Extra margins with assume thrust

[Life on top]

Hello you all! I am flying the 737NG:

I was told that if you use assume thrust, you will have the additional margin for take off between the density of the assume temp and the colder OAT. If i understand it correctly, if you have flat rated engines at 30 degrees C, the engines will adjust N1 and EGT to give a flat rate whenever it is colder than 30 degrees outside. Therefore you cannot select a colder assume temp than 30. But in my mind then, and here is the real question; you will only have the density margin from the assume temp down to 30 degrees then, and not all the way down to lets say 4 degrees C?

I hope this makes sense, here the mathemathical way of asking the same:

With assume thrust of 40 degrees, and OAT 4 degrees, flat rated engines at 30 degrees, Is the density margin then:
A: 40-30=10 degrees colder with the better density that gives, or
B: 40-4=36 degrees colder with the better density that gives?

[galaxy flyer]

The air, on the wing and in the inlet, are at 4C in your example; not at the assumed temperature. You will always have that density difference on your side.

[Life on top]

Yes, but my question is that if i understand it correctly with a flat rated engine, it will compensate and reduce EGT if temp is below it's flat rated temp. So will you then have the margins all the way down to 4 degrees? Only talking about the engines now, not the wings..

[Meikleour]

Life on top:

Think of it this way. Up to the flat rated temperature, the engine is able to produce its stated rated thrust.
Now, a TOGA departure at 4C will achieve the same thrust as one at 30C
HOWEVER the engine will be using less fuel to achieve that same thrust. In other words there will be no performance difference - simply a lower EGT at the lower temperature.

When using assumed temp. methods then there will be a "density margin" as you point out. So, by my reasoning that will only apply for the range above the flat rated temperature.

Note: we are only talking about engine performance here!

As a historical footnote - on the B707 with JT3D (no FADEC) engines we had approval to operate the engines at HIGHER than rated thrust in limited circumstances. ie. the F/E over EPR'd the engines to achieve extra thrust. This was at the expense of engine life. Only used departing Nairobi.

[FE Hoppy]

Normally the term Margin refers to engine temperature. The difference between the ITT/EGT achieved when setting thrust and the limit for that thrust.

The greater the difference between actual and assumed temperature, the greater the margin.

This also applies to any actual temperatures below the flat rated temp. A take off with full thrust at 4°C will have a lower ITT than a take off at 30°C.

So the flat rated temperature of an engine does not define the Margin when using assumed thrust. It's the difference between actual and assumed which defines the margin.


Now, if it's density you are interested in then we can say that we gain uncorrected benefits in terms of Lift and TAS when we use an assumed temperature compared to taking off at the equivalent actual temperature. This performance gain is also proportional to the difference between actual and assumed temps.


The only real significance the flat rated temperature has is to define the minimum acceptable assumed temperature.

Setting an assumed temperature of 25°C on an engine which is flat rated to 30°C is simply asking for max take off thrust. i.e. no reduction. If you could do this you would find that the N1 at assumed temperature would be higher than the N1 at actual temperature. You would then correct this N1 for the difference in density between actual and assumed and if you did the sums correctly you would get the same N1 as for your actual temperature.

Because the thrust scheduled at actual and assumed is the same and therefore the N1 required to achieve that thrust is the same.

No difference in thrust, N1 or ITT.



Bit of a ramble but hope it helps.

[Azzurri]

Hi guys.

I'm just wondering if I could get your best definitions of a 'flat-rated' engine.

[FE Hoppy]

An Engine who's rated thrust is fixed up to a published temperature.
Above this temperature the rated thrust will reduce as temperature increases.

[Azzurri]

Ok thanks man; I appreciate it.

[FE Hoppy]

@vilas
I think you may be mistaken.

[vilas]

Disregard my post and read below, FROM FLIGHT SAFETY FOUNDATION
Effect of True Airspeed


Pilots who are skeptical about reduced-thrust takeoffs often sense that something very important is being taken away. However, there is absolutely no loss of any necessary performance margins involving field length, screen height,1 climb or obstacle clearance. If the airplane’s weight and power setting satisfied the certification standards at the higher temperature, then they certainly will do so at the lower temperature.
Although the takeoff speeds used by the flight crew are indicated airspeeds, actual performance is determined by true airspeed, which is a function of air density. Because we are operating at an actual temperature that is lower than the assumed maximum, true airspeed likewise will be lower.
Because of this true-airspeed effect, we enjoy a great deal of cushion between what the airplane must do and what it actually is doing. We are, in reality, using less runway and achieving a higher climb gradient, or obstacle-clearance margin, than if the ambient temperature was at the maximum for that same weight. Depending on conditions, the effect can be considerable — on the order of several hundred feet in field length. The benefit increases as the difference between the actual and the assumed temperatures increases.

[FE Hoppy]

As stated.

One European airline I know uses a take-off software which shows the crew the TAS margin when assumed temp calculations are done. It also gives them the choice of V1s when a range is available.

Not sure it's necessary but some of the crews understand it. Others just shrug shoulders and go. ;)

[Meikleour]

vilas: in post 3 you will see that the poster is asking only about the consequences for the engine thrust. He is not asking about the TAS benefits to which your posting refers.

[de facto]

1% /5c away from IsA..easy.

[vilas]

Life on top
The margin you are talking about comes from difference between take off speeds in IAS and the TAS at which the aircraft is travelling because of higher density due to lower temperature but the example you have chosen is not correct. If you choose ass. temp. of 50 degrees for OAT of 35 degrees( which has to be higher than Tref). You will have performance margin as compared to the take off done at actual OAT of 50 degrees. Reproducing from my earlier post:
Because we are operating at an actual temperature that is lower than the assumed maximum, true airspeed likewise will be lower.
Because of this true-airspeed effect, we enjoy a great deal of cushion between what the airplane must do and what it actually is doing. We are, in reality, using less runway and achieving a higher climb gradient, or obstacle-clearance margin, than if the ambient temperature was at the maximum for that same weight. Depending on conditions, the effect can be considerable — on the order of several hundred feet in field length. The benefit increases as the difference between the actual and the assumed temperatures increases.

[Chu Chu]

As SLF, I probably have this entirely wrong, but let me try to put this down the way I understand it.

As far as the airframe itself is concerned, what matters is IAS, not TAS. Air density has the same effect as the wings as it does on the pitot tube, so drag, lift, stall speed, etc. will be the same at a given IAS, regardless of the density and corresponding TAS.

But when you're talking about the amount of runway needed for takeoff, what counts is the required ground speed, which corresponds to TAS (assuming calm winds). At lower density, an aircraft needs to reach a higher TAS to obtain the IAS required for takeoff. Reaching that higher TAS requires more acceleration and therefore more runway.

[Meikleour]

Why does nobody bother to read what the poster is ACTUALLY asking!!!!

[FE Hoppy]

Why does nobody bother to read what the poster is ACTUALLY asking!!!!

There is no such thing as density margin in relation to thrust.


When calculating thrust for assumed temperature take off method. The N1 is corrected for the difference between the actual and assumed temperature. This means you get exactly the same level of thrust as if it were the assumed temperature.

The density is corrected out.

The margin appears as lower ITT/TGT. This is entirely dependent on the difference between actual and assumed temperature and the flat rated temp makes no difference.

[FE Hoppy]

@Chu Chu

Lower TAS for same lift = higher climb gradient. They tend to be rather important for take-off performance.

So you get better stop and better go performance.

[Meikleour]

FE Hoppy: Here is my take on what I think is being asked....

The OP correctly identifies that with a TOGA takeoff at 4C and another at 30C then the thrust used will be the same albeit with a lower EGT due to the greater air density and lower fuel flow at the lower temperature.

Now, step to the FLEX case. At 40C the FADEC computes the N1 setting as if the air temp. was 40C. OK so far?

Ignore the TAS issue.

He wants to know if the FADEC calculated N1 for 40C will benefit more from the 4C air that is being taken in (ie. more dense) or just from the 30C flat rated air density.

My question to you is this: when using a FLEX setting does the FADEC actually compensate for the air density differences between the ambient or is it simply programmed to work using the top end of the flat rated values?

This, I think is what is being asked, not the margins inherent with the IAS/TAS margins.

[Gysbreght]

The article from the Flight Safety Foundation is not entirely correct. The difference in TAS due to air density results in conservative takeoff distance, accelerate-stop distance, and horizontal acceleration segment in the takeoff flight path, but the climb gradient is the the same for the assumed temperature and the actual temperature.

[FE Hoppy]

@ Meikleour

The fadec corrects for the full difference. The N1 is corrected for the difference between ambient and assumed.

@Gysbreght
If for example the perf at assumed temp was WAT limited second segment and we use that perf at a lower actual temperature the TAS difference will give us a higher gradient.
The actual gradient we will achieve is higher than the gradient we would make at assumed.

[vilas]

Life on top
You are not clear about this topic. Google this document it is from Boeing.


PDF]B737 Reduced Thrust Considerations - SmartCockpit (http://www.smartcockpit.com/download.php?path=docs/&file=B737-Reduced_Thrust_Considerations.pdf)
www.smartcockpit.com/download.php?path...Reduced_Thrust...pdf

[Gysbreght]

the TAS difference will give us a higher gradient.No, that is not correct. The lower temperature will give you a lower TAS and a lower rate-of-climb. The gradient is not changed by TAS, it depends on the thrust-to-weight ratio and that is equal for the assumed and the actual temperature because you set the same thrust.

Likewise, the acceleration in terms of kts TAS per second does not change, the number of seconds changes and therefore the distance.

[FE Hoppy]

@ Gysbreght

Take a look at the climb gradients for your aircraft at rated thrust below flat rated temperature.

Same thrust to weight ratio but the gradient is higher as temperature reduces.

[Gysbreght]

@ FE Hoppy,

sorry, I don't fly an aircraft and don't have access to an AFM.
The B777 Ops manual doesn't support your assertion.

Can you give an example?

P.S.
Have just looked at the Boeing presentation for the B737-800 linked in Vilas' post #22 above.

Page 18 shows that for that airplane there is an increased gradient at the lower actual temperature, but that is due to a higher thrust, not the difference in TAS.

[Goldenrivett]

Hi Gysbreght,
Page 18 shows that for that airplane there is an increased gradient at the lower actual temperature, but that is due to a higher thrust, not the difference in TAS.
Try reading a bit further: e.g. Slide 21

"Climb Gradient Margin Due to the True Airspeed Effect Increases With Higher Assumed Temperature"

[vilas]

Gysbreght
If you go through the entire document carefully you will get all the answers you are looking for.

[Gysbreght]

Try reading a bit further: e.g. Slide 21
I did. Can you explain that graph to me?

[Meikleour]

FE Hoppy:Because the thrust scheduled at actual and assumed is the same and therefore the N1 required to achieve that thrust is the same.

Sorry to bang on about this however - reference to Villas's link pages 7 & 10
suggest that the density issue is not fully factored out by the FADEC. Boeing say that there is in fact more thrust produced at the assumed temp. than would be at the actual higher temp. This I think is what the OP was after.
So, the "density" issue with respect to the engine thrust would be from the actual lower ambient temp rather than the top of the flat rate?

PS Keith Williams or Old Smokie please feel free to intervene!!

[vilas]

Gysbreght
gradient= change in height/distance travelled. If ass. temp is 40 degrees at actual temp of 15 degrees TAS at 15 is less than what would be at actual 40 degrees. So distance travelled is less and higher gradient.

[Gysbreght]

Vilas,

Read my post #23 again. TAS and V/S are both speeds, and change at the same rate with ambient temperature.

For constant weight, CAS and thrust, gradient and acceleration do not change with temperature.

I honestly don't understand what figure 21 is trying to show. In figure 18 the weight is 71000 kg, i.e. the climb-limited weight at 35 deg C. In figure 20 (titled "Lower Takeoff Weight ...") the climb-limit weight at 45 C is 65100 kg. What is the weight in figure 21? Why is the gradient constant above 45 C?

[Chu Chu]

How about this: An aircraft has the same lift, weight, and drag at a given IAS regardless of the density and TAS. This means that the rate of climb (in feet per minute) is also the same.

But at a higher density, the TAS will be lower, and so will the ground speed. Since the aircraft is gaining the same amount of altitude in the same time, but covering less ground, the climb gradient is higher.

[Gysbreght]

This means that the rate of climb (in feet per minute) is also the same.

(...)Since the aircraft is gaining the same amount of altitude in the same time, but covering less ground, the climb gradient is higher.

Wrong statements .....

[FE Hoppy]

@Gysbreght

e190 single engine climb gradients. Sea Level 40 tonnes

temp-----------gradient
0---------------6.03
2---------------6.02
4---------------6.01
.....
20-------------5.88
22-------------5.86
24-------------5.84
.......
30-------------5.79---Flat rated temp
32-------------5.42
34-------------5.05
36-------------4.71
38------------4.42



Note the gradient loss with increase in temperature up to flat rated temp.
Same thrust, same weight, same IAS.

The difference is TAS. (well it's rho really but that's reflected in TAS)

[Gysbreght]

@FE Hoppy,

Since the change in gradient for flat-rated temperatures is not caused by TAS, the explanation must be found in the flat-rated thrust not being truly constant for this airplane.

[keith williams]

This is certainly a curious one.

If we look at a couple of equations for % Gradient.

Climb gradient = 100% x ( (Thrust – Drag) / Weight)………Equation 1.

Climb Gradient = Approximately 100% x ( ROC / TAS)……Equation 2.

Strictly speaking it should be (ROC/Ground Speed) in the equation 2, but for small angles in still air the Ground Speed is approximately equal to TAS.

Both of the above equations are equally valid, so it must be possible to use both equations to explain the reason for the reduction in gradient shown by FE Hoppies post.

Looking at equation 2, if the TAS increases due to increased OAT, while the ROC remains constant, then the % gradient will indeed decrease.

Looking at equation 1, the increasing OAT will not change the weight, so if the flat rating keeps the thrust constant, the % gradient will decrease only if the drag increases.

One possible explanation might be that the increasing OAT causes the KIAS value of V2 to decrease. V2 is less than Vmd, so this decrease will increase the drag. This increased drag at constant thrust would cause a direct reduction is the % gradient in equation 1. It would also reduce the ROC, which would in turn cause a reduction in % gradient in equation 2.

I’m not stating that the above explanation is a fact. I am simply musing over the matter.

[vilas]

Gysbreght
One thing is certain it is an official document so it's veracity is not in question. Some of the assumptions in your argument may be incorrect.

[latetonite]

Fact is that the aircraft operates in a lower density altitude then calculated for.
Actual performance will thus be better.

[Owain Glyndwr]

@FE Hoppy

I'm with Gysbrecht. If you plot out the gradients listed you will find they vary directly with temperature. TAS however varies with the square root of temperature.
There is nothing in Keith Williams equations to link gradient with TAS - on the contrary, Equation 1 excludes any such relationship.
Checking the net for data on the E190 speeds I found that V2 at a given TOW is constant EAS over the flat rating temperature range.
So if it isn't TAS and it can't be drag at a constant EAS then it must be something in the way the engine is flat rated.

[john_tullamarine]

One thing is certain it is an official document so it's veracity is not in question.

I admire your faith in the OEMs of the world.

Your comment doesn't necessarily follow as day follows night ... over the years I have referred a variety of OEM Manual errors back to the relevant OEM for subsequent correction. Indeed, I have picked up a number of Regulator errors in Flight Manuals and referred them back to the source for correction - the fact is that none of us is incapable of error ... doesn't matter for whom one works.

Some of the assumptions in your argument may be incorrect.

While errors are always a possibility for any of us, Gysbreght has a great many runs on the board .. I'd err on the side of presuming him to be correct until proven wrong. On this point, Owain Glyndwr (another with many runs to his credit) agrees.

[vilas]

john_tullamarine
This is not simply a technical error but if it is it will be a conceptual error and since approval of assumed take off may be connected with it I am not inclined to think manufacturers and regulatory bodies can be building their case on a blunder. Also Flight safety article says the same thing.How ever let's wait till someone comes with more plausible explanation.

[Gysbreght]

I've no reason to doubt the authenticity of the gradient information provided by FE Hoppy. We differ in the explanation for the decrease with temperature.


Many aircraft exhibit this, perhaps not always as pronounced as the E190. As explained by Keith Williams, elementary flight mechanics indicate that it is not caused by the increasing TAS, so it must be caused by decreasing thrust. A possible explanation is that the thrust of the uninstalled engine is flat-rated but installation effects, such as bleeds and the power absorbed by the accessory gearbox, increase with increasing ambient temperature, so that the installed thrust decreases.

[Chu Chu]

Equation 1 has some assumptions baked in -- try applying it to an aircraft accelerating in level flight.

[Goldenrivett]

Hi Gysbreght,
I did. Can you explain that graph to me?
Please have a look at Page 7.3, Eq 7.7 "Climb correction factor" (CCF)
http://www.aviation.org.uk/docs/flighttest.navair.navy.milunrestricted-FTM108/c7.pdf

If the aircraft was flown at constant TAS then Keith Williams equation
Climb gradient = 100% x ( (Thrust – Drag) / Weight)………Equation 1
would hold true.

Since we fly a constant IAS during the climb, then TAS is increasing and there is an additional Kinetic Energy contribution which needs to be considered and appears as a CCF.

i.e. If we gained X% TAS during the climb, then the incremental increase in TAS is greater when the initial TAS is bigger (when the temperature is warmer). The additional KE is proportional to TAS squared, so the CCF is further away from unity when it is warmer, hence the climb gradient is less.

Edit, How many can remember density being expressed as:
ρssl (rho) Standard sea level air density = 0.0023769 slug/ft3 ?

[Gysbreght]

Goldenrivett,

Good point. I've thought about that, but estimated that the change of CCF with temperature would be too small to explain the change of gradient in the example given by FE Hoppy in post #34. If FE Hoppy can provide the IAS associated with those gradients I can do the sums. (Maybe you can do that yourselves?).

[No Fly Zone]

Too much nit-picking! IMO, the smart/safe pilot uses - and understands - ALL of the numbers available.... It, as mentioned in one reply, a range is given, that may help the driver understand the size of his/her fudge factor. And, at the end of the day... when rolling down that always too short runway, do you want to test the limits of those numbers, or do you want to go flying? If the purpose is to go flying, it seems that the prudent routine (supported by Big Birds' engineers and test pilots) is to rotate as soon a reasonably able, establish PRC, continue acceleration and FLY the SOB. Don't be a ground hog. Why? Both climb and control are functions of speed when still at the low end. Given stable thrust, speed will increase faster with a moderate AOA and wheels off the ground, than with them still in contact. That think is no a casino bus, but an airplane with real wings; it works better when flying than it does in high-speed taxi. Although a very different can of worms, consider how the military boys and girls do a tactical departure: Make it fly, speed it up, clean it up and look for the heavens. Perhaps not the most comfortable departure for for the pointy-end fare-paying SLCs, but with all engines burning, it seems to be safest method for leaving the ground. Humph! If you want to do a high-speed taxi test, do it. If your plan is to fly, get the airplane off the ground and into flying mode a quickly as is reasonably possible.
Blast me if you will. I can take it.:ok:

[Owain Glyndwr]

@ Golden Rivet, Gysbrecht

I don't think CCF will explain it.

the CCF is [1+(V/g)*dV/dh]^-1

If I apply that at 140 kIAS @ T=0 and T=30 I get:

CCF = 0.9824 and 0.9801 respectively (H check my sums?)

That's only 0.2% difference but the gradients differ by 5.79/6.03 = 4%

[Gysbreght]

@Owain Glyndwr:

I agree with your conclusion that the CCF does not explain the variation of the E190 gradients at flat-rated temperatures. Therefore I'm sticking with my explanation based on the variation of thrust due to installation losses.

[FE Hoppy]

Someone asked for the speeds?
Here is some data for those with time to chew on. I've come to the conclusion that at least some of it must be down to thrust having played with the numbers and tried to make CCF fit. It doesn't :-( This is approach climb gradients at Sea Level, One engine inop. Rated Thrust no bleeds.

Vac.SAT.T kelv.rho................TAS ............% ...TAS / IAS.....1/2rhoV^2 .... Ang RAD............Ang DEG...........GS
135 00 273.16 1.292200348 131.4428255 5.62 0.973650559 11162.8125 0.056140944 3.216639136 131.0728578
135 02 275.16 1.282807992 131.9231414 5.61 0.977208455 11162.8125 0.056041258 3.210927565 131.6061694
135 04 277.16 1.273551187 132.4017149 5.61 0.980753444 11162.8125 0.056041258 3.210927565 132.083593
135 06 279.16 1.264427021 132.8785648 5.59 0.984285665 11162.8125 0.055841883 3.199504233 132.6558063
135 08 281.16 1.255432661 133.3537096 5.58 0.987805256 11162.8125 0.055742194 3.193792471 133.1720684
135 10 283.16 1.246565359 133.8271674 5.56 0.991312351 11162.8125 0.055542813 3.182368757 133.7159262
135 12 285.16 1.237822440 134.2989561 5.54 0.994807082 11162.8125 0.055343427 3.170944790 134.2411078
135 14 287.16 1.229201306 134.7690932 5.53 0.998289580 11162.8125 0.055243732 3.165232712 134.731437
135 16 289.16 1.220699430 135.2375960 5.51 1.001759970 11162.8125 0.055044340 3.153808366 135.2275058
135 18 291.16 1.212314353 135.7044813 5.50 1.005218380 11162.8125 0.054944642 3.148096100 135.7016115
135 20 293.16 1.204043686 136.1697658 5.48 1.008664932 11162.8125 0.054745243 3.136671378 136.1681169
135 22 295.16 1.195885103 136.6334659 5.46 1.012099747 11162.8125 0.054545840 3.125246407 136.615212
135 24 297.16 1.187836341 137.0955975 5.45 1.015522945 11162.8125 0.054446136 3.119533828 137.0622441
135 26 299.16 1.179895197 137.5561767 5.43 1.018934642 11162.8125 0.054246727 3.108108483 137.4790706
135 28 301.16 1.172059527 138.0152188 5.42 1.022334954 11162.8125 0.054147020 3.102395719 137.9092091
135 30 303.16 1.164327243 138.4727392 5.40 1.025723994 11162.8125 0.053947604 3.090970004 138.2953483

Sorry about the format :-(

[keith williams]

Most ATPL level text books use the simplifying assumption that the thrust produced by jet engines is constant at all airspeeds. But in reality the thrust is maximum when TAS is zero (static thrust), then decreases as the aircraft accelerates down the runway. This is because the increasing speed of the incoming air decreases the overall acceleration given to the air as it passes through the engine. This effect can be seen in slide 10 of the link in Vila’s post 22. The magnitude of the thrust loss will increase as the OAT, and hence the TAS increases at any given EAS.

It may be the case that flat rating compensates fully for the temperature-induced loss of static thrust before brake release, but does not compensate for the thrust reduction caused by increasing TAS during climb out. If this is the case, then the thrust available during climb out will be less than the rated value and will decrease with increasing OAT even within the flat rating temperature range.

[Owain Glyndwr]

Originally posted by Keith Williams


It may be the case that flat rating compensates fully for the temperature-induced loss of static thrust before brake release, but does not compensate for the thrust reduction caused by increasing TAS during climb out. If this is the case, then the thrust available during climb out will be less than the rated value and will decrease with increasing OAT even within the flat rating temperature range.I wondered about that - net thrust is gross thrust minus momentum drag and the flat rating relates to static gross thrust. But the momentum drag is mass flow*TAS, so although the effect you describe is I think there, the magnitude will also depend on how the engine mass flow varies with temperature in the flat rating zone. From what I have read the CF34 is flat rated to constant N1/root theta, which (I think!) would mean actual mass flow reducing with increasing temperature and the gross thrust flat rating being maintained by increasing TET.


If I'm right then the mass flow would go down as root theta and the speed go up as root theta so the thrust lapse rate would not be affected by ambient temperature, if the mass flow stays constant then your explanation could be the answer. But I am not an engine man and I stand to be corrected !




[Gysbreght]

@Keith:


Nice try but no, I'm with Owain. If you are familiar with non-dimensional representation of turbojet engine performance, then it will be apparent that gross thrust and net thrust at a given altitude are defined by N1/root theta and Mach number. Mach number at a given altitude and IAS does not change with temperature.

[keith williams]

Yes, looking at Vilas’ link again I see that the thrust loss between V1 and Vr at 15C is 4027 lbs while that at 38C is 3998 lbs. That’s a difference of only 29 lbs. That’s not enough to make any significant change to climb gradient. But it is curious that the thrust loss is greatest at the lower of the two temperatures.

The figures in the link also look a bit dubious in that at both temperatures the thrust decreases a lot between V1 and Vr (by 4022 lbs at 38C and by 4042 lbs at 15C), then these losses are almost completely recovered between Vr and V2. Given that the differences between V1 and Vr are only 2 knots and the difference between Vr and V2 are only 7 knots, these effects look very strange.

[vilas]

Another technical article on assumed take off. It appears to be a translation from possibly Chinese. May be the mathematicians amongst us can explain to us.
http://www.icas.org/ICAS_ARCHIVE/ICAS2002/PAPERS/P16.PDF

[Skyjob]

All computations displayed involve various areas for corrective factors, as slowly is beginning to emerge from this thread.

The one factor not yet attended to is the difference in pitch attitude and thrust vector direction as a result of that, affecting the forward thrust vector and conversely has a vertical element.

All those guys having worked out the tables have made many iterations having based their data on flight tests etc, give them credit where it's due and let us accept their derived and published data rather than try to find the loops in the simplified equations presented to us simplistic pilots (compared to those in the know).

I'm sure there are more and unmentioned (this far) variables which may contribute as well, but let us get to grips with the fact that we are not going to find out ALL the variables and get access to test data to look over.

Basic question on page 1 about margins when using assumed thrust has been answered. Several factors have been mentioned which affect it.

[Gysbreght]

Skyjob,


The AoA and L/D are defined by weight and IAS, the gradient by the thrust/weight ratio, all of which do not change with temperature. Therefore pitch attitude and thrust vector direction do not change with temperature.

[Goldenrivett]

Hi Gysbreght, Owain & Keith,
I agree with your conclusion that the CCF does not explain the variation of the E190 gradients at flat-rated temperatures.

Sorry I wasted all your time. I made a simple maths error when I tested some figures and thought I was on to something.

[john_tullamarine]

But the initial question/error/whatever often generates a very useful and interesting discussion.

Often appears that the journey is far more interesting than the destination ?

[Skyjob]

Gysbrecht:
The AoA and L/D are defined by weight and IAS, the gradient by the thrust/weight ratio, all of which do not change with temperature. Therefore pitch attitude and thrust vector direction do not change with temperature.

But the thrust is a variable in this due to the assumed temperature method, thus has an impact on the thrust/weight ratio, therefore pitch attitude and direction.

[Owain Glyndwr]

But the thrust is a variable in this due to the assumed temperature method, thus has an impact on the thrust/weight ratio, therefore pitch attitude and direction


But the thrust component that matters is that which is opposing drag; that is along the flight path, not the horizontal component. That means the thrust vector has to be resolved through AOA (which is constant) not through pitch attitude (which varies)

[Gysbreght]

The whole point of this discussion is that if the thrust is constant for flat-rated temperatures, or with the assumed temperature method, the gradient is constant (i.e. does not change with TAS). If the thrust is not constant, the gradient is not constant.

[Meikleour]

Gysbreght: As others have pointed out - although the STATIC thrust in the flat rated regime may be constant, it changes by a variable amount with temperature during the takeoff roll. Hence thrust variation. Add to that, ref. to the Boeing paper (Vilas posting) shows also that there is a thrust difference at FLEX with respect to the ambient temperature.
Thus the consensus seems to be that, yes there is a variation in gradient!
Which I think is what you said.

[Gysbreght]

Thus the consensus seems to be that, yes there is a variation in gradient!
Which I think is what you said. Correct, there is a variation in gradient due to the variation in thrust.

[vilas]

Gysbreght
CFM document on smart cockpit gives better explanation. According to that:


If performance is limited by the one engine inoperative minimum climb gradient requirements, the higher actual thrust will result in a higher climb gradient
If performance is limited by obstacle clearance, the higher climb gradient combined with the shorter takeoff distance will result in extra clearance margin

[vilas]

Gysbrehght
The CFM document on smart cockpit gives clearer explanation according to that:
Due to lower ambient air temperature and higher air density in the actual take off conditions, actual TAS is lower and actual thrust is higher and
• If performance is limited by the one engine inoperative minimum climb gradient requirements, the higher actual thrust will result in a higher climb gradient


• If performance is limited by obstacle clearance, the higher climb gradient combined with the shorter takeoff distance will result in extra clearance margin