You may have heard the term "alpha" as well as "beta" when discussing the aerodynamics of your airplane. Your experience with either term may be limited unless you are operating a fly-by-wire aircraft and the manufacturer decided to give you a look inside all those fancy control laws. If even your aircraft is "fly-by-cable," you should consider alpha and beta. The aircraft may do something you don't expect if you neglect either concept.
— James Albright
Updated:
2022-07-01
So what are alpha and beta? You can think of alpha as Angle of Attack and beta as sideslip. I am sure there are finer distinctions to be made on both, but those should do for us pilots. We pilots usually focus our aeronautical engineering concerns with the need to avoid an aerodynamic stall, and that is key to understanding alpha. "Alpha protection" is another way to say "stall protection." So far so good, right? Now, did you know that beta impacts alpha? Your sideslip can impact when your aircraft stalls. And this is especially true for swept wing aircraft.
This came to sharp focus for many in the Gulfstream GVII series in 2020 and again in 2022. I wrote an editorial for Aviation Week about this, reprinted below.
1 — Viewpoint: Not All Airplanes Fly Alike!
3 — The impact of beta on alpha
4 — Crosswind approach and landing technique
5 — Automatic alpha protection
6 — The "holistic" conclusion and how you should fly your aircraft
1
Viewpoint: Not All Airplanes Fly Alike!
Aviation Week
You may have heard that the Gulfstream GVII world is under FAA scrutiny these days and that the feds are “cracking down” on this new technology aircraft in what many see as an over-reaction after the Boeing 737 MAX certification debacle. Where the 737 MAX fleet was grounded for more than a year, the GVII’s penance seems to be nearly debilitating wind limits. If you aren’t operating either variant of the GVII, the G500 or G600, you might think this doesn’t concern you. But if you are flying an aircraft with any kind of computerized flight control system, even a simple “black box” yaw damper, it concerns you a great deal. To understand why, we need to look at the common pilot attitude that “all airplanes fly alike,” how that caught two pilots in the GVII, and how it could catch anyone flying a new aircraft type.
When the only thing in my logbook was a Cessna 150, I often heard from those flying complex aircraft with retractable landing gear and variable pitch props, that it was a whole new ball game. Those comments came again with the instrument rating and when moving on to twins. Then a curious thing happened: pilots started saying, “she flies like any other airplane.” I’ve heard this about jets--heavies, and even the supersonic aircraft that I’ve flown. The point seemed to be summed up in the old pilot joke made while motioning with an imaginary yoke, “houses smaller, houses bigger.” Perhaps it is just false humility, showing younger pilots that anyone can master the next step up in airplanes. But to understand why the thought can be dangerous, consider the Gulfstream GVII type.
The GVII type is the second from Gulfstream to be completely fly-by-wire and the first to be controlled with a sidestick. Earlier Gulfstreams, such as the GIV, are “fly-by-cable” and are controlled with a more conventional yoke. It is said that the GIV flies like a tank and is built like one. The controls were heavy; it sometimes felt you were in a wrestling match when landing in a gusty crosswind. But the airplane could be flown smoothly if you knew how. The key point here, however, is that it could survive pilots with zero finesse.
The GVII, in stark contrast, does not fly like a tank and it certainly isn’t built like one. In 2020 a highly experienced Gulfstream pilot caused the aircraft to land so hard, that a landing gear door contacted the runway. It was a night landing at Teterboro Airport, New Jersey, in a gusty crosswind: from 60 deg. right of the nose, at 15 knots, gusting to 27 knots. I’ve landed in similar winds in both the GIV and GVII and believe the GVII handles the wind better, provided you fly the aircraft as it was designed. But you must first understand that a GVII does not fly like a GIV. Why is that? It is a matter of design.
The GVII can fly further, faster, more comfortably and use less gas than its older sibling. Flying from the London to New York, for example, the GIV struggles to maintain 0.80 Mach after climbing directly to 41,000 ft., makes it to its destination with minimum fuel reserves, while providing its passengers a cabin pressure around 6,000 ft. The GVII will do the same trip starting with less than a full tank of gas, climbing to 43,000 ft., cruising immediately at 0.90 Mach, and doing all this with a cabin pressure of just over 3,000 ft. All this economy and efficiency means the newer GVII is built lighter and, as much as the manufacturer would dispute this, more fragile. The flight control computers not only provide much of this efficiency, but act to protect the airframe from “ham fisted” pilots. The aircraft is designed to be flown with a light touch with the hand low on the stick. Pilots are told to operate the stick using pressures, not displacement.
In flight, the GVII is operating in normal flight control law, where stick position results in a g-response (short term) and speed stability (longer term). When warranted, the control law will transition to an angle-of-attack (AOA)-limiting sub mode, where stick position is used to command a target AOA. In this mode, full aft stick gives maximum allowable AOA, which may not be as much as the pilot intended. When aircraft pitch and sidestick input rates are high, the transition to AOA-limiting occurs earlier to avoid overshooting the limit. When this happens, an initial nose down input is commanded. In other words, if a pilot becomes too rough on the controls, a function of the flight control computer takes over. And that takes us back to the Teterboro incident.
The accident aircraft was flown at VREF+5, at the correct speed for a light wind day but 15 knots too slow for the winds that night. The airplane flight manual (AFM) at the time specified that “In strong wind conditions, add to VREF 1⁄2 of the steady state wind plus the gust increment to a maximum VREF 1⁄2 of the steady state wind plus the gust increment to a maximum additive of 20 knots.” With a 15 gusting to 27 knot wind, depending on if you round up or down, the correct speed should have been VREF+19 or VREF+20.
On short final, around 150 ft., the aircraft was flown with a crab established at about a 7-deg. sideslip in the conventional “wing low” crosswind technique. Gulfstream and many manufacturers of aircraft with wide wingspans recommend their aircraft be flown in a crab until initiating the flare to avoid a wingtip strike while landing wing low. Watching a parade of aircraft landing at Teterboro, I think most pilots hold on to the tried-and-true wing low method taught in their primary aircraft trainer. You can get away with this in the flying tank that is the GIV; the “fly-by-cable” simply obeys the pilot. In the GVII, AOA-limiting happens sooner if you have more than 4-deg. of sideslip and the pilot may not have the expected pitch authority when that happens.
Data analysis of the event also shows the pilot was using a series of rapid, large, alternating pitch inputs at low altitude followed by full aft stick through touchdown. This caused the AOA-limiting to occur even sooner and robbed the pilot of more available nose up control just prior to and during touchdown. Rapid control reversals are never a good thing in any axis, even on a conventionally controlled aircraft.
After the dust had settled, it was clear that the pilot used poor technique and violated required AFM procedures. The FAA’s reaction was almost predictable, requiring a new set of restrictions on the G500 only, even though the flight control system is identical to that on the G600. The recommended approach speed additive became mandatory, and the crosswind limit was reduced from 30 to 22 knots. The GVII AFM added this warning: “Rapid and large alternating pitch control inputs, such as an abrupt pull-push-pull, may reduce the airplane response to subsequent control inputs to less than what may be required for normal airplane handling.”
Despite all this, two years later, another G500 experienced a hard landing in similar conditions after the pilot used a series of large, rapidly alternating pitch stick inputs. It appeared the approach speed additives and crosswind restrictions alone were not enough to counter the stick techniques. The FAA reacted with the most draconian restrictions available, short of grounding the fleet. Both the G500 and G600 are now limited to landing in winds up to 15 knots with no more than a 5-knot gust. Night landings must be made using vertical path guidance, such as with an ILS glideslope. Approaches must be stabilized by 1,000 ft. These restrictions will remain in effect until the flight control software is updated to allow for ham-fisted pilots. To date, the GVII fleet has had over 37,000 landings of which two have resulted in hard landings due to the AOA-limiting mode of the flight control computer. That’s just 0.005%--and 100% of those were by pilots ignoring one or more AFM procedures.
Derrick Hodges' "G-VII No Fly Zone"
How severe are these restrictions? GVII pilot Derrick Hodges provides an application called the “G-VII No Fly Zone,” available at http://nfz.hdgs.me/. The first time I tried the application in May the answer was that more than half of the GVII capable airports in the continental United States had winds half of the GVII capable airports in the continental United States had winds that either exceeded the 15-knot total wind or the 5-knot gust.
Many Gulfstream pilots blame Gulfstream for all this. I don’t. Given the FAA’s mindset following its poor handling of the Boeing 737 MAX issues of a few years ago, Gulfstream must give its unreasonable masters a penance. No, for this mess, I blame two Gulfstream pilots who believed the GVII flies like any other airplane, when clearly it does not.
The GVII is the nicest flying airplane I’ve ever flown, and I’ve flown a lot of nice airplanes. But I learned early on that I need to greet each new aircraft type as a new learning experience. A manufacturer’s recommended technique almost always becomes my recommended technique. In many cases, I had to give up procedures I had been using for decades. But that is the price of learning to fly something new. The lessons here are both old and new, and they apply to all pilots flying all aircraft:
- No matter what aircraft you are flying, it is never a good idea to use large, rapid, alternating control inputs in any axis.
- Techniques learned in one aircraft, or even all aircraft you’ve flown previously, may not be advisable in your next aircraft.
- Even if you’ve been able to ignore AFM procedures and limitations with great success for a very long time, you may find a day where the results are not so kind. You might as well learn to fly the aircraft as designed on day one.
I implore all professional pilots to understand that not all airplanes fly alike. My reasons are purely selfish. Pilots who don’t understand this have already cost my flight department a trip because the winds were gusting above 5 knots. But I also worry that I will someday be a passenger in a large commercial jet flown by a captain who believes his Boeing or Airbus flies just like a Cessna 150.
Source: Aviation Week Network, 2022 Q2
2
Alpha and beta, explained
Alpha
Angle of Attack (AOA, or alpha, α). The acute angle between the relative wind and the chordline of an airfoil.
Source: Dole, p. 28
We pilots devote a fair amount of time studying and watching our angles of attack. We understand that the higher the AOA, the more of the aircraft's available lift we are using. We also know that there comes an AOA where we have no lift remaining.
I won't devote a lot of time to AOA here, I've already done that elsewhere: Angle of Attack, Stall Recovery, and "Everybody has an angle (of attack)"
I would like to emphasize, however, that AOA isn't something you set and forget, it is a result of not only how you fly the aircraft, but how the environment impacts the aircraft. In our GVII-G500, for example, VREF occurs at 0.67 AOA. But we never fly VREF, we are required to add between 5 and 20 knots CAS, depending on the winds. In the accompanying video, notice the AOA (bottom left of the HUD and the PFD), that AOA bounces between 0.41 and 0.75.
It was a gusty wind day and we had the full 20 knot additive. Let's say that our average AOA was 0.58 so it increased as much as 0.17. Had we flown VREF instead, our 0.67 AOA might have increased to 0.84. You might think this is no big deal, because the stall occurs at 1.00. (It doesn't, but let's say it does.) So no problem, right? It depends on the aircraft. In the case of the GVII, there are many other considerations, such as beta.
Beta
Beta, or Sideslip Angle,
Dole, fig 8.31
Sideslip angle β (beta) is the angle between the relative wind and the airplane's longitudinal axis. When the relative wind is from the right, the sideslip angle is positive in value. Figure 8.31 shows a positive sideslip angle.
Source: Dole, p. 262
In most aerodynamic textbooks, the importance of beta is covered as it relates to Stability and Control and very little else. But betas which vary from zero can impact alpha, especially on swept wing aircraft. (As we shall cover next.)
3
The impact of beta on alpha
Davies, pg. 97
- By sweeping a wing significantly, it will be remembered, the velocity vector normal to the leading edge is made less than the chord wise resultant. In [the figure] AC is shorter than AB. As the wing is responsive only to the velocity vector normal to the leading edge, for a given Mach number the effective chord wise velocity is reduced (in effect the wing is persuaded to believe that it is flying slower than it really is).
Source: Davies, pg. 96-99
GVII sideslipping into crosswind to provide a straight ground track
The first impact of beta on alpha is that on a swept wing aircraft, the wing on the side the aircraft is sideslipped into (the upwind side) produces more lift because it is closer to being perpendicular to the airfoil, it is closer to being spanwise. The opposite wing produces less. Your AOA indication may or may not reflect this. The net result is you have less than all the lift available from both wings.
GVII crabbing into crosswind to provide a straight ground track
If, on the other hand, the aircraft is crabbed into the wind, more of the relative wind is spanwise to the wing, providing more lift. In the exaggerated drawing, the large crab angle equals the crosswind angle and both wings are producing lift equally.
Note that this also happens on straight wing aircraft, to a lesser degree, because part of the wing is "blanked" by the fuselage when sideslipped. A swept wing aircraft has the additional problem that a sideslip can induce an unwanted roll.
Davies, pg. 98
Source: Davies, pg. 96-99
4
Crosswind approach and landing technique
"Wing low" sideslip
A Cessna 150 sideslipping for a wing low crosswind landing
You might think of a sideslip as flying sideways, and in many ways that is true. But it is flying sideways relative to the airmass. If you are making an approach to a runway on a calm wind day, the fuselage will be aligned with the runway and you are most definitely not flying sideways. What about with a crosswind? If you are flying the standard "wing low" method taught to most beginning flight students, you are actually sideslipping into the wind. The fuselage is aligned with the runway, but you are flying sideways nonetheless. This is precisely how many of us were taught in our Cessna 150s or Piper Cherokees how a proper approach and landing in a crosswind should be made.
A Gulfstream GVII sideslipping for a wing low crosswind landing
The "wing low" sideslip tends to be the technique of choice for many in the world of flying larger iron. Some manufacturers allow for this, some discourage it, but most are silent on the subject. Boeing, for example, permits with wing low sideslip, but recommends other techniques such as an approach and landing with the airplane crabbed into the wind, or with the crab removed at the last moment. For a full discussion about these methods: Crosswind Landing.
"De-crab"
Decrabbing a B-737
The following 737 technique can be found in other Boeing manuals and may not apply, word-for-word, to other aircraft that specify a de-crab of some sort. But if your manual doesn't offer any advice at all, or if you are looking for how "the big boys" do it, it gives you more information than you had.
Boeing 737 NG
- The objective of this technique is to maintain wings level throughout the approach, flare, and touchdown. On final approach, a crab angle is established with wings level to maintain the desired track. Just prior to touchdown while flaring the airplane, downwind rudder is applied to eliminate the crab and align the airplane with the runway centerline.
- As rudder is applied, the upwind wing sweeps forward developing roll. Hold wings level with simultaneous application of aileron into the wind. The touchdown is made with cross controls and both gear touching down simultaneously. Throughout the touchdown phase upwind aileron application is utilized to keep the wings level.
Source: Boeing 737 NG (TM), page 6.45
What you should be doing
Your manufacturer should have a recommended crosswind landing procedure, but it may just be assumed knowledge. In most Gulfstream manuals, for example, the method of choice is the de-crab. Flying an approach in a wing low sideslip erodes your stall margin, makes the aircraft less stable, and makes the ride in the cabin uncomfortable for your passengers. There is also an increased risk of having a part of the aircraft other than the wheels contact the runway. Many older Gulfstreams, however, tolerate the wing low method without complaint. That changes with the fly-by-wire Gulfstreams and alpha protection.
5
Automatic alpha protection
I think most, if not all, fly-by-wire aircraft have some form of alpha protection that serve to protect the aircraft from a stall. The system can be called alpha protection, AOA-limiting, or some other name which tells you the computers are monitoring your AOA and are prepared to do something when your AOA is too high. Unfortunately, few manufacturers give you a lot of detail about how this happens.
Example: Gulfstream
Gulfstream provides a very good set of manuals for most of its aircraft and starting with the GVII, the explanations given for the fly-by-wire system are quite good. You might have to dig, however:
Takeoff
Pilot has direct control over the elevator when on the ground, once above 10 feet AGL, the aircraft transitions to the NzU control law and AOA limiting protection is provided.
Source: GVII OM, §02-10-70
"NzU control law" is not explained in the manual; I presume it means "Normal Control Law."
Climb
If the Auto-Pilot is off, and the pilot is manually tracking the flight director, then the pilot will be unable to pull past AoA limiting and the nose will drop with the pilot on the limiter. A simultaneous roll input, while on the AoA limiter, can cause the stick shaker to activate.
Source: GVII OM, §02-10-140, ¶ 1.f. and 1.g.
Summary of NAOA Values of Interest:
0.66
Approximate NAOA for VREF
0.75
Path Limit Indicator (PLI) appears, PLI removed at 0.73 (hysteresis)
0.85
Stick Shaker activates for all non-normal flight control laws (Alternate, Direct, Backup)
-- No AOA limiting present in non-normal (Alternate, Direct, Backup) flight control laws
-- No Auto-Pilot available in non-normal laws
0.88 - 0.93
Entry into AOA limiting normally occurs at an NAOA between 0.88 and 0.93, depending on how rapidly airspeed is decreasing. In addition, when AOA is increasing rapidly, AOA limiting entry may occur at a considerably lower NAOA than 0.88.
-- CYAN CAS message – FCC AOA LIMITING 0.95
Full-Aft Stick – Maximum AOA achievable in Normal Law with pure pitch input 0.97
Stick Shaker activation in Normal Law; Normally only seen when on aft limit and attempt a large roll input or sideslip
Source: GVII OM, §02-10-160
Gulfstream makes a point that AOA displayed to the pilot is actually Normalized AOA (NAOA), a ratio and not an angle. I've never seen an AOA gauge that wasn't really NAOA.
40-degree bank turn (at a constant flight path angle) can be maintained using full aft stick, while in AOA limiting mode (0.95 NAOA).
Source: GVII OM, §02-10-170, ¶3
The top of the yellow band indicates the minimum speed at which a 30 or 40-degree bank turn (at a constant flight path angle) can be maintained using full aft stick, while in AOA limiting mode (0.95 NAOA).
Source: GVII OM, §02-10-170, ¶3
AoA Limiting occurs (CYAN CAS message)– no shaker with pure pitch input
(a) AOA limiting between 0.93 and 0.95 NAOA
(b) Can’t get to 0.97 NAOA with pure pitch input (no shaker)
(9) Sample roll +/- 5 degrees bank (slow) – no shaker
Source: GVII OM, §02-10-190, ¶3(8)c. Low Speed Awareness Alert with Auto-Throttle failed
AoA Limiting occurs (CYAN CAS message)– no shaker with pure pitch input
(a) AOA limiting between 0.88 and 0.95 NAOA based upon rate of deceleration
(b) Can’t get to 0.97 NAOA with pure pitch input (no shaker)
(9) Sample roll +/- 5 degrees bank (slow) – no shaker
Source: GVII OM, §02-10-190, ¶3(8)d. Low Speed Awareness Alert with A/P-off and A/T-off
The 2020 and 2022 incidents mentioned above in the "Viewpoint article shed a little more light on when alpha protection occurs and what happens as a result:
- The sidestick transitions from providing g-response and speed stability to an AOA-limiting submode under certain conditions.
- Though the "book" answer is that AOA limiting occurs between 0.93 and 0.95, it could happen down to 0.88 and lower when decelerating.
- AOA-limiting can happen sooner when sidestick input rates are high, when the pilot becomes too rough on the controls. (This prevents overshooting the limit.)
- AOA-limiting will also happen sooner when sideslip angles exceed 4 degrees. (I believe this happens because a sideslip can cause one wing to stall sooner than the other, sooner than the indicated AOA would predict.)
- When AOA limiting occurs, pulling full aft on the stick results in no more pitch than the maximum AOA or a value short of that determined by the software laws. This may sometimes result in an initial nose down pitch movement.
What about other fly-by-wire aircraft?
If you've not flown other fly-by-wire aircraft, you might think the information provided by Gulfstream to its pilots is sparse. But I think Gulfstream's publications are quite good compared to others that I've flown.
In 2021, I flew the Dassault Falcon 8X for Aviation Week / Business & Commercial Aviation magazines: Pilot Report: Falcon 8X. The alpha protection idea appears to be similar but not well documented.
Flying the 8X at altitude revealed the aircraft was quite stable with full aft stick and slow speeds. The aircraft showed no tendency to roll and the resulting flight path was a gentle descent with the pitch attitude remaining positive. But what if that happened in the flare? I am told the aircraft has a landing submode which would prevent the pilot from running out of pitch authority as appeared to have happened in the Gulfstream incidents.
What about non-fly-by-wire aircraft?
Even without the flight control computers operating behind the scenes, most transport category aircraft do have what could be called a "dumbed down" version of alpha protection system, using what some systems call stick pushers. It may be nothing more than a mechanical vane on the wing or as sophisticated as multiple AOA vanes which collaborate before deciding it is time to reduce the pitch of the aircraft. When you get right down to it, that is all alpha protection is: a very smart stall barrier system.
6
The "holistic" conclusion and how you should fly your aircraft
We often say in computerized aircraft that "everything is connected to everything else." Once computers get interconnected, it is hard to isolate any one system to just that system. But this type of holistic interaction isn't limited to the the electrons, it can also be found in the airflow which allows the aircraft to fly. Flying the aircraft in a sideslip impacts how well it flies in pitch, and that greatly affects how much control you as a pilot have. The lessons learned in the GVII incidents apply to all aircraft, no matter how the flight controls are connected to the stick or yoke:
- Stall protection goes under many names — such as stick pushers, nudgers, stall barriers, alpha protection, and AOA-limiting — and must be respected in a way many of us do not anticipate. If stall protection happens low to the ground (takeoff or landing), your options become limited. What you are doing, essentially, is running out of flight envelope.
- You can further reduce your flight envelope by flying with large sideslip angles. In a conventional flight control aircraft, this could mean one wing stalls before the other. In a fly-by-wire aircraft, it could mean the computers preclude that by limiting your pitch authority.
- No matter how the flight control system is built, it is never a good idea to use large, rapid, alternating control inputs in any axis.
References
(Source material)
Albright, James, Viewpoint: Not All Airplanes Fly Alike! Aviation Week Network, 2022, Second Quarter.
Dassault Aviation, Focus on Digital Flight Control System, DGAC-DMF-5170, January 2018.
Davies, D. P., Handling the Big Jets, Civil Aviation Authority, Kingsway, London, 1985.
Dole, Charles E., Flight Theory and Aerodynamics, 1981, John Wiley & Sons, Inc, New York, NY, 1981.
Falcon 8X Crew Operational Documentation for Dassault EASy (CODDE) 1, Airplane Description, Revision 04: September 10, 2020.
Gulfstream GVII-G500 Issue 1 Operating Manual, Revision 8, October 28, 2021.
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