Some further answers.

3. In your post number 17, in the second picture you make the statement that "if the datum is out to the nose, somewhere, the envelope slopes bottom left to upper right (blue line)." I see the envelope going from bottom center to upper right. What am I missing here ?

4. In the same picture, what would happen if the datum was moved further toward the aircraft tail ?

With reference to the following graphic



If the datum continues its aftwards movement, then the envelope just continues to rotate. The green envelope indicates the situation for a trim datum location at FS140. Clearly, as there is no advantage in moving the trim datum aft of a suitable point for an upright, boxy envelope, we don't normally give any thought to such aft datum positions.

For interest, I have continued the envelope graphics to the zero weight point which may make the shapes a little more easily understood. As one would realise, if either weight or arm is zero, moment or IU must be zero.

The previous graphic will be recognised as the upper RH box in pink. The typical POH presentation for the nose datum situation is given by the truncated khaki box in the extreme upper RH position. I should have been clearer with my previous description .. apologies for that oversight.

7. You then say that care must be taken with using straight lines to simplify the curves. Can you give an example when there would be a problem doing this ?

Reference the following graphic I have presented a made up CG envelope designed to demonstrate the curve and linearisation problem.



The region of interest is that where the forward and aft limits diverge from the main envelope.

If we then recast the envelope into a suitable IU form, we obtain



The blue line represents the "correct" envelope. In the central regions, I have added straight lines in purple.

As can be seen, quite easily, the two lower straight line segments (label "A") are outside the correct line segments and, hence, are non-conservative. We shouldn't linearise these segments.

The two upper segments (label "B") are inside the correct line and these linearised segments may be used in lieu of the correct curved line.

In summary, if the line segments move away from the central envelope region as weight increases, we have the linearisation problem. If they move in towards the central region, we can use the straight line simplification.

Clearly, for the envelopes discussed to date, the difference due to linearisation is minor .. if sufficiently so, it really doesn't matter if the line segment is linearised for trim sheet completion as the error is within the "noise" of the drawing.

However, it is important that the designers be aware of the problem. Where the difference does become significant is for the sort of GA envelope characterised by a relatively long, sloping upper forward limit line segment.

The following graphic demonstrates a made up example for illustration. You may well have seen this sort of envelope in your flying to date.



Clearly, in this case, if one uses a straight line segment, there is a moderate usable region of the envelope lost to us for loading.

Thanks so much for the additional explanation. I now have the trim sheet which caused me the greatest confusion originally. My colleague used to fly the aircraft and, for his own reasons, wished to de-identify the sheet. I look forward to your explanations of how this sheet works.

Am following this thread with interest. I have a couple of questions regarding trim sheets.

First, the attached sheet, below, appears to be rather less well defined than the others discussed above. Further, when I have used it for calculations, I get answers which are different to a normal arithmetic calculation. Perhaps you can offer some thoughts on the matter, please ?

Ref post #22

The sheet is a conventional trimsheet essentially following the AN/TN styles described earlier.

It does have a couple of unusual characteristics, though -

(a) the fuel grids are much the same as the AN 727 sheet, although the RH grid is tweaked somewhat to provide a better accuracy for this particular aircraft Type. Not a technique which you are very likely to see, in general, but there do exist a few aircraft for which it may be appropriate .. basically to do with a rescaling of the IU.

(b) the envelope grid is a bit unusual in that only the ZFW case has an explicit envelope. Just the way the OEM went about the exercise, I guess.

As previously done, best I run up some diagrams to assist explanation ... I'll cover the sheet in more detail in a subsequent post.

Ref post #23.

This document is a real worry

Although it describes itself as a "Load and Trim Sheet" it is nothing of the sort and might better be described as a nonsense drawing. There is no indication who "designed" it, nor is there any indication if anyone has approved or authorised its use. In the respect of the latter, I would be horrified to think that a CASA WCO would not have seen its deficiencies at a glance.

Reference to the CASA Aircraft Register indicates that a PA28 of this registration has been around since the mid-70s. I have no idea if the posted document is the current POH loading system but, if it is, then it CANNOT function as such and MUST NOT be used for loading calculations. If you have an involvement with the aircraft, I would urge you to draw this to the attention of those folks responsible for the aircraft and suggest that they have a competent WCO replace it with something which will work. That you have discovered discrepancies in its use surprises me not in the slightest.

The main problems with the sheet suggest that whoever designed it has little, if any, understanding of how trimsheets function.

One might be inclined just to dismiss the document as nonsense. However, if one such as this exists out there, then there may be others. Better that Bob's students be shown how to recognise the main errors in this sheet so that they can avoid potential problems with the use of other sheets of similar ilk.

Rather than describe the problems in text, which may just serve to confuse folks, it may be better if I run up a few diagrams to illustrate what the main problem is in a subsequent post.

(Due to system limits, this post has too many graphic links for one post so it is spread over two posts to circumvent the limit).


Following on from post #24

In keeping with the OP's mate's desire not to identify the aircraft too closely we will limit the ID to the Type. Actually, I recognise the trimsheet as I designed it in 1980 for an operator based at Essendon which used to operate a number of corporate aircraft for larger resources companies.

Looking at the trimsheet, it is clear that the drawing has been done by hand using drafting pens and lettering stencils. This dates it, almost certainly, to pre-early/mid 80s. The aircraft, fairly obviously, is a corporate swept wing jet in the 60.000 lb MTOW class. It is, indeed, a Gulfstream GII and a quick look at the TCDS (which can be found via the FAA website at rgl.faa.gov/Regulatory_and_Guidance_Libr...ILE/A12EA_Rev_48.pdf) confirms that.

The trimsheet is quite conventional other than for the matters referred to in the earlier post.

Looking at the sheet, from the top down ...

(a) the IU entry line uses the IU shift constant to keep those pesky negative numbers out of the way.

(b) the individual loading lines follow the sloping tick line technique as in the TAA B727 sheet we looked at earlier

(c) when we get to the fuel grid, things are a little unusual.

The left hand IU lookup grid is quite standard and runs like the AN B727 sheet discussed earlier. As a side note, the observation that the fuel line comes back to a zero IU change at full tanks indicates that the trimsheet datum is the arm for full fuel. This is deduced easily as zero IU requires either weight or arm to be zero so that the product (multiplication of the two) is zero.

The right hand IU summation (in this case the IU is subtracted) starts off as in the AN B727 trimsheet style but is tweaked somewhat to give better accuracy for the GII. This technique, which we will look at below, is not common but may be useful for a few of the corporate jets where the ZFW limits are low (it's a corporate pocket rocket, after all) and the the total fuel is a significant fraction of the MTOW. If the ZFW and MTOW envelopes are mismatched (compared to the usual arrangement) it can be quite difficult to get a "nice" and accurate trimsheet loading system. How can we get around this ? Easy .. we rescale the MTOW IU grid and, if necessary, reposition the rescaled grid to cause the two envelopes to sit over each other .. which allows us to get the best accuracy result for trimsheet completion. That's the basics of the story for this GII sheet. How we might go about that is shown below ...

First, let's consider the basic (ie the usual, standard) grid pattern for the right hand fuel grid. The IU scale (black) comes down from the final ZFW calculations for the fuel calculations and then both continue down to the envelopes. The left hand fuel grid IU lines (blue) come across from the left. This is shown in the first graphic



In the next graphic, we put in the fuel IU summation lines (red) and a typical example usage is shown - we come down from the ZFW calculations and continue (purple) until we intersect the IU line from the left hand fuel look up grid (orange) and then continue down (paralleling the IU gridlines) to the MTOW envelope (green). [The line from the ZFW calculations also continues straight through the fuel grid to the ZFW envelope but this is not shown here to keep the graphic somewhat simpler.]



Now comes the interesting part - how to get the IU rescale and shift. In the next grid we go back to the previous graphic without the example so that we have a starting point.



In the next grid, we rescale the IU scale. Typically, one has to reduce the scale for the MTOW envelope. Notice that the black IU scale above the fuel grid is wider than that below. The black lines in the fuel grid simply act as guide lines to show the rescaling from top to bottom.



If, as is often the case, we need to move the output scale left or right to end up with the two envelopes more or less one above the other, we just move the output scale left or right to suit the need. In this example, I have moved the output scale to the right.




(Post content continues at post #27)

(Post content continued from post #26)


Next we tidy up the lines coming from the left hand fuel IU lookup grid (blue lines)



and then reposition the fuel grid guidelines, maintaining the same plotted relationship as in the original grid



Notice that the fuel guide lines now become curved, rather than the original, straight lines. The graphic now looks a lot like the GII sheet shown previously.

In the final graphic of this sequence, I have run an example. While it looks quite different to the example in the standard fuel grid, it follows exactly the same pattern of use.



Looking at the example in detail

(i) we come down from the ZFW calculations (purple) and follow the (red) fuel grid guide lines until

(ii) we intersect the IU lookup line from the left hand fuel grid (orange), and then we

(iii) follow the iU guide lines (black) down to the bottom of the grid and then

(iv) continue following the IU guidelines (black) into the envelope region. (green line)

It is worth noting that we could have done the rescale exercise in two stages .. the basic fuel grid (as in the AN 727 example) and then the rescale grid as a separate grid. While this is a little less confronting to the user, it has little real advantage and one significant disadvantage .. it squanders sheet real estate and that is always a precious resource when designing trim sheets as the bigger the picture, the better the accuracy.


(d) now we are in the envelope region and the following points are noted for this sheet

(i) the envelope shown is for the ZFW case. The outer limits are the AFM limits while the inner limits are the curtailed AFM limits. The curtailment results from an error analysis for the sheet conducted by the designer.

(ii) the GII is unusual in that there is no prescribed TOW envelope. If the CG is in the ZFW envelope for the ZFW case, then one can add fuel safe in the knowledge that the TOW CG will be within acceptable limits. Hence the only information for the TOW case is the takeoff trim setting grid (which is an MAC grid labelled with trim settings rather than %MAC CG values)


That is to say, this trim sheet is a standard trim sheet ... with a few little changes to suit the particular aircraft.

As it appears that quite a few folk are following this thread, please feel free to raise any questions or concerns you may have with weight and balance. If the concerns relate to trim sheets, we'll sort them out here .. otherwise, I'll answer them in another thread so that other folks can search more easily for different questions. If the questions relate to the usual exam matters, I have no doubt that Bob or Rich will jump in with the relevant answer per Bob's exam techniques.

Following on from post #25

The principal fatal flaw with the document identifying itself as a trim sheet is that it purports to obtain a final CG by the addition of arms.

Thinking back to your basic theory training, we calculate CGs in the following manner -

(a) add all relevant weights

(b) calculate and add all relevant moments

(c) determine the resulting CG by calculation. The calculation is the divisor total moment/total weight. Nowhere does addition of arms figure in determining CG positions for loading problems.

It is useful to detail the deficiencies in the document to give you some "back of the mind" basis for assessing the likelihood that a trim sheet with which you might be faced is reasonable or not.

The following deficiencies are noted -

(a) the document contains no evidence as to provenance. By that I mean there is no information relating to

(i) the designer and/or drafter. This is not essential but is a typical drawing requirement.

(ii) whoever may have given authorisation or approval for the document's use. This is essential, either explicitly or implicitly (if the document is a controlled part of another approved and controlled document, eg part of the approved AFM). I draw your attention to CAO 20.16.1.3.

(iii) issue reference. This is essential so that one can determine whether the document proposed to be used is that cited per (ii).

(b) the top entry line has neither entry argument (ie the starting IU or moment scale) or other means of correctly entering the sheet (eg a grid of empty weight versus CG - this is rather untidy but you will see some sheets with this approach). This sheet has a line which appears to be identified as a CG (presumably the current CG for calculation purposes). This defeats a principal purpose of having a trim sheet, viz., once it is designed it doesn't need to be changed unless either AFM limits or aircraft configuration details are changed.

I note that there is a (CG - incorrect) scale at the bottom of the sheet. This is both unconventional and a recipe for error compared to the normal presentation.

(c) the individual trim lines have insufficient range. Indeed, the row 1 line is unworkable if there are two occupants other than pygmies.

(d) the CG envelope at the bottom of the sheet is a weight by CG envelope, rather than the required weight by moment (or IU) envelope.

This can be checked by reference to the AFM/POH (or TCDS) CG data. For the purpose of helping you detect flawed documents, such as this one, the shape of the envelope gives the deficiency away at a glance.

If one refers to post #21 it is clear that, in general, the envelope lines are not vertical. For the typical light aircraft envelopes, you will never have both extreme forward and aft CG lines vertical simultaneously - generally neither will be vertical unless the trim sheet datum is chosen to be located at one of these positions. For example, I have plotted the correct envelopes, below, for trim sheet datum positions at the forwardmost arm, a central envelope arm, and the the aftmost arm.

As you will observe, one can make either the forward or the aft limit line vertical but not both simultaneously. The spurious trim sheet envelope has both limit lines vertical. That says weight by CG, not weight by moment (or IU).

Datum at the forward limit -



Datum at a mid-envelope position -



Datum at the aft limit -





(e) the background sheet gridlines match the weight by CG envelope, confirming that the sheet purports to add arms rather than moments.


This sheet must not be used for operations.


My suggestion to you is that, if you are handed a sheet containing these sorts of deficiencies, you should request evidence that the sheet complies with the requirements of CAO 20.16.1.3.

Thanks, John. I was starting to think that the problem was just my lack of ability.

The reason I asked the question is that I have become interested in trimsheets recently as an alternative to the other calculation methods. I found a local pilot training and charter operator website which contained several light aircraft trimsheets and decided that they would be a good start to learning the method. However, I kept getting different answers using both methods.

Your explanation for the Warrior gives me some comfort as the sheet itself presents the problem. Another sheet on the same site is for a twin commanche and it has the fan shaped envelope lines unlike the Warrior yet I still keep getting different answers between a mathematical calculation and using the trimsheet. Perhaps you can look at this one for me.

Looks like you're having a run of bad luck there, mate. As for this document .. same, same, more or less. I wouldn't waste any more time playing with it .. perhaps the next one might be of more use to your plans ?

The document, again, is a nonsense loading system and must not be used for loading calculations in operations as it will give you incorrect answers.

Deficiencies -

(a) the document contains no evidence as to provenance.

There are sufficient similarities to the Warrior document to infer that the two may have been drawn by the same person. I can only hope that that person is not a CASA approved WCO. One of the problems with the present system is that the WCA process only really looks at aircraft weighing and basic loading systems competence. The more complex systems, such as trim sheets, tend to relate more to larger, more complex aircraft which, generally, are looked after by appropriately trained engineers. CASA is looking at changing the system to cover this deficiency.

(b) while it is difficult to work out just what the document is trying to do, it appears to be working on the addition of arms ... somehow.

(c) the top entry line has no entry data other than an arrow line which bears no relation to anything much at all .. in the absence of any rational vertical scale, it is hard to work out just what the "designer" had in mind

(d) the envelope appears to have been lifted from a POH document. It is, indeed, a weight by IU graph .. but the wrong type altogether.

While the shape of the graph is a red flag for me, I wouldn't expect the typical pilot to see the problem at a glance. Might I ask if you see anything in the graph which would cause you to recall some discussion earlier in this thread ? It might help if I overprint the IU scale (red line grid) which has been left out.



Does it not now look very much like the skewed envelope discussed at post #14 and subsequent ?

(e) the envelope doesn't apply to the specified aircraft.

The document professes to cover both PA-30 and PA-39 models. Unfortunately, the envelopes are different for each per the TCDS which can be reviewed at rgl.faa.gov/Regulatory_and_Guidance_Libr.../A1EA%20Rev%2018.pdf. Reference to the CASA Register indicates that there is a VH-ICS, a PA-39. The correct TCDS envelope cutoff is shown in the above graphic in blue.

A look at the bottom of the envelope (2200lb weight line) suggests that the vertical scale may have been chosen as the CG values for this weight. If that is the case, I have no idea why that might have been done.


Overall, as for the Warrior document, this document must not be used operationally as it will result in incorrect answers for loading calculations.

Hopefully, your other sheets may offer a more valuable training aid for your desires.