What is the maximum safe bank angle of a 747?

Question

This question arose during the comments of another question, linked for the curious: What does it take to turn a 747 around 180 degrees?

Because the discussion was interesting, (and to avoid congesting the comments of another user's question), I reposted it here.

Does anyone know the answer to this? Official sources/experience are preferred, but I'll take what I can get.

If I was at altitude and suddenly realized we were about to cross into airspace that might get us shot down, I would, smoothly, do 3 things simultaneously: (1) start the nose down to around 25 degrees down, (2) start a roll to a bank angle of 60-80 degrees, and (3) start the power back to idle. At the same time, I'd ask the first officer to deploy the speed brakes, which would give me great roll response. – Terry

To which I replied:

80 degrees of bank would be a bit excessive no? 60 might be reasonable for an emergency turn, but certainly no more in a 747? (G-forces aside) – HCBPshenanigans

Terry's reply:

I was thinking of a range because, in an emergency turn, hitting an exact degree of bank would be hard. I would, however, not want to go beyond 90 degrees because of the possible disorienting nature for the flight crew. At 60 degrees, approximately 87% of the wings lift would be turning the airplane. At 80 degrees, about 98% of the lift would be turning the airplane, so the lesser bank would sacrifice 11% of the turning force. I would expect to lose a lot altitude in the turn. I can't think of a reason not use 80 degrees. Pax comfort would be a non-issue. – Terry

My most recent response:

Idk if you are a real 747 captain (there are quite a few on here), but iirc many 747 crashes have happened because when the aircraft banks so hard that it loses that much vertical lift, it is very difficult to recover from. In addition, some flight systems might malfunction under these rather extreme conditions. 60, hell even 70, is much steeper than it seems. I seem to remember seeing an episode of that old Air Disaster show about just this. – HCBPshenanigans

Edit: What kind of difference would the difference between 60 and 70 or 80 degrees of roll make in time to turn 360 degrees?

Answer 1

The descent angle helps to reduce the lift that the wing needs to provide, in two ways. It leads the aircraft into higher density air, where more absolute lift is possible at the same Mach number. That takes a while, but a more immediate effect comes from pointing the aircraft's nose downwards. Then, part of the gravity-induced forces can be counteracted by drag (D in the sketch below). This is similar to a glider, only with much lower aerodynamic efficiency and steeper angles. Terry reduces thrust and opens the speed brakes to avoid overspeeding, so he can dive as steeply as possible, thus reducing lift requirements. Now more of the wing's lift L can be employed for turning the aircraft around. If he wants to achieve a constant sink rate, he still has to produce enough lift to balance weight, but reduced by the cosine of the glide path compared to the level flight condition. At 25° nose down, this is a reduction by 10%.

Now you are concerned about his roll angle. Please note that he wants to create as much sideways component of lift as possible, which will look like gravity to all onboard. At 60° roll angle (I think his 80° are a bit extreme), this works out to twice the normal vertical acceleration, and with the dive actually just 1.8 g, so everyone will feel almost twice the force of normal gravity. With the 80° roll, this will not be a stationary turn and not enough lift will remain to counteract gravity, so the aircraft will accelerate downwards during the turn. It will actually fall out of the sky. When already at Mach 0.85, I would be more careful than Terry, because things get ugly very quickly when Mach goes further up.

The term $m\cdot\frac{v^2}{R}$ is the centrifugal force which can be afforded by the horizontal component of the lift and which needs to be as big as possible for tight turns (a smaller radius R helps). This is the lift component that Terry needs to pull the aircraft around.

If we stay with stationary turns (without the "falling out of the sky" part), the maximum bank angle is given by the maximum load factor of the 747. At 400 KEAS, this is just 1.5g, so even with the 25° nose down attitude the maximum bank angle would be 53°. If you fly slightly slower, the load factor goes to 2g (equals 63° in a 25° descent) and tops out at 2.5g at 310 KEAS (68.7° in a 25° descent). Flying at Mach 0.85 in 30.000 ft will produce an equivalent airspeed of 306 kt in normal atmospheric conditions. The precise value varies with the actual flight speed, and the maximum safe bank angle is in the region of 60° to 70°.

I expanded my answer to the original question, and I hope in combination with this I can cover your questions. If not, please keep asking!

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EDIT: I see, now you want to know the time to turn around. All I can do is calculate it under the assumption that enough lift is available, regardless of buffeting. In reality, I doubt that even the 48° case will give you a pleasant ride. All results are for the 30.000 ft case, because at 36.000 ft those higher bank angles will not be cleanly flyable due to compressibility effects.

At 60° the airplane flies with 2g, and with 25° nose down still at 1.8g. The turn rate would be 3.77°/s and 180° would be completed after 48 s.

At 70° it flies with almost 3g, and with 25° nose down at 2.65 g which is a little outside of the g limits. The turn rate would be 5.98°/s and 180° would be completed after 30 s (plus the time to roll to 70°, which now starts to become important).

The 80° case becomes really hypothetical, because even with the 25° nose down attitude the load factor will be 5.2g if flown without sideslip and enough lift to prevent overspeeding. The 747 will be close to breaking apart, but maybe a future aerobatic version can fly this maneuver safely. It will result in a turn rate of 12.35° and need 14.6 s for a 180° turn. I would add at least 4 seconds to bank to 80°, but the turn can be completed within 20 s. Hypothetically.

What Terry hinted to when he said he would bank to 80° is not the clean turns I am calculating here, but a dynamic dive where the plane accelerates because not enough lift is left to keep it from falling. To compute this, I would need more aerodynamic data on the 747 and need to employ at least a finite difference algorithm or a lot of paper and pencils.

Just that much: If the 747 is rolled to 80° but the pilot pulls only as many gs as the aircraft can sustain (due to buffeting I doubt that even 2.5 g are possible), the lift will almost exclusively serve to fly a tight turn, but not enough will be left to counteract gravity. Therefore, the aircraft will slip sideways, and directional stability will turn the nose downwards. This will take a while (I am guessing maybe 12 seconds, really a guess), but the aircraft will pick up speed from the beginning of the maneuver. I am a little more scared of flying faster than Mach 0.85 than Terry is, and the various reports of 747s going up to Mach 0.98 support his view that a little overspeeding is OK. It is hard for me to guess how much time it needs to become uncomfortably fast, and then a lot of lift will be needed to pull out of the dive. On the other hand, when the airplane is diving, all it needs is a roll and a pull-out to come out at 180° to the previous course. The pull-out will be performed at a much lower altitude, and creating the gs there will not be a problem.

Answer 2

Some information in additional to the excellent answers already given:

First, let's say the need for the emergency turn occurred just after leveling from a typical step climb of 2,000 ft, which would probably mean you had only about 1.3g buffet limit protection, although in good conditions we often went up when we had only 1.2g. Given Murphy's law, let's say we're at 1.2.

Now the need for the turn comes. For the first several seconds, we dare not exceed 1.2g lest we enter a region of possible uncontrollability. We need to lose at least a couple of thousand feet as quickly as possible to get down to where we can start asking more of the wing. At the same time we want to use what the wing can safely provide to turn us. The steeper the turn the more that will be and the faster we will fall. Both good for a very short while. My seat of the pants guess is that we would roll to whatever extreme we were comfortable with, and then almost immediately start lessening the bank at a rate and to a degree dictated by what our speed was and how fast it was increasing.

The overspeed clacker should go off around mach 0.92, although in maintenance test flights I've seen it not start until almost 0.94. At whatever point it goes off, we'd want to start reducing the bank, and we'd want to replace the lost turning force and addressing overspeed by increasing the angle of attack to what the wing could safely do buffet-wise. By the time we'd dropped, say, 4000 ft, buffet speed would no longer be a factor, and we could safely pull something like 1.8g (or higher if necessary).

It would be a matter of playing our bank and angle of attack to get what we want. In thinking through this scenario, I'm informed (or at least I think I am) by two things.

First is the incident on Dec 12, 1991 described in this NTSB report (PDF) and in this article. I was a captain at Evergreen at the time (in fact had flown that very airplane a few weeks earlier and had noticed the autopilot anomaly which was to later cause the incident), and I knew and talked to the aircrew (as did everyone at the company).

Pertinent to this discussion is the fact that the aircrew did not notice what was happening until the INS gyros tumbled (old Carousel system with actual gyros), which happened as the airplane reached 90 degrees bank as I remember. Max bank angle prior to the start of recovery was 95 degrees. Also, the engines were at cruise power until the start of recovery. There's controversy as to the max speed reached; estimates ranged from mach 0.98 to 1.09 (a mach 1.25 report was spurious). Max nose down was 35 degrees. Altitude loss was approximately 10,000 ft.

Having read the previous answers, I'm a little less comfortable with the 80 degrees scenario, but I don't think that it would mean disaster. INS platforms would still be up. Speed I feel would be manageable given that we're going to idle thrust right at the beginning, and the speed brakes would help on that. The difference, though, between using 70 degrees and 80 degrees would probably be pretty small. The pdf referenced in the first link talks about another 747 going to 71 degrees as I remember.

Second, we had a simulator exercise in which we would sometimes exceed 60 degrees of bank, although I can't say for sure that I ever went to 80 degrees. The scenario would start with departure control saying, "You have a bomb aboard timed to go off in 5 minutes. Cleared to land any runway." The sim instructor, of course, would have put you in what he felt was as difficult but still doable situation as possible. So, what you did was power off, start throwing out all the drag you could (screw the speed limitations), and roll to whatever degree of bank would start you getting lined up. The exercise always started from a relatively low altitude, so buffet speed was not an issue.

Makes me teary-eyed thinking of fun times past.

Answer 3

What is the maximum safe bank angle of a 747?

That might depend on who is making the safety assessment and what the alternatives are. There might be circumstances where a pilot might feel that being the first pilot to bank a 747 at 70° would be safer than colliding with a mountain or another aircraft, or being shot down.

The FAA collect "Statistical Data for the Boeing-747-400 Aircraft in Commercial Operations". For example:

I think the FAA discard from the data any bank angles greater than 40. My guess would be that airlines and/or pilots consider angles greater than those shown in this graph to be unsafe (at that stage of flight?)

This data seems to be related to touchdowns. Perhaps greater angles are safely used at high altitude.

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JA8119, a 747 SR-100, after an explosive decompression and loss of vertical-stabilizer seems later to have briefly survived an 80° roll without the aircraft breaking up. In the accident report is this record from the flight data recorder.

This aircraft was essentially uncontrollable, experiencing phugoid cycles and dutch rolls and tragically crashed shortly thereafter. However maybe it suggests an undamaged 747 might be able to survive quite high bank angles (assuming RLL in the report means roll-angle). As Peter Kämpf noted in a comment, it may not be safe to draw conclusions about the flight characteristics of undamaged 747s from this data.

Answer 4

Normal operation, the 747 does not exceed 25 degrees angle of bank.

Steeper banks are done generally only in the simulator and will be up to 45 degrees of bank.

If radius of turn is to be decreased, then decrease speed. Depending on weight, altitude, and temperature, this may or may not be possible. Angle of bank that can be achieved will vary with altitude. At 10,000', a 45 degree bank can be done; at 41,000 this would be unwise.

10 degrees nose down is excessive in the 747. 25 degrees nose down is ridiculous. Especially while turning.

Speed is the key to reducing radius; there's only so much bank one will be able to achieve in the 747. It's not like flying a Cessna. If a reduction in speed is necessary per the original post, to achieve a minimum radius turn, a climbing turn would be in order, rather than a descending turn.

70+ degree turns are not going to be happening in the 747.

If the desire is to turn away from a political boundary from a given heading, a 360 degree turn will not be productive.