Hi Everyone. New to the Forum.

Studying for the Performance exam. Passed HF, Weather and Nav already.

Couple of questions on CPL performance regarding Ex 5.13.

I did equations 1 - 5 fairly easily, but on Q6, I went straight to using the flow chart method, instead of using the chart. I couldn't see when to know to use the chart. The text says to use chart when on AFW and outside the forward limit, but Q6 has 2400 and 590, which is not outside the limit, so I just went to the flow chart. What is the key to knowing to use the chart?

Q7, I used the chart (see attached), but could only come up with 8 or 10 KG. It seems almost impossible to plot A and B points, then find the intersection of the Forward limit, because the line is too shallow when intersecting. It's also hard to get correct position for weight lines like 2392kg, because of the gross weight scale. Whats the key to getting the correct answer of 20kg, and are there gonna be hard to draw graphs like this in the exam.

Cheers
Matthew

I don't have Bob's book to hand so I am unable to assist with the specific book-related questions - no doubt Bob/Stuart will be along soon enough and will be able to address that part of your post.

So far as the upper forward limit is concerned -

(a) this is a problem with most light aircraft

(b) the line is a curve rather than straight

(c) as you observed, with the usual GAMA POH arrangement and datum, the slopes of the some loading lines can present challenges when it comes to reading off intersections.

(d) the only way to run the calculation accurately and quickly is to use an algebraic solution which is way out of the pilot training league (although not intrinsically difficult).

(e) in practice (ie out flying on the line) one just plots accurately and reads the intersection as best as one can. The residual error is addressed by applying a suitable degree of conservatism to the answer.

(f) for the exam, we probably need to be a little more pedantic as we don't know, for certain, what sort of error tolerance the examiner permits.

My suggestion is to run (e) as a starting point - as accurately as you reasonably are able. Then, knowing the equation for the upper forward CG line from Bob's book you can run several additional iterations to home in on the real answer to an acceptable accuracy. The simplest way is to bracket the answer - this involves applying a small increment to the initial answer and then check what answer that gives. Then move one half of the increment in the direction of the correct answer and redo the calculation. This technique will home in very rapidly and you should need only a couple of iterations to get to a sensible accuracy. Obviously, you can fiddle the half increment according to the difference you see at each iteration but the principle is to use half as a protocol.

Hi John.

Thanks for the advice about comments about accuracy and real world stuff. I just read Bob's accuracy in calculations guide, that stated that CASA require accuracy that is way beyond 'real world'

If I do a few of those forward limit equations and find the moment too. I can see how your explanation works.

I also ran another drawing (attached). This time trying to decide the weight and moment scale a little more accurately and came up with a better answer, that more closely aligns with the books answer.

Still hard to see though. I hope the CASA exam has something easier to see

Matthew

CASA require accuracy that is way beyond 'real world'

I don't have a major problem with that, as the theory exam's intent isn't really to check on the candidate's ability to process real world stuff - that is the province of the relevant flight test for the qualification (albeit that the fact is a bit of a nuisance to the candidate).

If I do a few of those forward limit equations and find the moment too. I can see how your explanation works.

You may be missing the point, just a little ? albeit that it is difficult for me to assess at a remote distance.

In the iterations, you start with whatever the intersection value might be as you perceive/read it. The upper forward limit equation then gives you the correct CG for that weight and you can figure out the delta (error). That tells you whether you need to go higher or lower in weight (as the curve is monotonically increasing - ie the slope doesn't reverse along the way). So, from your assessment of your plotting, you take a punt and pick a weight increment to trial.

Repeat the exercise. This time, move half the previous increment in the appropriate direction (or some other proportion as you see fit to assess from the numbers).

Keep repeating the exercise until you get close enough and the answer is fit for purpose. In practice, this homing in will be pretty rapid and you should only need a couple of iterations to get there.

The technique comes from a simple computer programming process which has been used for donkeys' years and, for a computer, it doesn't matter if it takes a bunch of iterations to get to where you need to be.

I also ran another drawing (attached).

Although it is a case of splitting hairs if you are being careful, you may improve the initial result if you use two points reasonably distant from the limit line - that way the effect of any plotting errors can be minimised at the intersection. Similarly, there are graphical techniques which can improve your ability to estimate the weight value against the grid scale, as drawn. All a bit silly but the aim of the game is to get to an accuracy (or error) margin appropriate to what the examiner might be after.

Still hard to see though. I hope the CASA exam has something easier to see

Afraid you just have to put up with the exam presentation. Don't despair, though - heaps of folks pass so it's not all that hard to do. Probably the main problem is the candidate's trying to hurry too much and/or plain old carelessness and inattention to detail.

Thanks John.

Appreciate your reply. I'll practice the iterations process some more.

As for carelessness and intention to detail. I see that creeping in sometimes, so I'll keep practicing and stay on top of it. Thanks for the encouragement.

Cheer
Matthew

I'll practice the iterations process some more.

The main immediate value is that a few examples will allow you to see how accurate (or otherwise) your initial envelope plotting might be. If you take care and plot fairly accurately, then the subsequent iterations will demonstrate just how close you can get to a good answer first time around.

Hey mate, quick tip about accurately plotting stuff for this exam.

The scales are horrible and in unhelpfully large increments (e.g. 2000' of pressure height per line in some of of the p-charts where you're meant to plot a number like 1630 somehow, etc). The key to plotting this accurately is to measure the distance between the two lines with a ruler, then divide the number by however many millimetres fits into that section. This will tell you how many kgs/feet/whatever per millimetre, allowing you to plot your point extremely accurately.

The key to plotting this accurately is to measure the distance between the two lines with a ruler, then divide the number by however many millimetres fits into that section.

Not really.

Many of the carpets are characterised by non-linear parametric variables so all your technique is trying to do is linearise the carpet. If the parameter is somewhat near linear, a better technique (having played with it during your exam preparation) is to draw a suitable length straight line with scaled intervals (say 10). The drawn line then can be inclined against the printed axis scale (ie between consecutive grid lines) and used as a considerably more accurate scale than would be achieved using a rule in the manner you describe.

If the carpet parameters are obviously non-linear, you are out of luck unless you want to go to the trouble of cross plotting and reading off the required value from the cross plot graph. Generally, this takes too long to be of much use in the exam, although it is a standard technique for backroom work in the real world. If, on the other hand, you have done plenty of interpolation practice in your exam workup, you can estimate the intermediate parameter line reasonably accurately - easy for me to say, as I have been doing that for much of my engineering career.

Overall, don't rush and, when you have done it however you want, sit back and look at the carpet overall to assess whether your interpolation looks to be reasonable.

.. to plot your point extremely accurately.

Perhaps you might achieve moderate accuracy ... but, your technique, certainly, will not provide a result which is "extremely accurate".

I have genuinely no idea what you're talking about.

I have genuinely no idea what you're talking about.

Then, my apologies - I had presumed that the basics would have been clear as they are not uncommon, although probably more so at ATPL level than PPL/CPL. However, no matter, let's try again and I'll endeavour to make things a little easier and clearer for you.

Many of the carpets

A simple, single line graph will be presenting two sets of values.



Sometimes we see multiple single line graphs plotted on the one page.



Although each of the lines is unrelated (mathematically) sometimes, for convenience, they may all be plotted on the one graph.



Basically, each line gives us some two dimensional information for its particular value.

An example with which you will be familiar is in the CASA workbook at Loading System Echo Figure 10.

When we get to presenting more complicated data (ie the underlying equation is more complex with multiple variables), we could use a large number of two dimensional graphs at the expense of having many, many pages in the book. However, for many sets of data, it is far easier to plot in a three dimensional arrangement. This is very common in the presentation of aviation information such as in flight manuals or pilots' operating handbooks.



The difference between this and the previous graph is that the values for the various lines relate to one of the variables in the underlying equation whereas, previously, the various lines were unrelated mathematically.

(As an aside, the technique known as Dimensional Analysis was developed to allow us to represent hundreds, even thousands of tabular or graphical data in a single equation using what we refer to as a non-dimensional coefficient. Examples are Mach Number, Lift Coefficient, Drag Coefficient, and so on).

Let's look at the workbook at, say, the Takeoff Weight Chart Aircraft - Echo Figure 12 graph. This is the old DCA style P-chart presentation for the aircraft's takeoff weight information. The figure presents a vast amount of data in a fairly simple to use arrangement. When drawing up the various equations as graphs (and I have done quite a few of these in the dim dark past) the designer positions each separate graph according to background data values (which often are not shown) to make the whole thing work properly. Each separate graph, effectively, is a three dimensional graph in that there are three different, but mathematically related, values presented in the graph.

If we look at any one line, it is just a simple 2D graph. However, when we include a range of related value lines we obtain, in effect, 3D information. This style of graphing usually is referred to as a "carpet" graph/plot or, sometimes, just a "grid". Strictly, a carpet relates to a slightly different style of presentation but the basics are the same.

Just a mathematics buzz word. A related buzz word, for the lines as plotted, is that the line values (eg OAT variation in the density height carpet) are called "parameters".

are characterised by non-linear parametric variables

"Non-linear" refers to a line which is a curve as distinct from a straight line (which we refer to as being "linear"). "Parametric" means those items in a related set of things (ie the parameters) and "variable" a set of values.

So all your technique is trying to do is linearise the carpet.

If the carpet parameter lines are all separated by the same value, then they represent a straight line or linear variation and your technique works. If they aren't, then your proposed technique sets out to corrupt the data by forcing the region between each line to be linear rather than the correct curve shape. This will intentionally introduce errors varying in size depending on the actual data. The following example should make this clear -



This graphic makes use of the cross plot approach described below. The blue line is the correct curve while the red line segments are the separate linearising approach you are proposing. The extent to which any errors might be of practical importance will depend on the actual equations, values and so on.

So, how do we get around this ?

If the parameter is somewhat near linear, a better technique (having played with it during your exam preparation) is to draw a suitable length straight line with scaled intervals (say 10). The drawn line then can be inclined against the printed axis scale (ie between consecutive grid lines) and used as a considerably more accurate scale than would be achieved using a rule in the manner you describe.. This approach is shown below -



If the carpet parameters are obviously non-linear, you are out of luck unless you want to go to the trouble of cross plotting and reading off the required value from the cross plot graph.

Cross-plotting is a technique where you start with a graph of many lines, read off a bunch of points, and then re-plot those points on another, separate graph so that you can better extract desired information to an improved accuracy. With a reasonable amount of practice, you get to the point where you can eyeball where the interpolated line should go (and can rough it in freehand) but that probably will remain the province of techo folk who do this sort of stuff for a living.