Now that I have had a chance to run my eye over the CAA loading manual,
(a) I see that Tim's original question appears to relate specifically to the manual rather than the general question it appeared to be. See below for some suggestions.
(b) There may be some use for a few comments on the manual for those who are using it for their exams and will then have to rationalise some aspects when they get out into the real world. There appear to be a couple of strange things in the manual ...
Please note that exams are an artificial animal and my comments are intended to draw your attention to things which relate to the real world .. the exam world (with which I used to be involved years ago) is a somewhat different creature .... My comments are not exhaustive and only relate to those things which jumped out at me during a quick run through the booklet. For the exam you need to consider what the examiner wants to see as well as trying to learn some correct techniques for later life. So far as the CAA exam system is concerned ... I have no familiarity with it so I will leave it to Alex to offer comment on my comments in respect of what the CAA examiner might be looking for ...
(a) p3 a better definition for CG is that point about which (if taken as the datum) the sum of all moments is zero .. ie there is no residual turning tendency. Has the same effect but is often a bit easier to understand for the new kids on the block.
(b) p4 DOI. Tim may have misunderstood this definition .. an index is not the same as a CG or arm. If reworded one might describe the DOI as being the loading index which relates the DOM and DOCG. Specifically, the terms are related by
DOI = (DOM x DOCG)/reference moment used to convert moments to loading indices.
Note that, in the real world of trimsheets, the IU formula can get a bit more involved than this depending on what the designer is trying to achieve .. but the basic equation will be tucked away in there somewhere ...
(c) p4 conversion units .. I am staggered at the use of such inappropriate levels of significance for exam loading calculations even if it is relevant to ICAO Annex guidance. Be very aware that the conversion factors given ought not be used to infer that loading calculation are made to such levels of accuracy. There are so many sources of error in real world loading calculations that one is doing very well if the loaded CG calculation is within 5-10 mm of the actual.
(d) p5 for a light aircraft weighed on platform scales, the use of standard axle (wheel) arms is inappropriate as this will vary with oleo extension. However, for exam use, it is a convenient simplification. For weighing, the arms should be determined by measurement for each occasion. Same comment applies for p12.
(e) p5 BEM, BECG, BEM/100 (BEI, if you like) are individual to a given aircraft and will change any time that the aircraft configuration changes outside prescribed tolerances or is reweighed. Same comment applies to p12. It is quite possible that candidates could get the idea from the CAA manual that these numbers are fixed .. they are very variable and change regularly throughout the operating life of a typical aircraft.
(f) p6 baggage arms. Typically the arms quoted for any loading position will be to the centroid (think middle) of the load (considering the shape of the loading volume for baggage). Be very wary of just throwing things in the back of the aircraft if you are dealing with loads of moderate to high density .. your effective centroid might end up being a tad different to the one with which you presume to do your sums. More than a few aircraft have come to grief due to a combination of misloading, miscalculating, and overloading in the boot ...
(g) p6 while this aircraft has a constant fuel tank centroid, be aware that many light aircraft (and just about all larger aircraft) do not and the use of a constant fuel loading arm can prove embarrassing. With respect to the comment at p7 para 2.6, if the fuel arm is not constant it may not be adequate to check the correctness of loading only for TO, landing, and ZFM as there are aircraft where the fuel usage can take the CG outside and then back inside the envelope ... trap for young players ... Similar comment applies for p13 para 2. Generally a well designed trimsheet will allow for this sort of problem and protect against inappropriate loading.
(h) p9 the upper forward CG limit is a parabola not a straight line when you convert from mass plotted against CG to mass plotted against moment (or IU). Same applies to p15. One often sees the parabola approximated by a straight line which is OK provided that the slope of the mass by CG line is towards the middle of the envelope .. if it is the other way (as it is for some aircraft), the use of a straight line approximation is inappropriate and incorrect as the parabola curves inwards toward the envelope. Whether this is or is not significant depends on the individual geometry of the envelope but it needs to be kept in mind if you are playing with loading systems .. and some pilots do get co-opted to do some with smaller operators ...
(i) p13 standard masses. It is inappropriate to use standard masses for small numbers of occupants due to the variability of body mass within a given population. As the number of occupants increases the variability evens out a bit and the use of an appropriate standard mass becomes acceptable.
(j) p23 Fig 4.7 When using zone distributions, the loading is presumed to be evenly distributed throughout the zone so that the presumed centroidal loading arm is valid. It is very easy to generate a very incorrect loading by adopting an asymmetric loading distribution but doing the calculation using the zonal centroid loading arm. A well designed operator's trimsheet will consider the operator's loading practices and provide protection against this sort of misloading.
(j) p25 Item (h) I fail to see a schedule of fuel arm against volume (or mass) of fuel. I do hope that you good folk are not using the data p22 at Fig 4.5 for fuel loading arms ... that would be just a little bit naughty as this aircraft will not have a constant fuel arm. However, if that is the case, what explanation do your instructors give you when the longhand and trimsheet answers disagree to some extent ? Alternatively, have I overlooked a fuel arm table (intended for longhand calculations) tucked away somewhere in the booklet ?
An alternative is to use the trimsheet fuel data and reverse engineer the equations but I would expect that exam candidates are not required to have such a level of understanding of trimsheet design.
Perhaps someone out there might be so kind as to remove the confusion from my poor old brain and tell me what loading arm fuel data you use for the longhand calculation ... ? Alex ?
(k) For the manual calculation of loading on the twin jet, there is no indication of the starting data although there is for the trimsheet. I suspect that Tim's original question was driven by his frustration in not being able to find these data.
The general answer to the question is given in my previous post. For the specific case, there are several alternatives likely ..
(i) the data will be given in the exam
(ii) one can use the complement of Alex' suggestion ... starting with the trimsheet entry data read 34300 kg and 45 IU to give a CG of approximately 16%MAC (I did prefer life when I could read tiny numbers with the naked eye ..) and then calculate the CG to be 647.1 in. ... then do the longhand sum .. this would be my guess as to what the examiners are looking for.
(iii) alternatively, you could reverse engineer the trimsheet to get the numbers a bit more accurately. My quick back-of-a-fag-packet-looksee suggests that the trimsheet equation for DOI is something like
DOIU = 50 + (CG [in inches] - 650) x mass [in kg] /20000
Juggling the algebra a bit gives
CG = ((DOIU - 50) x 20000 / mass) + 650
.. for the same entry data as used above, this would give
CG = 647.08 which is pretty close to the figure obtained directly from the trimsheet of 647.1.
Sometimes the trimsheet IU equation can get a bit complicated depending on what the designer is doing or trying to achieve but the basics of mass x arm will be in there somewhere ... For the equation above,
(iv) 50 is a convenient number to shift the entry argument line to the left to get rid of the minus numbers .. quite arbitrary but it is normal to use a number which puts the zero point at the left of the entry line.
(v) 650 inches is the trim sheet datum. This is quite arbitrary (within a range of sensible options) and is intended to ensure that the envelope is fairly boxy or upright so that is can be stretched laterally on the sheet to maximise execution accuracy. In addition, with a complicated fuel line such as one sees with swept wing jets, it is convenient to put the trimsheet datum somewhere in the middle of the fuel grid to minimise the fuel index movement .. and this is what the designer appears to have done with this sheet ... The trimsheet datum is no different to any other loading datum .. it is just an imaginary nail in the side of the aircraft on which to hang the tape measure ...
(vi) 20000 is the moment chosen by the designer to convert moments to IU. Why 20000 ? Who knows .. and it doesn't really matter. My guess is that this sheet came out of Boeing ..
(vi) sometimes you will comes across mm-in and kg-lb conversion factors and sometimes, as in this sheet, you will see mixed imperial and metric units. Just a consequence of engineers being so comfortable with converting from one system of units to another (we have to work in all sorts of strange units ..) that often we forget it can confuse the living daylights of non-engineering folk ..
Note that one needs to be a bit careful extracting data from a trimsheet. When we design these, we often tweak the numbers for error control and it can be a bit difficult to work out just what is going on. However, I cannot think of any reason why the CG overlay would not be drawn "correctly" so extracting a CG in the manner described should be pretty safe.
Hopefully that sorts out Tim's initial question ?
Normally, I wouldn't bother correcting misconceptions with loading systems as they are just too endemic in the Industry. However, seeing Tim is a new chum and we ought not to add too much to his confusion, the following comments are relevant to the thread .. (no criticism of other posters intended at all)
(a) the moment of the CG at DOM is the DOI
Not quite.
Think in terms of the DOM, DOCG and DO moment being related by
DO moment = DOM x DOCG
and the DOIU coming in with
DOIU = DO moment / reference moment
(b) The DOW ( aircraft ready for service without fuel) is simply a sum of all the moments for catering, crew etc.
We know what the poster means but it is more accurate to say something along the lines of
The DO configuration index (DOI) is ...
(c) We actually have a laminated sheet in the cockpit with the weights and IU's.
Keep in mind that the entry data changes regularly and are just the numbers which represent the particular aircraft's configuration. The referenced laminated sheets would disappear and be replaced with new ones every time that the data changed.
(d) But I'm pretty sure that the DOI is = to the CG Position at dry operating mass in our case
This follows from a simple misreading of the CAA manual and a bit of bad luck. DOI can NEVER be equal to a CG position .. apples and oranges. It is feasible to generate systems where the numbers can come out the same but that is an artefact of the system only and not an equality.
Last edited by john_tullamarine; 14th Mar 2006 at 00:59.