2 kinds of yaw

2 kinds of yaw

Steve Seibel
www.aeroexperiments.org

This page is still under construction!
This page was last modified on August 24, 2006

 

The word "yaw" really has two different meanings with respect to flight.

One definition of yaw is a rotation about the aircraft's yaw axis in an absolute sense, i.e. in relation to the outside world. When the aircraft is in a wings-level attitude or is flying at a shallow bank angle, this type of yaw is essentially the same as a change in the aircraft's compass heading. In other words, if the aircraft's nose points toward a compass heading of 010 degrees and then moves to point toward a compass heading of 020 degrees, we can say that the aircraft has yawed 10 degrees to the right. As we emphasized in "What is a turn", this yawing motion may or may not produce an immediate change in the direction of the flight path, i.e. in the direction that the aircraft is moving through the airmass.

This kind of yaw always creates a difference in airspeed between the two wingtips. If the aircraft is yawing to the right in relation to the external world, the left wingtip is moving faster than the right wingtip. This is true regardless of whether the flight path is curving to stay "in synch" with the direction that the aircraft's nose is pointing, or not. In other words this is true both in a normal "coordinated" turn where the nose of the aircraft is fully aligned with the actual direction of the flight path and relative wind at any given moment, and in a "wing-wagging" motion where a pilot applies alternating left and right rudder and the nose swings alternately to the left and to the right with little change in the actual direction of the flight path and relative wind.

The above definition of yaw is really the most technically correct definition of yaw.

On many of the pages in this tutorial, we'll also be thinking about yaw in a different sense. For example we may say that adverse yaw, or a rudder input from the pilot, has "caused the nose to yaw to point 10 degrees to the right of the actual direction of the flight path, and the actual direction from which the relative wind is blowing, at any given moment". In such a situation we'll say that "the aircraft is flying with a yaw (slip) angle of 10 degrees to the right, in relation to the actual direction of the flight path and relative wind at any given moment". When we are using the word yaw in this way, we may mean either the angle between the aircraft's heading and the actual direction of the flight path and relative wind (e.g. "the aircraft is flying with a yaw (slip) angle of 10 degrees to the right"), or the change in the angle between the aircraft's heading and the actual direction of the flight path and relative wind (e.g. "the nose is yawing further to the right with respect to the actual direction of the flight path and relative wind at any given moment"). In the latter case, it's important to note that we don't necessarily mean that the nose is yawing to the right with respect to the outside world.

The relationship between these two kinds of yaw is a bit complex. For example, it's possible for the nose of an aircraft to end up pointing several degrees to the right of the actual direction of the flight path and relative wind at any given moment, without ever actually swinging to the right in relation to the external world. If the aircraft rolls into a left turn and the flight path starts to curve to the left but the nose of the aircraft lingers for a few seconds on its original heading, and then starts clocking around the horizon from right to left, this "lag" will create a temporary difference between the direction the aircraft's nose is pointing and the actual direction of the flight path and relative wind. When the aircraft's nose is "frozen" with respect to the horizon, it is yawing to the right in relation to the actual direction of the flight path and relative wind. The aircraft will temporarily have a yaw (slip) angle of several degrees to the right in relation to the actual direction of the flight path and relative wind, even though the nose has never yawed to the right in relation to the external world.

We've noted that the first definition of yaw--the rotation about the aircraft's yaw axis in relation to the external world, which for shallow bank angles is basically the same as a change in compass heading--is really the most technically correct definition of yaw definition of yaw. And bear in mind again that this is the kind of yaw that creates a difference in airspeed between the two wingtips. But the second kind of yaw--the difference, or the change in the difference, between the direction that the aircraft's nose is pointing and the actual direction of the flight path and relative wind--is what determines whether or not there will be a sideways component in the relative wind. So this kind of "yaw" is very important to an aircraft's flight dynamics.

Fundamentally, a pilot's rudder inputs really act to create "yaw" in the second sense, not the first. For example if an aircraft is banked to the left and the flight path is curving rapidly from right to left and the pilot applies a mild right rudder input, the nose of the aircraft will certainly yaw to the right in relation to the actual direction of the flight path and relative wind at any given moment, so that the airflow or relative wind strikes the left side of the aircraft, but it's quite possible that this yawing motion could be mild enough that the aircraft never actually yaws to the right in relation to the external world, and the left wingtip never actually moves faster than the right wingtip.

It would be better if our terminology could be clearer. Engineers often use the word "yaw" exclusively in the first sense that we've described here, and use the word "slip" to describe the difference between the direction that the nose of the aircraft is pointing and the actual direction of the flight path and relative wind. However this terminology has some ambiguities and limitations of its own. We'll try to be as clear as possible at all times. When we use the words slip and yaw together (e.g. "the aircraft is flying with a yaw (slip) angle of 10 degrees to the right), we'll always be referring to the orientation of the nose, or the change in the orientation of the nose, with respect to the actual direction of the flight path and relative wind at any given moment. When we are using the word "yaw" in the other sense, we'll generally add the phrases "in an absolute sense" or "in relation to the external world".

A typical "adverse yaw" motion involves both of these kinds of yaw. For example, as a pilot makes a left roll input and the flight path starts to curve to the left, the aircraft's nose may initially swing to the right both in an absolute sense, and in relation to the direction of the flight path and airflow at any given moment. Since the flight path is curving to the left, the rightwards yawing motion with respect to the actual direction of the flight path and relative wind at any given moment must be larger than the rightwards yawing motion with respect to the external world. Then the nose may "freeze" in an absolute sense for an instant, but as the flight path continues to curve to the left, the rightwards yaw (slip) angle between the aircraft's nose and the actual direction of the flight path and relative wind is continuing to increase. As the nose starts to swing to the left in relation to the outside world, there will be a moment where the nose is yawing to the left in an absolute sense, but not in relation to the flight path and relative wind, and the rightwards yaw (slip) angle in relation to the flight path and relative wind is remaining constant. As the yaw rotation rate to the left continues to increase in an absolute sense, the aircraft will also begin yawing to the left in relation to the actual direction of the flight path and relative wind at any given moment, and the rightwards yaw (slip) angle in relation to the flight path and relative wind will begin to decrease. Once the bank angle becomes constant and the rate of (leftwards) curvature in the flight path becomes constant, the aircraft will typically end up yawed just a few degrees to the right in relation to the actual direction of the flight path and relative wind at any given moment, unless the pilot maintains a touch of "inside" rudder to bring the nose fully into alignment with the actual direction of the flight path and relative wind at any given moment. All this takes place within just a few seconds.

As an aircraft rolls from wings-level into a constant-banked left turn without any rudder inputs from the pilot, the idea that first we'll see the nose yaw to the right in relation to the flight path and relative wind, and then we'll see the nose come back nearly into alignment with the actual direction of the flight path and relative wind at any given moment, is actually a slight oversimplification. At some point after we see the peak adverse yaw (slip) angle to the right in relation to the actual direction of the flight path and relative wind, there will typically be several oscillations where the nose actually swings to point slightly to the left of the actual direction of the flight path and relative wind, and then swings back to point to the right of the actual direction of the flight path and relative wind, etc, in a dampening series of yaw (slip) oscillations before the yaw (slip) angle in relation to the flight path and relative wind finally becomes small and constant. These yaw (slip) oscillations can be seen in the movement of a yaw (slip) string, but these yaw (slip) oscillations typically would not be so pronounced as to actually create any additional rightward swing of the nose in relation to the external world, after the first initial adverse yawing motion. Instead, the yaw (slip) oscillations would just create peaks and lows in the rate at which the nose was moving to the left in relation to the external world. These oscillations are particularly easy to see if we watch a centerline-mounted yaw string on a flex-wing hang glider with no fixed vertical fin, but they are also visible in other aircraft.

Here's another point that should help underline the importance of the difference between the two different kinds of yaw: when we speak of an aircraft's "yaw stability", we always are referring to the "weathervane effect", i.e. the aircraft's tendency to point its nose into the relative wind, so that the nose is aligned with the flight path through the airmass and pointing in the same direction as the aircraft is actually moving through the airmass. We don't mean that the aircraft has any tendency to hold a fixed compass heading in relation to the external world even if the flight path is curving!

In many ways we can often think of yawing motions in relation to the external world as being the accidental and relatively unimportant byproducts of yawing motions with respect to the direction of the flight path and relative wind at any given moment, plus curvatures in the flight path. Normally we are most interested in the yaw dynamics with respect to the direction of the flight path and relative wind at any given moment. This is especially true in cases where we are assuming that the aircraft has found a yaw (slip) attitude in relation to the flight path and relative wind where all yaw torques are in balance. (If the aircraft were flying through a very thick fluid, this would essentially be the case at all times, and we would never see yaw oscillations like we described above.) However, any time the yaw rotation rate with respect to the external world is changing rather than constant, we know there must be some imbalance in the yaw torques acting on the aircraft, and we also know that the aircraft's yaw rotational inertia must be playing some role in the dynamics that are taking place. Also, as we've already noted, at the end of the day it is the aircraft's rate of yaw rotation with respect to the external world that determines the difference in airspeed between the left and right wingtips.

We've undoubtedly hit the reader with far too much information at this early point in the tutorial pages! Many of these ideas will be re-introduced later in the tutorial pages. The idea for now is simply to drive home the point that we can think about yaw in two different ways. One kind of "yaw" involves the rotation about the aircraft's yaw axis in relation to the external world, which for shallow bank angles is essentially the same as a change in the aircraft's heading. This kind of yaw creates a difference in airspeed between the two wingtips. The other kind of "yaw" is the orientation or change in orientation of the aircraft's nose in relation to the actual direction of the flight path and relative wind at any given moment. We'll often use the word "slip" when we're discussing this kind of yaw. This is the kind of yaw that creates a sideways component in the relative wind, i.e. a sideways airflow over the aircraft.

(Diagrams to be inserted!)

 

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