A lengthy post, I’m afraid, but there’s no super short way to cover the problem you have raised. It would be far better to do this across the table or in a classroom setting but we shall work with what we have ..
We talked about several light aircraft sheets which appeared to be normal. They involved the loading positions having sloping lines. My colleague was not able to explain why these work the way they do.
I’ll take that to mean that you are somewhat comfortable with the smaller aircraft sheets. However, you should understand how the basics of the things work.
First, let’s start at the beginning .. not trying to teach Grandma to suck eggs .. rather making sure you are comfortable with the steps.
The normal longhand calculation involves a tabulation of loading arm entries each with the calculation –
Weight x loading arm = moment (you can make this an IU if you wish .. same principle applies).
Once each station is addressed, the weights and moments are summed (added to produce a total value) and the CG is determined by the simple calculation
CG = total moment / total weight
This is done for the zero fuel and loaded configurations. I presume that all of Bob’s students are familiar with this basic approach.
Now, just like with cuisinaire rods used in beginning number line studies, one can do the summations graphically .. normally we only do this for the moment as graphical summation of weights really doesn’t gain us much in the way of simplifying the process. Graphical summation of loading arm moments is what the trim sheet is all about .. the loading lines do both the sum (weight x arm) and the summation (moment 1 + moment 2 etc). This only works as the loading arm is constant .. ie it doesn't vary with the weight added.
If we have a look at the CASA PPL/CPL workbook (
www.casa.gov.au/sites/g/files/net351/f/_...ppl-cpl-workbook.pdf
) at page 10, we see a fairly standard, simple light aircraft trim sheet (I suspect this is one of Norm Overmeyer’s sheets from many years ago) labelled as Loading System Alpha. You will become familiar with the use of this sheet as you progress through your pilot theory studies with Bob.
If we look at a loading station, say, Row 1, we can compare the loading line ticks (on the 50kg line) with the IU scale at the top of the page and come up with a 50kg load corresponding to something in the order of -10.33 IU.
Moving to the left with additional load just means that the seat arm is forward of the datum used by the sheet designer. Note that, in general, trimsheets do NOT use the OEM datum from the POH. This is done to maximise the accuracy of the sheet in completion. As a result, it is very important that pilots do NOT try to apply “standard” data to a sheet. Just to note, the datum on this sheet is the CG appropriate to an IU of zero … ie somewhere near the aft limit of the CG envelope.
Using the sheet in the manner specified indicates that we come down from the start IU line and then move to the left one tick for each 50kg (ie -10.33 IU change to the total IU) and a part tick for a part of 50kg (and a similar proportion IU change). And so we continue on down the page
…
Now, let’s consider some errors associated with completing the sheet –
(a) The sheet is drawn to a background scale of IU, shown by the vertical lines between the loading arm lines. If the drop lines are not parallel to the grid, the calculation will be in error to some extent as the IU total will be changing a little between loading lines. Hence, it is best to use something like a Douglas protractor to run the sheet calculation. If you don’t have one to hand, an ID card is fine (and about the only useful value to ID cards).
(b) Generally, the drop line lands on a loading line somewhere in between two ticks so we have to do an interpolation to figure out the scale number (ie tick distance proportion) from which we are starting. There will be an error here and the only way we can minimise it for this style of sheet is by careful assessment of the scale.
(c) Similarly, the end IU change for the load generally will be in between two ticks and plotting it accurately will involve some degree of error. As with (b) the only defence is to exercise care with scale assessment.
Another sheet was a 727 which I have attached
You have cited the CASA ATPL training B727-200LR trimsheet (an old Ansett – an airline now gone - sheet). It will be convenient to compare this with a similar TAA (now the mainline domestic arm of Qantas) trimsheet (TAA didn’t operate LRs so that sheet is for the standard 727-200 .. the two are not all that much different for weight and balance – the LR has slightly higher weights and an extra auxiliary fuel tank).
The TAA sheet can be obtained with another download from the CASA website. The, now quite old, Pub 17 on Weight Control, although not directed at pilots, is a useful monograph and I recommend it for reading by pilots as part of their theory studies. The URL to locate the download is
www.casa.gov.au/files/weightcontrolpdf
and the trimsheet is at page 40.
This doesn't have the sloping lines for loading positions but does have sloping lines in the fuel area. There is an example diagram but it is not clear just why it works.
The value of comparing both the Ansett and TAA sheets is that, while they are, in essence, doing nearly the same job, they look somewhat different, use different stylistic approaches, and highlight the point that trimsheets can be made to look pretty well however the designer wishes.
Let’s have a think about the sloping loading arm lines. The Ansett sheet doesn’t use these (ie it’s much the same as the Loading System Alpha chart) but the TAA example does .. why ?
The sloping lines address error (b) in the previous discussion. They are just a draughting artefact which, in effect, “moves” the IU tick mark scale left or right so that the dropline has to hit a whole tick mark (ie one of the sloping lines). By this artefact, we make the loading line calculation start at a whole tick position and, in principle, error (b) ought now not to be a problem.
You can think of this in the following manner – where the dropline hits the sloping line, redraw the tick mark line horizontally and do the IU calculation in a manner similar to the Alpha sheet. It follows that these sloping lines
CAN NEVER be guide lines.
Is one style better than the other ? … largely personal preference but the sloping line model wins on error minimisation.
The next set of sloping lines is for the fuel grid. The Ansett sheet uses a separate graph to calculate the IU change for fuel load while the TAA sheet incorporates the IU change directly into the dropline section of the sheet.
You can see that the fuel grids are similar (the LR has an additional line segment at the higher fuel weight to allow for the additional baggage hold auxiliary tank) by rotating the Ansett sheet 90 degrees clockwise and comparing it to the TAA sheet. Ignoring the last segment for the additional auxiliary tank, and scaling effects, the lines are the same.
So how do both sheets work ?
For the Ansett sheet, the fuel chart on the left is a simple graph of weight (along the bottom axis) against IU (along the vertical axis – but not shown explicitly). This (hidden) IU scale is then joined up with the main trim section by means of the diagonal grid to the right of the fuel chart .. ie the fuel chart vertical IU scale is mapped to the horizontal IU scale on the main trimsheet so that the fuel IU scale is the same as the trimsheet IU scale. So, in effect, the diagonal grid is there just to skew the main sheet IU grid to the left. The reason for this will become clear in the next paragraph.
So, when we are using the fuel grid in the Ansett sheet, we
(a) run the zero fuel dropline down to the top of the diagonal grid (the line marked “fuel reference line”)
(b) continue the dropline down to the CG envelope to figure the ZFW CG
and, at the same time
(c) continue the dropline (from the fuel reference line) PARALLEL with the diagonal grid lines .. this is doing nothing other than skewing the dropline to the left while following the same IU scale value for the total IU at ZFW
(d) enter the fuel grid with fuel weight and then, from the intersection with the fuel line run across (and through) the unlabelled IU line
(e) where the two lines drawn in the diagonal grid intersect, continue the fuel dropline down to the CG envelope to figure the loaded CG.
In effect, what you have done is use the left hand fuel chart to do the weight to IU calculation and then use the right hand diagonal grid to do the addition of fuel IU to ZFW IU. This addition is done by moving the IU value from the fuel chart vertical axis to the main trimsheet horizontal IU scale.
It follows that, for any fuel calculation similar to this one, the diagonal grid sloping lines are
ALWAYS guide lines.
The reason for this complexity is simply that the fuel loading arm is not constant .. ie it varies with weight (more strictly, volume).
The only other sloping line grid on this sheet is the MAC grid overlay on the CG envelope. This allows you to read off the CG (in this case as %MAC) from the intersection of weight and IU. You could take the view than this is a guide line grid as you have to move in alignment with the grid lines to read the MAC value.
Looking at the TAA sheet fuel grid calculation, the fuel weight by IU variation is drawn directly on the main trimsheet. By paralleling the grid lines, one calculates the IU change and does the IU total addition in one process.
Which of the Ansett and TAA approaches is the better ? Again, largely a matter of personal preference, although the Ansett approach wins, marginally, on error minimisation (albeit at the expense of sheet real estate).
Again the TAA sheet has a similar MAC grid overlay on the CG envelope.
A long-winded post .. if anything is not clear enough, please say so and I’ll add some more/vary the detail and we’ll eventually get the story across. Like all weight control stuff, nothing in the way of rocket science .. just requires a bit of care and good housekeeping.
When you get a chance to post the final sheet, we can have a talk about that one as well.