative to the control bar, so that the bar is way out in front of his forehead. (We're thinking of something like a "Soarmaster", where the motor is on the keel, not on the pilot's harness.)
All the statements in the above paragraph true completely without regard to the aircarft's orientation to the outside world, and to the gravity vector. They are true even as the aircraft is inverted at the top of a loop, or going straight up or straight down at the 3 o'clock or 9 o'clock positions in a loop. That's why cloud flying without instruments for long periods of time is basically impossible-- to a first approximation, the basic forces "felt" by the pilot give no clue as to which direction is up, at least if we ignore the slight sideslip that usually accompanies even a constant-banked turn.
And what makes a pilot tend to fall toward the low side of the cockpit or control bar? Only a real aerodynamic sideforce generated by a real sideways airflow impacting the side of the aircraft. Nothing else.
(Qualification-- actually there is one other thing that can generate a real aerodynamic sideforce that will be "felt" by the pilot, and by the slip-skid ball. That one other thing is a strongly deflected rudder, shoving the airflow to the side. When a rudder is strongly deflected to counteract some other yaw torque-- such as the yaw torque from a failed engine on one wing in a multi-engined aircraft-- the aerodynamic sideforce generated by the rudder is significant, and the ball will be noticeably off-center even when the nose is pointing directly into the airflow. This is best dealt with by leaving the ball slightly off-center-- by just the right amount--and then raising one wing to stop the turn. The wing with the dead engine is the wing that will need to be raised. A pilot in this situation would be very well served to have an actual yaw string on the nose or windscreen of the aircraft, to verify that he is applying just the right amount of force on the rudder so that the nose is in fact pointing directly into the airflow or relative wind, for maximum streamlining and efficiency! Absent a yaw string, a pilot must rely on a rule of thumb like "leave the ball deflected one-half width toward the good engine." This can only be truly accurate at one particular thrust or power setting. In theory, these dynamics come into play whenever the rudder is deflected for any reason, so one can argue that the slip-skid ball never really should be moved all the way to the centered position, unless zero rudder deflection is required to do so. In practice, these dynamics are only significant with large rudder deflections.)
Back to hang gliding-- in the hang gliding context, only a sideways airflow over the aircraft can generate a sideways force that makes the pilot fall toward one side-- the "upwind" side-- of the control frame. Of course, we're assuming here that the sideways force generated by the airflow hitting the pilot's harness and body is small relative to the sideways force generated by the airflow hitting the rest of the aircraft-- if this isn't true, the pilot may not tend to fall toward the side at all, even in a severe sideslip!
Every force vector diagram that purports to show that some sort of "imbalance" between lift and gravity will make the pilot fall toward the low side of the aircraft is erroneous. And every force vector diagram that doesn't ultimately connect the sideways displacement of the pilot's body, or the slip-skid ball, to the real aerodynamic forces generated by a sideways airflow impacting the side of the aircraft, is also erroneous.
In summary, two common, intuitive ideas are actually wrong-- one, that an aircraft will "slip" sideways through the air whenever lift is "too small" for the bank angle, so that the vertical component of lift (plus the vertical component of drag or thrust) is less than weight. And two, that the pilot will tend to fall toward the low side of the cockpit or control frame whenever lift is "too small" for the bank angle. In truth, anyone who was ever experienced a barrel roll-- firsthand or in a movie-- knows that these ideas cannot be true. Of course, a barrel roll involves all sorts of complicated accelerations-- it's not the same as just suspending an aircraft in a banked attitude and then letting it fall earthwards under gravity's pull. It turns out that the same is true of an ordinary turn entry, as well as in more dynamic maneuvers like abruptly pulling in the bar while banked or while rolling into a turn. In these cases, just like in the barrel roll, the aircraft is accelerating in several directions at once, and we shouldn't expect to see a sideslip whenever lift is "too small" for the bank angle. Sideslip is driven mainly by adverse yaw from rolling motions.
Let's see these dynamics firsthand. It's time to stop pondering and go fly! Let's attach a yaw string to our glider-- on the far end of a dowel rod sticking straight forward from the center of the base bar, where we can easily see it in flight-- and go do some maneuvers. We'll see that sideslip is almost entirely caused by rolling motions, with higher roll rates causing more sideslip. As the glider rolls, it yaws toward the rising wing, so that the rising wing becomes the "trailing wing" or "downwind" wing, and the descending wing becomes the "leading" or "upwind" wing. We'll see that pitch inputs have very little effect on sideslip, except through their effect on roll rate.
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