VMO on the speed tape

[simonijs]

Good morning,

With a change in Outside (Static) Air Temperature [OAT/SAT], there will be a change in the speed of sound. For instance: 573 kts at -56,5 degrees C, 582 kts at -50 C or 566 kts at -62 C. Then the speed at which one would fly at 90 % (M0.9) of the speed of sound will vary as well with a change in temperature. For the examples above: 516 kts, 524 kts and 510 kts. These True Airspeeds [TAS] can then be converted into Calibrated/Computed Airspeeds [CAS], and I think they should vary accordingly.

In PSX, however, VMO as CAS seems to be fixed to a Flight Level. It does not change with changing temperatures. For instance at FL350: 319 kts; FL360: 311 kts; FL 370: 305 kts; FL380: 298 kts; FL390: 290,5 kts. These fixed values, converted into TAS, may then lead to Mach numbers in excess of M0.9.

One example of this:
- at FL380 - 275T - M0.837 - 493 kts TAS and -44 C --> VMO 298 kts results in M0.897
- at FL380 - 270T - M0.838 - 491 kts TAS and -47 C --> VMO 298 kts results in M0.903
- at FL380 - 265T - M0.844 - 488 kts TAS and -53 C --> VMO 298 kts results in M0.915
- at FL390 - 260T - M0.857 - 489 kts TAS and -59 C --> VMO 290 kts results in M0.927
- at FL390 - 255T - M0.862 - 488 kts TAS and -62 C --> VMO 290 kts results in M0.932

I haven't tested yet flying at or near VMO to see the PSX calculated values for TAS and Mach, maybe later today. For now, I can't see whether I am missing something in my understanding of high speed flight, and if so: what...?

The numbers for Low Speed Buffet Onset in PSX vary in accordance with changing weights, but seem to be higher than the numbers from my calculations and the ones on a KLM graph (that I will send you by separate mail, Hardy).

Kind regards,
Simon 

[Hardy Heinlin]

Hi Simon,

what do you mean by "results in"? Do you mean "should be" or "should not be"?

In PSX 10.29 I changed the CAS reference to pressure altitude because I thought it should be like that. Perhaps I should undo this modification. I tested it and it looked reasonable, but I didn't test excessive ISA deviations which I just did, and these are my results:

Load "Basic 011 - Approaching 2. step climb.situ"
On Weather > LPPD page:
Set QNH 914 hPa.
Click "To planet" and click "To zones".
On Weather > Planet page:
Set altitude of tropoause: Constantly 30000 ft
Set temperature at tropopause: Constantly -47c

Set flightdeck situation:
MCP: SPD 305 KIAS, ALT 35000
FMA: SPD | LNAV | ALT -- CMD

Check EFIS:

Result in PSX 10.28: CAS 305, Mach .885, TAS 519
Result in PSX 10.29: CAS 305, Mach .840, TAS 492

Which version agrees with your expectations?

Note that this difference just occurs due to the low QNH of 914 hPa.


Regards,

|-|ardy


P.S.:

For the speed of sound in knots I use this formula:
38.97 * sqrt( OAT + 273.2 )

In my performance/navigational model, TAS is the initial data source.
Mach is derived from TAS and speed of sound (which includes OAT parameter, see above).
ADC CAS is derived from Mach and pressure altitude (true altitude in PSX 10.28).
Standby instrument IAS is derived from CAS and Boeing's instrument error diagrams.

[Hardy Heinlin]

Maybe we're talking about two different things ...

[In PSX, CAS] ... does not change with changing temperatures.

Yes, it does change (in all PSX versions). Where on the Instructor screen do you change the temperatures?

When I'm at high altitudes and change the tropopause temperature, the CAS clearly changes.

When I'm at low altitudes and change the surface temperature, the CAS clearly changes as well. When you edit the inch or hPa box, the change happens promptly. When you edit the METAR text box, the change is slow and gradual. This is intentional because METAR updates need to be applied smoothly. Are you aware of this?


Regards,

|-|ardy


This is what I get in PSX; example:

270 tons, FL380, 1013 hPa at MSL:

SAT = -80c  --->  CAS = 290, Mach = .900, TAS = 488, speed of sound = 542
SAT = -25c  --->  CAS = 290, Mach = .900, TAS = 553, speed of sound = 614

If you maintain your CAS, your TAS changes with the SAT.
If you maintain your TAS, your CAS changes with the SAT.

[simonijs]

what do you mean by "results in"?

In the first line, FL380 at -44 C and a TAS of 493 kts, the CAS at that speed read 267 kts on the PFD. This CAS is well below the VMO of 298 kts. If I then translate this 298 CAS into TAS, this TAS = 529 kts, which can now be calculated as a Mach number. At this relatively high temperature, M0.897 is just fine.

In the last line, FL390 at -62 C and a TAS of 488 kts, the CAS read ± 270 kts on the PFD. Also well below VMO of 290 kts. A CAS of 290 kts then translates into a TAS of ± 527 kts and ± M0.932. Here, a TAS of 509,6 kts would have resulted in M0.9 and in a CAS of 279 kts. That is...: if my formulas are correct.

In the first three lines, all at FL380, the temperature decreases gradually. In accordance with this, there is a small increase in the current Mach-number (even though with decreasing weights the TAS is also slightly decreasing). My concern is, that the VMO as a number (298 kts at FL380 or 290 kts at FL390) is not changing.

SAT = -80c  --->  CAS = 290, Mach = .900, TAS = 488, speed of sound = 542
SAT = -25c  --->  CAS = 290, Mach = .900, TAS = 553, speed of sound = 614

I am getting the same results within 1 kt.

Result in PSX 10.28: CAS 305, Mach .885, TAS 519
Result in PSX 10.29: CAS 305, Mach .840, TAS 492

Which version agrees with your expectations?

The first result matches my Excel-numbers. I am using two different formulas to go from TAS to CAS. They both calculate with P0 (101325 Pa). I therefore cannot see why 913 hPa is important here.

When I'm at high altitudes and change the tropopause temperature, the CAS clearly changes.

I just changed the tropopauze temperature "in flight": indeed CAS changes. But not the number for VMO, it remains as it is.

Kind regard,
Simon (away from my computer for the next six days)

[John H Watson]

I just changed the trotropopause temperature "in flight": indeed CAS changes. But not the number for VMO, it remains as it is.

Perhaps my books are oversimplifying things, but they simply show that, above a certain altitude, Vmo (365kts) changes to Mmo (0.92). These numbers only change if the Gear Down Dispatch or 5th Carriage switches are selected.

[Hardy Heinlin]

So the actual subject of this discussion is not the TAS/Mach/CAS math of the flight model (which is correct) but the theory of the FMC's VMO computation.

I can confirm that in PSX the FMC uses fixed numbers as documented in some books.

5th engine carriage mode:
330 kt or M0.85, whichever is lower on the tape.

Normal mode:
365 kt or M0.92, whichever is lower on the tape.

When we're maintaining our command Mach while the speed of sound decreases due to a non-ISA temperature drop (higher air density), the TAS and EAS will decrease as well. This protects the aircraft structure automatically; we need not lower our command Mach. The EAS is the relevant speed to keep the aircraft within its structural limits. (The EAS is also used in the computation of the elevator feel force.)

365 is also a fixed reference number in the VNAV system. The FMC applies two limit modes:
349 (365 minus 16 for ECON speed)
354 (365 minus 11 for non-ECON speed)
The main limit in VNAV is M.892, so the Mach number again takes the decreasing or increasing speed of sound into account automatically. When the CAS at M.892 exceeds 349 (or 354), the CAS will be limited accordingly, and the Mach number will drop as well because the CAS limit is reached first.


Regards,

|-|ardy

[simonijs]

Hi Hardy,

I must apologize for my first post in this thread, which may have stirred up things. But for the high speed buffet onset value, expressed as a CAS number, PSX is modelled correctly indeed. Here is why I messed up:

In my Excel-sheet, I was using two different formulas to convert TAS into CAS, assuming they would both produce similar results (as they did with ISA conditions). One formula was used to calculate current CAS from current TAS, temperature and Mach-number, the second one was used to calculate the M0.9 number for CAS (from the value for TAS at M0.9). Based on this second one, I concluded that VMO (shown on the speed tape where the red blocks start) should increase or decrease with temperature changes. I was assuming that a change in TAS would also result in a change in CAS. Hence, my forum post. Wrong assumption, because not at a fixed Mach-number.

After some forum discussion, I started using the first formula as well to check calculated speeds at M0.9. In this way, a discrepancy showed up between the results of the first formula and the second one. Using the first formula, CAS at MMO remained a fixed number; using the second one, CAS would change with temperature.

The problem with the incorrect results from the second formula turned out to be the usage of ISA values for pressure and density at a specific flight level. But with temperatures deviating from ISA, so will density (ρ=P/RT). Using a temperature dependant density, both formulas now produce the same result: CAS at M0.9 remains fixed as temperature - and hence TAS for M0.9 - change. The dynamic pressure remains the same. Therefore, PSX is modelled correctly for the presentation of the high speed buffet onset CAS number. I am sorry to have created significant buffet onset here myself.

Humble regards,
Simon

[Hardy Heinlin]

No problem, Simon. Thank you for the clarification :-)


Cheers,

|-|ardy