# Calculate/Measure Sideslip Angle from Heading Track and Drift Angle

Is there a way to measure the sideslip angle during flight through the relationship of heading, track and drift angle? For example if you turn the aircraft into head or tailwind - does the sideslip angle equal the drift angle for establishing a steady heading sideslip through rudder and aileron input from this initial condition?

• Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer.
– Community Bot
Nov 17, 2022 at 15:14
• It's a little late now as several answers have been posted (including mine), but I'm realizing that I should have asked for a clarification of exactly what you mean by the "drift angle". Nov 18, 2022 at 13:34

Sideslip has nothing to do with wind, or drift. No matter what the wind is, unless you apply rudder or some other yaw inducing force, (Single engine p-factor or differential thrust on a multiengine aircraft), the aircraft will always weathervane into the relative wind, the ball will remain centered, and there will be zero sideslip.

• I would argue, that this does not answer the question. The question is how do you identify sideslip given these inputs, not how does sideslip work in motorized aicraft. You sentence is not true for example for rotorcraft such as helicopters or drones Nov 17, 2022 at 20:35
• I thought that saying that it has nothing to do with wind or drift implies the answer to the question..... It is a resounding, unequivocal NO! You can't use wind, heading, drift angle or anything like that to measure sideslip. The only way to measure sideslip (Helicopter or fixed wing aircraft) is with a ball or a yaw string... Nov 18, 2022 at 0:25
• ... and the sentence is true for helicopters! ... and drones. Unless there is some rotational torque on a Helicopter, like the torque from a single rotor, (Not a Chinook), or the torque from a tail rotor like on a conventional single rotor helicopter, a Helicopter will weathervane into the relative wind just like any other body free to move in a fluid. Nov 18, 2022 at 18:59
• You are right that the steady-state response will go to zero for all weathervaning aircraft, but the dynamic response is very much non-zero due to factors like transient wind or wind shear and due to mismatches in torque as a result of the extensive coupling in helicopters. This last point can be very nicely seen when looking at logged Beta data (I just took a look to make sure). Steady state is practically never reached, and the amplitude can be as high as 15° either side. Additionally, a lot of drones tend to not weathervane, e.g. the typical Quadrotor. Nov 19, 2022 at 9:27

No.

Drift angle is just the difference between your heading and your ground track. There is no way to know whether an aircraft's heading is different from its ground track due to wind, or due to full rudder input by the pilot.

More information would be needed to determine whether or not there is any sideslip angle.

Yes, in theory it would work to establish the sideslip angle from the difference in heading and track angle, if you are traveling exactly into the wind or downwind. In practice, the challenge will be to exactly determine the wind velocity, and making sure your track is exactly aligned.

The answer will depend on the definition of drift. So before answer, let me introduce my definitions of these terms, so it is clear what I am talking about.

• heading: the angle between the north (true or magnetic) and the x-axis of the body frame of reference of the aircraft. The x-axis is aligned with the fuselage.
• side slip: the angle between the incoming air and the plane of symmetry of the aircraft.
• drift1: the angle between the motion of air, relative to the aircraft and the motion of the ground, relative to the aircraft. Ignoring tectonic plate movement, drift is caused solely as an effect of wind.

A picture says more than a thousand words, they say:

So, if you align the track angle (relative ground motion) with the relative air motion (0 drift), and at the same time introduce a sideslip, the difference between the heading and the track, is purely caused by sideslip.

In practice, that will be extremely difficult to achieve that in a steady state.

When the track angle is not aligned with the relative wind motion, you can compute the side slip angle if you happen to know the exact magnitude and direction of the wind.

It is more practical to measure the sideslip angle by using a beta vane on the aircraft.

1 An alternative definition of drift is: drift the angle between the x-axis of the body frame of reference of the aircraft the motion of the ground, relative to the aircraft.

In that definition, drift is the combined result of sideslip and wind.

Terminology makes for such good internet discussion!

Calculate/measure sideslip angle

That means one plans to fly uncoordinated, using a sideslip to hold heading. While this technique works to keep the nose centered on the runway when landing, it is not the best way to fly a crosswind over distance.

What is more efficient is to fly a coordinated heading and let the wind "correct" the groundtrack.

the coordinated airplane has no crosswind relative to the airmass, the vector sum of aircraft velocity/direction and windspeed/direction determine groundtrack.

So, ground track is based on these two components, not the orientation of the aircraft. That's what this helps a pilot/navigator do.

Regarding calculation of bank angle vs crosswind in a slipping condition, side force from wing is readily available by decomposing the lift vector as sine bank angle × Lift. But one should keep in mind that crosswind forces are created by drag, essentially the wind hitting the side of the plane.

It would be easier to measure bank angle vs crosswind for a given aircraft, and one could expand the study to crab configuration, power on and off (I can see the graphs on slides and overhead projector already!), but, as wind varies, pilots generally must pilot by constantly adjusting control inputs to the weather conditions, not with data graphs.

Preface: The external, meteorological wind creates no tendency whatsoever for an aircraft to sideslip. Nor is sideslip an efficient or logical way to correct for a crosswind, except during the last stages of final approach, when there is a benefit to ensuring that the aircraft's heading is fully aligned with the ground track. "Crabbing" and "slipping" are two completely different techniques-- "crabbing" is a really no more than the selection of a particular heading to fly, and normally does not involve any sideslip at all.

Here are some related ASE questions whose answers may shed some light on these points:

Is drift and sideslip angle the same in the accompanied figure?

How does sideslip indicator react during crosswind?

Since we usually fly with zero sideslip as best we can, and experience no more particular tendency to slip when flying crosswise to the wind than any other time, your questions are pretty much moot as far as all practical flying and navigation is concerned.

Still, one could imagine a theoretical situation where a navigator was provided with a precise measurement of an aircraft heading, and a precise measurement of a (small but non-zero) sideslip angle, and was interested in computing the exact ground track and drift angle.1

Is there a way to measure the sideslip angle during flight through the relationship of heading, track and drift angle?

It depends on what you mean by the "drift angle".

If by "drift angle" you mean the angle between the direction of the flight path relative to the airmass, and the ground track-- i.e. the "crab angle" (or more precisely, the negative of the "crab angle") -- then the answer turns out to be "yes". See "Calculations part 1" for more.

But if you literally mean the angle that you would measure with a drift meter-- the angle between the aircraft's heading and the ground track-- then the answer turns out to be "no". See "Calculations part 2" for more.

The reason there is some ambiguity about which of these is the more appropriate definition of the "drift angle", is that sideslip is usually assumed to be zero in wind correction problems. But you aren't making that assumption, so we need to decide which definition to use.

Likewise, a word about "heading" -- what we usually call "heading" in wind correction problems, is really only heading if sideslip is zero. If sideslip is not known to be zero, a better term in many cases would be "direction of flight path relative to airmass" (dofprta). In this answer, I'll use "heading" to mean the actual heading. I'll also assume that that's the usage that was intended in the question.

Calculations part 1--

Here we define "drift" as the angle between the direction of the flight path relative to airmass (dofprta), and the ground track. This is simply the negative of the "crab angle".

(Note that by this definition, "drift" is zero at all times when we are flying in still air, even if we are sideslipping.)

Sign conventions used here:

A positive drift angle means that the ground track is clockwise of the dofprta. A positive sideslip angle means that the aircraft nose is pointing clockwise of the dofprta.

"Drift angle" and "crab angle" are essentially the same thing (more precisely, the "drift angle" is the negative of the "crab angle".)

Dofprta + drift angle = ground track

Sideslip angle = heading - dofprta

Therefore sideslip angle = heading - (ground track - drift angle)

Which means that sideslip angle = heading + drift angle - ground track

So yes, with this definition of "drift angle", we can calculate the sideslip angle from the drift angle, ground track, and heading.

For example if you turn the aircraft into head or tailwind - does the sideslip angle equal the drift angle for establishing a steady heading sideslip through rudder and aileron input from this initial condition?

It's a little unclear what "turning the aircraft into the wind" means. Here we'll assume that the questioner is envisioning that we have changed the flight path so that we are flying directly into the wind, before beginning a sideslip.

If we start by flying directly into the headwind (or tailwind), with zero sideslip, then heading, dofprta, and ground track will all be the same, and drift angle (and crab angle) will be zero. From this point --

a) If we keep the dofprta constant, and establish sideslip by changing to a new heading (while countering with bank to avoid any turn), then ground track will remain constant, and slip angle will equal heading - dofprta (which will also be heading - ground track), and drift angle (and crab angle) will be zero. (Using these terms as defined above.) So when we establish a sideslip while keeping the dofprta and the ground track pointing straight into the wind, the sideslip angle does not equal the drift angle.

b) If we keep the heading constant, and establish sideslip by using the controls in such a way that the flight path (dofprta) curves (turns) a bit before stabilizing in a slightly different direction, the situation has gotten considerably more complicated. Since the flight path (dofprta) now has a crosswind component, so does the ground track. The drift angle can no longer be zero. For a given angle between the wind direction and the dofprta, the resulting ground track (and therefore the drift angle) will depend on the relationship between the wind speed and the airspeed. It will still be valid to say that sideslip angle = heading + drift angle - ground track, which means that drift angle = ground track + sideslip angle - heading. So as far as case b) is concerned, as to your question "does the sideslip angle equal the drift angle?", the answer is "only in the specific case where the ground track and the heading are the same." But with the airplane pointing straight into the wind, this can actually never happen unless the sideslip angle and the drift angle (as we've defined it here) are zero. For all other cases, the answer to your question is "no -- when the airplane is pointing straight into the direction of the external, meteorological wind, the sideslip angle can not equal the drift angle".

In fact, regardless of wind direction or speed, it is always true that if the ground track and the heading are the same, then the sideslip angle must be equal to the drift angle, as we've defined it here, and vice versa. (There's no reason to ever fly an aircraft in this manner-- except on final approach, using the wing-down method of crosswind correction!) With a little reflection on the dynamics of wing-down crosswind landings, it becomes immediately obvious that to fly in a straight line with the ground track equal to the heading, with a sideslip angle other than zero, then the following must be true: 1) The ground track and heading cannot be directly aligned with the wind. 2) The direction of the flight path through the airmass (dofprta) cannot be directly aligned with the wind. 3) The dofprta must lie somewhere between the ground track and the wind direction. These conditions were not met in cases a) or b) above, hence the "no" answer to your question "does the sideslip angle equal the drift angle?" for either of these cases.

Calculations part 2--

Here we define the "drift angle" as the angle that we would measure a drift meter-- the angle between the aircraft's heading and the ground track. (This is arguably the best or at least the most widely-used definition of the "drift angle"-- for example, in the wing-down crosswind landing referenced immediately above, we would normally say our goal is to land with "zero drift", and this concept isn't really fully compatible with definitions used in part 1.)

(Note that by this definition, "drift" is not zero when we sideslip in still air.)

Sign convention used here:

A positive drift angle means that the ground track is clockwise of the heading. A positive sideslip angle means that the aircraft nose is pointing clockwise of the direction of the flight path relative to the airmass (dofprta).

Dofprta + (drift angle + sideslip angle) = ground track

Sideslip angle = heading - dofprta

With these equations, there's no way to state the sideslip angle purely as a function of the drift angle, ground track, and heading. All we can say is that Ground track = heading + drift angle, regardless of the sideslip angle. The "drift angle" gives us no new information that we don't already know from the heading and the ground track.

Therefore with this definition of "drift angle", there is no way to calculate the sideslip angle solely from the drift angle, ground track, and heading.

For example if you turn the aircraft into head or tailwind - does the sideslip angle equal the drift angle for establishing a steady heading sideslip through rudder and aileron input from this initial condition?

Again it's a little unclear what "turning the aircraft into the wind" means. Again we'll assume that the questioner is envisioning that we have changed the flight path so that we are flying directly into the wind, before beginning a sideslip. This introduces additional constraints to the situation. While flying directly into the wind or directly downwind, if we initiate the sideslip in such a way that the ground track (and therefore the dofprta) remain constant, rather than simply initiating a bank while holding aircraft heading constant, then and only then with this definition of "drift angle", can we say that the sideslip angle is also the drift angle. (Actually, there is one other case where we can make the same observation: if we know there is zero wind.)

Footnotes:

1. Here one is tempted to consider the case of a multi-engine aircraft with one engine failed, or with one engine intentionally shut down for enhanced range, but we must remember that in such a case the deflection of the slip-skid ball does not actually indicate the sideslip angle of the aircraft, i.e. the angle between the aircraft heading and the oncoming relative wind-- so how would the sideslip angle be known? And to the extent that it were known, why would it be allowed to be other than zero?
• Your explanation is sound, but the answer to the question, (as it is worded...) is NO. You cannot compute a sideslip angle from heading, track, and drift angle. Nov 17, 2022 at 18:20
• But the question wasn't about "DOFPRTA"... You state: "Since we usually fly with zero sideslip as best we can, and experience no more particular tendency to slip when flying crosswise to the wind than any other time, your questions are pretty much moot as far as all practical flying and navigation is concerned." This would seem to bolster my point. Nov 17, 2022 at 18:39
• Well, my comment stands. I think you have way over-answered a pretty simple question, going as far as inventing a new term to justify a possible yes answer… Nov 18, 2022 at 15:09
• (Continued in chat chat.stackexchange.com/rooms/140720/… ) Nov 18, 2022 at 16:10
• (Sorry, thought there was nothing more to say, but a new answer inspired a little more thought-- realized I hadn't specifically addressed the second sentence in the question, for the alternative (second) definition of drift -- ) Nov 21, 2022 at 12:38