Takeoff climb gradient

[Will]

The situation I'm going to describe could happen anywhere, but for comparison's sake:

RJBB Runway 6R
KANSAI 1 Departure
707,300 lbs at takeoff
Flaps 20
DTO-1, assumed temperature (recommended by PFPX) was 63C.
Autopilot engaged early, at about 800 feet.

The Jeppesen chart for departure doesn't mention anything about a required climb gradient. The FMC doesn't flag any climb alerts prior to takeoff.

The problem is that there is a waypoint a few miles away from the departure end of the airport, B6R11, that needs to be crossed at or above 2500 feet. When taking off with these parameters, the aircraft starts to accelerate as planned at 1000', but this kills the climb. The climb rate goes down from about 1650 fpm to about 400 fpm, and the it becomes clear that we won't make the altitude restriction at B6R11. The FMC shows UNABLE NEXT ALT.

One solution would be to speed intervene and climb at 200 kts; that brings the climb rate back up again, but not in time to make the crossing.

You can make the crossing, though, if you can predict the future... if you know it's going to happen, you can speed intervene earlier, instead of waiting for the FMC notice.

Another way to save the situation is to not put in such a high assumed temperature. With something like 30C, the climb gradient is preserved at the crossing restriction is easily made.

My question is about the lack of warning before starting the takeoff roll. First, PFPX was pretty zealous with the 63 degree assumed temperature. PFPX seems to know about runway length and weather, but it looks like it's not able to factor in a temporarily decreased climb rate while accelerating.

But I'd feel more comfortable if the aircraft also raised an alert, because it looks like you can't tell you're in this situation until it's too late to miss the crossing restriction. One way would be for the FMC to know that the climb would shallow out and display UNABLE NEXT ALT before takeoff. A different way would be for the FMC to predict that it won't make the crossing restriction and then slow down the acceleration until the altitude is going to be met, speed intervening on its own a little bit, to preserve the required climb rate to make the restriction.

Any thoughts?

In real life, how would you avoid this before falling into the trap?

[DougSnow]

The FMC doesnt know squat about any required climb gradient.  The FMC doesnt know about obstacles, required obstacle splay (ICAO or FAA).

It depends on the reason for the gradient requirement - if they are labeled as (ATC) then ATC can waive those as they are for airspace issues.

If the gradient is for terrain, ATC cant waive that.  At my airline we have a performance tool that will permit the crew to calculate their all-engine climb gradient (as well as E/O) to see if they can clear the charted gradients.

If you're concerned about meeting a gradient, plan a TO non ATM or derate takeoff or tell ATC "UNABLE" such as "UNABLE the 2500 ft restriction", that word works wonders.  All PFPX/TOPCAT is doing is getting you off the ground (like every other performance tool); once you're airborne you gotta do some of that pilot crap.  Sometimes they'll publish on the (Jepp) chart the required vert speed to meet a restriction, but the Japanese didnt do that here...

[Will]

Since there isn't a published climb gradient, I think that means that the "standard" IFR climb gradient of 200 ft/NM applies. Let's say the climb speed is 210 knots. We get, in a no-wind situation:

210 nm/hr * 1 hr/60 min = 3.5 nm/min, and 3.5 nm/min * 200 ft/min = 700 ft/min to climb safely.

In sum, no wind, at 210 kts, 700 fpm is needed.

But the FMC directs the aircraft to prioritize acceleration, and as it accelerates, the climb rate falls below what is needed for standard IFR performance.

This is what I'm asking; should the FMC recognize this and warn the crew? Or should the FMC recognize this and maintain 200 ft/nm by accelerating more slowly?

One would think the FMC wouldn't let the climb performance degrade below 200 ft/nm.

[Hardy Heinlin]

Two thoughts:

1) If "UNABLE NEXT ALT" could also refer to any constraint after the next constraint, the alert function should include a pointer to the referred constraint, e.g. "UNABLE 3000" or "UNABLE ENSUING ALT" or "UNABLE 5TH ALT" or whatever. But the message always reads "UNABLE NEXT ALT", so it must be the next and not any ensuing constraint.

2) As far as I know, VNAV SPD in climb will only go below the command speed when it's unable to maintain altitude. When that happens, it will go down to stick shaker speed and then allow a descent. Imagine you were climbing at your command speed of, say, 240, with good thrust, and suddenly your performance decreases from 2000 fpm to 300 fpm: If VNAV SPD would now focus on a higher climb rate, it would have to go below 240 KIAS. I can't imagine the FMC would do this. It may do this during descent, but not during climb -- as far as I know.


|-|ardy

[Will]

Just so we're talking about the same thing... if the aircraft held V2+10, it would make the crossing restriction.

The problem is that at the acceleration height, the nose lowers, and the FMC prioritizes acceleration over rate of climb, and thus the rate of climb falls briefly below the IFR standard of 200 ft/NM. The UNABLE NEXT ALT appears after the aircraft begins the acceleration at 1000', some seconds after the FMC has had a chance to realize that it won't make the restriction. By then, it's too late to save the situation. And there's no warning on the ground that this will happen.

If I were a Boeing employee and in charge of the FMC, I'd protect the 200 ft/nm climb (*not* factoring in wind, for simplicity's sake) and command the aircraft to accelerate more slowly if the 200 ft/nm is going to be breached. This should be simple, as the 200 ft/nm constraint is converts linearly to a ft/min climb rate based on airspeed.

[Will]

Another way to say the same thing is that at the acceleration height, the command speed jumps up to the next flap setting's maneuvering speed, which is of course above the speed where the aircraft is currently flying. So the aircraft pitches to increase speed.

Unfortunately, that pitch can result in a climb that is shallower than the IFR standard of 200 ft/nm.

If the FMC pitched less aggressively for speed, the climb could be protected.

[Will]

One last thought is that this doesn't have to do necessarily with a crossing restriction. Let's say there were no intermediate crossing restrictions, but there was a mountain in front of the aircraft. The "UNABLE NEXT ALT" would never appear, because there's no constraint, and yet the aircraft could still violate terrain clearance requirements if the FMC commands a shallow climb during acceleration.

[Hardy Heinlin]

For terrain look-ahead warnings you have the EGPWS :-)

My thought #2 refers to the logic of the target airspeed; when your target airspeed is captured and your climb rate has been fine, would your VNAV SPD design go below target airspeed when your climb rate decreases? Or would it only do this during airspeed acceleration? When necessary, just stop the airspeed acceleration, and never go below the current airspeed? E.g. when you have reached V2+30, don't reduce to V2+10, just maintain V2+30 (stop the acceleration). Is that your idea? I guess this will be tricky in turbulence. A minor positive windshear may put you 20 knots higher, and thereafter you would get the same poor climb rate because VNAV SPD would maintain that higher speed you've got after the shear. That's why I mentioned my thought #2 (may VNAV SPD also reduce the airspeed?).

[Will]

I'm talking about a situation where the initial pre-1000' climb speed has been captured, THEN, passing the acceleration height (1000'), there is a new target airspeed, which is not yet captured because it's much faster than the aircraft is currently going. Since we're already at target thrust, the aircraft has no choice but to pitch down to accelerate.

When the noes goes down, so does the rate of climb. The whole situation balances out once the new target speed is captured; when that happens, the nose comes up again to maintain the speed and thus the climb rate increases again, too.

For me, it would make sense to put a floor underneath the rate of climb during acceleration, so that the pitch for the acceleration doesn't result in a climb rate that's lower than the IFR standard gradient. The aircraft has the capacity to do this, as you can see by just hand-flying the departure. If you hand-fly it, you can accelerate more gently, and maintain 800 fpm climb throughout. But the autopilot wants to accelerate briskly, so the nose goes down, and the rate of climb decays to 400 fpm, leading to a situation in which the aircraft doesn't comply with the minimum IFM climb gradient.

So I'd limit the pitch during the acceleration, to protect a climb rate of 200 ft/nm as a minimum.

[Hardy Heinlin]

Yes, understood. My question is just this: When the climb rate suddenly drops below 800 fpm due to turbulence or thrust problem, would your design allow a mode change from airspeed acceleration to airspeed deceleration? Or would it just stop the current acceleration?

[dhob]

This requires a lengthy discussion, starting with takeoff performance.

There are several weights that must be considered for takeoff performance, Field Limit Weight, Climb Limit Weight, Obstacle Limit Weight, Tire speed Limit weight, and Brake Energy Limit weight. Field Limit Weight is a function of the maximum weight allowed for the runway length available, considering all engine accelerate-go, one engine inoperative accelerate-go, or one engine inoperative accelerate-stop. As such, this is what typically determines V-Speeds etc. If excess runway is available, takeoff thrust may reduced up to 25% off the rated thrust (TO, TO1, TO2). If excess runway is still available, then the V-Speeds may be unbalanced, either toward V1 min or V1 max.

Climb Limit Weight is the maximum weight at which, with one engine inoperative, meets all specified minimum climb gradients. In particular, it must meet the second segment climb gradient, which for a four engine airplane is 3.0%.

The Obstacle Limit Weight is the maximum weight at which the airplane clears all obstacles in the departure path, using gross and net clearance heights through the end of fourth segment climb (usually the higher of 1500' or Obstacle Clearance Height).

As such, takeoff performance does not consider required SID climb gradients, crossing restrictions, nor does it consider Noise Abatement Departure Procedures 1 or 2. However, since the engine inoperative second segment climb gradient must be at least 3%, one can assume the all engine climb gradient is easily in excess of 3.3% (200'/nm).

The standard SID climb gradient is 200'/nm, which is the same for TERPS Missed approach procedures (2.5% for ICAO MAP). A common misconception is the gradient must be maintained at all times, which isn't actually the case. The required climb gradient is a linear line drawn from the departure end of the runway, which maintains a slope of 200'/nm. The airplane only needs to stay above the line. During the initial climb to 1000' AFE, the airplane climb rate is high, and the airplane will be well above the line. Thus when VNAV commands the acceleration to UP + 20, the airplane easily stays above the required climb gradient line.

Again, nothing accounts for crossing restrictions however. The UNABLE NEXT ALTITUDE is only displayed for the next active altitude restriction. Until B6R11 becomes the active waypoint, the UNABLE NEXT ALTITUDE message will not display.

However, there is a technique to verify if the airplane will make the restriction. Enter 2500 on the fix page at 6R. This will display a green circle along the magenta line were the FMC calculates the airplane reaching 2500', it will either be prior to (which indicates meeting the crossing restriction) or after the waypoint. If the green circle is after the waypoint, then there are several steps to take to help meet the restriction. With a thrust setting of TO1, ATM 63C, then CLB 1 or CLB 2 is likely armed. Select CLB on the THRUST LIM page to arm full climb thrust, then look at the green circle, it will move, hopefully prior to the waypoint. If the green circle is still beyond the waypoint, then enter Flaps 1 speed and 2500' on the climb page at 4L (which is normally ---/-----). For example, if Flaps 1 speed is 210, then enter 210/2500 at 4L and execute. Now the green circle will be prior to B6R11.

Another good example is the Sunshine 4 Departure in KONT. The departure requires POM at 8000B, then NLAND at or above 14000. When heavy weight departing 26L/, the NLAND restriction will likely not be made unless the above technique is used. Further, it will not display UNABLE NEXT ALTITUDE until POM is sequenced.

[Will]

My question is just this: When the climb rate suddenly drops below 800 fpm due to turbulence or thrust problem, would your design allow a mode change from airspeed acceleration to airspeed deceleration? Or would it just stop the current acceleration?

I would try to protect acceleration, and to protect the 200 ft/nm gradient.

So I would not allow a mode that switched deliberately to deceleration, although gusts and turbulence can wobble the speed around. And I wouldn't move nose lower than the pitch for the 200 ft/nm gradient, but there can be turbulence here making bumps as well.

My fantasy logic would be to slow the acceleration to protect the climb, and in the extreme case, that would be holding the airspeed steady (delaying the actual acceleration, if needed), to keep the climb gradient above the minimum. The advantage here is that the flight path would be safe. The aircraft may not accelerate, because it's putting all of its energy into the climb, but that's safer than a below-gradient climb that may hit a very tall antenna or the Burj Khalifa.

Thus, I think this is safer. Of course, the crew would notice that the aircraft isn't accelerating. They could then decide to add thrust, or not, but along the way the minimum climb gradient would be preserved.

And, since this is my fantasy logic here, if acceleration was not possible and the minimum standard IFR climb gradient couldn't be protected, I'd have an EICAS alert called >UNABLE CLIMB. But the extreme end of the situation should be caught on the ground before departure.

[Britjet]

The green circle is one way of doing it - although I confess I've never tried it. It occurs to me that ATC turns etc might make this unreliable at the pre-take-off stage. I'm thinking of things like the easterly turn to the south of LAX on a westbound departure..
IMHO the best way of mitigating would be to set full CLB as discussed, with an ACCEL height of 3000 or so, and thrust reduction of 1500 or so.  Then when the aircraft starts to accelerate at 3000ft, only retract the flap to 5, and intervene at that speed. If you are still low then ask for relief from ATC - it's quite often only a light aircraft corridor below anyway..
You would have to do that anyway if you had an engine failure.
Peter

[Will]

I have an idea... I was thinking before that the FMC shouldn't command a pitch, while climbing, that results in a vertical speed below the no-wind VS needed for a standard IFR climb gradient (of 200 ft/nm). In my mind, I was picturing some kind of formula that constantly adjusted the minimum rate of climb as the aircraft accelerated.

But that seems like a lot of work.

It would be much simpler to just never command a pitch that would result in a vertical speed that doesn't provide standard clearance at the magenta command speed.

More lengthy explanation with an example: your command speed starts out at V2+10, or 165 kts in the case described above. Minimum vertical speed for a standard IFR climb would be 550 fpm. Then, at 1000 feet, the magenta command speed jumps to the flaps 10 maneuvering speed of 225 kts. Now, the minimum vertical speed for a standard IFR climb would be 750 fpm.

The FMC minimum vertical speed needn't be a moving target, because as long as 750 fpm was the minimum, you'd be protected throughout the entire acceleration from 165 kts to 225 kts. One calculation!

Again, the reason this is helpful is that the crew otherwise can't know before takeoff that the FMC is going to command a climb profile that will go below 200' per NM.

Bonus: what if the FMC can't protect the minimum vertical speed? That's when my (invented) ">UNABLE CLIMB" message would kick in. But of course that's fantasy-land, since the real FMC doesn't do this. (Right?)

So my full fantasy-land plan would be for the FMC to calculate the minimum VS needed for 200 ft/nm, pitch the aircraft to maintain at least that climb rate, and if, as a result, the airspeed stops accelerating or begins to decelerate, display >UNABLE CLIMB and pitch to maintain acceleration.

[Will]

So my full fantasy-land plan would be for the FMC to calculate the minimum VS needed for 200 ft/nm, pitch the aircraft to maintain at least that climb rate, and if, as a result, the airspeed stops accelerating or begins to decelerate, display >UNABLE CLIMB and pitch to maintain acceleration.

In the absence of my full fantasy-land plan, I'd just have the FMC command a pitch that preserves 200 ft/min at the magenta command speed, unless it can't.

:-)

[Hardy Heinlin]

I think this principle is more or less implied already. The complicated part of it is the super-fine adjusted work of the control loop that has to balance all parameters within 0.001% tolerance. A little drop here and you'll get a big drop there. And all this is running during airspeed acceleration; that is, not during a stable flight phase. On a 3° ILS path your airspeed is stable and so the 3° tangent in the triangle is stable as well. However, on a 3° to 5° climb path during airspeed acceleration the tangent fluctuates a lot. A fraction of a degree more or less causes a giant altitude difference at the target fix. The idea itself looks clean, but in practise in the real air there's always a tiny random fluctuation that amplifies itself through the tangent function, and it takes several seconds until the control loop can fully compensate for it.


|-|

[dhob]

This isn't how the airplane works. VNAV pitches over to accelerate at the all engine accel height, with no regard for a required minimum VVI residual climb. Again, the airplane out climbs the required 200 ft/nm SID climb gradient from lift off to the acceleration height. All that matters is the airplane stays above the linear obstacle clearance plane of 3.3%.

[G-CIVA]

The green circle is one way of doing it - although I confess I've never tried it. It occurs to me that ATC turns etc might make this unreliable at the pre-take-off stage. I'm thinking of things like the easterly turn to the south of LAX on a westbound departure..
IMHO the best way of mitigating would be to set full CLB as discussed, with an ACCEL height of 3000 or so, and thrust reduction of 1500 or so.  Then when the aircraft starts to accelerate at 3000ft, only retract the flap to 5, and intervene at that speed. If you are still low then ask for relief from ATC - it's quite often only a light aircraft corridor below anyway..
You would have to do that anyway if you had an engine failure.
Peter

Hooray for simplicity .... this is a tactical phase of flight SPD INTV on the MCP .... minimise on the 'heads down looking at the box' & keep a good look out ... simplicity wins.

[simonijs]

The Jeppesen chart for departure doesn't mention anything about a required climb gradient. The FMC doesn't flag any climb alerts prior to takeoff.

I am using LIDO charts. In the Departure notes (that should be somewhere in Jeppesen section 10.9, if I remember correctly), it says: MAX IAS 200KT at or below 3000 ft within CTR (APRX 5NM around ARP). Now that should probably get one above 2500 ft in time...

Regards,
Simon

[Will]

Another way out of the trap is for the pilots to just memorize some easy benchmarks, namely that 200 kts needs 650 fpm; 250 kts needs 850 fpm; 300 kts needs 1000 fpm, and then just monitor the vertical speed on the climbout.

Real-world pilots and instructors, can you tell me what you would do in this situation? You're heavy, so when the aircraft pitches down to accelerate, the vertical speed is dropping (and would drop to 400 fpm if you didn't do anything about it). I found that changing the climb mode to V/S and dialing in 1000 fpm saves the situation; the aircraft makes the altitude restriction, and continues to accelerate smoothly to the command speed. It's just a more gentle acceleration. Then I selected VNAV again once the crossing restriction was passed. It all worked fine.

I understand (and agree with!) the idea of managing this differently, like selecting a different derate for the takeoff. But assume you saw this situation developing, would anyone use V/S here? Or would you delay the acceleration with a speed intervention? Or add thrust by cancelling the derate? Or just hit Ctrl-Alt-Del and try again? :-)