Winds/Temps Aloft Discrepancy

[Chris Kilroy]

Hi Hardy,

I was doing a bit of island hopping today (Honolulu-Majuro-Kosrae) and ran into the pictured discrepancy. As you can see, the winds aren't too far off, but the temperatures aloft aren't close. This happened on both legs. I'm using PSX's built-in weather and (as far as I know) there's nothing else injecting anything as I don't believe Mark's P3D externalsim does anything of the sort.

The FMC didn't seem to know what to do with this scenario, so it dialed ECON CRZ speed back to about 2 knots above the lower yellow tape (~.79m). Easy enough to correct that with a manual entry, but just curious whether I've set something up incorrectly in the weather engine or what.

Any advice?

Thanks!
Chris

[Hardy Heinlin]

Hi Chris,

are you referring to the TAT indication on the EICAS?


Regards,

|-|ardy

[Chris Kilroy]

Hi Hardy,

Yes. I know that TAT reads higher than SAT, but that seemed extreme. I'll check the SAT in the CDU on my next flight.

Thanks!

[Hardy Heinlin]

Everything looks perfectly realistic on your photo.

Current sensed/computed wind on the ND is 142° true north at 37 kt (135° magnetic). FMC wind page refers to true north. 169°/36kt at STEFF. Although you're 65 nm from STEFF, the forecast wind direction differs by only 27°, and the wind speed by just 1 kt. Very good.

I don't know your gross weight. I guess you are at Mach .88. If that is too close to the minimum maneuver speed, you're simply too heavy for FL380. You need to descend.

Also, you're close to the equator and so the OAT is very high. When you're keeping your IAS constant while the OAT rises, the Mach number will decrease because the speed of sound is faster in hot air (lower air density) than it is in cold air. As you know, the Mach number is the ratio of your airspeed to the current speed of sound.

TAT is +1c, standby IAS is ca. 271 kt, standby FL is 379. I don't know the current baro pressure, but I guess your true altitude is close to 38000 ft. The forecast OAT at STEFF is -38c. These parameters all together produce a TAT of ca. +1c. Excellent.

Here you can check some formula; you will see your TAT indication is perfect:
https://en.wikipedia.org/wiki/Total_air_temperature

On Instructor > Model > Warnings under "EICAS" you may install the option "... SAT display". So you need not open the FMC PROGRESS page 2/3 to see the currently sensed SAT.


Regards,

|-|ardy

[Chris Kilroy]

Thanks again, Hardy.

ECON CRZ was actually around .79 mach for some reason. Cost index 80, FL380, and optimum was right in that ballpark on what was only a short 90 minute flight with ZFW around 560k LBs and landing with 23k lbs of gas.

I'm flying back to Majuro tomorrow so I'll re-check it then.

[Markus Vitzethum]

If I may comment on that ...

> ECON CRZ was actually around .79 mach for some reason.

I noticed that effect too, recently on Worldflight and also on some flights throughout the summer. When the OAT gets high (I'm usually using injected winds + temperature from P3D, controlled by the ActiveSky add-on) I find that the ECON CRZ speed can get "quite low", in many cases below M.80 for the CI I'm typically using (80-150).
Even for a high CI, I don't get Mach numbers beyond, say, .82 or .83.
Whenever I want to go fast e.g. M.85 I have to used the SEL SPD function on the VNAZ CRZ page to get the aircraft to this higher cruise Mach number.

For a 744 flying at around M.79 seems (just personal opinion, no facts) quite low to me - so I wonder: what is the reason for that? Is the influence of the OAT on the ECON CRZ documented somewhere? What does the real FMC box do in high OAT cases?

Thanks,
  Markus

[DougSnow]

CI80 for the 744 is too slow. So is M.79 unless you're near empty, at some altitudes and gross weights, that is well below max range cruise - and behind the power curve from the FMC Substantiation Documents - Boeing docs on all the painful math and cost index curves thats buried in the FMC. 

Aircraft with an FMC should almost never be flown in cruise slower than CI0. At work for example (I work at a big airfreight airline as an international standards dispatcher) we had dispatchers who would plan a 16 hour flight at slow constant mach to not arrive too early for ramp and download crew availability. In a recurrent training session I showed that while we managed our arrival time ok, we burned more fuel to do so because we were behind the power curve (and thus had a higher angle of attack) and underneath the CI0 curve by flying a slow constant mach. This was for a 777F but the concept applies to anything with an FMC. Plus, according to Bulfer, flying in constant mach takes the wind optimization routines in the FMC out of consideration, further impacting the fuel mileage. Our guidance at work is other than flying the North Atlantic, there is no valid reason to plan anything other than CI.

At the higher gross weights at any altitude, CI150 is a good rough ballpark number and approximates LRC for the 744. Its faster than LRC at lower weights, but approximates LRC at the higher weights for a given altitude.

[Hardy Heinlin]

Is the influence of the OAT on the ECON CRZ documented somewhere?

In PSX this OAT dependent Mach number is not a function of the ECON mode but a function of the Mach number. Mach is OAT dependent. At a certain grossweight, pressure altitude, wind, and cost index, the ECON mode in PSX keeps a certain TAS, not a certain Mach. When the OAT changes, it won't change its target TAS; only Mach will change as the speed of sound changes with the OAT. In performance tables for max range cruise and integrated range (to get the still air distance), for example, the data is based on TAS, not Mach. However, those tables contain a temperature correction factor: Increase ISA-TAS by 1 kt for each centigrade above ISA-temp. I'll have to recheck how this factor is applied in PSX (it's been a long time, I can't recall this detail off the top of my head). The cost index (CI) in PSX interpolates maximum range cruise data (CI 0), LRC data (CI 230), and high speed cruise data (CI 9999). (Data based on LH, CF6 engines). These data tables, too, have a temp correction factor; however this factor is not for speed corrections but for thrust and fuel flow corrections. And these tables refer to an IAS/Mach pair for ISA conditions. When the temp deviates from ISA, it is not clear which of the two parameters is supposed to change -- IAS or Mach? When the temp changes, the relation of IAS and Mach cannot be constant anyway. Either parameter of this pair must change. In PSX, as far as I recall at the moment, the constant parameter in this context is the airspeed (IAS, TAS), not the Mach number. So, in extreme hot weather at high altitudes it's possible that PSX's FMC lets the command Mach drop to the amber band (ECON SPD will change to LIM SPD) -- just to keep its internal performance based command IAS/TAS.


Regards,

|-|ardy


P.S.: The problem can be avoided by lowering the MAX ALT. I will soon try to make the MAX ALT calculation in PSX more precise. We'll see if this helps.

[Hardy Heinlin]

In performance tables for max range cruise and integrated range (to get the still air distance), for example, the data is based on TAS, not Mach. However, those tables contain a temperature correction factor: Increase ISA-TAS by 1 kt for each centigrade above ISA-temp. I'll have to recheck how this factor is applied in PSX.

This factor is applied in PSX (of course, when the temp rises, the ratio of TAS/IAS increases). For all kinds of airspeed relations PSX uses precise scientific formulas, so PSX is supposed to be even more precise than those linear thumb rules (which actually are sufficient because real empiric performance data are always just approximations anyway; every 744 aircraft is different).

In addition to the MAX ALT modification, I could add an OAT factor in the cost index stuff that leads to a higher TAS in warmer air. That would mean: In warmer air, at the same cost index, you will reach your destination earlier (with yet another increase in fuel consumption). -- But I won't add this factor unless someone can prove the real FMC does it.


Cheers,

|-|ardy

[simonijs]

Sorry for being late with my reply to these posts, but I really had no time available when this was "hot" a few days ago.

At a certain grossweight, pressure altitude, wind, and cost index, the ECON mode in PSX keeps a certain TAS, not a certain Mach. When the OAT changes, it won't change its target TAS; only Mach will change as the speed of sound changes with the OAT.

Flying in ECON mode, MRC or LRC assumes flying at a constant angle of attack (to be precise: a constant Coefficient of Lift and a constant ratio of Coefficient of Lift to Coefficient of Drag). If at a constant altitude, a certain weight and a constant Coefficient of Lift the temperature changes, then so will the density of the air. With all other factors in the Lift equation remaining constant (W, S, C of L), then an increase of the OAT (= a decreasing density of the air) means the velocity has to increase. So I think both TAS and Mach should change accordingly as OAT deviates from ISA.

When the temp deviates from ISA, it is not clear which of the two parameters is supposed to change -- IAS or Mach?

My "guess" would be: just Mach. IAS uses the ISA MSL value for density, so a change of OAT would not affect IAS (with all other factors being constant).

CI80 for the 744 is too slow.

Boeing used to publish AERO Magazines until late 2014, in 2007 with an article discussing just this: http://www.boeing.com/commercial/aeromagazine/articles/qtr_4_07/article_05_1.html. After downloading the article, have a look at figure 2 for typical airlines values of CI for the 747-400. It also confirms Hardy's CI figure for LRC.

In a recurrent training session I showed that while we managed our arrival time ok, we burned more fuel to do so because we were behind the power curve (and thus had a higher angle of attack) and underneath the CI0 curve by flying a slow constant mach.

Here, my "guess" would be, that the airplane was flying at Max Endurance speed (which on a Thrust-to-Speed curve would be the lowest point, occurring at minimum Drag = minimum Thrust required). This happens at the maximum ratio of Coefficient of Lift to Coefficient of Drag. Only at speeds below Max Endurance speed, one would get behind the "power" curve. Maximum Range Speed (CI=0) is well above this Max Endurance speed.
I am not sure what you mean by "behind the power curve and underneath the CI0 curve"... And do you really mean that the flight was planned at slower speeds than Max Endurance?
Flying at one altitude, both speeds decrease as weight decreases. Flying at a constant low Mach number, however, would implicate a constant low TAS (if temperatures do not change). If normally speeds decrease but in this case a constant speed was used (to obtain a constant Mach number) then the aircraft would eventually fly again at speeds above the Max Endurance speed, i.e.: away from the backside of the power curve 

Kind regards,
Simon

[Hardy Heinlin]

With all other factors in the Lift equation remaining constant (W, S, C of L), then an increase of the OAT (= a decreasing density of the air) means the velocity has to increase. So I think both TAS and Mach should change accordingly as OAT deviates from ISA.

I think so too. But there are two methods to increase the lift. Allow high altitudes and increase Mach -- or lower the MAX ALT and don't increase Mach.

Fact is that the FMC lowers the MAX ALT when Mach decreases, i.e. when the air density decreases.

So the FMC takes this effect into account already. Now the question is: Does the FMC provide a mix of solutions by lowering the MAX ALT a little (data is known) and by increasing the thrust a little (data unknown). Both factors lead to a higher Mach number.


Cheers,

|-|ardy

[simonijs]

There are two methods to increase the lift.

That puzzled me for some time, this morning. Why would Lift need to increase? In straight and level flight, weight is continuously decreasing and so is Lift. But maybe I misunderstood the context in which this was said.

While being puzzled, I entered several (scientific) formulas into an Excel sheet and had it calculate TAS, C(alibrated)AS and Total Air Temperature. Entering figures for whatever OAT, static pressure (taken from ISA) and pitot probe pressure produced results that exactly match PSX figures, taken from the FDR within PSX. They also match results, produced by the iPad/iPhone E6B app. So, our formulas obviously are correct (airspeed recovery Ct set at "1").

I entered these formulas, because I could not relate a TAS of 517 kts and -38 C (as shown on the photograph) to M0,79. Either Mach should have been ± 0,865 or TAS=472 kts. So, for a moment I thought that TAS was calculated, using the equation for incompressible flow (which produced an erroneous TAS of 510 kts..., close enough to 517 kts). Now I know: it does not, but maybe P3D is inserting "things" here...

With Excel being filled by these formulas anyway, I experimented a bit to see how things would change by inserting different values for OAT and altitude. Increasing altitude, using ISA density figures, and keeping Mach constant at 0,85 in ISA conditions: TAS (FL310 - 500 kts) decreased slowly with altitude until the tropopause, then remained constant at 487 kts. With temperatures of ISA+20 and Mach fixed at 0,84: TAS went from 514 kts at FL310 to 499 kts at FL390.
So I think speeds don't have to get as low as 472 kts/M0,79 in high OATs (as seen on some flights), but should profit from lower densities by increasing TAS. On the Thrust-vs-TAS graph I don't see how this this would increase fuel flow; it would, however, improve Fuel (lbs/kgs/N) per NM, hence Range.

Fact is that the FMC lowers the MAX ALT when Mach decreases, i.e. when the air density decreases.

FCOM tables for MAX ALT provide figures for Buffet Limit PA and for Maximum Climb Thrust limited PA, based on weight. Buffet Limit PA's are more limiting than Maximum Climb Thrust Limited PA's (Buffet Limit PA's are based on 1,3g at Mach 0,86). I need some time to think about how this all changes at lower Mach numbers. For now, I can only think of reduced climb performance with temperatures well above ISA, affecting only Max Climb Thrust Limited PA's.

Regards,
Simon

PS - My formulas were taken from "Introduction to Flight", fifth edition (McGraw-Hill, 2005), by John D. Anderson, Jr. - kind of my bible these days, with about just as many pages.





 

[Hardy Heinlin]

There are two methods to increase the lift.

That puzzled me for some time, this morning. Why would Lift need to increase? In straight and level flight, weight is continuously decreasing and so is Lift. But maybe I misunderstood the context in which this was said.

The context was the question how to keep the optimal AOA constant while the OAT is rising. (Rising OAT lowers density and lift.) Answer: Increase Machairspeed. Question: How? Answer: Descend or increase thrust.

Was that a typo? "... weight is continuously decreasing and so is Lift." You certainly meant to write decreasing weight increases lift(?)


Cheers,

|-|ardy

[skelsey]

Was that a typo? "... weight is continuously decreasing and so is Lift." You certainly meant to write decreasing weight increases lift(?)

No - in straight and level flight L = W. Therefore if W is reduced (i.e. due fuel burnoff) L must also reduce.

Likewise in a steady climb or descent, lift will always be slightly less than that in S&L as in a climb some of the weight is opposed by thrust and in a descent there is a forward component of weight aiding thrust which does not need to be balanced by the wing.

[Hardy Heinlin]

Of course, but in the context I'm thinking of, the "lift" is the lift produced at a certain AOA at a certain airspeed. Not the "lift" that is necessary to maintain the altitude.

If AOA and airspeed remain constant while just the weight decreases, the lift will increase, not decrease. So if you want to maintain altitude you need to change AOA or airspeed to lower the lift.

Sorry, in that quote I missed the words "In straight and level flight".

Back to the context, if it's not clear yet: The question is what shall we do if a rising OAT decreases the Mach number. How do we re-increase Mach? Not just increase, but re-increase after the rising OAT decreased it. I.e. "increase" is not the right word, it's rather "maintain". How do we maintain our Mach when OAT rises? We could stay at the same altitude and maintain our Mach by applying more thrust. Or maintain our Mach just by descending to thicker air which will also increase our IAS (however, the descent will also lower the Mach/IAS ratio a little).


P.S.: My own quote:

When the temp deviates from ISA, it is not clear which of the two parameters is supposed to change -- IAS or Mach?

Actually, the effect of the OAT change on the ratio of Mach to IAS is very small when the pressure altitude is constant. It's not about the pair Mach/IAS but Mach/TAS. If we maintain TAS while the OAT is rising, both IAS and Mach will decrease.

[Jeroen Hoppenbrouwers]

If AOA and airspeed remain constant while just the weight decreases, the lift will increase, not decrease.

When strictly talking terminology, lift depends only on AOA and airspeed then, not on weight. Lift remains constant, weight decreases, result is a force up, but not more lift. I don't know what to call this force. But it is not "lift".

It's the same as when you would say: reduce airspeed, there now is a resulting down force, so weight increases. Feel what I mean?


Hoppie

[simonijs]

I still have no idea how to insert images, so hopefully this dropbox link functions (it does in the preview...).

https://www.dropbox.com/s/77w9oo669veweps/Schermafdruk%202017-11-28%2013.54.18.jpg?dl=0

There are two ways to look at Drag, which has to be balanced by Thrust Required: using equation (3) or equation (4), that has been rearranged by inserting (2a) into (3).

Let's look at (3) first. Flying at one particular speed, Thrust Available (TA = position of the thrust levers) then has been set to match Thrust Required (TR). If, however, density becomes less because of temperature, so will Drag and TR in (3). If no changes are made to TA, then TA > TR. Hence, the aircraft will start to accelerate until a point where TA=TR again. And this happens at a higher True Airspeed.
NB - I am assuming that only maximum TA is heavily influenced by density, but that the set thrust (TA) is influenced by density to a much lesser degree than D although I might be wrong here...

Looking at (4), this simply tells that flying at a constant AoA (= constant Coefficient of Lift), Drag and TR will decrease as Weight decreases. Since Fuel Flow is proportional to Thrust (jet engines only), Fuel Flow will go down as well. (4) is used to compose the Drag(or Thrust)-vs-TAS graph.
To be complete: the Coefficient of Drag depends heavily on C of L. Therefore with a constant C of L, C of D will also be constant.
Just note, that density has disappeared in (4), indicating it is of no influence on Drag. This can only be explained by assuming a constant dynamic pressure in (3), i.e. a decreasing density has to be counteracted by an increasing velocity, as would then also be the case in (1) and/or (2b). 

If this all makes (some) sense, then maybe there is no need to increase thrust in order to maintain a Mach number. But maybe I am talking no(n)sense.

Now for MAX ALT...: as Skelsey wrote L=W. The load factor, however, is described as the ratio of L to W (n = L/W). Rewriting this results in: L = nW; inserting nW in (2b) would be more correct.
For 1,3g as Buffet Limit the velocity would increase by the square root of 1,3 (= 1,14). According to KLM's AOM, this Buffet Limit PA is set for M0,86. So a first thought is that margins would be better for lower Mach numbers (0,85 or 0,84 or ...), but I need to think about this more thoroughly since (2b) describes TAS, which is not what we see on the speed tape.

Kind Regards,
Simon

[Hardy Heinlin]

I feel what you feel, Hoppie. The up-vector is produced by aerodynamics, the down-vector by gravity. In this discussion about cost index and OAT, in pilot's language (not strict language), I would just focus the result and say "we gain some lift" rather than "we reduce some gravity".

If, however, density becomes less because of temperature, so will Drag and TR in (3). [...]

Looking at (4), this simply tells that flying at a constant AoA (= constant Coefficient of Lift), Drag and TR will decrease as Weight decreases.

Thanks for sharing your thoughts, Simon.

To avoid misunderstandings, I now avoid talking about lift and gravity; I just ask: What happens to the aircraft's vertical motion then? Will it move up, down, or remain constant? I say it will move down. The thinner the air, the faster the down motion. In vacuum, the down force is pure gravity.

Now the goal is to keep the vertical motion at zero while density and TR decrease.

To achieve this, the AOA needs to be increased. That in return increases the drag (exponentially). The thinner air also reduces the TA as in vacuum there is no TA at all. So the whole stuff is not linear. It's shaped in curves. The decrease of the TR is not linear either: The higher AOA increases the drag (requires more thrust again), and a fraction of the forward thrust vector is directed vertically. To keep the vertical motion at zero in vacuum, 90° AOA is required and TR just refers to vertical motion, and airspeed/Mach is 0/0 (which makes the AOA incomputable: no attack, thus no angle). I'm mentioning these extremes just to make whole picture plausible.


|-|ardy

[simonijs]

I find it quite hard to avoid thinking in terms of Lift and gravity, but I am trying to... 

As far as I know, the concept of MRC, LRC (or any other speed like Max Endurance speed) is based on a constant C of L (= constant AoA) to C of D ratio. Then, thinking in my terms (which we were to avoid now) there would be no need to increase the AoA. And with this constant C of L, nor would there be an increase in C of D. Looking at my formula (4), I would expect the TR to decrease in a linear way, as Weight is decreasing.
But this all taken from textbooks, the contents of which may have nothing to do with programming a simulation.

Perhaps you have seen this website before:

https://www.eurocontrol.int/eec/gallery/content/public/document/eec/other_document/2011/EEC-Technical-Report-110308-08.pdf

Not sure though, whether or not you (or me, the Public...) would be granted access rights for using the application, mentioned on PDF page 85 (or: document page 67). It's a nice document for today's weather. I am working my way through just to find out if if could be of any use for determining PSX MAX ALT calculations.

Regards,
Simon

[Hardy Heinlin]

As far as I know, the concept of MRC, LRC (or any other speed like Max Endurance speed) is based on a constant C of L (= constant AoA) to C of D ratio. Then, thinking in my terms (which we were to avoid now) there would be no need to increase the AoA. And with this constant C of L, nor would there be an increase in C of D. Looking at my formula (4), I would expect the TR to decrease in a linear way, as Weight is decreasing.

I agree, and this effect can be seen in PSX as well. But I think you're now talking about the effect of weight loss, not of density loss (air warmer than ISA). The original question was whether the FMC increases the ECON speed when the temperature rises above ISA while gross weight, altitude, and cost index are fixed.

It may be sufficient to just lower the MAX ALT. Actually, "lower density" (warmer air) means "higher density altitude", and that same higher altitude is something that needs to be decreased on the flight plan: Even though MAX ALT is a pressure altitude, not a density altitude, MAX ALT is the only parameter available that can be decreased to get the aircraft back down to a normal density altitude in case of a density loss (not weight loss).


Cheers,

|-|ardy

It's a nice document for today's weather. I am working my way through just to find out if if could be of any use for determining PSX MAX ALT calculations.

How the real FMC sets the MAX ALT is known. There is a graph for this in various manuals. That's not a problem (I'll make it more precise in the next update).