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Optimum Altitude

Started by simonijs, Mon, 2 Oct 2017 13:07

simonijs

Hello Hardy,

I have been looking for earlier threads on this subject but couldn't find any relevant to what I have seen in recent PSX-flights: a behaviour of the OPT ALT indications on VNAV page 2/3 that I could not account for, occurring on long trips. There is a steady increase of OPT ALT from the beginning of a flight onwards - consistent with a decrease in Aircraft Mass - until a point where OPT ALT seems to get stuck for a long period of time not consistent with the decrease in Aircraft Mass.

For example: On one flight I am cruising at FL370 with one final S/C to FL390 being predicted on VNAV page 2/3. FL390 is also shown on the LEGS page next to a waypoint with an ETO being ± 1H30' before the ETA (2252z) at destination.

When OPT ALT was showing FL377, however, things changed and OPT ALT started to indicate 376, 377, 376, 377 and so on, until a point where it finally became 378. Then it fluctuated 378, 377, 378 for another (long) period of time, eventually reaching FL379. But that's it. And definitely not consistent with the decrease in aircraft mass (see below).
Simultaneously, the estimated time for the next S/C started to fluctuate as well (i.e.: initially it indicated S/C at 2125z, later on it became 2152z, 2204z and finally NONE).

With the OPT ALT being FL377 for the first time, in this flight the aircraft mass was 258.4T (in KGS, at sim time 2047z), and still showing FL377 at a mass of 250.4T (at 2143z). At 65NM from T/D (at time 2222z), the OPT ALT indication was FL378 with a mass of 245.0T.
Since the aircraft (PH-BFY model) was remaining at FL370 with decreasing aircraft masses, ECON TAS and Mach-number became lower than would have been the case at FL390 and hence also the GS. In this particular case, temperatures were ± ISA+15° (which further lowered Mach-numbers).

I have been using data from the PSX Flight Data Recorder for several months now, and for recent PSX-flights it was used to take samples of the data whenever the OPT ALT changed numbers. These data are available in Excel documents that I can send by e-mail if you would like to take a look.

Kind regards,
Simon

Hardy Heinlin

Hello Simon,

in PSX the OPT ALT is -- in the first stage -- a function of the maneuver margin and the minimum rate of climb in CRZ or CLB set in the FMC's performance factors, and the current gross weight.

Since PSX 10.1.1-beta1 there is a second stage that limits the optimum altitude at 3500 ft below the current maximum altitude (and also limits it at the minimum cruise time performance factor).

Do you think that the maximum and optimum altitude curves should eventually coincide at very low gross weights? The logical problem here is that the maximum altitude is Mach dependent, and the optimum altitude is not. Yet, it would look bizarr if the optimum altitude indication was higher than the maximum altitude indication.


Regards,

|-|ardy



simonijs

Hi Hardy,

In my observations, the PSX OPT ALT indeed always was ± 3500 ft lower than MAX ALT (VNAV page 2/3). A picture in my KLM AOM showing VNAV page 2/3, however, only shows 1900 ft difference between MAX (376) and OPT (358) altitude (and same picture in the current FCOM) ... I haven't thought (yet) about coinciding curves but for now I do not think that the curves should coincide, whether at high or low gross aircraft masses.

What I noticed - and tried to describe - is that under "normal circumstances" the OPT ALT should go up as fuel is burned. PSX does so nicely until a point where - in the mentioned flight - 13,4 tons of fuel were consumed and the OPT ALT only increased from FL377 to FL378. That is not a normal condition, since in earlier stages of this particular (and other flights) the OPT ALT would go up one step for roughly every 1000 kgs of fuel burn.

From my notes on Aircraft Performance and Economy Cruise systems in modern Jet Transport: Optimum altitude is a function of gross weight only.
From my KLM AOM Volume I: "Optimum Altitude is based on the selected cruise mode and the flightplan distance. For economy cruise, this altitude is related to gross weight and cost index only."
Maximum Altitude is described in the AOM as: "the highest altitude to which the aircraft can climb for the corresponding weight, speed limit, Center of Gravity and rate of climb criteria.
The altitude is limited by:
- 1.3g load factor limited altitude based on mach .86 and default or manual entered Center of Gravity.
- Rate of climb of 300 fpm, available at the planned climb speed and maximum climb thrust.
- Rate of climb of 100 fpm, available at planned cruise speed and maximum cruise thrust.
The varying factor in the maximum altitude calculation is the Center of Gravity (CG) as a result of the
decreasing fuelload during cruise flight."

Based on these texts, I doubt if OPT ALT and MAX ALT do have a direct relationship on the real aircraft.

Kind regards,
Simon

Hardy Heinlin

OK, I'll try to reduce the 3500 limit in the next update.

The performance factors are, of course, airline specific as set on the PERF FACTORS page. I'm not sure how the word "only" is to be interpreted in your text. I think I got my source from Bulfer or Honeywell (or Boeing? I can't remember).


Regards,

|-|ardy

simonijs

Hi Hardy,

I don't think a revision of this 3500 ft is required, solely based on a picture in a manual. So maybe just wait with that.

The word "only" was used to clarify the following (but it seems that I am not clarifying my point at all  ;) ):

- approximately every 7-8 minutes, the OPT ALT increases by one bit (say: 325 becomes 326), for a large portion of the flight
- approximately every 7-8 minutes, the aircraft Mass is reduced by ± 1000 kgs, for a large portion of the flight (heavy: by some 1350 kgs; lighter: by some 1100 kgs); hence, OPT ALT can go up because it is based on weight/mass only
- all of a sudden, it takes 1H35' and 13,4 tons of burned fuel for the OPT ALT to go up one step, from FL377 to FL 378; that is a significant deviation from earlier stages of the flight
- At the same time, a predicted step climb to the next higher level (FL 390 in this case) is cancelled, because it never gets to the OPT ALT where such a S/C can be performed

And I think this is not correct. I have looked into this for nearly two weeks, analyzing data from the PSX FDR and trying to be thorough in my findings before writing the first post.

So what I am saying is, that I think that the PSX presentation of OPT ALT (and not MAX ALT) may not be modelled as it is in the real aircraft.

Regards,
Simon

Hardy Heinlin

This part was clear to me, Simon. Thank you.

I meant the word "only" in that other part:

Quote from: Simonijs on Mon,  2 Oct 2017 16:18
From my notes on Aircraft Performance and Economy Cruise systems in modern Jet Transport: Optimum altitude is a function of gross weight only.
From my KLM AOM Volume I: "Optimum Altitude is based on the selected cruise mode and the flightplan distance. For economy cruise, this altitude is related to gross weight and cost index only."

I think some variables on the PERF FACTORS page also influence the optimum altitude, as I wrote above. But this is just a side note re "only". Of course, the variables on the PERF FACTORS do not change during the flight. I just mentioned it to provide the complete picture. It does not affect the problem during the flight that you mentioned (I agree with you here).


Regards,

|-|ardy

simonijs

Sorry for this miscommunication:

"Only" with respect to my notes on aircraft performance: I could not find variables - other than weight/mass - that influence calculation of OPT ALT.
The second (or third) "only" was quoted from my KLM Aircraft Operations Manual [AOM] Volume I. I cannot reflect on that, I can "only" agree with this text...

It so happens, that I am tonights cook. I am picking up these duties now  ;)

Regards, and have a good night
Simon

United744

#7
I thought MAX ALT varied with weight vs. conditions, and OPT ALT was lower by some pre-determined factor, that was also based on weight vs. conditions, considering MAX ALT, but that this split was *not* constant (it could be 1000 ft, or it could be 3000 ft).

Ergo, both increase with reduced weight, with OPT varying with selected cruise Mach number, among other things.

Hardy Heinlin

Hi,

the modification is now available in PSX 10.2: http://aerowinx.com/board/index.php?topic=4191.0


Regards,

|-|ardy

United744

Great! Thank you Hardy!! :D

simonijs

Hello Hardy,

After having been away from home, computers and internet for several weeks, I finally did have time to look at modification 10.2 (on the same two routes that I did earlier). OPT ALT now increases nicely with a decrease in weight/mass. Thank you very much for this update (and the - already many - ones after 10.2).

My contact (as promised by separate e-mail) confirms that the link between OPT & MAX ALT is just weight. My "conclusion" to wrap it up: if a constant Cost Index figure (with CI = 0 resulting in MAX range) is used, then a given weight basically should result in the same OPT ALT on every single flight.

Boeing/KLM FCOM's show Long Range Cruise [LRC] tables for both the Passenger/Combi [PAX] and the Freighter aircraft, from which - for a given weight - the respective OPT & MAX ALT figures can be read. Figures for MAX ALT are given for Buffet Limit Pressure Altitude (1,3g maneuver capability) and for residual rates of climb, the latter being dependent of outside air temperatures. Buffet Limit Pressure Altitudes [PA] are more limiting than Max CLB Thrust limited PA.
For the PSX freighter PH-CKB, CI 250 (0 - 9999) seems to match LRC; for the PSX PAX PH-BFY aircraft CI 150 (0 - 9999) seems to match LRC. PSX values for LRC OPT & MAX ALT differ to some extend from these FCOM values. If you like, I can e-mail two FCOM screenshots for comparison with PSX.

QuoteDo you think that the maximum and optimum altitude curves should eventually coincide at very low gross weights? The logical problem here is that the maximum altitude is Mach dependent, and the optimum altitude is not. Yet, it would look bizarr if the optimum altitude indication was higher than the maximum altitude indication.

If we both talk about Aircraft Performance graphs: for Endurance and Range (or to obtain OPT ALT) graphs are composed of Thrust Required versus TAS. Buffet Limit (1,3g) would require CAS and/or MACH. For (Residual) Rate of Climb the graph to use would be Power versus TAS.
The Altitude figures, however, resulting from these different graphs and presented in the FCOM LRC tables, are getting closer and closer at very low gross weights: for the freighter at 200.000 kgs OPT ALT is 44200 ft, with Buffet Limit & Max climb thrust limit PA all at 45000 ft. This is where the table stops, hence very similar to 10.2.004.

Kind regards, and thanks again for this update
Simon