Question about OPT and MAX Alt

[tango4]

Good Morning,


I just observed a strange behavior and wanted to know if this was something to be expected or not.


Load a situ with an aircraft ready for departure, if possible with a low weight so it is even more obvious, for example the default Hofu Tokyo.
Go to VNAV CRZ page and observe OPT and MAX alt. In the Hofu Tokyo situ, you have CRZ ALT 390, OPT425 MAX450.
Now, change your CRZ ALT to FL300. OPT goes to 397, and MAX to 402.
I would have expected these values not to depend on CRZ ALT.


Am I missing something ?


Charles

[Hardy Heinlin]

Hi Charles,

planned Mach number is a function of planned altitude.

Planned altitude is CRZ ALT in ACT CLB, or current aircraft altitude in ACT CRZ.

MAX ALT is a function of planned Mach number.

The calculation of the planned Mach number at MAX ALT is slightly simplified in PSX (don't know if it's simplified in the real FMC as well); it uses the planned Mach number at the planned altitude, not at the MAX ALT, because at that point in the algorithm it doesn't know yet where the MAX ALT is (it needs a Mach number for this, and the Mach number at MAX ALT cannot be calculated yet as the MAX ALT calculation depends on the Mach number at MAX ALT):

The planned Mach number for MAX ALT depends on speed mode (ECON, LRC etc.).
Speed mode requires a reference altitude.
Reference altitude needs to be determined.
Speed is gross weight dependent.
Gross weight progress is fuel flow dependent.
Fuel flow is altitude and speed dependent.

Therefore:

Planned Mach number is a function of planned altitude.

Planned altitude is CRZ ALT in ACT CLB, or current aircraft altitude in ACT CRZ.

MAX ALT is a function of planned Mach number.


Optimum altitude remains at 425 in your example, but will not exceed MAX ALT - 5.

The above (simplified) effect can only occur before the CRZ phase activates as during ACT CLB the current aircraft altitude is not used for this.

To get more precision, I would have to extrapolate a climb profile in small segments (gross weight progress, climb rate etc.) and check at which point the resultant Mach number approaches the respective data point etc. pp.

You see the dilemma? When I go higher, Mach increases. When Mach increases, I can go higher. So I need a pre-determined fixed Mach to see how high I can go. For this purpose PSX uses the Mach number at the current aircraft altitude (or current CRZ ALT when that is not reached yet).


Regards,

|-|ardy

[Will]

That's a good explanation, Hardy.

[tango4]

Thanks for taking the time to give such a complete explanation. Once more a very interesting glimpse in the difficulties you must have faced many times while developing this software.


Just for a bit of context, the reason I asked is that I happened to be fiddling with cruise level on the ground while testing something totally unrelated. I initially had a flight plan with a CRZ ALT of 390, as computed by PFPX for that flight plan. Then, I edited the CRZ level for my tests without paying attention to OPT and MAX. And after a few minutes I went back to VNAV CRZ page and saw MAX 360 and thought holy cr** there must be something wrong with my PFPX profile. Only after a while did I realize it was me changing CRZ ALT that had modified this value.


Good night !


Charles

[Britjet]

I hear everything that you say Hardy, but changing the planned cruise altitude shouldn't change the predicted envelope for OPT and MAX ALT, surely?
MAX ALT is just a straightforward graph interpolation (it is available in the performance graphs in FCOM) which can be done on the ground. The only two factors are weight and required CRZ speed.
OPT ALT is more complicated of course because it depends on selected CRZ speed, CI, wind, LRC or whatever, but I don't think that just changing the CRZ speed on the ground or in flight should have an effect?
I am in a sim tomorrow and it will be easy to see what happens..
Peter

[Hardy Heinlin]

The only two factors are weight and required CRZ speed.

Peter, I know that the above effect is absurd and I wish I could get rid of it, but the big question is:

What is the definition of "required CRZ speed"?

It cannot be the required CRZ speed at MAX ALT because we have no MAX ALT yet. We first need the chicken which lays its own egg. And that egg is what we need first.


|-|ardy


As I wrote further above, a more precise solution would be this: On an altitude graph calculate a Mach and grossweight progress curve for a given cost index, or a given LRC or SEL, E/O, MCP SPD. And then search for the crossing point of that curve and the database MAX ALT curve.

[Britjet]

Let me have a play tomorrow - I have one of our very own forum members flying the sim so PSX will be mentioned quite a bit, I'm sure!
Will try to give some figures for comparison..
Peter

[Britjet]

Just had a short tryout on a GE Sim.
Anoyingly I left my hastily-scrawled notes in the sim, so figures from memory, but..
On the ground pre-departure. TOW 346T ISA. Cost Index in the FMC 350. Selected cruise level FL 310.
Econ speed at FL 310 .866Mach.

This gave an OPT OF (about)  FL 324 and MAX ALT (about) FL349.
Then reselected CRUISE alt to be at FL 290. - NO CHANGE TO THE OPT OR MAX ALTS.

Tried it again with a fixed cruise Mach of .80 at FL 310.
The new OPT and MAX ALTs were now lower, as would be expected (can't remember the values, I'm afraid)
Then reselected CRUISE alt to be at FL 290  - NO CHANGE TO THE OPT OR MAX ALTS.

I hope this helps..
Peter

[tango4]

Many thanks for chiming in and taking the time to look into this matter, Peter.
As always, your knowledge and helpfulness are much appreciated.


Charles

[Hardy Heinlin]

Thank you, Peter, for the confirmation.

I just figured out I can increase improve the MAX ALT resolution to ca. 78 ft by only 8 search iterations in the range between FL251 and FL451; starting in the middle at FL351, each iteration will halve the range (10000, 5000, 2500, 1250, 625, 313, 156, 78 ft). In other words: not a big task. The FMC indicates just 3 digits anyway.


|-|ardy

[Magoo]

So to be sure I get this right, the MAX ALT displayed by the FMC is the MAX ALT based on my cost index, i.e.: if I fly with a cost index of zero, my MAX ALT will be different from a cost index of say... 250?

[Hardy Heinlin]

Yes.

MAX ALT is speed dependent.
Speed is cost index dependent.

[Magoo]

Thanks Hardy!

[Hardy Heinlin]

More precise calculation of MAX ALT (and OPT ALT) is now available in PSX 10.14:

http://aerowinx.com/board/index.php?topic=4191.0


|-|ardy