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.

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.

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

Hi Gysbreght,
Please have a look at Page 7.3, Eq 7.7 "Climb correction factor" (CCF)
http://www.aviation.org.uk/docs/flig...-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 ?

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?).

Let's Beat it to Death!
 

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:

@ 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%

@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.

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 :-(

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.

Originally posted by Keith Williams


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 !




@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.

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.

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/ICA...PAPERS/P16.PDF

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.

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.

Hi Gysbreght, Owain & Keith,
Sorry I wasted all your time. I made a simple maths error when I tested some figures and thought I was on to something.

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 ?

Gysbrecht:
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)