Here is an extract from a reasonably old article I wrote a year or so back. It concerns the 777 specifically, but in general it is typeless. It (the article) is a bit "granny sucking eggs" and lacks meat (to be digestable). However if anyone is really interested - email me I will give you some real numbers to play with.
Interesting topic all the same and very valid when we start to talk about 7 hours +. The effect of a bad (nose heavy) trim on altitude selection is particularly important with modern jets, since the SFC penalties for flying over optimum are much more severe than the converse. Hope this makes sense in its' present form.
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Trim Drag
When the tail of an airplane carries some load, several drag components are increased: the tail itself has vortex drag and lift-dependent viscous drag, but the lift of the wing must be changed to obtain a specified airplane CL:
CLAirplane = CLAirplane + CLtail (Stail / Swing)
The increase in wing CL means that the wing vortex and lift-dependent viscous drag increases. In addition, wing compressibility drag is affected.
To compute this, we first must calculate the lift carried by the tail. For most transport aircraft without active controls this is about 5% of the airplane lift, but in the wrong (downward) direction. We could then compute the vortex drag of the combined wing/tail system and then add in viscous and compressibility increments. The difficulty with this is that unless we know the airplane center of gravity (CG) location, we cannot compute the tail load and in the early stages of the analysis, we do not know the airplane CG location. Sometimes we make rough estimates of the CG. When this is not possible, we can rely on more detailed computations done on other aircraft which show trim drag of about 1% to 2% of airplane drag.
Well that’s a mouthful, but it explains the thing quite well. In essence Trim Drag is a penalty that must be paid, in terms of increased Induced Drag (Lift Dependant) for the requirement to have the CofG forward of the CofP to provide dynamic pitch stability. Our modern B777 has everything going for it in this respect. The extra hold aft of the wing (to physically allow the CofG to be placed as aft as required. An active Pitch Control system and an all moving tailplane. However it’s still there and must be lived with. But what is this to do with this article? Well, quite a bit. Allow me to explain.
As far as I know, the FMC and the CFP both assume a CofG at 30%MAC and all performance calculations are based on that. If however the cruise CofG is away from 30% then the induced drag penalties are more or less than assumed. Please note we are discussing CRUISE CofG here, not Take Off.
Now let me say something here before we get deeper into this. Firstly, nothing here is significant numbers on the safety side of things - that is definitely not the issue. We have a 5% fuel buffer that looks after all of this with total ease. Also, the numbers that I will be using below are pure guesses, intelligent guesses (I would like to believe) but still guesses based on observation. So please treat what follows in the spirit in which it is offered. A guide, a thinking about point, maybe even something to examine further for yourself. On the shorter (<3 hours) sectors, none of this really makes any real difference. But longer sectors do show it all happening to a convincing degree.
Let me start by saying that our loading system is good and we mostly get a very good trim. Very good in the sense that it is better (more aft CofG) than the nominal 30% cruise MAC that is planned for. This is why we make a bit of fuel most of the time.
However now and then it’s worse. Then we lose a bit. But this “make a bit”, “lose a bit” is a little inexact to my mind, and I would like to be able to get a feel for what is going on even if I have no control over it. Well in this case you can. The very simple rule of thumb here is the position of the Trim Indicator; which is an analog of cruise CofG.
A cruise trim position of 4.7 seems to equate, almost perfectly, with the FMC/CFP figures. Each 0.1 unit shift represents an effective change in cruise AUW (due to tailplane loading / Wing CL) of 1 ton. Trim figures less than 4.7 equate to Less Weight and figures more than 4.7 are equivalent to More Weight. And of course this is a moving target again. As fuel burns off the CofG moves forward (trim moves back to higher numbers). The higher you fly (and the lower the IAS) the trim moves back also. Fly too high and the trim starts to eat fuel part of the reason for the WT figures.
So now we can start to put some numbers to the penalty or bonus. Assume we start our cruise with a GOOD trim of 3.7 on the indicator. This is roughly a 10 ton induced drag bonus over what the FMC and the CFP are working on. Look at the bottom of the CFP and it gives you a per ton adjustment for variations in AUW. Multiply this by your assumed trim bonus and then divide it by your cruise flight hours. Over the next hour you should see this on your fuel checks, everything else being equal. And it really is there. If you work at eliminating all the other factors - it will show. The CFP is a remarkable tool and accurate fuel checks show all this happening. The converse is also true with a BAD trim, in the same magnitude. However do not assume that the TOC trim will be there for the whole flight. The trim does move back. As of writing I am still working on that one.
OK, I agree, there is nothing that you can do about the trim of the aircraft. You are stuck with it. However this doesn’t mean that you cannot be proactive about the effects on Cruise Altitude selection. This is the link and it is really quite important.
Think back to the beginning of this article were we saw the penalties for flying too high. Remember also that 1 ton of AUW was equal to 100 ft of Optimum Altitude (and Maximum Altitude but more on that later). The FMC does not know about your Cruise Trim / CofG it assumes 30%, so all the altitudes are calculated to that. However an intelligent application of a suitable adjustment would give the wise pilot a definite edge. We are not talking big numbers here. It is rare to see a trim of 3.7 or 5.7, but in between is a whole world of variations. As with everything else we have discussed here, these are small effects with correspondingly small variations in performance. But in the long term they do add up, either for the good or the bad. As I stated above, there is nothing here that is not generously catered for in the 5%, but on a redespatch day, sensible application of this knowledge can make that critical few 100kgs difference sometimes.
My last word is on Maximum Altitude. The bad old days of “coffin corner” are mostly behind us, but the beast is still alive and waiting for the unwary. Do be aware of your trim when you venture to the top corners of the flight envelope for whatever reason. If you have a BAD trim then you could be working a perfectly acceptable performance margin (as far as the QRH / FMC) is concerned and actually have a pair of wings that are much closer to performance limits than you would knowingly want. This is a “how long is this piece of string” issue again and the margins that are built in are more than adequate, most of the time. The converse, of course, is also true, but that is definitely not an excuse to go higher than the FMC/QRH altitudes.
MG